The Myth of the Postmodern: Lyotard and Too Many Truths
In 1979 a provincial government paid a French philosopher to report on the state of knowledge in the developed world. What it received was…
The Myth of the Postmodern: Lyotard and Too Many Truths
In 1979 a provincial government paid a French philosopher to report on the state of knowledge in the developed world. What it received was a slim, elegant, uncooperative book announcing that the great stories humanity had been telling to justify its knowledge — progress, emancipation, the eventual unity of science — had quietly lost their audience. The word postmodern entered the language and never left. Forty-seven years later it still works overtime, explaining architecture, elections, art markets, and the collapse of public trust, often in the same sentence.
This book takes that report seriously enough to answer it with another one.
Boris Kriger — theoretical physicist, philosopher of science, and a man who spends his mornings auditing cosmological preprints for conclusions their evidence cannot carry — accepts Jean-Francois Lyotard’s diagnosis at full strength, refusing every convenient caricature of it. Then he asks the question the last four decades of commentary somehow skipped. Was this a historical event or a structural law? The answer, established formally in the Theorem of Incompatible Truths, is unkind to the calendar. Any sufficiently complex domain necessarily admits mutually exclusive but individually valid descriptions that cannot be unified. Nothing began in 1979. A permanent condition of complex knowledge was mistaken for breaking news, and an entire vocabulary was built on the misfiling.
The grand narrative did not die, either. It compiled. It descended into the machinery of research, into priors and reference models and calibration choices, where nobody utters it aloud and everybody runs it. A story nobody tells is a story nobody can argue with. Using his own taxonomy of the measured, the declared, and the derived, and the Code of Practice built upon it, Kriger tracks the missing narrative to its new address, explains why it is so much harder to cross-examine there, and offers what Lyotard never did: instructions for a rational agent who has to decide something before lunch while the truths refuse to combine.
Sharp, funny, occasionally merciless, and unexpectedly generous to its subject, this is philosophy written by somebody with skin in the game.
Keywords: postmodernism, epistemology, philosophy of science, Jean-Francois Lyotard, incompatible truths, legitimation of knowledge, scientific pluralism
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Contents
Chapter One — The Report That Ate Its Commission. 16
Chapter Two — The Philosopher Who Taught in Constantine. 23
Chapter Three — Auguste Comte Writes the Story Lyotard Will Bury 30
Chapter Four — Incredulity, and What It Cost 37
Chapter Five — Games With No Referee. 44
Chapter Six — Performativity, or Knowledge Billed by Output 50
Chapter Seven — Knowledge as Merchandise, and the Receipts. 55
Chapter Eight — The Differend. 61
Chapter Nine — Paganism, or Judging Without a Ruler 67
Chapter Ten — The Author Would Like to Retract Some Footnotes. 73
Chapter Eleven — Something Is Always Missing. 79
Chapter Twelve — Truths That Refuse to Combine. 84
Chapter Thirteen — No Final Theory. 90
Chapter Fourteen — Plurality Is Not a Mood. 96
Chapter Fifteen — Provable Depends on Defined. 101
Chapter Sixteen — The Choice of Formal Realities. 107
Chapter Seventeen — The Condition That Never Began. 112
Chapter Eighteen — Measured, Declared, Derived. 118
Chapter Nineteen — The Grand Narrative Did Not Die; It Compiled. 123
Chapter Twenty — Ten Norms for Introducing an Entity. 128
Chapter Twenty-One — Role Without Referent 134
Chapter Twenty-Two — Myths the Predictive Mind Cannot Do Without 139
Chapter Twenty-Three — Totalities Fail Asymmetrically. 144
Chapter Twenty-Four — Irony Is Not a Style; It Is a Swap. 149
Chapter Twenty-Five — Absurdity as Mercy. 153
Chapter Twenty-Six — The Unpresentable, With a Proof 157
Chapter Twenty-Seven — Art When Everything Is Available. 162
Chapter Twenty-Eight — Power With Nobody in It 166
Chapter Twenty-Nine — Excluded Before Speaking. 171
Chapter Thirty — Hostile by Design. 175
Chapter Thirty-One — How to Act When the Truths Will Not Combine. 180
Chapter Thirty-Two — The Adaptive Observer 185
Chapter Thirty-Three — Communities That Were Never Grand. 189
Case Study One — The Afternoon Pluto Stopped Being a Planet 202
Case Study Two — Two Correct Measurements of the Same Universe 206
Case Study Three — The Threshold That Ate a Discipline. 210
Case Study Four — The Signal That Was Dust 214
Case Study Five — How Many People Are Out of Work. 218
Case Study Six — The Number That Runs the World and Was Never Meant To. 222
Case Study Seven — The Two Weeks That Separated Grief From Illness. 226
Case Study Eight — The Day the Kilogram Stopped Being an Object 230
Case Study Nine — The Rubber Ring and the Missing Qualifier 234
Case Study Ten — The Formula That Priced the Unpriceable. 238
Case Study Eleven — The Bridge That Nobody’s Model Contained. 242
Case Study Twelve — Seven Countries Out of Twenty-Two. 246
Case Study Thirteen — What Heritability Does Not Mean. 250
Case Study Fourteen — Three Instruments and Four Minutes. 254
Case Study Fifteen — The Doctor Who Was Right Without an Idiom 258
Case Study Sixteen — Two Systems That Both Predicted the Sky. 262
Case Study Seventeen — The Continents That Could Not Move. 266
Case Study Eighteen — The Bacterium That Was Not Supposed to Be There. 270
Case Study Nineteen — The Formula That Decides Cricket Matches 274
Case Study Twenty — The Baseline Question. 278
Preface
My working day begins with a list of things strangers discovered overnight. The astrophysics preprint server posts its new arrivals in the small hours, and by the time the coffee is ready there are forty or fifty fresh papers waiting, each announcing something about the universe that was not known, or at least not claimed, the previous afternoon. I read the titles. I read most of the abstracts. I read perhaps three of the papers properly, and of those three I am usually hunting for one specific defect, the way a building inspector walks through a beautiful new house looking only at the joists.
The defect is easy to describe and surprisingly hard to see. A team measures something real. They point an instrument at the sky, they collect light, they count galaxies, they record positions and brightnesses with genuine care, and the measurement is honest work done by honest people. Then, between that measurement and the headline in the abstract, there is a chain. The chain contains assumptions. Some of those assumptions were themselves measured elsewhere. Some were derived from the measurements by mathematics that can be checked. And some were simply announced. Somebody had to choose them, nothing in the data chose them, and the paper proceeds as though the choice had been handed down rather than made. When the conclusion at the end of the chain is loud — the universe has an age, the dark energy is evolving, the cosmos has a preferred direction — and one of the links carrying that weight was announced rather than found, the paper has a joist problem. It may still be standing. It may stand for decades. But it is standing on something that was put there by a person, and the reader is not told which person or why.
I have spent a good part of the last several years writing short notes about exactly this, one paper at a time, and the notes all use the same three words. A quantity is measured when an instrument produced it and somebody could in principle produce it again. A quantity is derived when it follows from measured quantities by steps that can be audited. A quantity is declared when a human being chose it and wrote it down. That is the whole apparatus. It is not deep. It is the same distinction any competent accountant makes between a receipt, a calculation, and an estimate written on a napkin, and the reason it produces so much trouble in physics is that the napkins are typographically indistinguishable from the receipts. In a published paper everything is set in the same typeface. The measured, the derived, and the declared all wear the same suit.
This is a book about a French philosopher who died in 1998, and I should explain how a person with the morning routine described above ended up writing it.
The explanation is that Jean-Francois Lyotard asked my question first, in a much grander register, and got a famous answer that I believe is half right in a way that matters. His question was: who authorizes knowledge? Not who produces it, not who funds it, not who teaches it, but who or what gives it the standing to be believed. For a long time the answer had been a story. Science was legitimate because it was part of the emancipation of humanity, or because it was the self-development of the human spirit, or because it was the steady accumulation of a single true picture toward which everything converged. Lyotard’s claim was that nobody really believes those stories anymore, that the culture had quietly stopped being able to tell them with a straight face, and that knowledge had therefore been left standing without the thing that had been holding it up.
I ask the same question at a considerably lower altitude. When a paper tells me that the universe is 13.8 billion years old, what authorizes that number? Not the telescope alone. Somewhere in the chain there is a declared component, and behind the declared component there is a convention, and behind the convention there is a whole way of doing things that nobody in the paper defends because nobody in the field currently disputes it. That is a legitimating story. It is just not told in narrative form anymore. It is executed rather than recited, and it lives in software.
What you are holding is a counter-report. Lyotard’s most famous book was, in its original life, a commissioned document: a government wanted to know the state of knowledge and paid to find out. Forty-seven years later, this is a second opinion from somebody who works inside the machinery the first report was describing from the outside. I have tried to write it the way a serious report should be written, which is to say with a stated mandate, an honest account of method, findings that can be checked, and a section at the end about what should actually be done. I have also tried to make it funny, because the alternative is a book about the impossibility of universal justification written in the tone of universal justification, and there is only so much irony one volume can support without buckling.
Some disclosures are owed to the reader before we start.
I am not a Lyotard scholar. There are people who have read every essay, every interview, every marginal note in the archives, and who can tell you which of his positions belongs to which year. They are useful and I have used them. What I bring is not philological. It is the view from inside the pipeline, from somebody who has to decide, this morning, whether a particular claim about dark energy is worth carrying in his own work, and who therefore cannot enjoy the luxury of treating legitimation as a topic.
I also have a program of my own. I work on a cosmological framework that competes with the standard one, and this creates an obvious temptation. A man who argues that mainstream cosmology rests on declared components is a man with a motive. I have tried to manage this the only way I know, by adopting a rule I hold myself to in the technical work and will hold myself to here: a pipeline diagnosed as unreliable cannot then be cited in support of a conclusion I happen to like. Declarations cut both ways, or they cut nothing. When my own framework has a declared component in it — and it does — I will say so.
The central claim of this book can be stated in one sentence, and since I dislike books that make you wait three hundred pages for the point, here it is. The postmodern was never a period. What Lyotard described in 1979 as an epoch that had arrived is a permanent structural condition of any sufficiently complex field of knowledge, and it had been there all along, unnoticed, the way a permanent condition tends to be.
This is not a rhetorical flourish. It is a formal result, and I will lay out the argument in ordinary language in the middle third of the book. The short version is that when a domain is complex enough, and when the descriptions of it must compress — which is another way of saying that they must be theories rather than infinite catalogs of instances — then those descriptions will necessarily disagree with one another in ways that cannot be repaired by more evidence, more goodwill, or more meetings. They will each be internally consistent. They will each be correct within their scope. And they will contradict each other where their scopes overlap. This is provable, it is provable in several independent ways, and it has nothing whatsoever to do with the twentieth century, the Second World War, the computerization of society, or the mood of the French intelligentsia. It follows from complexity and compression, which have been features of the world for rather longer than the Sorbonne has existed.
If that is right, then a great deal follows, and most of it is inconvenient for everybody. It is inconvenient for Lyotard’s admirers, because the historical drama evaporates. Nothing collapsed. There was no fall from the age of grand narratives into the age of small ones, because the age of grand narratives was itself a story people told about a situation that had never actually permitted a single unified account. It is even more inconvenient for Lyotard’s opponents, the ones who have spent four decades insisting that postmodernism is a fashionable disease and that a properly rigorous discipline would simply converge on the truth. They now have to explain away a theorem rather than a Frenchman, which is much harder work.
And then there is the second half of the argument, which is the part I could not have written without the morning routine. If the great legitimating stories really had disappeared, we would expect to find modern science operating without any. We do not find that. We find the opposite. The narrative has not vanished. It has been compiled. It went down into the machinery, into the standard model that everybody assumes, into the priors that everybody uses, into the reference cosmology that gets loaded before the analysis starts, and there it does exactly what a legitimating story always did, with one important difference. A story that is told can be doubted. A story that is executed cannot be, because there is no moment at which anybody says it. It has no author present in the room. You cannot cross-examine a default setting.
That is the finding of this report, and everything else in the book either leads up to it or follows from it. The chapters before the midpoint present Lyotard at full strength, because a critique that begins by weakening its subject is not a critique but a performance. The chapters after the midpoint do the work he did not do, which is to say they ask what a reasonable person should actually do in a world where the truths will not combine. There is an answer, it is neither relativism nor stubbornness, and it turns out to look a great deal like what competent people already do without having a name for it.
A word about method, since I claimed this was a report. I use a procedure I have come to call the tree-top method, which sounds more picturesque than it is. You climb a claim upward toward greater generality, one branch at a time, until the next step up would make the claim so general that it stops saying anything. That is the top. Then you come back down with a map of everything the ascent passed through, and the map is the useful object, not the summit. It is a good discipline for a subject like this one, where the temptation to keep climbing past the point of meaning is enormous and where the view from the very top is always the same white nothing.
There is no mathematics in these pages. This is a genuine constraint and not a marketing decision, and I want to be clear that the arguments here have formal versions, published elsewhere, with axioms and proofs and all the usual furniture. What is absent is the notation, not the rigor. I have found that equations in a book like this function mainly as a status display, a way of signaling that the author could have been harder to read if he had wanted to be. The reader is invited to check the formal papers if the plain-language version seems too easy. It usually is too easy. That is the point of writing it.
Finally, on tone. Lyotard wrote difficult prose, and a certain kind of homage would be to write difficult prose back at him. I have declined. Partly this is temperament and partly it is theory: I hold that irony is not a stylistic preference but a structural necessity for any system that predicts, since a predictor must be able to hold a model and its own failure at the same time, and that operation, performed out loud, is what we call a joke. So the jokes in this book are load-bearing. When one of them collapses, something behind it has probably collapsed too, and the reader is entitled to say so.
What follows is an argument that a very famous diagnosis was correct about the symptom, wrong about the date, and silent about the treatment. The correction is not a demolition. Lyotard saw something real, described it with more precision than his imitators ever managed, and had the honesty, late in life, to disown parts of the book that made him famous. That is more intellectual courage than most people manage in a lifetime, and it deserves a serious answer rather than either a monument or a sneer.
So let us begin where he began, with a purchase order.
Chapter One — The Report That Ate Its Commission
Governments commission reports the way anxious people buy exercise equipment. The purchase is an act of hope, the object arrives, and then it sits there. Somewhere in the late nineteen seventies the Conseil des universités of the province of Quebec decided that it wanted to know what was happening to knowledge in the most developed societies, and that a philosopher should tell them. The philosopher was Jean-Francois Lyotard, then in his mid fifties, a professor at the experimental University of Paris VIII at Vincennes, a man with a long record of political militancy and a modest record of publishing. He accepted. He delivered. The resulting document was a little over a hundred pages, arrived with the subtitle a report on knowledge, and did not contain a single enrollment projection.
It is worth pausing on what a body like the Conseil des universités would reasonably have expected. Such councils exist to advise ministers on where to put buildings and money. The natural deliverable is a survey of trends: how many students, in which disciplines, with what employment prospects, and what the new computing machinery would mean for the way universities store and transmit what they know. The commission was not frivolous. The question of what computers would do to institutions of learning was, in 1979, urgent and unresolved, and one of the intellectual events of the moment was another government report entirely, the one Simon Nora and Alain Minc had produced for the French president the previous year on the computerization of society, a document that took seriously the idea that data networks would reorganize national life. France was about to put terminals into people’s homes. Somebody had to think about what that meant.
There is a further irony in the choice of client that nobody involved appears to have noticed. Quebec in the nineteen seventies was the most interesting possible place to ask a question about the legitimation of knowledge, because Quebec had recently changed its answer. Within living memory the education of the province had been substantially in the hands of the Catholic Church, which supplied not only the schools but the story that made the schools make sense. Then, over a single decade, the province dismantled that arrangement with startling speed, built a ministry of education where none had existed, and created a public university network. A society does not do that without replacing one legitimating narrative with another, and the replacement in this case was the confident modern story of a secular technocratic state educating its citizens into prosperity. Fifteen years later, the institutions born of that replacement paid a French philosopher to tell them what was happening to knowledge, and he told them that stories of exactly the kind they were living inside had stopped commanding belief. There is no evidence that anyone laughed.
What Lyotard delivered was a philosophical argument dressed in the clothing of an administrative document, and the disguise was so effective that almost nobody noticed it was a disguise. He accepted the premise that knowledge was being transformed by computerization. He agreed that what could not be translated into quantities of information would be abandoned. And then, instead of drawing the operational conclusions his employers were paying for, he asked a question no procurement officer has ever asked, which is why anybody should believe any of it. Not whether the knowledge was correct. Whether it had standing. Whether there existed, anywhere, a reason to accept the authority of the whole apparatus, and if so, where that reason lived.
His answer was that the reason used to live in stories, and that the stories had stopped working. This is the famous sentence about incredulity toward metanarratives, and I will unpack it properly later. What concerns me here is the collision between that answer and the form it arrived in. A report is a genre with obligations. It has a mandate, a method, findings, and recommendations, and the recommendations are the reason the mandate existed. Lyotard supplied the first three and quietly declined the fourth. He told a government that the legitimating stories underwriting its education system had lost their audience, and then he did not say what the government should do on Monday morning.
I want to be careful here, because there is a cheap version of this observation and I am not making it. The cheap version says that Lyotard defrauded his patrons and ran off with the fee. He did not. What he wrote was more useful to them than a set of enrollment tables would have been, and it was more honest than the confident forecasting that such documents usually contain. The expensive version of the observation is more interesting: the missing recommendations are not an oversight but a symptom. If you have just argued that no story remains that could justify a direction, then recommending a direction is awkward. The genre demands a conclusion and the argument forbids one. Something has to give, and what gave was the genre.
The book that resulted has had a career its author did not plan. Translated into dozens of languages, it supplied a word that escaped into general circulation and has been doing unskilled labor ever since. Postmodern now describes buildings, novels, hairstyles, marketing strategies, political movements, and the general sensation that things have gotten strange. Very little of this has anything to do with the argument. The word travels; the argument stays home. This is a common fate for technical terms that sound like moods, and it is one reason the book is more cited than read, and more read than checked.
There is also the matter of the checking. A report is a document whose claims can be audited, and Lyotard’s report makes claims about science. It talks about instability, about catastrophe theory, about undecidability and quantum limits and the search for paradoxes rather than for laws. These were, in 1979, fashionable topics in the popular scientific press, and they appear in the book as evidence that science itself had abandoned the search for a single unified account. Whether the evidence supports the weight placed on it is a question I will take up when we get to the part of the argument that needs it. The short version is that a certain amount of the scientific material is decorative, and that the author himself later said something considerably harsher about it than I have just said.
Two of the report’s substantive claims deserve to be put on the table now, since the rest of this book will keep returning to them. The first is that knowledge was being detached from the people who hold it. Learning had traditionally been inseparable from the formation of a mind: you knew something because you had become the sort of person who knew it. Once knowledge is stored, transmitted, and sold as quantities of information, that link is cut. The knower becomes optional. What survives the translation into a database is knowledge; what does not survive is discarded, and nobody sends a memo announcing the discard. The second claim is blunter and, to my mind, the most durable sentence in the entire book: the question of who decides what counts as knowledge and the question of who has power are not two questions but one. That is not a fashionable provocation. It is an accurate description of how research funding, editorial policy, and peer review actually operate, and it was written before any of those systems acquired their present metrics.
The report does end with something that looks like a recommendation, and honesty requires me to acknowledge it. Lyotard proposes that legitimation might be sought in what he calls paralogy: the invention of new moves, the deliberate cultivation of disagreement, the refusal to let a field settle into consensus that merely reproduces the powerful. It is a beautiful idea. It is also, as stated, a mood rather than a mechanism. Nothing in it tells an editor which paper to accept, a committee which grant to fund, or a reader which of two incompatible cosmologies to carry into his own work tomorrow. I will come back to paralogy near the end of this book with something more operational, and I will try to do it without patronizing the original, because the original was pointing at the right vacancy.
Notice what has happened structurally, because it will happen repeatedly in this book and I would rather name the pattern once than describe it forty times. A loud conclusion was reached. The conclusion rests partly on a component that was announced rather than established. And the announcement was made in a register that made it look like a finding. This is the same defect that occupies my mornings when I read astrophysics preprints, appearing here in a book about why nobody can trust anything anymore. The situation is funny, and I intend to enjoy it, but the joke has a barb in it. The report was right about the disease and caught it.
None of which means the diagnosis was wrong. A doctor with a cough can still read a chest film. The claim I will be defending is not that Lyotard was mistaken about what he saw, but that he misdated it, misattributed it, and stopped one chapter before the useful part. He saw an actual feature of the world. He announced it as news. And then he handed in the report without recommendations, which left four decades of readers holding a diagnosis and no prescription, an experience that tends to make people either cynical or shrill.
What I propose to do, across the chapters that follow, is finish the assignment. Not because the original author was incompetent, but because the assignment turned out to be much larger than the Conseil des universités realized when it approved the budget line. They asked what was happening to knowledge. It is a good question. It has an answer. The answer takes a while.
Chapter Two — The Philosopher Who Taught in Constantine
In the autumn of 1950 a newly qualified French philosophy teacher, ranked fourth in the national examination that year, was posted to a lycée in Constantine, in the eastern highlands of Algeria. Algeria was not then a foreign country in the eyes of French law. It was administratively part of France, which is a sentence that sounds neutral until you consider what it was doing in practice, which was governing a large Muslim population as subjects while calling their territory a set of French departments. Into this arrangement walked a twenty six year old graduate of the Sorbonne, hired to teach the philosophical inheritance of the metropole to the children of both communities in the same classroom.
He stayed two years. Those two years reorganized him. He would later describe the experience in terms that leave no doubt about what he understood himself to be looking at: a colonial situation being maintained by a republic that described itself, without apparent embarrassment, as the homeland of universal rights. The universalism was not a lie exactly. The people who believed it mostly believed it. But it was being recited in a place where its application was visibly rationed, and a young man of a certain temperament, standing in front of a class in which the rationing was represented by the seating, does not forget that.
Everything that followed grows out of that room. In 1954, the year the Algerian war began, he joined the group called Socialisme ou Barbarie, founded a few years earlier by Cornelius Castoriadis and Claude Lefort as a revolt against the orthodoxies of Trotskyism. The group’s distinctive position was that the Soviet Union was not a workers’ state that had gone wrong but a system of exploitation with a new managerial class in the seat previously occupied by owners. This was, in the France of the nineteen fifties, an unpopular thing to say in both directions at once. It annoyed the Communists, who had numbers, and it annoyed the anticommunists, who had power. Lyotard spent roughly a decade as the group’s principal writer on Algeria, producing analysis, agitation, and the kind of prose that has to be right by Thursday.
For a man who would become famous for doubting grand stories, this was a period of remarkable narrative commitment. Revolutionary Marxism is a metanarrative in the strict sense: it explains where history is going, why the suffering along the way is intelligible, who the subject of emancipation is, and what any particular act means in the light of the whole. Lyotard did not merely study this story. He worked for it. He wrote in its idiom, argued inside its assumptions, and organized his life around its calendar.
He also wrote much of it under another name. In the militant press he signed himself Francois Laborde, a common enough precaution for a state employee publishing revolutionary analysis about a war his employer was prosecuting, and a detail I find impossible to leave out of a book about a thinker who would later insist that the speaking subject is not a fixed point from which sentences issue but a position produced by them. He had held two names at once, in earnest, with legal consequences attached. Whatever else his later theory was, it was not naive about the situation it described.
The Algerian writings themselves, later gathered into a single volume, are worth a moment because they are unlike anything in his famous period. They are patient, empirical, and almost journalistic: analyses of land tenure, of the composition of the nationalist movement, of the gap between the FLN leadership and the peasantry it claimed to represent. There is no play in them. A man who spends a decade producing that kind of prose and then produces a philosophy of language games has not changed hobbies. He has changed his estimate of what prose of that kind can accomplish.
Then it stopped working. Not all at once and not because of a single disappointment. The Algerian revolution succeeded and produced a one party state. The French working class declined to perform the role assigned to it by theory. The group itself split, in the way that such groups do, over the question of whether the party form was itself part of the disease, and in 1963 Lyotard left with the faction that founded Pouvoir Ouvrier, which he in turn left a few years later. By the time the students of Nanterre lit the fuse in 1968 he was teaching on that campus, a veteran of the previous revolution watching the next one arrive with different vocabulary.
Vincennes deserves a sentence of its own, because it explains the tone of everything he wrote afterward. Created in the immediate aftermath of 1968 as a concession and an experiment, it admitted students without the usual qualifications, ran classes at odd hours, and assembled a faculty that would later be exported wholesale to American humanities departments. It was chaotic, politically inflamed, and academically serious in a way that outsiders found impossible to credit. A philosopher formed in that building does not write for a committee. He writes for a room that may or may not be listening and that is entitled to walk out.
The thesis he defended in 1971 belongs to this period and is the least read of his major works, which is a pity, because it announces the obsession that outlasted every political affiliation he ever held. Its subject is the quarrel between discourse and the visible: between what can be said in sentences and what a painting or a dream does to a viewer without passing through sentences at all. Structuralism was then at its zenith, converting everything into language and its rules. He objected that something in seeing refuses that conversion. Hold that objection in mind. Twenty five years later it becomes an argument about what cannot be presented, and I will need it in a much later chapter.
I have a personal reason for finding this trajectory legible, since I made a version of it myself, from a very different starting position, and I know what the inside of a departed conviction looks like. So I will state the point plainly rather than pretending to neutral distance. Incredulity toward grand stories reads very differently depending on who is doing the disbelieving. From a person who never believed any of them, it is a shrug. From a person who spent fifteen years writing for one, it is testimony. Lyotard’s famous formula is not the cool observation of a spectator noticing that the fashion has changed. It is a report from somebody who was inside the machine when it seized.
This matters for the argument of this book in a specific way. Testimony of that kind is enormously valuable and systematically unreliable in one direction. The person who has lost a faith knows things about it that no outside observer can know, and is also inclined to believe that its collapse was an event, because in his own life it was one. A conviction that ends in a particular decade feels like something that ended in that decade. The temptation to promote a personal chronology into a historical one is almost irresistible, and I am going to argue that Lyotard did not resist it.
The rest of the biography can be summarized briskly, since it is the ordinary shape of a French academic career, with detours. There were the years teaching in provincial lycées, including a stretch at the national military academy at La Flèche, which is a placement of considerable comic value for an antiauthoritarian Marxist and which he seems to have handled with the deadpan competence of a man who needed the salary. There was the Sorbonne, then Nanterre. There was the doctorate, defended in 1971, on the relation between discourse and the figural, supervised by Mikel Dufrenne, which is a book about aesthetics that most of his later admirers have not read. There was Vincennes, the experimental university created after 1968, where the faculty list read like a directory of everything that would later be exported to American literature departments. There were the visiting appointments in California and Brazil and finally Atlanta. He died in Paris in April 1998 of a leukemia that moved fast, while preparing a conference on postmodernity and the media, and he is buried at Père-Lachaise.
The private life can be given in a line or two, since he kept it out of the work and I see no reason to drag it in. He married twice, had children by both marriages, and one of his daughters became a philosopher and a specialist in his writings, which is either the happiest or the most alarming outcome available to a parent in that profession.
What I want to preserve from this chapter is not sympathy, though he earns some, but a methodological warning. When a thinker announces that an epoch has ended, it is always worth asking what ended for him. The question is not a smear. It is a control experiment. If the epoch really ended, we should be able to find its ending in places where our thinker never was, in disciplines he never studied, in centuries before he was born. If we cannot, then what we have is not an epoch but a biography with excellent prose style.
Chapter Three — Auguste Comte Writes the Story Lyotard Will Bury
To understand what it means for a grand story to lose its audience, it helps to watch one in perfect health, with its color high and its confidence intact, and for that there is no better specimen than Auguste Comte. He was born in 1798, worked for years as secretary to the utopian planner Henri de Saint-Simon, quarreled with him permanently over credit, suffered a severe mental collapse, threw himself into the Seine, was fished out, and then delivered a course of lectures that founded a discipline and gave the modern world its most durable picture of intellectual progress.
The picture is the law of three stages. Human thought, according to Comte, passes through a theological phase in which events are explained by the will of persons or gods, a metaphysical phase in which the gods are replaced by abstractions such as nature or essence, and finally a positive phase in which we stop asking why and start describing how, contenting ourselves with the relations among observable phenomena. Every branch of knowledge makes this journey, and they make it in a fixed order, because the simpler and more general sciences mature first. Mathematics and astronomy arrive early. Physics and chemistry follow. Biology takes longer. And at the end of the queue, arriving last because it depends on all the others and is the most complex thing in the universe, stands the science of society, which Comte was obliged to name himself, and which he called sociology.
Consider what this story does. It takes a chaotic accumulation of human inquiry and gives it a direction, a sequence, and a destination. It explains why old ideas were not stupid but immature. It tells any working scientist that his particular labor, however narrow, is a contribution to a single ascending movement. And it delivers a legitimating verdict at the end: the knowledge produced by positive science deserves belief because of where it stands in the story. This is exactly what a metanarrative is for. It does not add a single fact. It confers standing on facts obtained elsewhere.
Comte then did something that his admirers have been apologizing for ever since, and that I regard as the most intellectually honest act of his career. He noticed that a story of this kind cannot survive on argument alone, and he built it a church. The Religion of Humanity had a calendar of thirteen months of twenty eight days, each month named for a benefactor of the species, so that one might find oneself living through the month of Gutenberg or the month of Shakespeare. It had saints, sacraments, a catechism, and a High Priest, a position Comte generously agreed to occupy. It had a private devotional practice organized around the memory of Clotilde de Vaux, the woman he loved briefly and idealized permanently after her death. Thomas Huxley described the result as Catholicism minus Christianity, which was meant as an insult and functions perfectly well as a definition.
It is easy, and pleasant, to laugh at this. The temptation should be resisted for about ten minutes, because within those ten minutes Comte is telling us something that the whole subsequent history of the legitimation problem has struggled to hear. He understood that a story which authorizes knowledge has to be told. It needs occasions, repetitions, a community that rehearses it, and a form in which the young receive it before they can evaluate it. A legitimating narrative that exists only as a proposition in a book is not doing any work. Comte’s calendar is absurd, but it is absurd in the direction of a real requirement.
It is worth recording what the word positive was doing in all this, since it has drifted. Comte did not mean cheerful and did not mean confirmed. He meant the renunciation of a certain kind of question. The positive mind gives up asking what things are and why they exist, and confines itself to how they covary, because the first sort of question has no procedure attached and the second does. This is a genuine act of intellectual discipline and a genuine loss, and Comte knew it was both. He also coined altruism, a word we now use without any memory of the system it was built to serve, which is roughly the fate of everything he made.
The quarrel with Saint-Simon that preceded all this was the ordinary tragedy of an assistant who has become a rival. Comte spent seven years as secretary to a man whose ideas he was partly generating, and the break came over whose name would appear on the work. He spent the rest of his life insisting on the originality of a system that had grown in another man’s greenhouse, which is neither unusual nor discreditable, but which does illustrate something about legitimating stories: they are always, in part, stories about who is entitled to speak.
Two features of the system deserve mention because they show how thoroughly Comte had thought about the boundaries of his own construction. The first is his treatment of psychology, which he refused to admit into the hierarchy of sciences at all. Introspection, he argued, is structurally impossible: the organ cannot observe itself in the act of observing, and the attempt produces not data but an echo. Whatever one thinks of the conclusion, the reasoning is a genuine piece of epistemology and it anticipates by a century the difficulties that experimental psychology would have with self report. The second is the practice he called cerebral hygiene, by which he meant that he had stopped reading. Not casually, but as a policy: after a certain point in his career Comte deliberately avoided the works of contemporaries in order to keep his own system free of contamination.
Cerebral hygiene is the funniest thing in nineteenth century philosophy and also the most instructive, because it is what a declared foundation looks like when a man is honest enough to admit he is declaring it. Comte knew that his system rested on choices which no evidence had forced upon him, and he protected those choices by sealing the input. Every thinker does some version of this. Almost nobody labels the bottle. When we reach the machinery of contemporary science and I start pointing at conventions that are protected from revision by the simple fact that nobody names them, I want the reader to remember that Comte at least had the courtesy to name his, and to install a doorbell that did not work.
The story was enormously successful in its serious form. It shaped positivist movements across Europe and, remarkably, in Latin America, where it took institutional root in Brazil among the military officers who overthrew the empire in 1889 and where it left a permanent souvenir: the words order and progress on the national flag, lifted from Comte’s own formula. The flag is still flying. The metanarrative that generated it is, as a living object of belief, gone.
The afterlife is instructive in both directions. Comte’s disciples split almost immediately between those who wanted the science and those who wanted the church, with Emile Littre leading the party of embarrassment and the priesthood carrying on regardless. In England John Stuart Mill admired the early work, corresponded warmly, and then recoiled from the later system with the particular horror of a liberal who has watched a friend invent a state religion. Durkheim inherited the sociological program while quietly dropping the calendar. In Brazil the church actually got built, and its temple in Rio still stands. The lesson is not that Comte was a crank with one good idea. It is that the scientific content and the legitimating apparatus separated cleanly, and that everybody kept the content and nobody kept the apparatus, which left the content standing on a foundation that had been carted away while the building remained occupied.
So we have a control case. Something did in fact happen to the story Comte told, and it happened before anybody was talking about postmodernity. By the end of the nineteenth century, professional scientists had largely stopped needing the three stages. They did not refute them. They simply proceeded without them, in the way that a grown child stops citing the family myth about how the business was founded. The narrative was not defeated. It became unnecessary to say aloud, and it was gradually replaced by something quieter that did the same job.
This is where a rereading becomes possible, and where I will introduce, briefly and without ceremony, a distinction I use throughout my own technical work. Comte’s real discovery was not the sequence of three stages, which is a piece of nineteenth century philosophy of history that has aged as badly as the calendar. His real discovery was that inquiry requires an organizing structure which persists while its contents are replaced, and which holds the enterprise together across the failures of any particular theory. Call this the persistence requirement. What makes a body of knowledge one thing, rather than a heap of results, is that something invariant survives the churn. Comte thought that something had to be a narrative with priests. He was wrong about the priests. He was not wrong that something has to be there.
The question this book pursues is what occupies that position now. Lyotard’s answer was that nothing does, that the position stands empty, and that we have all quietly adapted to the vacancy. My answer is that the position is fully occupied, that the occupant is extremely difficult to see, and that the difficulty is not an accident. But we are not there yet. First we have to give the case for the vacancy its strongest possible statement, which is the business of the next several chapters, and which requires taking Lyotard more seriously than his enemies and more literally than his friends.
Chapter Four — Incredulity, and What It Cost
A metanarrative is not a big story. It is a story about stories, and its job is not to entertain but to authorize. When a chemist tells you what happens when two reagents meet, that is a narrative in the ordinary sense: this, then that, for this reason. When somebody explains why you should believe chemists in general, why their institution deserves your tax money and your children’s attention, and what the whole enterprise of measuring things is ultimately for, that is a narrative of the second kind. It sits above the first, contributes no reagents, and decides who gets to speak.
Lyotard identified two such stories running underneath modern knowledge, and their difference matters more than their similarity. The first is political and, in his telling, essentially French. Knowledge is justified because it frees people. The subject of the story is humanity, or the citizen, or the worker, and the plot is emancipation: ignorance is a form of bondage, education is a form of liberation, and the state that funds the laboratory is discharging a debt to the future. This is the story printed on the founding documents of every public education system on earth, including the one that was paying for his report.
The second story is philosophical and essentially German. It descends from the reorganization of the Prussian university in the early nineteenth century and it says something quite different. Knowledge is justified not because it liberates anybody but because it is a single thing gradually coming to know itself. The disciplines are not a collection of trades; they are organs of one developing intelligence, and the university exists to keep them in the same building so that the unity can be maintained. This is why a research university has a philosophy faculty at all, and it is why the word doctorate is attached to chemistry, history, and musicology alike, as if these were all the same activity performed on different material. They are not the same activity. The story says they are.
The second story has an address and a date, which helps. In 1810 a new university opened in Berlin under a plan largely written by Wilhelm von Humboldt, with Fichte and Schleiermacher arguing over its shape, and its founding idea was that teaching and research belong in the same institution because both are moments of a single unfolding. The professor is not a transmitter of settled results but a participant in an inquiry that the student joins. Nearly every research university on earth is a descendant of that building, including the ones in countries that have never heard of Humboldt, and the family resemblance is visible in the architecture of the doctorate.
Incredulity toward both is a specific mental state and it is worth describing precisely, because the usual paraphrase gets it wrong. Incredulity is not refutation. Nobody disproved emancipation. No committee sat down and demonstrated that knowledge is not the self development of spirit. What Lyotard claimed had happened was smaller and much worse: the stories could no longer be told without embarrassment. A minister can still say that education liberates, and does, at graduation ceremonies. The sentence retains its ceremonial function and has lost its capacity to settle anything. Everybody present knows that the university is also a sorting mechanism, a credentialing monopoly, and an employer with a real estate portfolio. The story survives as etiquette.
He attributed a good deal of this to the twentieth century’s demonstration of what an emancipatory project can do when it is fully equipped. If the story says that history moves toward the liberation of humanity, then a great deal of what happened between 1914 and 1945 has to be either explained or absorbed, and the explanations available were not honorable. This is the point at which his writing loses its lightness. He was not making a debating move. A generation of European thinkers came out of that period unable to say certain sentences aloud, and he was one of them.
At this point a reader with any philosophical training has an objection loaded and ready, and it is such an obvious objection that it deserves to be fired early rather than left to fester. The claim that all grand narratives have lost credibility is itself a grand narrative. It tells a story about all of human knowledge, assigns it a plot with a before and an after, and asks to be believed on grounds it has just declared unavailable. This charge was pressed hard, most famously by Jurgen Habermas, who regarded the whole enterprise as a fashionable abandonment of the unfinished project of modernity, and it has been repeated ever since by people who have not read either party.
The objection is correct as stated, and Lyotard’s various answers to it are not his best work. He tried to say that his own account was a small story rather than a large one, which is unconvincing given its scope. He tried to say that it was a report rather than a philosophy, which is a jurisdictional dodge. My own answer is different from his and will take the middle of this book to develop, but I can indicate its shape now: the diagnosis survives the objection precisely when it is detached from the historical claim. A structural condition that has always held is not a narrative about anything. It has no plot, no before, and no after. What cannot survive the objection is the periodization, and the periodization is the part I intend to remove.
Now the bill. It is customary to treat the loss of grand narratives as a liberation, a clearing away of oppressive universals so that difference may flourish, and there is something to that. But a legitimating story is load bearing, and when you remove it, several things you liked come down with it.
One more clarification before the tally, since the term gets used loosely. Losing a metanarrative is not the same as disbelieving the science it authorized. Nobody stopped believing in thermodynamics. What lapsed was the second story layer, the one that explained why the whole enterprise deserves its position in a society. Results kept their credibility; the institution lost its warrant. That combination is unstable in an interesting way, because an institution with unquestioned results and no warrant is exactly the sort of thing that gets managed by whoever pays for it.
The first casualty is critique. If you want to say that an institution is unjust, you need a standard that the institution does not itself supply, and the standards available in modern political language mostly came from the emancipation narrative. Take away the story and the sentence this is oppressive becomes a report on the speaker’s preferences. Lyotard saw this coming and spent a good part of his later career trying to build an ethics that would work without a universal, which is the subject of a later chapter and is by some distance the most impressive thing he attempted.
The second casualty is the unity of the university. If there is no story in which chemistry and musicology are organs of one intelligence, then a university is an accounting convenience holding a set of unrelated professions, and it will eventually be managed as one. Anybody who has watched a dean explain why a language department must demonstrate its contribution to regional economic development has seen this play out. The reorganization is not a betrayal of the institution’s values by philistines. It is what happens to a building when the story that put the rooms next to each other stops being told.
The third casualty is the argument for public patience with useless research. Curiosity driven work is expensive, most of it leads nowhere, and its defense has always been narrative: this is how knowledge grows, and knowledge growing is good in itself. Without that, every project must justify itself by its expected yield, which is a different criterion with different winners, and which is the subject of the sixth chapter.
There is one more cost, and it is the one that irritates me most, because it is a cost that the doctrine imposes on its own admirers without their noticing. If the grand stories are gone, then any claim to have discovered something general looks like a relapse. A whole intellectual generation learned to hear the word universal as a warning siren, and so learned to treat every structural argument as an attempted power grab in fancy dress. This makes certain true things very difficult to say. I am going to have to say some of them in the middle third of this book, and I would rather deal with the siren now than pretend it will not go off.
The peculiar thing about the reception of all this is how thoroughly the mourning was mistaken for celebration. Lyotard is filed, in the popular imagination and in a good many undergraduate courses, as the man who cheerfully announced that everything is relative and nothing is true. Read the actual sentences and you find something closer to a coroner’s report written by a relative of the deceased. He had believed one of these stories, professionally, for fifteen years. He was not dancing.
Chapter Five — Games With No Referee
Chess and poker can be played with the same brain, in the same room, on the same evening, and there exists no move that is legal in both. This is not a defect in either game. It is what it means for them to be different games. Ludwig Wittgenstein, in the work published after his death, used exactly this sort of observation to dismantle a picture of language that had held philosophy for three centuries, including his own earlier picture, and he did it with an unhurried cruelty that still makes the book uncomfortable to read.
The picture he attacked says that words get their meaning by standing for things, and that sentences are true when they correspond to arrangements of those things. Wittgenstein’s counter proposal was that meaning is not a relation between a word and an object but a matter of use within an activity. Language is not one instrument but a toolbox, and the tools are not variants of the hammer. Asking, thanking, cursing, praying, greeting, joking, ordering, reporting, calculating: these are different activities with different rules of success, and the rules are not written anywhere. They are exhibited in the playing. He called these activities language games, and he was careful to add that the family of games has no single feature common to all of them, only overlapping resemblances, the way members of a family share a nose here and a laugh there without any one trait running through the whole line.
Wittgenstein’s examples are deliberately unglamorous, which is part of the method. He opens with two builders, one of whom calls out the name of a stone and the other of whom brings it, and asks whether the shout is a word, a command, a description, or the whole of a language. He asks what game is being played when a child is taught to count, when somebody guesses a riddle, when a man reports a dream. And he refuses, throughout, to supply the general theory that his readers keep waiting for, on the grounds that the demand for one is the disease.
Lyotard borrowed this and did something to it that Wittgenstein would probably have refused. Wittgenstein was describing a fact about how language works, with no political charge attached. Lyotard made it structural and, eventually, judicial. In his hands the different modes of speech become what he called regimens of phrases and genres of discourse, and the crucial claim is not that they differ but that there is no move above them. There is no metalanguage. There is no referee’s rulebook standing outside chess and poker in which the question of whether a bluff beats a knight has an answer. Each genre supplies its own criterion for what counts as a successful move, and criteria do not travel.
Consider what this does to an argument. Two parties dispute a case. One speaks in the genre of cognition, where the winning move is a demonstration, and the other speaks in the genre of prescription, where the winning move is the establishment of an obligation. Nothing derived from what is the case will settle what ought to be done, a point Hume made in a single paragraph and which philosophy has been failing to get around ever since. If the two parties are locked into different genres, the dispute is not hard. It is not even a dispute in the ordinary sense. It is a situation in which one party’s best move does not register on the other’s scoreboard.
This is where the philosophical literature has been circling ever since, mostly without knowing that it was circling. In 1985, an American philosopher named Robert Fogelin published a short paper introducing the notion of deep disagreement, and it has been generating commentary for forty years. His claim was that ordinary argument presupposes shared ground: to argue about whether a policy is just, we must already agree about what justice is for, which considerations count, and how to weigh them. Where that ground is absent, argument does not merely become difficult. Its preconditions fail. He borrowed from Wittgenstein’s late notes on certainty the idea of propositions that are not themselves defended but hold everything else in place, the way a door needs hinges that do not turn.
Fogelin’s examples were the disputes over abortion and over affirmative action, and he chose them for a specific reason that is usually lost in summary. His point was not that these debates are heated. It is that both sides reason competently. Take the moral status of the fetus as the primary consideration and follow the argument carefully, and you reach one conclusion. Take bodily autonomy as the primary consideration and follow the argument with equal care, and you reach the opposite one. Neither party has made a logical mistake. Neither is being stubborn. The disagreement lives one level below the arguments, in the choice of what is fundamental, and that choice is not itself the kind of thing that arguments are built to adjudicate.
Subsequent work has sharpened Fogelin’s picture in ways that matter for the argument I will be making. Scott Aikin has argued that the original examples run together several distinct species: disagreements where the parties use different logical principles, disagreements where they weigh evidence differently, and disagreements where the same word is doing different work in each mouth. Chris Ranalli has connected the whole discussion to the epistemology of hinges, arguing that a disagreement rooted in different hinge commitments is irresolvable in a way that a merely stubborn disagreement is not, because hinges are not the sort of proposition for which reasons can be offered. Jan Albert van Laar and Erik Krabbe have taken a more practical line, asking what a dialogue can still accomplish when the frameworks diverge, which is closer to the right question than anything else in the literature.
An analogy from a duller profession may help. Two accountants examine the same company and produce different valuations. Neither has made an arithmetical error. They are working under different accounting standards, one of which requires a class of assets to be carried at historical cost and the other at market value. Both sets of books can be audited clean. The disagreement is real, the numbers are incompatible, and no amount of recounting will fix it, because the divergence is in the standard rather than in the counting. The interesting question is not who is right. It is what a person should do who has to make a decision using both sets of books.
The literature that followed divides, as literatures do, into optimists and pessimists. The optimists point out that the parties still share a great deal: rules of consistency, standards of evidence, a common language, an interest in not being ridiculous. Surely these shared resources give some purchase. The pessimists reply that shared logic settles nothing when the premises diverge, and that a disagreement rooted in what one takes as bedrock is by construction beyond the reach of reasons.
Here is what I want the reader to notice, because it is the hinge of this book. In four decades, neither side proved anything. The optimists assert that resolution is possible without ever specifying the structural conditions that would permit it. The pessimists assert that resolution is impossible without identifying the conditions under which impossibility actually holds. Both positions are stated with great sophistication and neither is stated with a theorem. And neither camp has offered a word of practical advice to the person who has to act this afternoon inside a disagreement of this kind, beyond the counsel to agree to disagree, which is not advice but a description of the problem in a soothing voice.
The same gap runs through Lyotard. His claim that there is no metalanguage is asserted, illustrated, and made vivid. It is not demonstrated. He offers no account of why complex domains should generate incompatible genres rather than converging on one, and no account of what happens to a rational agent who has to live in several at once. That absence is not laziness. Nobody in his tradition had the tools, and the tools that existed in the neighboring tradition were pointed elsewhere. It took a rather different sort of argument to close the gap, and closing it changes what the whole diagnosis means. That is the business of the twelfth chapter, and I promise to arrive there without further teasing.
Chapter Six — Performativity, or Knowledge Billed by Output
Suppose the stories really have stopped working, and suppose there is no referee above the various genres of speech. A practical problem arises immediately, and it is not philosophical. Somebody still has to decide which laboratory gets the money. Committees meet. Budgets close. The question of legitimation may be theoretically homeless, but the administrative question it used to answer is due on Friday.
The answer that filled the vacancy is the one Lyotard named performativity, and his description of it is the most prescient passage he ever wrote. In the absence of a story that says what knowledge is for, the criterion becomes the ratio of output to input. A claim, a program, or a whole discipline earns its standing by being efficient: by producing more result per unit of resource than the alternatives. Truth does not disappear from this arrangement. It is demoted. It becomes one of the things that efficient research tends to produce, valued for its contribution to performance rather than the other way around.
The elegance of this solution should not be underestimated, and most critics of it are too indignant to see how good it is. Performativity requires no narrative whatsoever. It needs no account of humanity’s destiny, no claim about the unity of the sciences, no shared conception of the good. It needs a numerator and a denominator. It can be applied by people who disagree about everything else, it is portable across cultures and languages, and it produces a ranking, which is what committees exist to consume. As a replacement for a collapsed legitimating story it has the enormous advantage of being installable.
What Lyotard could not have known in 1979 is how thoroughly it would be installed, and with what instruments. The bibliometric apparatus that now governs academic life was then a specialist curiosity. Citation indexing had been invented in the previous decade as a tool for librarians deciding which journals to buy, and the impact factor was a number about periodicals, not about people. The index that ranks an individual researcher by the intersection of paper count and citation count was proposed only in 2005, by a physicist, in a paper that has since been cited tens of thousands of times, which is either an endorsement or a very long joke. Whole national systems now exist to evaluate university departments by periodic assessment of research output, distributing money accordingly. None of this was imposed by a conspiracy of accountants. It was adopted with enthusiasm, largely by academics, because the alternative was a return to patronage and the judgment of eminent men, and nobody wanted that either.
It is worth seeing what the alternative looked like when it was still available. In 1945 Vannevar Bush delivered a report to the American president under a title borrowed from the mythology of the frontier, arguing that basic research should be funded generously by the state precisely because nobody can say in advance what it will yield. The argument was frankly narrative: knowledge is a frontier, the nation advances by exploring it, and the explorers must not be asked for a business plan. That document created the postwar research system. Try submitting it as a funding proposal today and see how far it travels.
Lyotard added a darker observation about how the new criterion enforces itself, and the word he used was terror. Not in the political sense, but in a structural one: the efficiency criterion does not argue with an unproductive player, it removes him from the game. There is no debate, no refutation, and no verdict. There is a line item that does not appear in next year’s budget. A criterion that eliminates rather than persuades is unanswerable in a specific technical sense, since being eliminated is not a position from which one can reply.
The trouble is a piece of folk wisdom that has been independently discovered in half a dozen fields and is usually credited to a British economist who observed it in monetary policy. When a measure becomes a target, it stops measuring. Any number used to allocate resources will be optimized by the people whose resources depend on it, and optimization does not respect the difference between the thing measured and the thing intended. The literature on this in science is now enormous and thoroughly documented. Papers are sliced into the smallest publishable units, because count is the numerator. Groups agree, sometimes tacitly, to cite one another. Analyses are run repeatedly with small variations until a statistically significant result appears, which is not fraud in the eyes of most who do it, merely diligence pointed in a convenient direction. Whole industrial operations exist to sell authorship on manufactured papers. And a large fraction of published findings in several fields turn out, when somebody bothers to repeat the experiment, not to repeat.
I want to be careful about the moral tone here, because there is a version of this complaint that is simply nostalgia for a golden age that never existed. Science before bibliometrics was not a republic of disinterested truth seekers. It was smaller, more closed, more dependent on personal reputation and the good opinion of a handful of men in a handful of countries, and it excluded almost everyone. Metrics were introduced in part to break that. They did break it. The system that replaced it is more open and more measurable and has its own characteristic disease, which is that it rewards the visible form of scientific activity rather than its content, and that the two come apart under pressure.
There is a further consequence that concerns me directly and that Lyotard did not anticipate at all. Performativity does not merely decide which projects get funded. It shapes what a finding is allowed to look like. A result that says the data cannot presently distinguish between these two accounts is a true statement about the world and a poor performer: it cites badly, headlines badly, and funds worse. A result that says we have determined the value of this quantity to unprecedented precision performs beautifully, even when the precision rests on choices that were made rather than measured. The criterion does not corrupt anybody. It quietly reweights the space of publishable conclusions, and after two decades of reweighting, an entire field can find itself unable to say certain honest sentences without professional cost.
There is one more thing to say, and I will say it briefly because it belongs to a chapter much later in this book. The most remarkable property of performativity as a legitimating principle is that it does not require anyone to advocate it. A story needs a teller: somebody has to stand up and say that knowledge serves emancipation, and can be argued with when he does. A ratio needs only a spreadsheet, and the spreadsheet is now a piece of software that runs on the university’s servers whether anybody believes in it or not. Lyotard predicted that efficiency would replace the story. He did not predict that it would stop needing a mouth.
Chapter Seven — Knowledge as Merchandise, and the Receipts
Prophecies are usually judged too generously, because the people doing the judging are fans. The honest procedure is to write down what was predicted, wait, and then check the receipts without adjusting the wording afterward. Lyotard made a specific, checkable forecast about what knowledge would become, and it has now had almost half a century to come true or not. The forecast was that knowledge would be produced in order to be sold and consumed in order to be valorized in a new production, that it would cease to be an end in itself, and that it would lose what he called its use value. He added that states would one day contest control of information the way they had contested control of territory and then of labor.
The receipts are unambiguous, and they are more interesting than a simple confirmation.
Consider what happened to the scholarly journal, an institution invented in the seventeenth century as a way for gentlemen to inform one another of experiments. In its modern form it works like this. A researcher, paid by a public institution, performs work funded by a public grant, writes it up without payment, and assigns the copyright to a commercial publisher. Other researchers, also publicly funded, review it without payment. The publisher then sells access back to the institutions that produced the whole thing, at prices negotiated under conditions that have prompted competition authorities in several countries to take an interest. The operating margins in this industry have at times exceeded those of the large technology firms, which is remarkable for a business whose two principal inputs are donated. When the reform movement finally arrived, it did not abolish the toll. It moved it: instead of the reader paying to get in, the author now frequently pays to get out, a fee that runs into thousands per article and which is, of course, drawn from the same public grants.
I record this without much indignation, because indignation is cheap and the situation was not built by villains. What matters for the argument is the structure. A thing that used to circulate as a contribution now circulates as a commodity, and the transformation happened without anybody deciding it should. There was no moment at which the community of scholars voted to sell its output back to itself.
The second half of the forecast concerned the knower rather than the merchandise, and it has come true in a way that is harder to see because it happened to people rather than to institutions. The older European idea of higher education held that a student was being formed, not filled: the point of the exercise was a mind of a certain shape, and what it contained was secondary and replaceable. Detach knowledge from the knower, package it as transferable content, and that idea has nowhere to live. The vocabulary of the last two decades records the shift with brutal clarity. Institutions no longer speak of forming students; they speak of delivering learning outcomes, of stackable credentials, of skills that can be acquired in modules and verified by badges. Every one of those words assumes that the substance is separable from the person and can be moved without loss. Some of it can. The interesting question, which nobody in the credential business is paid to ask, is what happens to the part that cannot.
Two features of the modern arrangement would have delighted him for their sheer economy. Journals are sold in bundles, so that a library wishing to subscribe to the four titles its faculty actually reads must purchase several thousand it does not, an arrangement whose logic is drawn directly from cable television. And the metric that determines a journal’s price commands, its position in the ranking, is computed from citations, which are contributed free by the same academics who will later pay to be published in it and pay again to read it. The circuit is closed and every node in it is a public institution. If a satirist had proposed this in 1979 he would have been told it was too broad.
The larger version of the forecast has aged even better. Nations now do contest information as they once contested territory: through export controls on the machines that process it, through restrictions on where data may be stored, through the treatment of certain model weights as objects of national security. Corpora of text assembled from the writings of everybody who ever posted anything have become capital assets of a size that has no precedent, and the litigation now working through the courts is, in substance, a dispute about whether the exteriorization of knowledge from its knowers has a limit. Lyotard would have recognized every element of this except the scale.
There is one measurement of my own that belongs here, and since we agreed to use my terminology openly I will not disguise it. I have studied what I call the time density of the information environment: how much of the interval between the appearance of a piece of information and its assimilation into general circulation has been compressed, and how strongly the sources of that circulation have converged. The two findings are related and they cut against the intuition most people carry. The interval has collapsed dramatically, which everybody expects. What is less expected is the convergence: as the volume of available information rises, the number of effectively distinct channels through which it reaches anyone falls. More information, arriving faster, through fewer paths. That combination has a name in engineering, and the name is not diversity.
Note what this does to the picture of the small stories flourishing after the fall of the big one. The postmodern promise, as it is usually retailed, was a garden of local narratives, each cultivating its own patch, with nobody in a position to impose a single account. What actually developed was a global infrastructure that distributes local narratives at industrial scale through a handful of pipes, and that ranks them by a criterion nobody chose deliberately. The micronarratives are real. They are not autonomous. They live in a warehouse.
A last observation on the physical side of all this, which I mention because it embarrasses a certain kind of talk about the immateriality of the information age. Storing and processing knowledge costs energy, and the cost is not metaphorical. There is a hard thermodynamic floor beneath the erasure of a bit, established long before anybody built a data center, and the systems we now use to compress the world’s text into models sit above that floor by a margin that is shrinking as engineering improves. Knowledge became a commodity, and commodities have shipping costs. The postmodern condition has a cooling bill.
It is only fair to record where the forecast went wrong, since I have been generous about where it went right. He expected the nation state to lose its grip on information to firms that operate across borders, and to become a spectator to a contest between commercial powers. That is half of what happened. The other half is that states discovered they could regulate the firms, subsidize them, buy from them, and in several cases depend on them for defense, which produced not a retreat of the state but a fusion that nobody at the time had a category for. He also expected the merchandising of knowledge to render the teacher obsolete, replaceable by machines and memory banks. Instead the teacher was retained and reclassified as a producer of content, which is worse than obsolescence in every respect except the one that matters to a payroll department.
None of this refutes Lyotard. All of it confirms him, which is precisely why I am spending a chapter on it. The reader should be clear that I am not building toward the conclusion that he was a fraud whose predictions failed. He was, on this point, better than almost anybody writing at the time. The problem with the report lies elsewhere, and I would rather establish his credit before drawing on it.
Chapter Eight — The Differend
Some wrongs come with a receipt and some do not. If a contractor takes your money and does not build the deck, you have a grievance and also the apparatus for pressing it: a contract, a court, a standard of evidence, a rule that both parties recognize. The system may fail you in practice, but it exists in principle, and your complaint is expressible within it. Lyotard called this situation a litigation, and he was not very interested in it.
He was interested in the other case, and he gave it the name that became the title of the book he considered his real work of philosophy. A differend arises when two parties are in conflict and there exists no rule of judgment applicable to both, so that the resolution of the dispute in the idiom of one party automatically wrongs the other. What makes it more than a hard case is the second half of the definition. The party who suffers is deprived of the means to demonstrate the suffering, because the only available means belong to the tribunal, and the tribunal speaks the language in which the wrong is invisible. A plaintiff who loses the ability to argue his case does not merely lose. He is converted into a victim, which is Lyotard’s technical term for someone whose damage cannot appear as damage.
The word itself is ordinary French legal vocabulary, meaning a dispute, and the choice is deliberate. He is not inventing a mystical category. He is pointing at something that the machinery of dispute resolution encounters constantly and has no name for, because naming it would require the machinery to admit that some cases arrive in a language it does not process.
The book opens with an example that is designed to be unbearable, and I want to handle it with care because it is easy to misrepresent. In the years before Lyotard wrote, a French academic had achieved notoriety by denying the existence of the gas chambers and by proposing a criterion for evidence that was constructed to be unsatisfiable: he would believe in the gas chambers when he met a witness who had personally been killed in one. Lyotard’s use of this is not a concession to the denier and is the opposite of one. He takes the argument apart to show its shape. A rule of evidence has been proposed which guarantees in advance that no evidence can qualify, since the only qualified witnesses are precisely those the machinery destroyed. The reality of the crime is then declared unproven, by a standard designed so that proof is impossible. This, he says, is what a differend looks like in its pure form: the extermination of the witnesses and the demand for witnesses in the same act.
What follows from this in his hands is not despair but an obligation. If a wrong exists that has no available idiom, then the task is to invent one. New phrases, new genres, new procedures of testimony, so that what could not be said becomes sayable and the victim can become a plaintiff again. He describes literature, philosophy, and sometimes politics as the workshops where this invention happens, and he treats the invention as an ethical duty rather than a creative option. It is the most morally serious thing in his work and it is almost entirely absent from the popular image of the man.
The second example he uses is drawn from his old political vocabulary and translates the concept out of atrocity into ordinary life. In a labor dispute, the employer’s idiom treats the worker’s capacity to work as a commodity with a price, exchanged under a contract freely entered. Within that idiom, everything is in order: an offer was made, accepted, and honored. The worker’s idiom treats his working time as a portion of his life, not as a good he owns separately from himself. There is no neutral courtroom in which these two descriptions can be compared, because every available courtroom is built out of contract law, which has already adopted the first description before the parties arrive. The worker is not being cheated by a corrupt judge. He is being processed by a jurisdiction that cannot hear his sentence.
There is a further move in the book which strikes most readers as a piece of avant garde provocation and which is, I think, an exact technical observation. Lyotard insists that silence is itself a phrase. When somebody does not speak, something has been communicated, and the interesting work is determining what the silence denies. It may deny that the addressee is the right one to hear this. It may deny that the situation is of the kind the tribunal thinks it is. It may deny that the speaker has the standing to say it. Or it may deny that the thing has a formulation at all. Four different silences, indistinguishable from the outside, requiring different responses. Anyone who has sat in a meeting where a person who obviously has an objection declines to state it will recognize the taxonomy immediately, and will also recognize that guessing wrong about which silence it is makes everything worse.
It is not difficult to see where the concept came from. A man who spent his twenties teaching in a colony under a republic that described itself as universal had watched, at close range, a jurisdiction in which certain grievances could not be phrased without first being translated into the language of the party causing them. He did not invent the differend at a desk. He met it in a classroom.
Once you have the shape, you find it everywhere. Land claims brought by peoples whose relation to territory was never a property relation, argued before courts that recognize only property. Testimony about experiences for which the diagnostic manual has no entry, offered to a clinical system that records only entries. Complaints about the harms of a technology, made to a regulator whose statutory mandate covers only quantified risks of specified kinds. In each case the tribunal is not necessarily hostile. It is deaf in a particular direction, and its deafness is constitutive rather than accidental.
I will make my own use of this concept much later in the book, and it would be dishonest not to signal now what that use will be, because it has been sitting under every chapter so far. When a scientific paper reports a result, the result is expressed in a language that has room for measurements, for derivations, and for uncertainties attached to both. It has no room at all for a sentence spoken by an assumption on its own behalf. A quantity that was chosen rather than found cannot say so. It cannot object that it is being loaded beyond its capacity, and there is no procedure by which its objection could be entered into evidence, because the entire apparatus of statistical reporting is built to describe the behavior of measurements. The wrong, if there is one, is done in a jurisdiction with no clause covering it. Whether that is a genuine differend or merely an untidy convention is a question I will argue properly in its place. I raise it here so that the reader can watch for it.
There is a criticism of all this that deserves an airing, and it is not the usual one about relativism. It is that the concept, once you have it, is too easy to apply. Any party losing any argument can claim that the tribunal’s language is rigged against him, and the claim is unfalsifiable by construction, since the absence of expressible evidence is exactly what the concept predicts. Lyotard has no procedure for distinguishing a real differend from a convenient one, and he does not appear to have looked for a procedure very hard. This is a serious gap. Somebody has to be able to tell the difference between a witness who genuinely has no words and a litigant who has run out of arguments. I intend to supply a criterion in due course, and I intend to apply it first to my own case.
Chapter Nine — Paganism, or Judging Without a Ruler
In the same year the report on knowledge appeared, Lyotard published a second and much stranger book, a set of conversations with a younger colleague who plays the part of a patient student pressing an evasive teacher for definitions. It is the most enjoyable thing he wrote, mostly because the interlocutor keeps asking reasonable questions and keeps not getting answers, and the reader is permitted to sympathize with him.
The subject is justice, and the position defended goes under a name chosen for its capacity to annoy: paganism. The pagan, in this usage, is not somebody with an interest in Norse gods. He is somebody who judges without possessing the criterion by which he judges. He decides case by case, in the situation, without the comfort of a rule that would have decided the matter for him if only he had looked it up correctly.
The choice of the word is a joke with a point in it. A pagan world has many gods, with overlapping and competing jurisdictions, none of whom outranks the others, and a mortal facing a conflict between two of them cannot appeal to a higher court because there is not one. That is precisely the structural situation of somebody caught between two genres of discourse. Monotheism, by contrast, is the theological form of the metanarrative: one authority, one standard, one final appeal. He is not making a claim about religion. He is using the oldest available diagram of the situation he wants to describe.
The contrast is with Plato, and the accusation against Plato is precise. In the Platonic arrangement, there exists an Idea of justice; the just act is the one that copies it; and the expert is the person who has contemplated the Idea and can therefore certify the copy. Everything about this is attractive and, on Lyotard’s account, everything about it is a mechanism for transferring authority to whoever claims to have seen the original. The pagan alternative is closer to Aristotle in his practical mood, where the person of good judgment reads a case correctly, weighs what is before him, and produces a decision that could not have been derived in advance from any rule, because the relevant rule is exactly what the case was about.
He also has a Kantian source, and it is worth naming because it makes the position respectable rather than merely defiant. Kant distinguished two operations of judgment. In the first, you have the rule and you file the case under it, the way a clerk applies a regulation. In the second, you have the case and no rule, and you must go looking for the universal that would fit it. The second operation is what happens in aesthetic judgment: nobody can hand you a rule that makes a painting beautiful, and yet the judgment that it is beautiful is not a report on your private twitches, since you make it while expecting others to agree. Lyotard takes this structure out of aesthetics and installs it in ethics and politics, which is either the boldest or the most reckless move in his corpus, depending on the reader’s temperament.
Dialectic in this book does not mean what Hegel meant by it and the confusion has cost readers a great deal. Lyotard uses the word in its older sense, the one it carries in Aristotle: the discussion of opinions, reasoning from what people actually hold rather than from established first principles, in the domain where certainty is unavailable and a decision is nonetheless required. Rhetoric, in that tradition, is not the art of deceiving people but the art of arguing well when proof is not on offer. This is a rehabilitation of an entire discipline that modern philosophy had spent three centuries treating as a subject for the second rank.
The obvious objection arrives immediately, and it arrived immediately in the conversations themselves. If there is no criterion, what distinguishes a judge from a man with strong opinions and a room to shout in? The answer offered is that the Idea of justice continues to operate, but as a horizon rather than a template. One is obliged to judge as if under a demand for justice that can never be possessed, satisfied, or converted into a procedure. The obligation is real; the specification is unavailable. If that sounds like a description of how conscientious people actually behave under pressure, it is, and that is the strongest thing in its favor.
It is also, I have to say, inadequate as it stands, and the inadequacy is of the same species as the one I flagged in the previous chapter. A horizon does not tell you what to do this afternoon. It tells you the direction in which the thing you cannot reach is located, which is not nothing, but a person deciding whether to authorize a treatment, publish a paper, or admit a piece of testimony needs more than a direction. He needs to know which considerations to hold fixed, which to trade, and how to notice when he has made a mistake. Lyotard is admirably clear that no rule can be supplied. He is much less clear about why this leaves us with nothing but tact.
One more objection deserves a hearing, and it comes from the direction of consensus. Lyotard was implacably hostile to the idea that rational agreement is the goal of discussion, on the grounds that a consensus reached among parties with unequal power is a settlement disguised as a discovery, and that the demand for agreement is the polite face of the demand for submission. His preferred word for the alternative is dissensus. I have sympathy for this and I think it goes one step too far, for a reason that has nothing to do with politics. A blanket preference for disagreement is itself a rule applied without regard to the case, which is exactly what paganism was supposed to forbid. If judgment is genuinely case by case, then sometimes the case calls for agreement, and a thinker who has ruled that out in advance has smuggled a criterion back in while insisting he has none.
It may help to see the position operating in a place where nobody is being clever. A physician performing triage in a crowded emergency department is judging without a criterion in exactly the sense at issue. There are guidelines, and the guidelines run out precisely where the difficult cases begin. He is weighing incommensurable things, under time pressure, with incomplete information, and he cannot suspend judgment because suspension is itself a decision with consequences. Nobody watching him would describe what he does as relativism. They would describe it as competence, and competence of that kind is real, teachable, and improvable, which is the fact that any adequate account of judgment has to explain.
And yet I want to defend the pagan against his more confident critics, because on one point he is simply right, and the point is technical rather than temperamental. If several genuinely incompatible descriptions of a domain are each valid within their scope, then a decision procedure that ranks them globally cannot exist, and the demand for one is not rigor but nostalgia. Judging case by case is then not a failure of method. It is the only method the situation permits. What Lyotard lacked was the argument that would turn this from a stance into a result, and therefore the further argument that turns the result into a practice with structure, error correction, and something a committee could actually adopt on a Tuesday. Those arguments exist now. They are not his, they do not come from his tradition, and they arrive in the middle of this book, at which point the pagan will turn out to have been right for reasons he never gave.
Chapter Ten — The Author Would Like to Retract Some Footnotes
Eight years after the report on knowledge appeared, its author gave an interview to a small art magazine in Australia. He was by then internationally famous, the word he had launched was in every seminar room in the English speaking world, and the book was being assigned to undergraduates who would carry its central sentence with them for life. Asked about it, he said it was “the worst of my books,” adding that almost all of them were bad but that this one held the record. He said he had told stories in it. He said he had cited a quantity of books he had never read. He remembered an Italian architect who had upbraided him for making the whole thing needlessly complicated. And he said that the work belonged to the satirical genre.
It is worth sitting with that for a moment, because there is no comparable event in modern intellectual history. The founding document of a movement was disowned by its author, in print, while the movement was still assembling, and the disowning changed nothing whatsoever.
There are three ways to read the remark and I think all three are partly right.
The first is deflationary. French intellectuals of that generation practiced a highly developed form of self deprecation, and a man asked for the fortieth time about a book he wrote to order, in a hurry, for a provincial education council, may reasonably reach for the nearest available shovel. Nobody likes being reduced to a single title, least of all somebody who considers his real work to be elsewhere. The remark may be a mood.
The second reading is literal and, in my judgment, mostly correct. He said he had referred to books he had not read, and the passages where this shows are exactly the ones a working scientist would flag. The report’s account of contemporary science, with its instability, its undecidability, its catastrophes and its search for paradoxes, reads like a summary of the popular scientific press of the middle nineteen seventies, because it is one. The material is not fabricated. It is unweighted: results of very different standing are lined up as though they were interchangeable evidence for a single trend, and the trend is one the author needed. Anybody who has ever written a literature review under deadline knows exactly how this happens and it does not require dishonesty.
The third reading is the interesting one, and it is the reason this chapter exists rather than being a footnote. He said the book belonged to the satirical genre. On his own theory, that is not a modest aside. Genre determines what counts as a successful move. In the genre of the report, a citation is a claim, and a false citation is a defect. In the genre of satire, a citation is a prop, and the question of whether the cited author actually said the thing is beside the point, in the way that it is beside the point to complain that the horses in a fable do not really talk. If the work belongs to the satirical genre, then a whole class of objections to it are category errors, and so is a whole class of endorsements.
The trouble is that no reader was informed of this at the time of purchase, and that the book was commissioned, delivered, and shelved as something else entirely. Which produces, within the career of the man who invented the concept, a textbook instance of the concept. He is a party with a grievance: the world has misclassified his work and is drawing conclusions from it that its genre does not support. He states the grievance clearly. And it has no effect at all, because the tribunal in which the matter would have to be settled does not exist. There is no court of genre. A correction issued in an art magazine has no jurisdiction over a paperback in its ninth printing, and by the time the correction circulates, the word has been adopted by architecture critics who never read the book and are not going to start.
He is, in short, the victim of a differend of his own making, and I would be lying if I said this were not funny. It is funny in the way that only real intellectual history is funny, which is to say without anybody having arranged it.
Now, what am I entitled to do with this? Less than the reader might expect, and I want to be strict about it, because there is an obvious temptation and taking it would wreck the book. The temptation is to treat the retraction as a refutation: the author says it is bad, therefore we may stop taking it seriously, and four decades of citation collapse in a single paragraph. That would be cheap, and it would also be a mistake of exactly the kind this book is about. Whether an argument is sound has nothing to do with its author’s later opinion of his own prose. Newton thought a good deal of his alchemy. A retraction is evidence about a man’s confidence, not about the world.
What the retraction does license is a narrower and more useful move. It tells us which parts of the report were load bearing in the author’s own mind and which were decoration, and it tells us on his authority rather than by my inference. The scientific material was decoration. The historical periodization, the claim that something changed and that we are living after the change, was written quickly and defended casually, and its author was perfectly willing to describe the whole framing as a satirical performance. The diagnosis of legitimation, on the other hand, he never took back, and he spent the following fifteen years developing it with enormous care in books he did rate.
That is the division of the estate I will be working with. The diagnosis is the inheritance. The date on the tombstone is decoration, and the man carving it said so.
A brief word about what he did next, since the record is often presented as though he simply walked away. He did not. Between 1982 and 1985 he wrote a series of letters, later collected, in which he tried to explain the postmodern to a general readership and to correct the two misreadings that had already hardened: that he was announcing an era, and that he was recommending an anything goes attitude toward truth. The letters are patient and, in places, exasperated. They also failed, in the sense that both misreadings are still the standard ones forty years later, which tells us something discouraging about the relative velocities of a slogan and its correction.
This is not a phenomenon confined to French philosophy, and I mention it because the pattern will recur in a technical setting later in this book. A compressed formulation travels. Its qualifications do not. What arrives at the far end of a long transmission chain is the proposition with its boundary conditions stripped away, and the stripped version is not false so much as unmoored: it now applies everywhere, including in all the places where the author explicitly said it did not. Lyotard’s own most famous sentence is the leading exhibit. It was written about the legitimation of knowledge, and it is now quoted in support of the view that nothing means anything.
There is one further thing to admire here, and I say it without irony. He could have kept quiet. The incentives for keeping quiet were overwhelming: the book had made him, the misreading was profitable, and correcting it cost him status while gaining him nothing. He corrected it anyway, in public, to a journalist, knowing it would not work. That is a rarer quality than any of the ideas discussed in this book, and I would trade several of the ideas for more of it.
Chapter Eleven — Something Is Always Missing
Consider a mapmaker commissioned to produce a complete map of an island, with everything on it, at a scale that omits nothing. Halfway through he notices a problem. The map is on the island. A complete map must therefore include a picture of the map, which must include a picture of the picture, and so on. There are famous literary versions of this joke, and it is usually told as a joke, which is a pity, because at the bottom of it there is a structural fact about any system that contains its own observers, and the fact is not funny at all.
Let me state the question carefully, stripped of paradox mongering. Suppose a physical world that behaves consistently, and suppose that somewhere inside it there is an observer: not a disembodied intelligence contemplating the world from a balcony, but a genuine part of the system, made of the same material, obeying the same rules, occupying a finite region and possessing a finite number of distinguishable internal states. This is not an exotic assumption. It is a description of every observer that has ever existed. The question is whether such an observer can, in principle, gain access to the complete content of the world it inhabits.
The answer is no, and the reason is architectural rather than technological. For the observer to hold a full description of the world, its own internal states would have to distinguish every distinguishable state of the whole. But the observer is part of that whole, so its states are among the things to be distinguished, and holding a description of itself changes what there is to describe. The pursuit does not fail by a narrow margin that better instruments might close. It fails by a structural margin that grows as the instrument improves, because every improvement adds to the system being described. There is content in the world which no observer inside the world can reach, and this remains true no matter how many observers there are, how long they work, or how good their equipment becomes.
It may help to run the argument through a machine rather than a mind, since machines have no dignity to defend. Imagine a computer whose task is to hold a complete and current description of the room it sits in, updated continuously and accurate to the last atom. The computer is in the room. Its memory is part of the room’s atomic inventory. Writing the description alters the states it must describe, and the alteration must itself be recorded, and the recording alters things again. This is not a race the machine loses because it is slow. It is a race in which the finish line is attached to the runner. Build a faster machine and you have added mass to the room. There is no configuration of hardware for which the task closes.
Notice also that adding observers does not help, and this is the point that separates the result from an ordinary complaint about limited instruments. Two observers can cover each other’s blind spots in the everyday sense, and science is largely the institutionalized practice of arranging exactly that. But two observers inside the world are two parts of the world, and their combination is a larger part, facing the same relation to the whole that each faced separately. Distributing the problem does not dissolve it. A committee is not an exception to physics.
Several precautions are necessary here, since this is exactly the sort of statement that gets adopted by people I would rather not be adopted by.
It is not a claim about quantum mechanics, and it does not depend on any particular physics. The argument is about the relation between a whole and a proper part that models it. It would apply to a purely classical world.
It is not the same as the famous results in logic about the limits of formal systems, though the family resemblance is real. Those results say that within a sufficiently rich consistent system there are statements neither provable nor refutable there. This is a statement about description rather than proof, and about physical embedding rather than syntax. The distinction matters, and I will need it again in a few chapters, because philosophical discussion has a bad habit of collapsing every limitation into an appeal to a single Austrian logician who did not say most of what he is credited with.
It is not a license. The inaccessible content is not a room where anything you like may be kept. This is the crucial guard and it is worth stating in the strongest terms. From the fact that something is unreachable it does not follow that any particular unreachable something exists. The result establishes a residue, not a repository. Nobody may point at the gap and place his preferred entity in it, and if I catch myself doing that with my own physics, I hope somebody will tell me.
And it is not a counsel of despair, which is the point most often missed. A limitation that is structural is also, for the same reason, predictable. If you know that a residue must exist, you can ask where it will show up, what its signature would look like, and which of your conclusions are standing on the near side of it. That is useful. An unknown unknown that has been shown to be necessary has been partly domesticated, in the way that knowing your blind spot is behind your right shoulder is useful even though you still cannot see into it.
There is a further consequence which I will only flag here, since a later chapter is built on it. A structural residue of this kind is exactly what a certain tradition in aesthetics has been circling for two hundred years under the name of the sublime: the experience of running into something that cannot be presented, and of registering its existence precisely by the failure to present it. That tradition has usually been treated as a matter of feeling, as a report about what large mountains do to sensitive persons. It may instead be a report about architecture. If so, the most notoriously unrigorous concept in the whole of aesthetics turns out to have a rigorous address, which would be an unexpected outcome for everybody concerned.
What I want the reader to carry out of this chapter is a single sentence and a single expectation. The sentence is that any consistent world containing observers made of the same stuff necessarily contains content that no observer within it can reach. The expectation is this: if that is true, then the descriptions available to those observers are fragments of something they cannot assemble. Fragments that cannot be assembled might merely be incomplete, each true as far as it goes, quietly waiting to be joined by the next generation. Or they might be worse than incomplete. They might actively contradict one another, so that the joining is not merely unfinished but impossible.
It is worse. That is the next chapter, and it is the chapter this entire book was written to reach.
Chapter Twelve — Truths That Refuse to Combine
The Earth is round, and every flat map of it lies. This is not a defect in cartography and it is not a scandal. A sphere cannot be laid out on a plane without something giving way, and which thing gives way is a choice the mapmaker must make. The projection used on nautical charts preserves angles, so that a straight line drawn on it is a course a ship can actually steer, and the price is that it inflates areas grotesquely as you move toward the poles, which is why generations of schoolchildren have believed Greenland to be the size of Africa. Other projections preserve area exactly, and the price is that shapes are wrenched and no straight line on the chart corresponds to a heading. There are hundreds of these, each a different bargain.
Now ask the obvious question. Which one is true?
The question is malformed, and everyone feels that it is malformed, but it takes a moment to say why. Each projection is valid: it can be checked, it has determinate content, and a navigator using the wrong one will run aground in a way that demonstrates the difference between validity and preference. Each is also incomplete, and the incompleteness is not a gap that a better cartographer might fill. And crucially, they are not merely different. Where they overlap, they contradict. Two atlases can each be internally consistent, each correct within its own conventions, and disagree about a measurable quantity, with no third atlas available in which both are right.
That is the shape of the result I now have to present, and the reader who has grasped the map is most of the way there.
The formal apparatus begins with five notions. A domain is a region of reality with states, some dynamics relating them, and stable observables: features that can be assessed and that behave reproducibly. Two domains overlap when they share at least one such observable, which is to say when they both make assertions about the same feature of the world. A description of a domain is a finitely specified account with a language, a set of basic commitments, and a way of drawing consequences from them. A description is valid if it is internally consistent and correct about the observables it addresses within its scope; validity does not require completeness, but it does forbid being wrong. Two descriptions are compatible if there exists some single consistent account whose consequences include all the consequences of both. That is a demanding requirement, and the demand is the whole story.
Four assumptions do the work.
The first is that a serious description cannot be silent about the observables in its own domain. A moral position that has nothing to say about consequences is not a modest moral position; it is not one at all.
The second is the load bearing assumption, and it is the one to interrogate. A description must compress. Its specification must be shorter than a list of every case it covers. This is what makes something a theory rather than a catalogue. A person who has memorized ten thousand individual verdicts without any principle organizing them does not have a position; he has a filing cabinet, and you cannot disagree with a filing cabinet, only consult it. The requirement is not smuggled in to force the conclusion. It is the precondition of there being anything to disagree about.
The third is that in a sufficiently complex system, domains overlap. The parties are talking about the same thing.
The fourth is that at least two of the descriptions genuinely differ: they are not the same account in different vocabulary.
From these, with the complexity above a threshold, the result follows: the descriptions cannot be compatible. The reason is what compression actually is. To compress is to take some features as basic and derive the rest from them, and the choice of what is basic is not a matter of style. It is a claim about the domain, and it has consequences. Take welfare as basic and rights come out as instruments; take rights as basic and welfare comes out as a constrained residue. Both accounts can be internally flawless. Both can be correct about the cases each was built for. But where they address the same case, the feature that one treats as fundamental and the other treats as derived will be assigned inconsistent values, and no single consistent account can contain both assignments. This is not a failure of goodwill. It is what having a position costs.
An example less abstract than moral philosophy may secure the point, and I will take it from a domain where nobody suspects the participants of postmodern sympathies. Consider two accounts of a volume of gas. One describes it as an enormous number of particles with positions and velocities, evolving by mechanical rules that run equally well forwards and backwards in time. The other describes it in terms of temperature, pressure, and entropy, and includes a law stating that certain processes go one way and never the other. Both accounts are valid within their domains, and both have been tested to a precision that would satisfy anybody. They also make incompatible claims about the same system: one says the evolution is reversible, the other says it is not. Physics has spent a century and a half producing extremely sophisticated accounts of the relation between them, and those accounts are illuminating, and they involve additional assumptions about initial conditions and about coarse graining that are not derivable from the mechanics alone. The two descriptions are not merely at different levels of detail. Each takes as basic something the other derives, and the choice cannot be adjudicated by the phenomena, because the phenomena support both.
Two things about this result matter more than the result itself.
The first is that it has been reached by several independent routes. There is the compression argument just given. There is a route through the logical independence of what each description holds basic. There is a route in the language of category theory, which asks whether the two descriptions have a least common refinement and shows that in the relevant conditions none exists. There is a route through topological obstruction, in which the local patches are individually fine and cannot be glued into a global object. And there is a route through predictive performance, in which a description tuned to one set of observables necessarily loses accuracy on another. Five roads, five starting points, one destination. In my experience of formal work, that is the strongest signal available that a result is about the structure of the situation and not about a quirk of the formalism.
The second thing matters even more, and it is the reason I insist on stating the theorem conditionally every time. The result holds when the four assumptions hold. Each one is therefore an escape route, and each escape route has a toll. You may deny that descriptions must compress, at the cost of trading your theory for a catalogue. You may deny that the domains really overlap, at the cost of admitting the parties are not disputing the same thing, which ends the dispute by dissolving it. You may propose that the two accounts are approximations arranged in a hierarchy, one reducing to the other in a limit, which is a genuine and honorable escape that works in some famous cases in physics and fails wherever the coarser account has content the finer one cannot express. And you may propose a shared underlying ontology in which both are grounded, at the cost of showing that the grounding preserves what each account claims, which is precisely what nobody has managed for the interesting cases.
The escapes are real. That is what makes this a result rather than a mood. A claim you cannot get out of is not saying much; a claim whose exits are all mapped and priced is doing work.
And now the punch line, which I have been walking toward since the first page. Every one of these assumptions was available in the eighteenth century. Compression is what a theory is. Complexity is a property of the world. Overlap is what it means for two people to be discussing the same subject. None of it has anything to do with computers, with the Second World War, with the exhaustion of European politics, or with the mood of any decade. If the argument is right, then incompatible and individually valid descriptions have been a permanent feature of every sufficiently complex domain for as long as there have been domains and describers.
Which means that the thing announced in 1979 as an arrival was not an arrival.
Chapter Thirteen — No Final Theory
Temperature does not exist for a single molecule. This is not a limitation of thermometers. A lone molecule has a velocity, and velocity is not temperature; temperature is a property of a population, defined by a distribution, and asking for the temperature of one particle is a grammatical mistake wearing a lab coat. Nobody finds this troubling, because everybody has quietly accepted that some descriptions belong to some scales and not to others.
What almost nobody accepts is the consequence.
The consequence was stated with unusual bluntness in 1972 by the physicist Philip Anderson, in a short paper whose title has outlived most of the theories of its decade. His claim was that the ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe, because at each level of complexity entirely new properties appear, and understanding them requires research as fundamental as any other. He was arguing against a hierarchy in which particle physics sits at the top handing down truths to chemistry, which hands them to biology, which condescends to psychology. Nothing in the hierarchy was false. The direction of the arrows was fantasy.
Against this stands one of the most powerful stories modern science has told about itself, the dream of a final theory: a single set of equations from which, in principle, everything follows. It has motivated an enormous amount of first rate work and it deserves to be stated at full strength rather than mocked. The claim is not that a physicist could calculate the behavior of a badger from first principles. It is that the badger contains nothing that is not, in principle, entailed by the fundamental laws, and that the failure to perform the calculation is a matter of computational capacity rather than of principle.
The law of scale specific principles denies exactly this, and it denies it with a technical argument rather than a shrug. Passing from a finer description to a coarser one involves coarse graining: many distinct microscopic configurations are mapped onto a single macroscopic state. That mapping is many to one, and a many to one mapping cannot be inverted. Information is not hidden in the transition; it is destroyed. Consequently the coarse description cannot in general be recovered from the fine one by any procedure, and where stable, reproducible phenomena persist at the coarser scale while extrapolation from the finer scale fails, the principles governing the coarse scale must be different in kind rather than merely different in detail.
The mathematics that makes this precise came from an unexpected direction. In the middle of the twentieth century, physicists studying phase transitions found that systems made of completely different materials behaved identically near their critical points, with the same exponents governing the same relationships, regardless of what they were made of. The apparatus developed to explain this, which examines how a description changes as you deliberately blur it, showed that most of the microscopic detail becomes irrelevant to the large scale behavior. Irrelevant is a technical term there, and it is doing exactly the work I need. The details do not merely fail to matter in practice. They drop out of the equations that govern the scale in question.
There is a name for what working physicists actually do about this, and it is not a compromise but a methodology. An effective theory is one that is explicitly valid up to a certain scale and is not expected to hold beyond it, with the influence of whatever lies below appearing only through a handful of parameters that the theory itself cannot compute. Almost all successful physics has this form. The theory of fluids does not know about atoms and does not need to. The theory of atoms does not know about quarks and does not need to. Each is honest about its ceiling. What is striking is that a discipline whose public story is the search for a single account of everything conducts its daily business in a manner that presupposes the opposite, and does so without any apparent discomfort.
Biology offers an even sharper case, because there the units themselves refuse to stay put. The gene was defined as a unit of heredity, then as a stretch of sequence coding for a protein, and then, as the molecular details accumulated, as something that overlaps other genes, is read in pieces, is spliced into several products, and is regulated by material that is not part of it under any definition. There is no single correct answer to how many genes an organism has, and the disagreement is not ignorance. Different research programs need different units, each unit is well defined within its program, and the programs are all producing results.
Three consequences follow, and each one takes a hammer to something the reader may be attached to.
The first is that laws are scale relative. A law is not a proposition true everywhere; it is a proposition true within a regime, and its truth outside that regime is not guaranteed by anything, least of all by the impressiveness of its performance inside.
The second is that no final theory can encompass all scales at once. Not because we are not clever enough, but because the encompassing would require an invertible map between levels, and the map is not invertible. There may well be a deepest layer of physics, and finding it would be a magnificent achievement, and it would not entail the layers above it.
The third is the one I want to defend most carefully, because it is where every reader who has been made nervous by this book so far will look for reassurance, and I intend to give it. Scale relativity of laws is not relativism. Within a scale, the constraints are rigorous, the tests are real, and a wrong answer is wrong in a way that will eventually break something expensive. Objectivity is preserved not by holding across all levels but by holding firmly within one. A structural engineer does not become a relativist upon learning that his equations fail inside a neutron star.
A reductionist reply is available and deserves to be met rather than ignored. It grants everything about practice and insists on principle: whatever the coarse description says is, in the end, made true by the fine one, however unrecoverable the derivation may be. I have some sympathy with this, and it has one fatal weakness. A claim about what holds in principle, where the principle can never be exhibited even in outline, has no consequences that anybody could check. It is a statement of faith about the architecture of the world, held for reasons of taste, and it is doing exactly the job that a legitimating narrative does: it confers standing on an enterprise without adding to its content. That is not an insult. It is a classification.
Now connect this to the report on knowledge. One of the two great legitimating stories, the reader will recall, was that the disciplines are organs of a single developing intelligence, which is why they are housed in one institution and why they all award the same degree. That story does not fail because European intellectuals lost their nerve after the war. It fails because the sciences are not organs of one intelligence. They are descriptions of different scales, they are not derivable from one another, and the unity that the university was built to embody is not merely unachieved but structurally unavailable.
Delegitimation, in other words, happened. It just did not happen for the reasons given, and it did not happen in the twentieth century. It has been happening since the first time somebody noticed that the rules for describing a crowd are not the rules for describing a man.
Chapter Fourteen — Plurality Is Not a Mood
Take a piece of music. Now describe it. You may write a score, which captures pitch, duration, and instruction, and which is silent about the specific warmth of the third clarinet in the fourth bar. You may record a waveform, which captures everything the microphone received and knows nothing whatever about which note is the tonic. You may write a harmonic analysis, which reveals the architecture of the thing and cannot tell you how loud it is. You may write a dance notation for how bodies should move to it. Each of these is a complete description of the music in some respect and a hopeless one in others, and no procedure exists for merging all four into a super description that keeps everything.
The observation is not a lament about the ineffability of art. It is an instance of a general result about what formalization is, and the result comes in three parts.
The first part is the least expected and the most useful, because it clears away a great deal of romantic nonsense. Anything with determinate structure can be formalized. When somebody claims that a domain resists formalization by its nature, that consciousness or aesthetic value or moral experience is intrinsically beyond the reach of formal treatment, the claim is almost always a claim about the absence of an adequate set of constraints, and it should be relocated accordingly. The failure is in the tooling, not in the world. This matters because the opposite belief has done real damage: it has allowed whole territories to be declared off limits to careful thought, which is convenient for everybody currently occupying them.
An example makes the first part concrete and shows how much is at stake in it. For most of the twentieth century, consciousness was routinely described as intrinsically resistant to formal treatment, a subject on which precision was inappropriate by the nature of the case. What has happened since is instructive. Nobody solved the problem. What people did was build constraint sets: measures of integration, frameworks of prediction and error, accounts that specify what would count as evidence for what. Several of these are probably wrong. All of them are arguable, which the previous situation was not. The move from a domain declared unformalizable to a domain with several competing formalizations is not the achievement of certainty. It is the achievement of the conditions under which one can be shown to be mistaken, which is worth more.
The second part concerns what a formalization costs. Any statement is verifiable only relative to a set of boundaries that fix the domain, the scale, and the admissible procedures of checking. Without those boundaries, verification is not difficult. It is undefined. From which follows a sentence that ought to be carved over the entrance of every philosophy department: removing the constraints from a claim does not make it more true, it dissolves its truth. A claim that applies everywhere, without conditions, has not achieved universality. It has lost the machinery that would let anybody find out whether it holds.
Anybody who doubts that verification requires boundaries should try to evaluate the sentence this object is heavy without knowing whether the speaker is a jeweler, a mover, or an astrophysicist. The example is childish and the structure is not. A great many public disputes consist of two parties evaluating an unbounded claim against silently different boundary sets and each concluding that the other is being obtuse.
The third part is the one that concerns this book. For any phenomenon with determinate structure, there exist at least two distinct adequate formalizations, corresponding to different choices of boundary. Each is faithful to certain structural features and blind to others, and the blindness is not a defect to be repaired in the next version. It is the price of the fidelity. To see one aspect sharply is to place another out of frame, and the trade is built into the act of representation rather than into the incompetence of the representer.
I want to guard immediately against the misuse of this, since it is the point at which a certain kind of reader begins to rub his hands. Plurality does not mean parity. The claim is that no single formalization can be exhaustive, not that all formalizations are equally good. Some capture more structure, generate more testable consequences, connect to more neighboring domains, and survive more attempts to break them. A description that fails on the observables it addresses is not an alternative perspective; it is wrong. The space of adequate formalizations is a space, and it has a boundary, and most proposals fall outside it.
It is worth asking why this needs saying at all, since stated plainly it is obvious. The reason is that the three laws have an unfortunate resemblance to a slogan that circulated widely in the late twentieth century, according to which all descriptions are constructions, all constructions serve interests, and therefore the choice among them is political rather than epistemic. The first clause is true, the second is often true, and the conclusion does not follow from either. A construction can serve an interest and still be checkable. The tide tables published by a naval authority serve the interest of a navy and are also right about the tide, and a rival authority with opposite interests will produce the same numbers or run aground.
What distinguishes the position I am setting out from that slogan is the existence of the boundary. The slogan says the space of descriptions is unbounded, so that anything can be defended by anyone with sufficient motivation. The laws say the space is bounded by adequacy, and that within the boundary there are several genuinely different options, none of which can be eliminated by evidence. Those are opposite claims that happen to sound similar when compressed, and the compression is why the last forty years of argument about this have been so unproductive.
With that guard in place, notice what has been established and by what route. The plurality of valid descriptions is not a historical development. It is not the residue left behind when the grand stories evaporated. It is entailed by the structure of formalization itself, which means it was as true of Aristotle’s physics as of ours, and would be true in a civilization that had never heard of Europe.
This is the second time in three chapters that a supposedly postmodern condition has turned out to be a permanent one, and the reader may be starting to see the shape of the argument. But the demolition is not finished. There is a third result, and it is worse than the first two, because it does not merely say that our descriptions must be plural. It says that whether a given claim can be proved at all depends on a choice that somebody has to make and that nothing in the world makes for him.
Chapter Fifteen — Provable Depends on Defined
Here is a toy that will do more work than its size suggests. Consider the statement that there exists a number greater than two with a certain property, and leave the property temporarily unspecified. Now specify it two ways. If the property is being even, the statement is provable, and the proof takes one second: four. If the property is being both even and odd, the statement is refutable, and that proof also takes one second. The sentence did not change. The arithmetic did not change. Only the definition of the property changed, and the status of the claim moved from proved to refuted.
This is trivial in content and not at all trivial in structure, and it is the seed of a principle I use constantly. For any statement whose formulation involves a term admitting several admissible definitions, the provability of that statement is a function of which definition is chosen. Where the function is constant, nothing interesting is happening. Where it is not constant, a claim that looks like a claim about the world is partly a claim about a decision, and arguing about the world will not settle it.
Two guards are needed before this becomes useful rather than corrosive.
The first is that not every stipulation counts. A definition is admissible if it preserves the inferences competent users of the term actually make, classifies the obvious cases correctly, and does not collapse the term into a triviality or a contradiction. You may not simply define your opponent into defeat. The space of admissible definitions is bounded, and the interesting cases are the ones where it contains more than one member and the provability function is not constant across them.
The second guard is a distinction that philosophical writing collapses constantly, to its cost. There is a famous species of unprovability, established in the last century, in which a precisely defined sentence is neither provable nor refutable within a specified consistent system, and no amount of redefinition will fix it, because the obstruction lies in the system rather than in the vocabulary. That is one thing. Definitional indeterminacy is another thing entirely: here the terms admit several specifications, and the status of the claim moves as they vary. The practical rule I follow, and recommend, is that when an inquiry becomes irresolvable, the first question is which of the two you have hit. Almost everybody assumes the first, because it is more glamorous. Almost always it is the second.
A third feature deserves mention because it makes the principle self limiting rather than a universal solvent. The criteria of admissibility can themselves be disputed, at which point the principle applies to the dispute about admissibility, and so on. Some readers find this alarming, as though an infinite regress had been discovered. It is a regress, and it terminates in practice for the same reason that legal proceedings terminate: at some level the parties either agree or the matter is decided by something other than argument. What the principle supplies is not a guarantee of resolution but an accurate account of where the argument actually is, which is usually two levels below where the participants think it is.
There is also a heavier case, which arises when the competing definitions are not variations within one framework but arrive attached to different frameworks. Approximate truth defined through a completed theory of reference belongs to one intellectual world; defined through mappings between mathematical structures it belongs to another; replaced entirely by predictive reliability it belongs to a third. These are not three ways of saying one thing. Each brings its own commitments, and the same phrase does different work in each. When that happens the shift in provability is not a subtlety at the margin. Whole classes of claim change status at once.
Now apply this to a debate that has been running for half a century with no visible movement: whether the theories of mature science are approximately true.
The realist says that the success of our best theories would be a miracle unless they were getting something right about a world we cannot observe. The antirealist replies that the inference is unwarranted, and offers a catalogue of once successful theories whose central entities turned out not to exist. Both sides are sophisticated. Neither is winning. And the reason, I claim, is that the central term is definition dependent in exactly the sense just described.
Watch it move. Under one specification, approximate truth is a matter of distance in a space of possible states, with a theory counting as closer to the truth when the set of possibilities it permits narrows correctly around the actual one. On that reading, the historical sequence of theories does look convergent, and the realist claim is supported. Under a second specification, approximate truth requires that the entities a theory posits continue to be recognized by its successors. On that reading, the record is a catalogue of eliminated furniture, and the realist claim is refuted. Under a third, deflationary specification, approximate truth means empirical adequacy within the tested domain, on which the claim is easily provable and completely vacuous, since the antirealist has been asserting it all along.
Three admissible definitions, three different verdicts. And the same exercise works on every other load bearing term in the debate. Novel prediction shifts its extension depending on whether novelty means the phenomenon was unknown when the theory was built, or merely was not used in building it, or must have played a particular role in the derivation; each reading admits a different roster of historical cases and therefore a different strength of evidence. Structural continuity, the concept invented to rescue realism from the historical record, is secure but empty under a permissive reading of structure and substantive but vulnerable under a strict one, with no stable position in between. Empirical adequacy, the antirealist’s own instrument, requires a line between the observable and the unobservable that nobody has managed to draw without controversy.
The practical protocol that falls out of this is short enough to memorize and has saved me a great deal of time. When an argument has been running long past the point where new evidence is arriving, stop arguing about the world and locate the term that is carrying the weight. Write down the admissible definitions of it. Determine, for each, whether the disputed claim comes out true, false, or undetermined. If the answers differ, the dispute is definitional, and the honest move is to say so and to argue about which definition to adopt and why, which is a different and much more tractable conversation. If the answers agree, the dispute is substantive and somebody is simply wrong, which is also useful to know.
The diagnosis, then, is that the stalemate is not a failure of argumentation. It is a structural consequence of definitional multiplicity. The parties are not making mistakes. They are computing correct answers to slightly different questions and reporting them as answers to the same one.
This is, I hope the reader notices, a considerably more precise version of something we have already met. Lyotard said the parties to a dispute may inhabit different genres with no common tribunal. Fogelin said deep disagreements bottom out in framework propositions that argument cannot reach. Both were pointing at this, from outside, without a mechanism. The mechanism is that the provability of the disputed claim is a function of a choice which the evidence does not make and which each party has already made before the argument begins.
Which raises the question that occupies the next chapter, and that neither Lyotard nor Fogelin ever asked. If the choice must be made, and the world does not make it, what governs it?
Chapter Sixteen — The Choice of Formal Realities
Somebody has to choose, and nothing chooses for him. That is the situation the previous chapter left us in, and it needs a vocabulary before it can be handled.
Call a formal reality a complete specification of the apparatus within which claims get evaluated: a logic, a set of basic commitments, and definitions for the terms that carry weight. Inside a given formal reality, well formed claims have determinate status. Between formal realities, the same claim can have different status, not because the world differs but because the machinery used to assess it differs. The phrase is deliberately unromantic. What is being described is closer to an operating system than to a worldview, and like an operating system it is mostly invisible to the person using it, right up to the moment he tries to run somebody else’s software.
Four constraints govern the choice, and they are results rather than recommendations.
The first is that the choice cannot be avoided. For any task rich enough that changing the logic or the definitions would change what can be established, neutrality is not an available position. Declining to choose is choosing, and what one then gets is the default configuration of one’s intellectual community, adopted without examination and defended with the special ferocity reserved for commitments one does not know one has. This is the single most useful thing in the framework, and it is worth pausing on. The person who says he is simply following the evidence, with no prior commitments, is not describing a superior method. He is describing a machine whose settings he has not read.
The second constraint is that no task determines its own formal reality uniquely. More than one adequate configuration exists for any sufficiently rich problem, which follows directly from the plurality law of the previous chapter. Therefore the dispute between two well developed positions is not a dispute about which one is correct, since correctness is assessed inside a configuration and there is no configuration outside them both. It is a dispute about which to adopt, which is a different kind of question with different kinds of reasons available.
The third constraint is that every configuration has costs, and that the costs come in a small number of currencies that trade against one another. Strengthen the assumptions and you can prove more, at the price of committing yourself to more entities being real. Reduce the ontological commitment and the proof power falls. Buy tractability and you generally pay in fidelity. No configuration minimizes all costs at once, which means the choice is a genuine trade rather than a mistake made by whoever chose differently. The realist about scientific theories buys explanatory power and pays with vulnerability to the historical record of abandoned entities. The antirealist buys immunity to that record and pays by having no account of why the enterprise works so well. Both bills are real. Neither party enjoys receiving the other’s.
The fourth constraint supplies the thing everybody has been looking for since the beginning of this book, and it supplies it in a modest form that will disappoint anyone hoping for a verdict. A result has structural generality when it survives every admissible variation of the configuration. That is a criterion, it is not arbitrary, and it can be applied. Claims that pass it represent genuine convergence and can be relied upon across the disagreement. Claims that fail it are configuration dependent and cannot settle anything, however vigorously they are asserted.
Notice what this does to the shape of an intellectual dispute. The question stops being which side is right, which has no answer, and becomes which claims in the neighborhood are robust across the admissible configurations, which has one. That question is laborious rather than glamorous. It produces a map instead of a verdict. And it is, so far as I can see, the only form of progress available in any domain where the parties have been arguing well for a long time without moving.
There is a further result here that I find genuinely uncomfortable and include for that reason. It concerns what would happen if one of these long disputes were actually settled. In any complex adaptive system operating under real uncertainty, the variety of configurations maintained within the system carries information about the part of the environment that nobody has mapped. Eliminate the variety in favor of the currently best option and you have optimized for a landscape you do not know, and you have destroyed the mechanism by which the error would have been detected. The result establishes that the damage from eliminating the variance exceeds the damage from tolerating it, whenever the gap between what the system understands and how things actually are is larger than what the system can learn before the variance is gone.
Applied to a philosophical debate, this says something that sounds like an excuse and is not. The diversity of positions is not a scandal awaiting resolution. It is the field’s instrument for detecting its own errors, and a resolution would remove the instrument. I want to be precise about the scope, because this argument could otherwise be used to protect any unresolved question from ever being answered, which would be intolerable. It applies only where the unknown is genuinely unknown and the uncertainty irreducible. It does not apply to empirical questions with accessible answers, or to mathematical questions inside a fixed system. Whether a particular protein binds a particular receptor is not protected by this result and never will be.
And now an old acquaintance returns. Judging case by case, without a criterion that would have decided the matter in advance, refusing the demand for a final consensus on the grounds that the demand serves something other than knowledge: that was the pagan position of the ninth chapter, asserted there as a stance and defended by nothing but its author’s considerable taste. Here it arrives as a consequence. The difference is that the consequence comes with instructions. It tells you which claims to trust across the disagreement, what the cost of each position is, and when the disagreement should be preserved rather than settled. Lyotard could tell you to judge without criteria. He could not tell you when you had judged badly.
Chapter Seventeen — The Condition That Never Began
Everything necessary has now been assembled, so let me put it on the table at once and then defend the arrangement.
Complex domains necessarily admit descriptions that are individually valid and mutually incompatible. Coarse graining is not invertible, so the principles governing one scale are not recoverable from another. Formalization is always bounded and always plural. Whether a claim can be established depends on definitional choices the evidence does not make. And the configuration within which such choices are settled cannot be avoided, is not unique, carries costs, and is only transcended by those rare claims that survive every admissible variation.
Read that list again and look for a date. There is none. Not one of these results mentions a century, an event, a technology, or a mood. They are consequences of complexity, of compression, and of the relationship between a describer and what he describes. They held during the Bronze Age. They will hold in whatever comes after us. And every one of them was needed to reach the situation that a report to a Canadian education council in 1979 described as the condition of knowledge in the most highly developed societies.
The condition is real. The word beginning with post is a filing error.
I should say precisely what I am and am not claiming, because the sentence just written is the kind that gets quoted without its neighbors. I am not claiming that nothing changed in the twentieth century. A great deal changed. I am claiming that what changed was the visibility of a permanent condition rather than the condition itself, and I can name three specific changes that produced the new visibility.
The first is arithmetic. In 1900 the number of people employed to produce systematic knowledge was small enough that they could largely be introduced to one another. By 1979 it was in the millions, and the number of distinct research programs had grown accordingly. Incompatible descriptions require describers, and the probability that two well developed and genuinely incompatible accounts of the same domain will both exist, and will meet, rises steeply with the number of people building accounts. Nothing about the world changed. The population of mapmakers did.
The second is maturity. Two descriptions cannot collide until both are precise enough to disagree. Vague accounts pass through one another without contact, which is why disciplines in their early phases feel so companionable and why the arguments start when the measurements get good. Much of what looked in the twentieth century like the fragmentation of knowledge was the opposite: it was fields becoming sharp enough that their disagreements finally had edges.
The third is transmission. A disagreement between two schools of thought used to be a private matter conducted in journals read by a few hundred people. It is now conducted in public, at speed, in front of an audience that has no way to evaluate it and every reason to conclude that the experts are in disarray and therefore that expertise is worthless. What the public experienced as the collapse of authority was, in large part, the removal of a wall that had concealed how knowledge has always been produced.
So the phenomenology was accurate. It felt like something was happening, because something was: people were seeing a thing that had previously been out of view. Announcing that the thing had just come into existence is the same error as concluding that the far side of the mountain was created by your climbing the near side.
Now the test that any claim of this sort must pass. If incompatible valid descriptions are permanent, they should be findable in periods that never heard of any of this, in cultures with no connection to European intellectual history, and above all in institutions that were built to handle them. If we find none, my argument is a rationalization. Let us look.
The rabbinic tradition preserved minority opinions in its central legal texts alongside the majority ruling, deliberately, as part of the record, and produced a famous formula to the effect that two contradictory schools were both speaking the words of the living God while practice followed one of them. That is a two thousand year old institutional technology for holding incompatible valid descriptions without collapsing them and without pretending they agree. Islamic jurisprudence developed four schools of law, all regarded as orthodox, each internally rigorous, differing in their rulings, with the differences understood as legitimate rather than as evidence that three of them were in error. Roman law had its competing schools. The medieval universities ran on the disputed question, a format in which the strongest case for each side was constructed and the outcome was often a distinction rather than a victory.
In the sciences the pattern is just as clear once you look. The dispute over the nature of light ran for two centuries between two accounts, each of which explained phenomena the other could not, and it was not resolved by one side winning. Newton and Leibniz disagreed about whether space is a container or a system of relations, and each position was internally coherent, and the argument was still live in the twentieth century under new names. Astronomy in China and in Greece developed geometry of the heavens along different lines, each accurate enough for its purposes, with neither reducible to the other.
None of these people were relativists. Most of them would have been appalled by the suggestion. They were practitioners who had noticed, from experience, that a complicated subject supports more than one rigorous account, and who built procedures for working under that condition instead of waiting for it to end.
Which puts the twentieth century in a rather humbling light. What was announced as the crisis of modernity was a rediscovery of something that jurisprudence had known since antiquity, made in a culture that had spent three hundred years insisting on a single unified account of everything and was therefore genuinely shocked to find it unavailable. The shock is real. The novelty is provincial.
Two conclusions follow, and they are aimed in opposite directions.
To those who have built careers on the postmodern: the diagnosis survives, and it is stronger than you thought, because it is now a structural result rather than a period claim. What does not survive is the drama. There is no rupture, no epoch, no before and after, and consequently no cultural authority attached to being on the near side of the break. The historical framing was, as its own author eventually said, a satirical performance, and it should be released without regret.
To those who have spent forty years insisting that all this was a fashionable disease imported from France: you are now obliged to argue with a theorem rather than with a Frenchman, and the theorem does not care about your opinion of continental philosophy. The plurality of incompatible valid descriptions is not a doctrine invented by people who were bad at mathematics. It is a consequence of what a theory is.
Both parties, having been relieved of their positions, may now be asked the question that actually matters. If this is the permanent condition, and if it never began, then it never ended either, and there is no crisis to survive. There is only the practical problem of working well inside it, which people have been doing successfully for millennia without ever having a good account of what they were doing. The remainder of this book is about that account, and it begins with the place where the missing story went.
Chapter Eighteen — Measured, Declared, Derived
Three words, and the rest of this book depends on them.
A quantity is measured when an instrument produced it and the production could in principle be repeated by somebody else. A quantity is derived when it follows from measured quantities by steps that can be written down and checked. A quantity is declared when a person chose it and wrote it down, and nothing in the data forced the choice.
That is the entire apparatus. It has no mathematical content, it would be recognized instantly by any competent auditor, and I have watched it cause more trouble in more fields than any other idea I use.
The trouble originates in a typographical accident. In a finished piece of work, all three kinds of quantity appear in the same typeface. The number that came out of the detector, the number computed from it, and the number somebody picked because everybody picks it are set identically, punctuated identically, and carried forward identically into the arithmetic. Nothing in the visual grammar of a scientific paper distinguishes a receipt from an estimate. In a financial statement the distinction is mandatory and its absence is a criminal matter. In a research paper it is a matter of taste.
Let me make this concrete with the case I know best. When a telescope observes a distant galaxy, one thing that is genuinely measured is the extent to which its light has been shifted toward the red end of the spectrum. That is an observation, it has an error bar, and another team with another instrument can check it. What is usually wanted, however, is not the shift but the distance, and the distance is not measured. It is obtained from the shift by way of a model of how the universe expands, which contains parameters, which were themselves obtained from other observations analyzed under a model, which contains assumptions about what the universe contains. Somewhere in that chain there are quantities nobody measured. There is a choice of which model to assume while processing the data, standard in the field and rarely defended, because defending it would require the paper to admit it was made. There is a choice of prior probability distributions, which formally encode what one believed before looking, and which determine the answer in exactly those cases where the data are weakest and the answer is therefore most interesting. There is a choice of which epoch to use as the reference point for calibration, and in some analyses that choice alone can flip the sign of a reported trend.
None of these choices is dishonest. Most are the accumulated sediment of decades of reasonable practice. Each one is a declaration.
The distinction is not confined to astronomy, and I do not want the reader who has no interest in galaxies to feel this is somebody else’s problem. A poverty line is declared. The basket of goods used to compute inflation is declared, and the choice of basket determines whether a decade looks prosperous. The baseline against which excess mortality is calculated is declared, and different defensible baselines have produced pandemic death tolls differing by large factors. The threshold at which a laboratory value becomes a diagnosis is declared, and moving it converts millions of healthy people into patients overnight without a single cell changing. In each case there is a real measurement underneath, a legitimate derivation in the middle, and a human decision that the final number depends on and that the final number does not display.
Here is the test I apply, and it takes about ten seconds. Ask whether a competent, honest person could have made a different choice at that point without contradicting any observation. If yes, the quantity is declared. Then ask what would happen to the headline conclusion if the alternative had been chosen. If the answer is nothing much, the declaration is harmless and needs only to be recorded. If the answer is that the conclusion changes, then the conclusion is standing on the declaration, and the reader is entitled to know that before he is asked to believe anything.
Three characteristic failures follow from ignoring all this, and they have distinct signatures.
The first is declaring and forgetting. A choice is made explicitly at the beginning of a research program, for good reasons, in a paper that says so. Twenty years later it is a default in a piece of software, and the graduate student running the software has never seen the argument and does not know there was one. Nothing was concealed. The declaration simply aged out of view.
The second is laundering, and it is the one that does real damage. A quantity is derived from a declared component, and then reported in the same voice as a measurement, with an error bar that describes only the noise in the instrument and says nothing about the choice. The error bar is not a lie. It is an answer to a question nobody asked.
The third is overloading, which is the specific defect my working notes exist to catch. A declared component is asked to carry a conclusion far heavier than anything that could be justified for it. The paper is not wrong about the measurement. It is loud about something that rests on a choice, and the volume of the conclusion bears no relation to the strength of what supports it.
Honesty requires me to apply this to myself, and it is worth doing publicly rather than in a footnote. The cosmological framework I work on contains a declared component of its own: an assumption about the global shape of space, which is not measured, which was chosen because it makes the rest of the structure work, and which could in principle be replaced by another assumption with different consequences. It is a declaration. I say so in the papers, and I will say so again in this book whenever the topic arises, because a man who builds an instrument for detecting undeclared assumptions and then exempts his own has not built an instrument. He has built a weapon.
And now the connection that this whole book has been walking toward. The great legitimating story, the one that supposedly evaporated in the second half of the twentieth century, does not appear in modern research as a narrative because narratives can be doubted. It appears as a declared component. The choice of standard model to assume while processing the data is a story about what the universe is like, told in the imperative mood, executed rather than asserted, and inherited by everyone in the field without a moment of decision on anyone’s part. It has no author present in the room. It cannot be cross examined, because it never makes a claim.
That is where the metanarrative went, and the next chapter follows it there.
Chapter Nineteen — The Grand Narrative Did Not Die; It Compiled
A story that is told can be argued with. Somebody stands up, says that knowledge serves the emancipation of humanity, and at that moment he becomes answerable: he can be asked which humanity, emancipated from what, and at whose expense. The vulnerability is built into the act of speaking. This is why legitimating narratives were always fragile and why the twentieth century was able to demolish them so thoroughly. They had mouths.
What replaced them has no mouth, and that is the whole of my finding.
Begin with an ordinary morning in observational cosmology. A team wishes to know something about the distribution of galaxies. Before any of their own data are touched, a reference cosmology is loaded: a specified model of the universe with specified parameter values, used to convert the angles and redshifts that were observed into the distances and volumes that the analysis requires. This is called the fiducial cosmology, and its selection is not usually presented as a result of the paper, because it is not one. It is infrastructure. It arrives with the pipeline.
Now ask what a fiducial cosmology is, considered as a piece of speech. It is a complete account of what the universe is made of, how it began, and how it develops, adopted in advance of the investigation and used to make the investigation possible. Strip away the file format and it is a cosmogony. It is the same kind of object as the opening chapter of a sacred text, performing the same function: it tells you what sort of world you are in so that you can get on with living in it. The difference is that nobody recites it. It is a configuration block, and the analysis will not run without it, and the person running the analysis frequently could not tell you which parameter values are in there without opening the file.
This is what I mean by saying the metanarrative compiled. It did not die and it did not go into exile. It moved from the register of assertion, where it could be contested, into the register of infrastructure, where contesting it is not so much forbidden as unformulated. There is no meeting at which the reference model is defended, because there is no meeting. There is a default, and defaults do not make claims.
Four properties make this new location much stronger than the old one, and they should be set out plainly.
It is invisible in the output. A paper reports its measurements, its statistical treatment, its uncertainties, and its conclusions. The infrastructure appears, if at all, as a sentence in the methods section stating which model was assumed, in the tone one uses for describing which brand of telescope was booked.
It is inherited rather than adopted. A researcher entering a field receives the configuration along with the software, the file formats, and the conventions about which plots go in which order. He does not choose it, so he never has the experience of having chosen, and one does not doubt what one has never decided.
It is enforced by cost. Rerunning an entire analysis under a different assumed model is expensive in time and computing, and produces a result that is harder to compare with everybody else’s, which is the currency of the field. The alternative is not forbidden. It is merely priced out, and pricing is a far more reliable mechanism than prohibition, as the previous chapters on performativity should have prepared us to expect.
And it is self confirming in a way that is genuinely difficult to escape. When a model is assumed in order to process the data, and the processed data are then used to constrain the model, the loop is not necessarily vicious, and there are careful techniques for handling it. But the techniques are themselves configured, and the configuration comes from the same lineage. A field can spend decades tightening its error bars around a value while the choice generating that value sits in a file nobody has opened since 2004.
I want to be careful, because there is a paranoid version of this chapter that I refuse to write. Nothing here implies a conspiracy, and nothing implies that the reference models are wrong. They are, in most cases, the best available summary of a great deal of honest work, and adopting a common standard is what allows results from different groups to be compared at all. A field without shared infrastructure would not be more open minded; it would be unable to communicate. What I am describing is not a crime but a relocation, and the relocation has an epistemic consequence that would be present even if every parameter in the file were exactly right.
The consequence is this. A legitimating story in narrative form generates dissent, because it can be heard and disliked. A legitimating story in infrastructural form generates no dissent at all, because there is nothing to hear. The absence of controversy is then read, quite naturally, as consensus. It is not consensus. It is silence of the fourth kind, the kind Lyotard identified: not the silence of parties who agree, but the silence of a situation in which the objection has no available formulation.
Nor is any of this peculiar to physics, and I would be doing the reader a disservice if I left him thinking that it were. The same architecture governs the credit score, where a model trained on past decisions determines future ones and no applicant is told which features carried his refusal. It governs the actuarial tables underlying insurance, the risk models underlying capital requirements, the triage algorithms in emergency departments, and the ranking function that determines which sentences a person reads today. In each case a substantive account of how the world works has been embedded in a procedure, and the procedure is executed rather than argued, and its embedding was performed by people who were mostly trying to be helpful.
Here is the summary I would put to the Conseil des universités if they were still asking. Legitimation did not disappear. It descended. It is now performed by software, inherited by apprenticeship, protected by cost, and rendered invisible by the conventions of publication. The old grand narratives at least had the decency to be wrong out loud.
What follows from this is not despair but a specification. If the trouble is that declarations have gone underground, the remedy is a procedure that brings them back to the surface, and such a procedure can be written down. It has ten clauses, it fits on two pages, and it is the subject of the next chapter.
Chapter Twenty — Ten Norms for Introducing an Entity
Every so often somebody has to add a new thing to the world’s inventory. A new particle, a new field, a new social force, a new mental disorder, a new asset class. The proposal is usually made because something needs explaining and the existing furniture will not explain it, and the proposal is usually reasonable. What is missing, almost universally, is a procedure: an agreed set of clauses that the proposer must satisfy, so that the community can tell the difference between an entity that has been earned and one that has been installed.
I wrote such a procedure, deliberately stripped of any connection to my own physics, so that it could be used against me as easily as by me. It has ten clauses in four groups, and I will give them here in plain language rather than in the form they take in the original, which is drier and has proofs attached.
The first group concerns declaration.
Clause one. State what the entity is supposed to do. Not what it is, which is often unavailable, but which observations it accounts for that would otherwise be unaccounted. An entity with no assigned job is not a hypothesis; it is furniture.
Clause two. State, for every quantity in the argument, whether it was measured, derived, or declared. This is the clause that does most of the work, and it is the one that meets the most resistance, because it is embarrassing to write down how many of the numbers were chosen. The embarrassment is the point. If a paper cannot survive its own inventory, the inventory is not what is wrong.
Clause three. State the alternatives that were available at each declared choice, and say why this one. Not a defense, necessarily. A sentence will do. The purpose is to record that a choice existed, so that a reader ten years later knows there was a fork in the road.
The second group concerns capacity.
Clause four. Do not load a component beyond what its own evidence supports. If a parameter is constrained loosely, a conclusion that depends sensitively on it inherits that looseness, and no amount of precision elsewhere in the pipeline repairs it.
Clause five. Distinguish the case where a referent is deferred from the case where it is foreclosed. This clause was added after a public criticism of an earlier draft, and I record that because a code of practice whose own history is concealed would be a poor advertisement. The distinction matters enormously and I give it a chapter of its own next.
Clause six. Report what the conclusion would look like under the leading alternative declaration. This is the single most useful clause in the whole document and the least often obeyed. It costs one paragraph.
The third group concerns the relations among results.
Clause seven. Do not present as independent confirmations several results that descend from the same underlying quantity. If four predictions all follow from one functional choice multiplied by fixed profiles, their agreement with data is one success reported four times, and a joint fit that treats them as independent will report a confidence it has not earned. I hold myself to this one with particular attention, because my own framework produces a family of predictions from a small number of structures, and the temptation to count them separately is constant.
Clause eight. Where a result depends on a convention shared across the field, name the convention and cite where it was established. Infrastructure that cannot be traced to a decision is infrastructure nobody can revise.
The fourth group concerns the disposal of the entity.
Clause nine. Specify what observation would remove it. Not a ritual gesture toward falsifiability, but a concrete statement: this measurement, at this precision, would leave the entity with no remaining job.
Clause ten. Apply all of the above symmetrically. A diagnosis that a pipeline is unreliable disqualifies that pipeline as support for any conclusion, including conclusions the diagnostician likes. This is the clause I care about most and it has cost me things I wanted. There have been results congenial to my own framework which I could not use, because I had already argued that the analysis producing them was not sound. Declarations cut both ways or they cut nothing, and a critic who applies his instrument selectively is not a critic but a partisan with a vocabulary.
A word about what the document is not, since codes of practice attract a predictable suspicion. It is not a method for producing truth. Nothing in it will tell anybody whether a theory is correct, and a paper can satisfy all ten clauses and be entirely wrong, which is as it should be. What the clauses do is make a paper legible: they ensure that a reader can reconstruct what was assumed, what was found, and which of the two the conclusion is standing on. Legibility is a lower ambition than truth and a great deal more attainable, and in a field where the errors that survive longest are the ones nobody can see, it is the more urgent of the two.
It is also not a novelty. Every mature discipline that handles money, medicine, or aircraft has evolved something similar, and the resemblance is not accidental. An audit trail, a chain of custody, an as-built drawing showing where the construction departed from the design: each is an instrument for keeping declarations attached to the objects that depend on them. Research is the largest enterprise in the modern world that has not developed one, and the reason is straightforward. In those other fields somebody eventually gets sued.
Now, what is this document, considered philosophically?
It is an attempt to build the missing idiom. That is not a decorative comparison; it is the specification. Lyotard defined the differend as a wrong that cannot be expressed in the language of the tribunal, and defined the ethical task as the invention of phrases that would let the wronged party speak. In a scientific paper, the party with no available phrase is the declared component. It cannot say that it was chosen rather than found. It cannot object that it is bearing more weight than it can support. The genre has no slot for such a sentence, and so the objection is not overruled; it is unformulable, which is worse.
Clauses two, three, and six create the slot. That is all they do. They are not a theory of anything, they establish no new results, and they are unglamorous to the point of tedium. They convert a differend into a litigation, which is precisely the operation Lyotard called for and never specified, and they do it not by moral exhortation but by adding three paragraphs to a document template.
I have no illusions about adoption. Norms of this kind spread when a journal requires them or when a scandal makes them cheap to demand, and neither can be arranged by writing a book. But the objection that such procedures cannot be enforced is not an objection to their correctness, and the objection that they are obvious is the highest praise available for a piece of practical philosophy. Structured reporting formats already exist in medicine, in clinical guidelines, in the uncertainty language of climate assessments. They were all obvious too, once somebody had written them down, and every one of them was resisted first.
Chapter Twenty-One — Role Without Referent
Consider an object that has never been observed, that may never be observed, and that is doing indispensable work in a successful theory. What is its status?
The question sounds like scholasticism and is in fact the daily condition of theoretical physics. Something is required by the structure of an explanation; it has a role, precisely specified, with consequences that can be calculated. What it has not got is a referent: an item in the world one could point at, weigh, or photograph. And the interesting discovery, once one starts sorting such cases, is that they are not all the same kind of case. They come in two kinds, and confusing them is responsible for a remarkable amount of bad philosophy on both sides of every argument about scientific realism.
In the first kind, the referent is deferred. The theory says there is something occupying this role, describes what it must be like, and the failure to observe it is a fact about our instruments, our era, or our luck. The neutrino spent a quarter of a century in this condition. It was proposed to save a conservation law, it was expected by its own proposer never to be detected, and it turned up. The positron was deferred for four years, the top quark for eighteen, gravitational waves for a century. During the waiting period a critic could correctly say that nothing had been seen, and a defender could correctly say that the theory had specified what to look for. Both were right, and time settled it.
In the second kind, the referent is foreclosed. Here the structure of the theory itself excludes any observation, so that the waiting is not long but infinite. The role is filled by construction, and the filling is a bookkeeping operation rather than a bet on future instruments. There is nothing disreputable about this either, provided it is labeled. Plenty of indispensable machinery in mathematics and physics has no referent and needs none.
What is disreputable, or at any rate confusing, is the systematic failure to say which kind one is dealing with. The two cases have entirely different epistemic profiles. A deferred referent generates a research program: build the detector, wait, and find out. A foreclosed referent generates nothing, and a community that treats it as deferred will spend decades and considerable money waiting for a knock at a door that has been bricked up.
The distinction also settles a dispute that has consumed a great deal of energy for no result. When a critic complains that some theoretical entity is unobservable and therefore illegitimate, and a defender replies that unobservability is no objection since science is full of successful unobservables, both are talking past each other because neither has specified the kind. The critic is usually thinking of foreclosure. The defender is usually citing deferral, and his examples are always the same handful of eventual triumphs. Ask which case is at issue and the argument either resolves or becomes an argument about something real.
A worked example may help, and I will take one where I have no stake at all. In the standard account of the very early universe, a period of enormously rapid expansion is invoked to explain why the sky looks the same in opposite directions and why space appears geometrically flat. The mechanism requires a field, and the field has a role of great precision: it must have certain properties, evolve in a certain manner, and deposit its energy at a certain moment. Its referent is a matter of genuine dispute among competent people. Some regard it as deferred, expecting that the pattern it left in the microwave background will eventually pin down which version of the field it was. Others regard it as effectively foreclosed, on the grounds that the family of admissible versions is large enough that no observation will select among them, so that the field is a name for a requirement rather than for a thing. Notice that this is not a dispute about the data. It is a dispute about which of two categories the entity belongs in, and until somebody states the categories the parties cannot even agree about what they are disagreeing over.
There is a further refinement that I find useful and that costs nothing. Between the two kinds sits a third condition, which one might call conditionally deferred: the referent is unobservable given the current theory, but the current theory is not the only admissible one, and under a plausible alternative it would become observable. This is the most interesting case of all, because it converts a metaphysical dispute into a comparison between two research programs, which is a competition that can actually be run.
Now the reason this chapter sits here rather than in a technical appendix.
Everything in the second half of this book has been about a wrong that cannot be phrased: the declared component with no way to speak on its own behalf. The distinction between deferral and foreclosure is the first piece of vocabulary in that missing language. It gives the silent party two things to say. It can say: I am a placeholder awaiting an instrument, and here is the instrument. Or it can say: I am a placeholder that no instrument will ever fill, and you should stop treating my eventual arrival as a reason for patience.
It also supplies a test that can be applied from the outside, which is the property I care about most in any piece of philosophical machinery. Ask the proponent of an entity what would count as its arrival. If he can describe the instrument, the measurement, and the value that would settle it, the referent is deferred and the entity is doing honest work on credit. If he cannot, and if on examination the structure of his theory is what prevents him, the referent is foreclosed, and the entity should be relabeled rather than removed. If he cannot, and the obstacle is merely that nobody has thought about it, then what he has is not an entity but a habit.
The same test applies outside physics with no modification. An economist invoking a natural rate of unemployment, a psychiatrist invoking an underlying chemical imbalance, a critic invoking the author’s intention: in each case the entity has a well specified role, and in each case the question of whether its referent is deferred, foreclosed, or merely unexamined is answerable, and answering it changes what the surrounding discipline is entitled to claim.
Two sentences, neither of which existed as an available move before somebody wrote them down. That is what building an idiom looks like in practice. It is much less dramatic than the phrase suggests, it consists mostly of drawing distinctions that could have been drawn at any time, and it is the only thing anybody has ever done about a differend that actually worked.
Chapter Twenty-Two — Myths the Predictive Mind Cannot Do Without
A physicist explaining why a heavy nucleus splits will tell you that the thing behaves like a drop of liquid, wobbling until surface tension loses to electrical repulsion and the drop tears in two. There is no liquid. There is no surface, no tension in the ordinary sense, and nothing that a drop would recognize as a relative. The metaphor is nonetheless doing real work, has been doing it since the nineteen thirties, and generated quantitative predictions that were checked and found correct.
This is a nuisance for anybody who believes that mature science replaces stories with equations. The equations are there. So is the story, and removing it does not leave a purer science; it leaves a set of relations nobody can think with.
The thesis I want to defend in this chapter is that metaphor, narrative, and ritual are not residues of a prescientific past that a sufficiently rigorous discipline would eventually shed. They are structural necessities of cognition in any system that has to predict a world larger than itself. If that is right, then the central move of the postmodern diagnosis, the announcement that the great stories have been retired, is not merely mistaken about the date. It is proposing something that cannot happen.
Start with metaphor. A mind with finite capacity confronting a world of effectively unlimited complexity must compress, and compression means mapping the unfamiliar onto structures it already handles. The nucleus as a drop, the atom as a solar system, the gene as a text, the brain as a switchboard and later as a computer, the market as an organism, the immune system as an army with a memory: none of these is decorative. Each imports a body of inference wholesale, so that a researcher who has accepted the mapping already knows a hundred questions to ask. This is why a good metaphor is worth a decade of work and a bad one costs a generation.
The costs are real and worth naming, since I am about to defend the practice. Every metaphor smuggles. The solar system atom carried an implication of definite orbits that took twenty years to remove. The brain as computer imported a separation of hardware from software that neuroscience has spent decades trying to unlearn. The gene as text implied an author, a reader, and a fixed message, none of which survived contact with the molecular details. A metaphor is a loan of structure, and the interest is paid by whoever comes next.
The proper conclusion is not to abolish the metaphors, which cannot be done, but to declare them, which can. A discipline that knows which of its metaphors are load bearing can audit them the way it audits its instruments. That sentence should sound familiar by now. It is the same operation as before, applied one level up: the metaphor is a declared component of the theory, and a metaphor whose declaration has been lost is exactly as dangerous as a parameter whose provenance has been forgotten.
Narrative next, and here the case is even stronger. An explanation is not a list of correlations. It is a sequence with a direction, in which something happens because something else happened, and the direction is not present in the data, which contain only associations. When a geologist accounts for a landscape, the account is a story: this ocean closed, that range rose, ice came and went. When an evolutionary biologist accounts for a structure, the account is a story with selective pressures playing the part of motives. When a cosmologist accounts for the abundance of the light elements, the account is a story with a beginning, a middle, and a cast. Each is testable, each is revisable, and none of them is expressible without narrative form, because the causal ordering that makes an explanation explanatory is a narrative property.
There is a serious body of work arguing that this reflects what brains are for. A predicting system generates expectations, meets the world, and updates on the difference, and the cheapest way to generate expectations about a complicated environment is to run a model in which things have roles, tendencies, and consequences. That is a story. The organism telling it is not being primitive; it is being efficient, and the alternative, tracking every correlation without any organizing structure, is not available to a finite creature.
Ritual is the part that makes scientists uncomfortable, and it should not. Consider what happens around a major result: preregistration of what will be looked for, blinding of the analysts so that they cannot see what they are producing, the unblinding performed at an appointed moment before witnesses, the circulation of a draft, the review by anonymous strangers, the correction, the publication, the replication. Every element of this is functional. Every element is also ceremonial, in the strict sense that it is a prescribed sequence of actions performed at prescribed times whose correct execution confers a status that the underlying facts do not confer by themselves. The same measurement, obtained by the same instrument, has a different standing depending on whether the sequence was followed. That is what a rite does.
I am not sneering. I think the ceremonies are among the finest inventions of the species, and I would like more of them rather than fewer. The point is that a community which believes it has no rituals cannot examine them, and an unexamined ritual drifts. The peer review ceremony, in particular, has drifted a long way from anything its designers would recognize, and the drift went unnoticed largely because nobody could admit that a ritual was what had been drifting.
Now bring this back to the argument. The postmodern diagnosis says the metanarratives have gone. This chapter says that a knowledge producing system cannot operate without metaphor, without narrative, and without ceremony, because these are the mechanisms by which a finite mind handles a world it cannot enumerate. Both cannot be true in the simple form.
The resolution is the one this book has been building toward, and it now falls out with no effort at all. The stories did not go anywhere. What went was their audibility. Metaphors that everyone shares stop being noticed as metaphors and start being experienced as descriptions. Narratives that everyone assumes stop being told and start being presupposed. Rituals that everyone performs stop being ceremonies and become procedure. In each case the thing survives in full working order and loses precisely the property that made it contestable.
A field with no metanarrative would be a field that had stopped thinking. What we actually have is a field whose metanarrative has become too familiar to hear, which is a different condition with different remedies, and the remedy is not to invent a new grand story. It is to make the existing one audible again.
Chapter Twenty-Three — Totalities Fail Asymmetrically
There is an argument for tolerance that everybody has heard and nobody believes: that we should permit dissent because we might be wrong. It fails as a practical matter because the people in a position to suppress dissent are precisely the people who do not think they are wrong, and telling them they might be is not an argument but a mood.
There is a better argument, and it is not about humility at all. It is about information, and it works even for a ruler who is completely confident and entirely well intentioned.
Take any system that has to adapt to an environment it does not fully understand: a species, an economy, a research field, an institution. The variety of configurations present in that system is not merely tolerated diversity. It is a measurement instrument. Each configuration is a probe, quietly testing a slightly different hypothesis about the environment, and the pattern of which ones flourish and which ones fail is data about the shape of a world nobody has mapped. Now suppose an authority, having identified the best current configuration, eliminates the deviations in order to optimize. It has achieved efficiency against its current model. It has also disassembled the only apparatus capable of detecting that its model is wrong.
The asymmetry is in the payoff. If the model is right, the cost of maintaining variance is modest: some resources spent on approaches that were never going to work. If the model is wrong, the cost of having eliminated variance is catastrophic and, worse, undetectable from inside, because the signals that would have revealed the error were the deviations that were removed. One error is bounded and visible. The other is unbounded and silent. A rational agent facing that payoff structure maintains the variance regardless of how confident he is, and confidence does not enter the calculation.
This is a general structural law, and it is startling how many separate literatures have been circling it. Ecologists describe the way monocultures collapse under a stress that a mixed system absorbs. Engineers build redundancy into systems whose failure modes they cannot enumerate. The most careful students of institutions have shown that rules for governing shared resources work when they are locally adapted and fail when a single scheme is imposed from above. In each case the mechanism is the same: variety is not waste, it is the sensor array.
The application to intellectual life is direct and, for anyone who likes tidy conclusions, unwelcome. A field in which one framework has eliminated the alternatives is not a field that has achieved consensus. It is a field that has lost its instrumentation. It will continue to produce results, and the results will get more precise, and there will be no mechanism by which anybody notices if the whole enterprise has been aimed slightly wrong for thirty years, because the people who would have noticed were the ones working on the abandoned approaches.
I want to state the limits of this argument with some force, because in the wrong hands it becomes a charter for every crank who has ever been rejected by a journal.
It applies only where the uncertainty is genuinely irreducible. Whether a particular vaccine reduces a particular mortality is not protected by this result. It is an empirical question with an accessible answer, the answer is obtainable by trials, and maintaining diversity of opinion about it after the trials have reported is not adaptive variance but negligence.
It does not imply that all positions deserve support. A position that has failed on its own terms, that makes no predictions, or that survives only by retreating whenever it is tested is not a probe; it is a corpse being carried by relatives. The variance that matters is variance among live approaches, each of which is doing work and could be wrong in an informative way.
And it does not imply that resolution is bad when resolution is available. The claim is precisely restricted to those questions where the underlying situation is not accessible, where the competing positions each capture something real, and where the appearance of resolution would be produced by fashion or authority rather than by evidence.
With those limits in place, look back at what has just happened to the argument of this book. In an earlier chapter I said that the plurality of incompatible descriptions is structurally necessary. I am now saying that the elimination of that plurality would be actively harmful even where it could be achieved. Those are two independent results converging on the same conclusion from opposite directions, one from the nature of description and the other from the dynamics of adaptation, and the convergence is the strongest evidence I have that the conclusion is about the world rather than about my preferences.
And now the barb, which points at the position I have been defending. If totalizing ideals fail asymmetrically, then anti-totalization is not exempt. A movement that eliminates every unifying framework in the name of difference has produced a monoculture of anti-monoculture, with exactly the same loss of variance and exactly the same blindness to its own error. The intellectual history of the last forty years contains more than one department where this occurred, and where a young scholar proposing a systematic account of anything was corrected with the reflexive certainty of a catechism.
The structural law does not take sides. It says maintain the variance, and a variance that has been purged of unifiers is as depleted as one that has been purged of skeptics. Which means, awkwardly for everyone, that the correct configuration of an intellectual field includes people who think this entire book is wrong, working seriously on the assumption that a final unified account is available. I am not required to agree with them. I am required to want them funded.
Chapter Twenty-Four — Irony Is Not a Style; It Is a Swap
Somewhere in the nineteen nineties, irony became a personality. It was diagnosed as the ailment of a culture that could no longer say anything without quotation marks, blamed for political apathy and bad architecture, and periodically declared dead, usually by columnists announcing that some recent catastrophe had made sincerity mandatory again. Sincerity did not become mandatory. Irony did not die. The diagnosis was wrong in a way that is worth correcting properly, because the correction reveals a mechanism rather than a mood.
Begin with what irony does, mechanically, leaving aside every question of taste. A statement is made. Attached to it is a role: this is an assertion, offered as true, by a speaker who stands behind it. Irony swaps the role while leaving the content untouched. The words stay put and the position from which they are spoken moves, so that the listener receives both the statement and a signal that the speaker is not standing where a speaker normally stands.
For that to work, three things must be true simultaneously. The listener must possess the expected model. He must detect that the speaker’s actual position departs from it. And he must be able to hold both at once, since dropping either one destroys the effect, leaving either a lie or a puzzle. Irony is therefore not available to a system that can hold only one model at a time. It is a native operation of a system that maintains several and can compare them.
Which brings the argument round to a familiar place. A predicting system generates expectations and measures the world against them. Such a system must, structurally, maintain both a model and the record of its departure from the model, because the departure is the only thing it can learn from. That is precisely the configuration irony requires. To be capable of irony is to be capable of holding a description alongside its failure without collapsing into either, and that capability is not a stylistic option for a predictive mind. It is the thing the mind is made of.
The consequence is that a culture cannot decide to stop being ironic, any more than it can decide to stop having peripheral vision. What it can do is change what irony is aimed at, which is what actually happened in the periods when commentators announced its death and its resurrection.
Now put this next to the situation the last several chapters have described. A person living among incompatible valid descriptions has to hold more than one model of the same domain and to know that each of them fails somewhere. That is the ironic configuration exactly, arrived at not through sophistication or fatigue but through the structure of the epistemic situation. The much discussed irony of the late twentieth century was not a decadent affectation. It was the natural posture of minds that had noticed the plurality and had no theory of it, and it looked like decadence because they had no theory of it. A person who holds two accounts and knows why he holds them is doing something respectable. A person who holds two accounts, cannot say why, and is embarrassed about it retreats into quotation marks. Same operation, different amount of understanding.
This also explains the failure of every campaign to restore sincerity, and there have been several, each announcing that the age of detachment was over and that we would now say what we mean. The campaigns fail because they misidentify what they are fighting. They think irony is a refusal to commit. It is in fact the ability to run a commitment and its known failure modes at the same time, which is not the opposite of seriousness but its most advanced form. A surgeon who is fully committed to a procedure and simultaneously tracking every way it could go wrong is in the ironic configuration, and he is the person you want holding the instrument.
Two limits, since I am defending something that has been justly criticized.
Irony has a pathological form, and it is not the excess but the collapse. When the second model becomes fixed and universal, when every possible assertion is received as merely a position somebody is occupying, the comparison stops doing any work, because a comparison requires a standard and a stance held permanently at a distance from all standards has none. That configuration is genuinely sterile, and it accounts for the specimens of the nineties that the columnists were complaining about. The complaint was correct; the diagnosis blamed the mechanism instead of its degenerate case.
And irony fails as a public instrument the moment it is transmitted beyond an audience that shares the expected model, which is the situation created by every general purpose communication network ever built. Detached from the community that could detect the swap, an ironic statement arrives as a sincere one, and the swap is lost in transit. This is not a modern discovery in principle and it is a modern catastrophe in practice, and everybody who has watched a joke travel and return as an accusation has observed it directly.
None of which touches the structural point. Irony is a swap of attributed role with the content preserved, it is available to any system holding multiple models, it is required by any system that learns from prediction error, and it is therefore permanent. Which makes it, I note with some satisfaction, one more thing that the postmodern was said to have introduced and that turns out to have been here all along, waiting for somebody to describe the machinery.
Chapter Twenty-Five — Absurdity as Mercy
There is a moment in the collapse of a difficult conversation when somebody says something ridiculous and the room laughs and the temperature drops. Everyone has experienced this. Almost nobody treats it as anything but a social lubricant, a bit of luck, the sort of thing a skilled chairman supplies by instinct. I want to argue that it is a mechanism, that it has a function, and that the function is not comfort but repair.
Consider an interpretive system under load. A mind, or a committee, or a discipline is trying to make sense of a situation in which the available frames all fail in different places, the evidence supports several incompatible readings, and every additional piece of information makes the picture worse rather than better. This is not confusion in the ordinary sense. Confusion is not knowing enough. This is the opposite condition: knowing too many things that will not sit together, with the interpretive apparatus running continuously and converging on nothing.
Such a system has a characteristic failure mode, and it is not paralysis. It is premature closure. Under sufficient interpretive load, a mind will seize the first frame that reduces the load and defend it with a ferocity out of all proportion to the evidence, because what is being defended is not the conclusion but the relief. This is where conspiracy theories come from, and where a great deal of ideological rigidity comes from, and where the sudden and total conversions come from. The mechanism is not stupidity. It is an overloaded system taking the exit.
Now the claim. Semantic destabilization, which is to say the deliberate introduction of the absurd, interrupts that seizure. A frame that has been building pressure toward premature closure is knocked off balance by a statement that fits nowhere: nonsense, a joke, an image so incongruous that no reading survives it. The interpretive machinery, which was about to lock, is forced to release. And in the interval, the situation can be looked at again without the pressure that was about to determine the outcome.
This is why absurdity clusters in exactly the places one would predict if the account is right, and I offer the distribution as evidence. It appears in the traditions of religious instruction where the objective is to break a student’s grip on a concept he holds too tightly: the puzzle with no answer, the deliberately unanswerable question, the master’s reply that has nothing to do with what was asked. It appears in the humor of soldiers, of surgeons, of emergency workers, of people who work with the dying, and it appears there in a form that outsiders find shocking, which is the point, since the shock is the release. It appears in the folk tradition of the sacred fool, licensed to say what nobody else may. And it appears in literature at precisely those historical moments when the available accounts of the world had visibly failed and no replacement was in sight.
The nonsense verse of the Victorians is not children’s entertainment that grew up. It arrived alongside the collapse of natural theology and the arrival of a universe with no obvious moral architecture. The theater of the absurd in the middle of the twentieth century was not a stylistic preference. It was written by people who had watched the collapse of every available narrative and who found the honest response to be a stage on which two men wait for someone who does not come. In each case the absurd is not describing the failure of meaning. It is performing the release that lets an overloaded interpreter keep working.
Hence the name I use for the principle: absurdity as mercy. The mercy is not consolation. It is more like the release valve on a boiler, and it is aimed at the same organ that would otherwise seize.
Two consequences follow, and both bear on the argument of this book.
The first concerns the reception of postmodern culture, which has been consistently misread by its detractors and, in a different way, by its admirers. The irreverence, the pastiche, the refusal of the straight face: this is the signature of an interpretive system under load, doing the thing that such systems do to avoid locking. It is not decadence and it is not nihilism. It is what a culture does when the available frames have stopped fitting and no replacement has arrived. The detractors were right that something was wrong and wrong about what it was. The admirers mistook a coping mechanism for a philosophy.
The second is a warning about my own recommendations, and I would rather issue it myself than wait for somebody else to. This entire book has been arguing for a disciplined way of working under plurality: declare your components, map the provability landscape, maintain the variance, judge case by case with a procedure. That is a demanding regime. It requires holding several incompatible descriptions simultaneously and refusing the relief of choosing one, which is precisely the load I have just described as dangerous. Any regime of that kind must include its own release valve or it will produce exactly the rigidity it was designed to prevent.
Which is my defense, if one is wanted, of the tone of this book. The jokes are not a marketing decision and not a personal weakness. A book that argued for holding contradictions open, in a voice of unbroken solemnity, would be recommending a discipline while demonstrating its failure mode on every page. If I am right about the mechanism, then a serious book about incompatible truths has an obligation to be funny, and the obligation is structural.
Chapter Twenty-Six — The Unpresentable, With a Proof
Late in his life, having been famous for two decades for a book he disliked, Lyotard spent most of his energy on aesthetics, and specifically on a concept borrowed from Kant that nobody outside the field had thought about for a century. The concept is the sublime, and the reason for his interest is the reason this chapter exists.
The eighteenth century distinguished the beautiful from the sublime with some care. The beautiful is what pleases through form: a proportion, a harmony, something the mind takes in and finds fitting. The sublime is what happens when the mind meets something it cannot take in. Confronted with a magnitude beyond its capacity to assemble into a single image, the imagination fails, and in the failure the mind becomes aware of a demand it cannot satisfy, and the awareness is not merely painful. There is an odd exaltation in it, because the failure reveals the presence of something the failing faculty was reaching for.
Lyotard’s contribution was to take this out of the mountains and put it to work as the central category of modern art. On his account, what the serious painting of the last century has been doing is not representing objects and not expressing feelings but presenting the fact that there is something which cannot be presented. The blank canvas, the monochrome, the vast field of a single color that produces vertigo rather than decoration: these are not failures of representation and not jokes at the expense of the public. They are attempts to make the existence of the unpresentable perceptible without presenting it, which is a paradoxical assignment and precisely the assignment.
He also curated an exhibition on this theme, in 1985, at the Pompidou Centre in Paris, about the new immaterial technologies and what they were doing to our sense of what an object is. I mention it because it is the only case I know of a major philosopher testing a concept by building an environment for it rather than by writing another book, and because the exhibition asked visitors to move through spaces in which the material carrier of information kept receding, which is a physical demonstration of an argument that would take forty pages in prose.
Now, the problem. This is the part of his work most easily dismissed, and the dismissal is not stupid. A concept that names what cannot be named, that is verified by the failure of verification, and that finds its evidence in the inability to produce evidence, has the formal structure of an unfalsifiable claim. If every failure to present is evidence for the unpresentable, then nothing counts against it. The critic who says this is a mystification dressed as a theory is making a legitimate objection, and neither Kant nor Lyotard answered it in a way that a skeptic would accept.
I propose to answer it, and the answer was established eleven chapters ago in a completely different register.
Any consistent world containing observers made of the same material as the world necessarily contains content that no observer within it can access. That is not an aesthetic claim, it involves no feeling, it makes no reference to art or to mountains, and it follows from the relation between a whole and a part that models it. The unreachable content is a structural consequence of embedding, and its existence is established by an argument that a hostile logician can check.
Set that beside the aesthetic tradition and the correspondence is exact. The sublime, in the Kantian analysis, is the experience of a mind encountering the limit of what it can assemble. The structural result says that such a limit exists necessarily, for any embedded observer, in any consistent world. What the eighteenth century described from the inside as a feeling, and what the twentieth century took as an unfalsifiable posture, turns out to be the phenomenology of a fact about architecture.
This changes the status of the concept in three specific ways, and I want to be exact about what is and is not delivered.
It supplies an address. The unpresentable is no longer a name for whatever eludes us. It is the residue that follows from embedding, and it has a location in the argument: it is what an internal observer cannot reach precisely because he is internal. That is a definite thing to have said.
It supplies a limit. And here the aesthetic tradition loses something it will not enjoy losing. If the unpresentable is a structural residue, then nothing may be placed in it. Not God, not the Real, not the unconscious, not any of the various items that two centuries of writing have quietly deposited there on the grounds that the space was available. The result establishes that a residue exists. It says nothing whatever about what is in it, and the inference from unreachability to any particular content is invalid.
And it supplies a test, which is what the critic was asking for. An artist or a philosopher who claims to be working with the unpresentable can now be asked which limit he means: the limit of a technique, which is a craft problem; the limit of a period’s imagination, which is a historical problem; or the structural limit, which is the only one that is permanent. Most of the work that has invoked the term is doing the first two, and there is nothing wrong with that, and calling it by the name of the third has been the source of an enormous amount of intellectual inflation.
So the concept survives, considerably smaller and considerably harder. Lyotard was right that something cannot be presented, right that this is not a temporary shortfall, and right that the encounter with it is a real experience rather than a confusion. He had no argument for any of it. The argument existed, in a different building, among people who would never have read him, and it says what he said with none of his authority and all of his conclusion.
Chapter Twenty-Seven — Art When Everything Is Available
Every recording ever made is now on the same device, in the same list, at the same price, which is nothing. Every painting is a search away. Any competent request produces an image in seconds. The scarcity that organized aesthetic life for the whole of human history has simply been removed, and it has been removed within the lifetime of most people reading this.
The interesting question is not whether this is good or bad. It is what happens to a faculty that evolved under scarcity when the constraint is lifted, and the answer is not the one either the optimists or the pessimists expected.
Start with why art exists at all in structural terms, because the usual accounts are unusable here. A mind that models a world larger than itself is under permanent pressure from two directions: it must compress, and it must remain sensitive to the parts of the world its compression has discarded. Those requirements pull against each other. A model good enough to act on is a model that has thrown away most of what it received, and a system that only ever refines its model becomes progressively better at a world that may have moved. Something has to keep the discarded material in play.
That is what aesthetic engagement does. An artwork is an object that resists immediate assimilation into the model and rewards continued attention with structure that was not apparent at first. It is calibration equipment for a compressing system: it exercises the capacity to perceive what has not yet been categorized, and it does so in a setting where the cost of failure is zero. This is why art is not optional in any known society, why it appears before agriculture, and why nobody has ever found a group of humans who decorate nothing and sing nothing.
Now lift the scarcity.
The first thing that happens is the one everybody noticed and misdiagnosed. Abundance does not produce more aesthetic experience; it produces less per unit of material, because the limiting resource was never the supply of objects. It was attention, and attention is not merely finite but rivalrous with itself: the knowledge that ten thousand alternatives are one gesture away changes the quality of engagement with the one in front of you. A person who owned four records heard them differently from a person with everything, and the difference is not nostalgia. It is a real change in the depth of processing, and it can be measured.
The second thing is more interesting and it is where the generative machinery becomes relevant. When the production of competent work becomes cheap, competence stops being the scarce quantity, and the value migrates. It migrates toward the things that cannot be produced on demand: provenance, the fact that a specific person made this at a specific cost; occasion, the fact that it happened once, in a room, with people in it; and duration, the fact that somebody spent a portion of a finite life on it. None of these is a property of the object. All of them are properties of its relation to a life, and none of them can be synthesized, because synthesizing them is exactly what would destroy them.
This predicts several things that have in fact occurred, which is the only reason to advance it. It predicts the extraordinary resurgence of live performance in an era of perfect reproduction, and the willingness of audiences to pay sums for presence that they will not pay for recordings. It predicts the return of formats whose only advantage is inconvenience. It predicts that the first question asked about any striking new image will become a question about how it was made rather than about what it shows. And it predicts a rising premium on work whose production is verifiably expensive in human time, which is a peculiar thing for a civilization to reward and is what a civilization rewards when everything else has become free.
The third consequence returns us to the argument of this book, and I will not labor it. A mind that must hold several incompatible descriptions, refusing the relief of collapsing them, is performing an aesthetic operation as much as an epistemic one. The capacity to hold a form in view without resolving it, to keep attending to something that will not settle into a single reading, is exactly the capacity that art trains, and it is not trained anywhere else. This is not a metaphor and it is not a compliment paid to the arts by a physicist in a generous mood. The discipline recommended by this book requires a faculty, the faculty is developed by aesthetic practice, and a culture that eliminates the practice on the grounds that it produces nothing will find, some years later, that its scientists have become unable to tolerate an open question.
Lyotard, who spent his last years writing about painters while the world asked him about postmodernism, would have been pleased by that conclusion and irritated by the route. He thought the aesthetic was where the unpresentable made itself felt. I think the aesthetic is where a compressing system maintains the equipment it uses to notice what it has thrown away. These are not the same claim. They are, however, both claims that the arts are load bearing, and I am content to arrive at his conclusion by a road he would have disliked.
Chapter Twenty-Eight — Power With Nobody in It
The classic complaint about power is that somebody has it. There is a person, or a class, or an institution, and the analysis consists of identifying who benefits, tracing the mechanism, and naming the interest served. Two centuries of political thought are organized around that assumption, and the assumption is what makes the thought actionable: once you know who is doing it, you know whom to negotiate with, vote against, or replace.
The arrangement that now governs a great deal of daily life does not have that shape, and the mismatch is why the standard vocabulary keeps sliding off it.
Consider what happens when a system decides which items a person sees. The system was built by engineers who were given an objective, usually some measure of engagement, and who optimized against it with no view about content whatsoever. The objective was set by managers responding to advertisers responding to a market. The training data are the recorded behavior of the users themselves, so that the system’s model of what people want is assembled from what people did, which was itself shaped by what previous versions of the system showed them. Every participant in this loop is behaving rationally within his role. Ask who decided that a particular kind of material would flourish and a particular kind would vanish, and there is no answer, because nobody decided. The outcome was produced by an optimization nobody supervised against an objective nobody examined.
This is power in the strict sense: it shapes what people believe, want, and do, at scale, in a direction. It simply has no subject. There is nobody in it.
The consequences are worth setting out carefully, because they are not the ones the dystopian version predicts.
Attention becomes the contested resource, and the contest is asymmetric in an unusual way. The system has a complete record of what has held attention in the past and unlimited opportunity to experiment; the user has one lifetime, no record, and no control condition. This is not a fair fight and describing it as manipulation misses what is odd about it. Manipulation implies a manipulator with an intention. What is present instead is a gradient, and the user is a ball on it.
Suppression happens without prohibition. Nothing is banned. Material that performs poorly against the objective is shown less, and being shown less is functionally identical to not existing, and no record is generated of the non-event. A censor produces a list, and lists can be litigated. A ranking function produces nothing at all, and the material it declined to distribute has no standing to complain, having never been rejected.
Behavioral lock-in emerges without anyone locking anything. A system that predicts what a person will engage with and supplies it will progressively narrow the range it offers, not because narrowing was an objective but because the estimate is most confident where the evidence is thickest, and the evidence gets thicker wherever the person was already going. The result is a groove, cut by a process with no view about grooves.
Now the connection to this book, which the reader has probably already made.
This is the same structure I described earlier in the machinery of research, appearing in a different domain and at a vastly larger scale. A substantive account of the world has been embedded in a procedure. The procedure is executed rather than asserted. Nobody defends it because nobody states it. It is inherited by everybody who uses the system, enforced by cost rather than by rule, and invisible in the output. A reference cosmology and a recommendation engine are the same kind of object, differing in subject matter and in the number of people affected.
And the epistemic property that matters is identical in both cases. A story that is told can be contradicted. A story that is executed presents nothing to contradict. What Lyotard called the differend was a wrong for which the tribunal had no language; what we have here is a wrong for which there is not even a defendant, since the party who would have to answer does not exist as a party. The objection cannot be phrased, and there is nobody to phrase it to.
Some cautions, because a chapter like this attracts a readership I would rather not have.
The absence of a subject does not mean the absence of responsibility. Somebody chose the objective. Somebody decided that engagement was the quantity to maximize and that the decision did not require justification because it was technical. That choice is a declared component of the largest experiment ever run on human attention, and it is undeclared in every sense that matters: unstated, undefended, and mostly unexamined by the people who set it.
Nor does any of this require the systems to be malevolent, and the assumption that they are is the most effective protection they have. A conspiracy can be exposed. An optimization cannot, because there is nothing to expose; the whole thing is documented, published, and often open source, and knowing exactly how it works changes nothing about its effect on the person who knows.
And the remedy is not to smash the machinery, which will not happen and would not help. It is the same remedy as everywhere else in this book, and it is unglamorous to the point of anticlimax. Name the objective. State what is being maximized, who set it, what the alternatives were, and what the system would do differently under each. Make the declaration visible in the output rather than in a document nobody reads. That is not a solution to the problem of power without a subject. It is the construction of a party who can be addressed, which is the precondition of every other remedy anybody might want.
Chapter Twenty-Nine — Excluded Before Speaking
Institutions rarely defeat their opponents. Defeating an opponent is expensive, produces a record, and leaves the opponent alive and aggrieved. What institutions do instead, when they are working well by their own lights, is arrange matters so that the opponent is not present.
The mechanism is worth studying without indignation, because it is not primarily a technique of the wicked. It is a stability property, and stable institutions have it for the same reason that stable buildings have expansion joints.
Consider how a body maintains coherence over time. Every member admitted brings preferences that may diverge from the institution’s operating assumptions, and divergence has a cost: deliberation slows, coalitions form, and the shared understandings that let a group act without renegotiating everything begin to erode. A body that admits everyone must spend most of its energy on internal negotiation. A body that admits nobody ossifies and dies. In between there is a management problem, and the solution that emerges almost everywhere is selection at the boundary rather than suppression on the inside.
Selection at the boundary takes forms that are individually defensible and cumulatively decisive. There are qualification requirements, which are genuinely necessary and which encode the assumptions of whoever set them. There are procedural norms, so that a case arrives in the correct format or not at all, and formatting is not neutral, since some claims have no correct format. There are costs of entry in time, money, and credentials, which filter by resources and by tolerance for the institution’s particular tedium. And there is the most effective mechanism of all, which requires no action by anybody: self exclusion, in which a party surveys the arrangement, concludes correctly that his case cannot succeed there, and does not come.
The result is that the institution’s deliberations are conducted among parties who already share its foundational commitments, and the deliberations therefore have a striking quality that observers routinely misread. Debate within is vigorous and often bitter, which everyone experiences as evidence of openness. The vigor is real. It is also confined to a range that was fixed before anybody arrived, by a selection process invisible to those selected, since the parties who would have raised the other questions are not in the room to be noticed as absent.
This is the differend converted into an operating procedure and running as designed.
The literature on scientific institutions supplies examples that are not controversial in retrospect. A funding body evaluates proposals by expected productivity, and productivity is estimated from track record, and track record accrues to those who have already been funded, so that the process is stable and the questions nobody has worked on remain the questions nobody has worked on. A journal defines its scope, and work that falls between two scopes falls out of both. A peer review system asks whether a submission engages adequately with the existing literature, which is an entirely reasonable requirement and which means that work proceeding from a different starting point will be judged inadequate by a criterion it never claimed to satisfy.
I have opinions about this that are not disinterested and I will state the interest rather than pretend to have none. I work outside the institutional structures of my field, my papers do not arrive with an affiliation that reviewers recognize, and I have accumulated the usual collection of responses that decline to engage on grounds unrelated to content. That is my situation, and it is exactly the situation in which a person is most likely to mistake his own inadequacy for structural exclusion. So let me supply the discipline rather than the grievance, since a chapter like this one is worthless without it.
There is a test that distinguishes a genuine exclusion from a convenient one, and it is not difficult. Ask whether the excluded claim can be stated in a form the institution could evaluate. If it can, and the institution declines to evaluate it, the exclusion is real and the institution is failing by its own standards. If it cannot be so stated, ask why. If the reason is that the claim requires assumptions the institution has ruled out in advance, then there is a genuine differend and the honest move is to say precisely which assumption is at issue rather than to complain about closed minds. And if the reason is that the claim is not yet in a condition to be evaluated by anybody, then what is being described as exclusion is unfinished work, and the correct response is to finish it.
I apply that test to myself regularly and it comes out three ways. Some of my work has been declined for reasons I regard as poor and could argue about, and arguing about it is legitimate. Some of it depends on assumptions that mainstream practice excludes at the outset, and there the disagreement is real and locatable and I should be naming the assumption instead of complaining about reception. And some of it, at various times, has simply not been finished, and the reviewers who said so were right.
The general point outlives my case. An institution’s health cannot be assessed from the vigor of its internal disagreements, because that vigor is compatible with any degree of prior selection. It can only be assessed by examining the boundary: what arrives, what is turned away, what never applies, and whether anybody is keeping a record of the last of these. Almost nobody keeps that record. It is, by construction, a record of things that did not happen, and no institution has ever been rewarded for maintaining one.
Chapter Thirty — Hostile by Design
It is possible to build an environment in which nobody can find out what is true, and it is not necessary to lie in order to build it.
This is the finding that I regard as the most practically urgent thing in this book, and it requires distinguishing three mechanisms that are usually discussed separately and that only make sense together.
The first is noise. The channel between the world and the observer is flooded with material, not primarily false material but simply an overwhelming quantity of assertion, so that the cost of determining which items are supported exceeds any individual’s budget. The classical propagandist wanted you to believe a particular falsehood, which required his falsehood to be findable and therefore refutable. The modern operation has no such requirement. It needs only that the true account be one item among a hundred thousand, and it achieves that without asserting anything.
The second is the stigmatization of doubt. Here the pressure is social rather than informational, and it operates on what a person will admit to perceiving. Certain questions are marked in advance as the questions asked by a disreputable kind of person, and the marking does its work before any evidence is considered, because the cost of being taken for that kind of person is immediate and the benefit of asking is speculative. This mechanism is the most interesting of the three, because it is usually deployed by people defending something true. The defense is sincere, the target is often genuinely disreputable, and the effect is to make an entire region of inquiry expensive to enter regardless of what is in it.
The third is algorithmic filtering, which I have already described in another connection: selective disclosure performed by a system with no view about the material, producing a personalized picture of the world whose selection principles are unavailable to the person looking at it.
Each of these has a substantial literature. What that literature lacks is the observation that the three form a cycle, and the cycle is why interventions against any one of them tend to fail.
Watch it turn. Noise raises the cost of independent verification, which makes people rely on social signals about which sources are respectable. Reliance on social signals amplifies the stigmatization mechanism, since the cheapest signal is the reputational one. Stigmatization suppresses the expression of doubt, which removes doubt from the observable record, which means the filtering systems, trained on expressed behavior, learn that the suppressed questions have no audience and stop distributing them. Reduced distribution means the material that would have addressed those questions is produced less, which leaves the field to whoever is producing noise. And around again.
The practical consequence for policy is severe and explains a great deal of recent failure. An intervention against disinformation that operates by marking whole categories of inquiry as illegitimate strengthens the second mechanism while weakening the first, and the net effect can easily be negative, since it confirms for a substantial audience that the institutions cannot tolerate questions. Conversely, a defense of open inquiry that ignores deliberate flooding leaves people with no navigational resources at all. Each remedy feeds the mechanism it does not address. This is not a coincidence; it is what a cycle does.
Now a corrective that runs against the mood of everything I have just written. There is a systematic reason why environments of this kind are perceived as more hostile than they are, and it follows from an asymmetry in what gets observed. Successful deception is invisible: if a manipulation works, it is not registered as a manipulation. Detected manipulation is highly visible and highly discussed. So the observable record consists of failures, and a population that sees a great many detected manipulations is seeing evidence of detection capacity, which it interprets as evidence of manipulation prevalence. The same asymmetry operates for institutional failure. Every discovered error in a scientific field is evidence that the field discovers errors, and every one of them is read as evidence that the field is unreliable.
This does not make the hostility imaginary. It means the perceived level is an upper bound and probably a considerable overestimate, and that a person calibrating his trust from the observable record will be systematically too cynical. That correction is worth carrying, because the cynical error is not the safe one. A person who trusts nothing has not achieved skepticism; he has achieved unavailability, and unavailable people are the easiest of all to move, since a mind that credits no source will eventually credit whichever one is closest.
Which leaves the question of what to actually do, and the answer I propose is a discipline rather than a technique. Call it epistemological patience: the deliberate maintenance of an unresolved state on questions where the available evidence does not support resolution, held open for as long as it takes, without the closure that the environment is engineered to produce.
Four things it is not, since each is a way of getting it wrong. It is not the ancient suspension of judgment applied to everything, which is a permanent posture and this is a temporary one, adopted per question. It is not relativism, since it holds that there is an answer and that we do not yet have it. It is not procrastination, because it is compatible with acting: one acts on the best available estimate while explicitly declining to convert the estimate into a belief. And it is not global skepticism, which is a claim about knowledge in general, whereas this is a decision about a particular question on a particular day.
It is also, I should say, extremely unpleasant. Holding a question open costs something continuously, and the cost is exactly the interpretive load described a few chapters ago, which is why the release valve of the absurd is not an optional extra but part of the equipment. The environment is built to make closure cheap and patience expensive. Nothing can be done about that except to notice it, and to recognize the sensation of relief, when a frame finally clicks into place, as a piece of data about oneself rather than about the world.
Chapter Thirty-One — How to Act When the Truths Will Not Combine
A ship’s navigator in the age before satellites carried several instruments that disagreed. The magnetic compass pointed at a pole that was not the one he wanted, wandering with local iron and with the year. The chronometer, which converted time into longitude, drifted. Celestial observation was exact and unavailable under cloud. Dead reckoning accumulated error at a known rate. No instrument was correct, no two agreed, and there was no master instrument to arbitrate. Navigators nonetheless crossed oceans and arrived, and they did it by a practice that had a definite structure and no theory whatsoever.
That practice is what this chapter is about, because it is the answer to the question the whole book has been circling, and because nobody has ever thought of it as philosophy.
Restate the problem exactly. Several descriptions of a domain are each valid within their scope, each incomplete, and mutually incompatible where they overlap. No description ranks them. A decision must be made anyway, this afternoon, with consequences. What should a rational agent do?
The wrong answers are worth naming first, since each is popular and each is a failure mode rather than a strategy.
Rigid adherence picks one description and uses it everywhere. This is the commonest response and it performs adequately for as long as the agent stays inside the region where his chosen account is accurate. Its failure is silent, since the account continues to produce confident outputs outside its scope, and there is nothing in the output to indicate that the boundary was crossed.
Forced unification refuses to act until the descriptions have been reconciled. Since the incompatibility is structural, this is a decision never to act, dressed as rigor.
Random selection alternates without principle, which sounds absurd and is in fact common in institutions, where it appears as inconsistency across departments and over time. It does have one virtue: it cannot be systematically wrong in a single direction. That virtue is not enough.
The strategy that outperforms all three is to maintain the incompatible models simultaneously and switch between them according to context. The switching is not arbitrary. Each description has a domain in which its accuracy is high, and the agent’s task is to know those domains, to determine which one he is currently in, and to apply the appropriate model, while continuing to maintain the others rather than discarding them.
This can be established formally, and I want to say what the formal result depends on so that it is not mistaken for a recommendation to be sensible. The advantage of contextual switching over the alternatives requires two conditions: that the descriptions differ in where their accuracy is high, and that the agent can obtain some signal about which context he is in. Where those conditions hold, the switching strategy dominates, and the margin grows with the degree of specialization. Where the second condition fails, and the agent has no way to tell where he is, the result does not hold, and honesty requires saying so. An agent with no context signal is in a genuinely worse position and should be told that rather than reassured.
Now the practical content, which is what the navigator had and no philosopher supplied.
He knew each instrument’s error profile. Not that it erred, but where, in which direction, and by how much: the compass by this many degrees in these waters, the chronometer by this much per week. Knowing where a description fails is a different kind of knowledge from knowing what it says, and it is the knowledge that makes switching possible. In research, this is the knowledge that lives in the informal culture of a field and almost never gets written down, which is why it is lost when a generation retires.
He cross checked deliberately, and he treated disagreement as information rather than as an embarrassment. When two instruments diverged more than their known profiles allowed, that was a signal about the situation, not merely a nuisance. The most valuable moment in the practice is the one where the descriptions disagree by more than they should.
He maintained the disused instruments. The compass was kept in working order through the days when the sky was clear, because the weather would change. This is the operational form of the argument about variance from an earlier chapter, and it is worth noticing that the practical people arrived there long before the theorists.
He acted on the current best estimate while holding it revisable, and he recorded the basis of the estimate so that a later correction could be propagated. That is a log. Every competent practice under uncertainty has one, and the function of the log is precisely to keep declared components attached to the conclusions that depend on them.
And he never confused a fix with the position. The fix was an estimate produced by a procedure, carrying a known uncertainty, and the ship was somewhere near it.
Set this beside what Lyotard offered, which was to judge case by case, without criteria, under an obligation to justice that can never be satisfied. He was not wrong. He was describing the navigator’s situation without the navigator’s equipment, and the equipment is the entire difference between a stance and a practice. Judgment without criteria is not the same as judgment without structure. There is no master instrument; there are error profiles, cross checks, maintained alternatives, logs, and the discipline of not mistaking an estimate for a location.
This is the answer, and I am aware that it will disappoint anybody who wanted a philosophy. It is a set of habits, most of which have been independently invented by every profession that operates under uncertainty and cannot wait for certainty: navigation, medicine, aviation, intelligence analysis, structural engineering. What philosophy can add is not the habits but the account of why they work, which matters because a practice that does not know why it works will be optimized away by the first administrator who finds it inefficient.
Chapter Thirty-Two — The Adaptive Observer
Something is still missing from the previous chapter, and a careful reader will have located it. The navigator knew his instruments’ error profiles because generations of navigators had drowned working them out. The strategy requires knowing where each description is accurate, and that knowledge is exactly what is unavailable when a domain is new.
So the question sharpens. Not what to do when you know the profiles, but how to acquire them: how an observer who is inside the system, cannot access all of it, holds several incompatible descriptions, and has to act, gets better over time.
Call such a thing an adaptive observer, and specify it plainly. It is embedded, so a portion of the content is permanently out of reach. It is finite, so it compresses, and compression forces the choice of what to treat as basic. It holds multiple descriptions, none authoritative. And it must act, which means its errors are not merely noted but suffered, which is the feature that makes learning possible at all.
Four capacities distinguish an observer that improves from one that merely persists.
The first is scope tracking. The observer maintains, for each description it holds, an estimate of the region in which that description performs, and updates the estimate from failures. This is the crucial move and it inverts the usual relation to error. In a system that holds one account, a failure is a refutation and is resisted accordingly, since the alternative to the account is nothing. In a system that holds several, a failure is a boundary marker: it does not say the description is wrong, it says where it stops, and it is therefore welcome. The same event is a threat to a monotheist and a survey instrument to a pagan, which is the most useful thing that word has done in this book.
The second is the recognition of surprise. A failure only teaches if it is registered as a failure, and an observer whose descriptions are flexible enough to accommodate any outcome after the fact learns nothing while feeling well informed. This is why the discipline of stating in advance what would count as a departure is not bureaucratic. It is the mechanism by which surprise becomes available as data, and a system without it has no error signal, only a stream of confirmations.
The third is cost accounting. The observer must know what each of its descriptions is buying and what it is paying: which conclusions it enables, what it commits to, and what it renders invisible. Without this the switching in the previous chapter degenerates into opportunism, in which the model chosen is the one that yields the preferred answer, and the agent cannot tell the difference from the inside. The defense against that failure is not virtue. It is recording the choice before the answer is known.
The fourth is residue awareness, and it is the one that connects this chapter to the beginning of the book. The observer knows that some content is structurally unreachable, and it therefore does not treat the union of its descriptions as complete. This sounds like a counsel of humility and is in fact a piece of engineering. A system that believes its models jointly exhaust the domain will interpret every anomaly as noise or as a local error. A system that knows a residue exists has a third category available, and the third category is where new physics has always come from.
Two things this account is not, and I want them nailed down.
It is not a theory of consciousness, and nothing in it requires the observer to be conscious, or human, or singular. A research community satisfies the specification. So, in principle, does an instrument.
And it is not a procedure for reaching the truth. The adaptive observer does not converge on a single correct description, because the results of the middle chapters establish that there is not one. What it converges on is an accurate map of where its descriptions work, which is a different achievement and the only one on offer.
Now step back and look at what has been assembled, because this is the point at which the argument of the book closes.
Lyotard’s diagnosis was that the stories which authorized knowledge had failed, that the domains of discourse have no common tribunal, and that we are left to judge without criteria. Each part is correct, none of it began in 1979, and he stopped there. The reason he stopped is that the third part looked like a terminus. If there is no tribunal and no criterion, what could possibly follow except tact, taste, and the invocation of a justice that cannot be specified?
What follows is this specification. An embedded, finite, multiply modeled, acting observer, tracking the scope of each of its accounts, arranging to be surprised, accounting for the costs of its commitments, and reserving a category for what it cannot reach. That is not a metanarrative. It legitimates nothing, promises no destination, and confers no standing on anybody. It is a description of what a knower has to be in order to keep learning in a world that will not resolve into a single account, and it is available to anyone, in any field, on any afternoon.
The report on knowledge asked what happens to inquiry when the great stories go. This is the answer, delivered forty seven years late. Inquiry carries on, rather better than before, without them.
Chapter Thirty-Three — Communities That Were Never Grand
The most durable collective experiments in Western history have been small, voluntary, and modest in their ambitions. Monasteries, mutual aid societies, cooperative settlements, congregations, kibbutzim, the associations that emerge in a neighborhood after a flood: none of them proposed to transform humanity, and several of them have outlasted every state that surrounded them.
The century that ended two decades ago ran the opposite experiment at civilizational scale, and the results are not in dispute. Attempts to install collective life through revolutionary seizure and central planning produced authoritarian governments, economic failure, and mass death, at magnitudes that are still being counted. That is the record, and no accounting of it should be softened.
The interesting question is what the record actually shows, and the usual reading gets it wrong in a way that matters for this book.
The usual reading is that collective ideals were tested and refuted. But the ideals were not the variable. Equality, shared ownership, and mutual aid are also the operating principles of the monastery and the cooperative, which did not produce famine. What differed between the cases was not the content of the ideal but the mechanism of formation: whether people arrived by choosing to and could leave, or were assembled by force and could not.
The mechanism does specific work and it can be stated without sentiment. In an arrangement with no exit, contributing is irrational for each individual, since the benefits of collective effort arrive regardless and the costs of contribution are personal. Everyone reasons this way, and the outcome is the shirking and quiet sabotage that characterized every coerced collective economy. Where participation is voluntary, membership is self selecting: the people present are the ones who value the arrangement enough to sustain it, and the community can exclude those who do not, which makes free riding unprofitable rather than dominant. Exit is what makes voice credible, and a community nobody may leave has no information about whether anybody wants to be in it.
Now the honesty that this argument requires and rarely receives, because I have lived on both sides of it. I spent time in a kibbutz as a very young man, and later, in Canada, I ran a communal shelter in my own home for nine years, for people in crisis: some homeless, some recovering from addiction, some simply out of options. Roughly two hundred people passed through it. Of those who stayed longer than a few months, about half went on to stable housing and work, and about half returned to the street or to institutions. Those figures are reconstructed from memory rather than from records, and I offer them as the testimony of a practitioner rather than as findings.
What that experience taught me is not that voluntary community works. It is where it stops working, and the boundary was sharp. The arrangement functioned when residents genuinely had somewhere else to go and chose to stay. It broke down, reliably and quickly, whenever somebody was present because he had no alternative. The formal condition and the lived one turned out to be identical: without a real exit, the same dynamics appeared inside a shelter of ten people that appeared in states of a hundred million. Free riding, the erosion of trust, and the quiet conversion of a common project into a resource to be extracted.
The wider evidence points the same way and is not flattering to enthusiasts. Most voluntary communes fail, and they fail within a few years, from leadership conflict, from economic non-viability, from disputes about who belongs, and from the ordinary difficulty of sustaining commitment across a generation. Even the successful ones change beyond recognition: the kibbutz movement, the most studied voluntary collective of the modern era, has largely privatized. Voluntariness is necessary and it is nowhere near sufficient. It requires governance, resources, realistic expectations, and mechanisms that sustain commitment, and where those are absent the good will of the members will not supply them.
Which brings this book’s argument to its social conclusion, and it is not the one either political camp will want.
A society composed of diverse coexisting community forms is more resilient than one organized on a single model, and the reason is the structural law from an earlier chapter rather than any preference for pluralism. Different arrangements fail under different pressures. A market shock devastates the commune that depends on selling its produce and leaves the subsistence settlement standing. A social crisis strains the small group and is absorbed by the large network. People at different stages of life need different things, and a society with only one available form condemns everyone to fit it. The variety is the sensor array, exactly as before, and eliminating it in favor of the currently best form is the same error at a different scale.
Which specifies a role for the state, and it is neither the enforcer of a single order nor the minimal watchman. It is the facilitator of variety: protecting the freedom to form, join, and leave associations; maintaining a floor beneath everyone so that the outside option is genuinely available, since a person with no alternative cannot voluntarily choose anything; reducing the cost of forming new arrangements; and preventing any single form from crowding out the rest.
I record the tension in that last function rather than smoothing it over. Preventing monopolization is an active intervention, and it requires judgments about the desirable composition of civil society that no neutral principle supplies. The facilitative state is not neutral between forms. It is committed to variety as a value, and that commitment has to be argued for and renegotiated continuously rather than settled by a formula.
And now the sentence this whole book has been walking toward, which I will let stand without decoration. The grand narratives failed. What did not fail, and never needed a grand narrative to begin with, are the small arrangements people build voluntarily and can leave: the shelter, the congregation, the cooperative, the research group of six people who trust each other. They were never legitimated by a story about the destiny of humanity. They were legitimated by the fact that everyone in them could walk out the door and did not.
Conclusion
A report is supposed to end with recommendations. The one that started all this did not, and I have spent a book explaining why its author could not supply them and why the omission was more interesting than a failure of nerve. It would be a poor joke to reproduce the omission.
So here is the part where I say what should be done, addressed to the same sort of body that commissioned the original: an education ministry, a research council, a funding agency, a scientific society, anybody whose job includes deciding how knowledge gets made and who gets to make it.
Begin with what has actually been established, since recommendations resting on nothing are the disease rather than the cure.
The condition described in 1979 is real and is not a period. Complex domains generate descriptions that are individually valid and jointly incompatible; the principles governing one scale are not recoverable from another; formalization is always bounded and always plural; the provability of a claim depends on definitional choices the evidence does not make; and the configuration in which such choices are settled cannot be avoided, is not unique, and carries costs. None of this began, so none of it will end. The word that made the author famous names a permanent condition and dates it to a decade, and the dating is the only part that has to go.
The legitimating stories did not disappear. They changed register. What used to be asserted, and could therefore be disputed, is now executed: embedded in reference models, default parameters, standard pipelines, and ranking functions. A story that nobody tells is a story nobody can contradict, and the resulting silence is routinely read as consensus by people who have never encountered the alternative.
And the practical question, which the original report raised and abandoned, has an answer. An observer who is inside the system, cannot see all of it, holds several incompatible accounts, and must act anyway, does have a way of proceeding, and it is not tact. It is scope tracking, arranged surprise, cost accounting, and a reserved category for what cannot be reached.
From which four recommendations follow. They are unglamorous. That is a feature; the glamorous version of this book would have been useless.
The first is a declaration requirement. Any report of a result should state, for each quantity carrying weight, whether it was measured, derived, or declared, and for the declared ones what the alternatives were. This costs a paragraph. Financial statements have required something equivalent for a century, and nobody argues that it has damaged accounting. The objection that it is obvious is not an objection; the objection that it is unenforceable is a statement about journals rather than about the proposal.
The second is a degradation audit at every point where a finding is transmitted into policy or into public communication. A scientific claim has four separable parts: the core proposition, the relational structure that connects it to other claims, the contextual qualifiers that specify when it holds, and the argumentative scaffolding beneath it. These degrade at different rates as the claim travels, and the qualifiers go first, because they are the hardest to compress and the least interesting to a non specialist. What arrives at the far end is a stripped claim: true, and severed from the conditions that make it true, and therefore dangerous in exactly the way a true statement can be. The most common failure at the science and policy boundary is not the transmission of falsehoods. It is the transmission of true things without their boundary conditions.
I know of no better illustration than one from the recent pandemic, and it is worth stating because it cost lives. Decades of careful public health messaging had established, correctly, that antibiotics should not be prescribed for viral illness in routine practice, in order to slow the development of resistance. Transmitted through institutional channels for thirty years, the qualifier fell away and the norm survived as a bare instruction: avoid antibiotics. Applied to patients with viral pneumonia complicated by bacterial infection, a context in which the original boundary condition explicitly did not hold, the stripped version was lethal. Nobody lied. The science was right. The conditions of its validity were lost in transmission, which is what a degradation audit is designed to catch.
The third is architectural rather than communicative, and it is the recommendation I would press hardest. Since translation errors cannot be reliably eliminated, design the system so that their consequences are contained. Measure how much of a system’s critical function depends on decisions made outside it, and reduce that dependency where the cost is bearable. A region that relies entirely on a central modelling group is helpless when the central guidance is late or wrong; a region with its own analytical capacity adapts. This is not an argument for decentralization as an ideology, since local capacity has real coordination costs, and I have no interest in trading one dogma for another. It is an argument that the trade-off is a design parameter, that it can be reasoned about, and that at present it is mostly not reasoned about at all.
The fourth is to protect variance deliberately, and to write the protection into funding rules rather than leaving it to the good will of committees. A field in which one framework has eliminated the alternatives has not achieved consensus; it has dismantled its own error detection. The recommendation is concrete: allocate a fixed and non-trivial fraction of funding to approaches that the dominant framework regards as unpromising, chosen by people who do not work in the dominant framework, and evaluate them on their own terms rather than by their contribution to the mainstream program. This will waste money. Wasting money in a controlled fashion is what an error detection system costs, and the alternative expense, which is thirty years of increasingly precise work aimed slightly wrong, is not visible on any budget line until it is far too late.
Now a word about what none of this achieves, because a conclusion that oversells is a conclusion that has forgotten its own argument.
None of these measures produces truth. A paper can satisfy every clause of a declaration requirement and be entirely wrong. What the measures produce is legibility: the property that a reader can reconstruct what was assumed, what was found, and which of the two the conclusion rests on. Legibility is a lower ambition than truth, and it is attainable, and in a system where the errors that survive longest are the ones nobody can see, it is the more urgent of the two.
Nor do these measures resolve any of the disagreements this book has described. They are not intended to. The incompatibility is structural and will outlast every reform anyone proposes. What the measures do is convert an unphraseable difficulty into a statable one, which is the whole of what Lyotard asked for when he defined the ethical task as the invention of idioms in which the wronged party can finally speak. He thought that work belonged to literature and to philosophy. Some of it does. A surprising amount of it turns out to belong to documentation standards, which is a less dignified home than he would have wished for it, and a more effective one.
Let me close where the book began, with the man who received a purchase order and delivered something else.
He was right that the great stories had lost their power to authorize, and he was right in a way he could not have known: not because a period had ended, but because they had never been able to authorize what they claimed to, and the twentieth century merely made this visible. He was right that the discourses have no common tribunal, and here he was more right than his own argument could establish, since what he asserted has since been proved. He was right that judgment must proceed case by case, and wrong to think that this leaves nothing but taste. And he was right about the differend, which is the most valuable thing he produced and the least read, and which turns out to describe not only the great historical injustices he had in mind but the small daily situation of an assumption that cannot testify on its own behalf.
He also wrote the book in a hurry, for money, in a genre he later described as satire, on a subject he had not studied, and then said so in public when it would have been far more profitable to keep quiet. I have come to regard that last act as the most admirable thing in the whole affair, and as the model for how this business ought to be conducted.
The postmodern was never a period. It was a discovery, misfiled as news, by a man who told us afterwards that he had not been entirely serious, and whom nobody believed, because by then the word was worth more than the argument.
That is the report. The condition it describes has no start date and no expiry. The work goes on, as it always has, in the only way it ever could: by people holding several incompatible accounts of the same world, keeping careful track of where each one fails, declaring what they have assumed, and deciding anyway.
Case Studies
Case Study One — The Afternoon Pluto Stopped Being a Planet
For seventy-six years the solar system had nine planets, and every schoolchild in the world knew their order. Then, on an August afternoon in 2006, in a conference hall in Prague, a show of hands reduced the number to eight. No object moved. No new observation was reported that day. What changed was a definition, and the definition changed what was provable about an unchanged sky.
The background is a discovery problem that had been building for a decade. Pluto had been found in 1930 by a young assistant at an Arizona observatory who was searching for a large body thought to be perturbing the outer planets. The perturbation turned out not to exist, and the object he found was far too small to have caused it, but it was there, it orbited the sun, and it was named and counted. As instruments improved, astronomers began finding other bodies in the same region beyond Neptune. By the early 2000s there were hundreds. In 2005 a team announced an object, later named Eris, which appeared to be more massive than Pluto.
The core challenge was not astronomical but definitional, and it had been avoided for as long as avoidance was possible. There had never been a formal definition of the word planet. The term was inherited from antiquity, where it meant a wandering light, and had been extended by custom to whatever the community agreed to call one. Custom works until the cases get hard. With Eris in hand, the community faced a forced choice: either the solar system had ten planets and would shortly have fifty, or Pluto was not a planet, or the word would have to be redefined so that it drew a line somewhere.
Notice the structure, because it is the one described in the chapter on definition-dependent provability. The claim under dispute was Pluto is a planet. That claim was not settled by any observation. Its status was a function of the definition assigned to a term, and the definition was not determined by the data.
The solution implemented was a vote. The definition adopted required three conditions: the body must orbit the sun, must have sufficient mass for its own gravity to have pulled it into a round shape, and must have cleared the neighbourhood around its orbit. Pluto satisfies the first two and fails the third, since it shares its orbital region with a great many other objects. A new category, dwarf planet, was created to receive it.
The measurable results were immediate and instructive. Textbooks were revised worldwide. Museums rebuilt exhibits. A substantial minority of professional astronomers objected, and the objection was not sentimental: the third criterion is worded in a way that depends on where a body is as much as on what it is, so that an Earth-sized object placed far enough out would fail it. One state legislature passed a resolution declaring Pluto a planet within its borders, which is a delightful piece of jurisdictional comedy and also an accurate demonstration that definitions are settled by authority rather than by nature. Fifteen years later a spacecraft flew past Pluto and returned images of a complex world with mountains of water ice, a nitrogen glacier, and evidence of geological activity, and a fresh round of argument began on the grounds that the object certainly looks like a planet.
What makes this a clean case study is that everybody involved was competent, nobody was dishonest, and no fact was in dispute at any stage. The disagreement was located entirely in the choice of a definition, and the choice was not arbitrary either: each proposal preserved some of the inferences competent users of the word wanted to keep, and none preserved all of them. A definition based on shape gives a tidy physical criterion and a solar system with dozens of planets. A definition based on orbital dominance gives eight planets and a criterion that depends on context. A definition based on cultural inheritance gives nine and no criterion at all.
The contemporary relevance is not confined to astronomy, and the same structure appears wherever a classification carries consequences. The definition of a species determines which populations receive legal protection, and biologists maintain several incompatible species concepts for good reasons, with conservation law forced to pick one. The definition of a recession determines when policy triggers fire, and the widely used rule of two consecutive quarters of contraction is a convention rather than a finding, as became publicly evident in 2022 when the convention and the official designation diverged and a technical dispute turned into a political one overnight. The definition of a planet cost nobody anything except pride. The others cost money, habitat, and elections.
The general lesson is the one this book keeps returning to. When a dispute will not settle, the first question is whether the parties are disagreeing about the world or about a word that carries a boundary. If it is the second, no further evidence will help, and the honest move is to state which definition each party is using and what each one buys. The astronomers, whatever one thinks of their vote, did that in public. Most fields do it in silence, if at all.
Case Study Two — Two Correct Measurements of the Same Universe
There is a number that describes how fast the universe is expanding today. It has been measured by two entirely different methods, both of them the product of decades of careful work by large teams. The two answers disagree. The disagreement has not narrowed as the measurements improved; it has sharpened, because the error bars have shrunk faster than the gap between the central values. This is one of the cleanest examples available of the situation this book describes, and it is unresolved as I write.
The background involves two independent routes to the same quantity. The first is a ladder built from the nearby universe outward. One begins with objects whose distances can be established geometrically, uses them to calibrate a class of variable stars whose brightness varies in a way that reveals their intrinsic luminosity, uses those stars to calibrate a class of exploding stars visible at much greater distances, and then compares distances with recession velocities. Every rung is a separate empirical achievement and every rung carries its own systematic uncertainties.
The second route runs from the other end of time. The pattern of temperature fluctuations in the radiation left over from the early universe encodes a characteristic length scale. Given a model of what the universe contains and how it has evolved, that scale can be projected forward to yield the present expansion rate. The measurement of the fluctuations is exquisite and the projection is arithmetic.
The core challenge is that the two routes give values that differ by roughly nine percent, with quoted uncertainties small enough that the difference amounts to a serious discrepancy rather than a rounding disagreement. Both communities have spent years hunting for errors in their own work, which is exactly what should happen. Neither has found one sufficient to close the gap.
The interesting part, for present purposes, is the asymmetry in what the two routes assume. The ladder is closer to a direct measurement, but it accumulates calibration choices at every rung, and each calibration involves declared components: which sample of stars to use, how to correct for the dust between here and there, how to treat the dependence of brightness on chemical composition. The early-universe route involves fewer choices in the measurement and far more in the projection, because projecting a length scale forward requires assuming the entire content and history of the universe in between. If that assumed content is incomplete, the projected value will be wrong while the measurement remains perfect.
The solutions attempted are a case study in how a mature field handles a genuine impasse. Independent calibrations were developed using different classes of star. An entirely third route was constructed using gravitational waves from merging neutron stars, which yields a distance directly from the shape of the signal and requires no ladder at all. Multiple teams reanalysed each other’s data with different pipelines. Systematic effects were hunted with a thoroughness that produced valuable science of its own.
The measurable results are that the discrepancy has survived every attempt to dissolve it, that the third route is not yet precise enough to arbitrate, and that a substantial theoretical literature has grown up proposing modifications to the assumed content of the early universe which would reconcile the two. Whether one of the measurements is wrong, or the model connecting them is incomplete, is not currently known.
What the case demonstrates is the practical difference between measured, derived, and declared quantities. Neither number is a measurement of the expansion rate. Both are derived, by long chains, from things that were measured, and the chains contain declared components. The community knows this, and the productive work of the last several years has consisted almost entirely of tracing which declared components each route depends on and how sensitive each answer is to them. That is precisely the discipline this book recommends, and it is worth noting that a field arrived at it by necessity rather than by philosophical argument.
The contemporary application is broader than cosmology. Any time two respected estimates of the same quantity disagree beyond their stated uncertainties, the productive question is not which team is more careful. It is which declared components each estimate depends on, and whether the two estimates share any of them. Two estimates that share a declared component are not independent, and averaging them produces a number with an uncertainty that has been understated. Two estimates that share none are genuinely independent, and their disagreement is information about something neither of them modelled.
Public health encountered exactly this during the recent pandemic, when case-based and excess-mortality-based estimates of deaths diverged by large factors in some countries. The instinct was to ask which was right. The productive question was which baseline each had declared, and what each was therefore measuring.
Case Study Three — The Threshold That Ate a Discipline
In 2015 a large collaboration published the results of an unusual project. One hundred teams had attempted to repeat one hundred experiments drawn from three leading psychology journals, using the original materials and, where possible, the advice of the original authors. Rather less than half produced results consistent with the originals, and among those that did, the effects were typically about half the size. The publication caused a crisis that the field is still working through, and the crisis has a technical origin that runs directly to the theme of this book.
The background is a number. In the 1920s the statistician Ronald Fisher, working out how to analyse agricultural experiments, needed a convention for when a result was worth a second look. He suggested that a result which would occur by chance less than one time in twenty might be treated as significant, and he was explicit that this was a convenience rather than a principle, and that no isolated experiment should be regarded as establishing anything. The convention spread. Within a few decades it had hardened into a threshold, and the threshold had become a condition of publication.
The core challenge is that a threshold applied to publication does not filter for truth; it filters for the crossing of a threshold. If a true effect is small and a study is small, the study will usually miss it. If an effect does not exist, one study in twenty will nonetheless cross the line. When only crossings are published, the literature fills with the fraction of results that happened to cross, and the published effect sizes are systematically larger than the real ones, because only the large fluctuations made it through.
Two further mechanisms make this worse and both were documented extensively after 2011. The first is the flexibility of analysis. Any real dataset can be analysed in many defensible ways: which outliers to exclude, which covariates to include, when to stop collecting data, which of several measures to treat as the primary outcome. Each choice is defensible, and an investigator who tries several and reports the one that worked has not falsified anything, but has multiplied his chances of crossing the line without any corresponding increase in evidence. The second is that a hypothesis formed after seeing the data, and then reported as though it had been formed before, converts an exploratory observation into an apparent confirmation.
The solutions implemented over the following decade are the most encouraging story in this book. Preregistration: the analysis plan is deposited publicly before data are collected, so that the distinction between what was predicted and what was noticed is preserved. Registered reports: journals accept a paper on the basis of its design, before results exist, which removes the incentive to produce a crossing. Sharing of data and code by default. Larger collaborative studies with sufficient sample size to detect the effects claimed. Estimation with intervals rather than binary verdicts.
The measurable results are mixed and real. Replication rates in fields that adopted preregistration have improved substantially. Effect sizes reported in registered reports are smaller and more stable than in conventional publications, which is what the diagnosis predicted. Several celebrated findings, taught for decades, have not survived: effects on willpower depletion, on posture and hormones, on priming behaviour with unrelated words. Other fields have run their own replication projects with comparable results, notably in cancer biology and experimental economics.
The case is a textbook demonstration of a declared component that was forgotten. The threshold was declared, explicitly, by a statistician who said it was a convention. Ninety years later it was operating as a law of nature enforced by editors, and the people it constrained had never seen the original argument. Nothing was concealed. The declaration simply aged out of view, which is the first of the three failure modes described in the chapter on measured, declared, and derived.
The contemporary relevance is immediate and extends well beyond psychology. Any field with a publication threshold, a target, or a scoring rule has the same structure. Clinical trials, where the choice of primary endpoint is declared in advance precisely because the profession learned this lesson earlier and at greater cost. Machine learning, where the benchmark on which models are compared is a declared component that determines which architectures appear to be improving. Education policy, where the assessment used to evaluate a programme determines which programmes look effective. In each case the question worth asking is not whether the threshold is correct, since thresholds are conventions and correctness is not the relevant category. It is whether anyone in the field can still say where it came from.
Case Study Four — The Signal That Was Dust
In March 2014 a team announced that it had detected the imprint of gravitational waves from the first instant of the universe. The announcement was made at a press conference, it was accompanied by a widely circulated video of a young physicist informing an elderly theorist that his life’s prediction had been confirmed, and it was reported worldwide as one of the great discoveries of the century. Within a year the result had evaporated. Nobody had faked anything. The failure was located precisely in a declared component.
The background is a prediction of considerable elegance. If the universe underwent a period of enormously rapid expansion in its first fraction of a second, that expansion should have generated gravitational waves, and those waves should have left a distinctive swirling pattern in the polarisation of the microwave background radiation. The pattern is called B-mode polarisation, and detecting it would be evidence for an epoch otherwise permanently inaccessible. A telescope at the South Pole, operating in exceptionally dry and stable air, was built to look for it.
The core challenge was foreground contamination. The microwave sky is not clean. Dust grains in our own galaxy, aligned by magnetic fields, emit polarised radiation that can mimic the sought-after pattern. Any claim to have detected a primordial signal is therefore a claim to have correctly subtracted a galactic one, and the subtraction requires a model of how much polarised dust lies in the direction observed.
Here is where the case becomes instructive. The team observed a patch of sky chosen for its low dust content. To estimate the residual dust, they used, among other inputs, a preliminary map presented by another collaboration in a conference talk. The numbers were extracted from a slide. The extraction was reasonable, the source was the best available at the time, and the resulting estimate suggested that dust could account for only a small fraction of the observed signal.
The declared component was the dust model. It was not measured in the patch observed; it was imported, from a preliminary source, and used to license a very loud conclusion.
The solution came from the other collaboration’s own data. When the full analysis of galactic dust polarisation was published later that year, it showed considerably more polarised dust at the relevant frequencies than the preliminary estimate had implied. A joint analysis followed, conducted by both teams together, using the same data and a proper treatment of the foreground. The conclusion was that the observed signal was consistent with dust, and that no detection of primordial gravitational waves could be claimed.
The measurable results include an upper limit rather than a detection, a joint publication that is a model of how such disputes should be handled, and a significant improvement in the field’s treatment of foregrounds. Subsequent experiments observe at multiple frequencies precisely so that dust, which has a different frequency dependence than the primordial signal, can be separated rather than assumed.
Three features make this the clearest case study in the collection.
The measurement was excellent. The instrument worked, the polarisation was real, and the data were sound. What failed was one link in the chain between the measurement and the claim.
The failure was invisible in the headline. The announcement reported a detection with a stated significance, and the stated significance described the noise in the instrument. It did not, and by its construction could not, describe the uncertainty in the imported dust model. That is the laundering failure described in the chapter on the three categories: a quantity derived from a declaration, reported in the voice of a measurement.
And the correction worked. This is the part that critics of science routinely omit. The system detected its own error within a year, the two teams collaborated on the correction rather than litigating it, and the field changed its practice. A case study in failure is also a case study in a functioning error-detection mechanism, and the mechanism functioned because the underlying data were shared.
The contemporary application is any high-stakes announcement in which a background must be subtracted before a signal can be claimed. Environmental contamination assessments, where a baseline level must be assumed. Drug efficacy in a population with an assumed placebo response. Detection of anomalies in financial transactions against a model of normal behaviour. In each case the question to ask is the same one that would have caught this in advance: where did the background model come from, was it measured in the same conditions as the signal, and what happens to the conclusion if it is doubled.
Case Study Five — How Many People Are Out of Work
Every month, governments publish an unemployment figure, markets move on it, and politicians are held responsible for it. The number is not a count of people without jobs. It is the output of a set of declared definitions, several of which could reasonably be drawn otherwise, and the alternatives produce numbers that differ by a factor of two.
The background is a definitional problem that any statistical agency must solve. To be counted as unemployed under the standard international definition, a person must be without work, currently available for work, and actively seeking work during a specified recent period. Each of the three conditions requires specification. What counts as work: an hour of paid labour in the reference week is generally sufficient, which means a person working two hours is employed. What counts as available: usually able to start within a specified short period. What counts as seeking: certain activities qualify, others do not, and merely wishing to be employed does not.
The core challenge is that reasonable people can draw each boundary in more than one place, and the boundaries determine who is counted. A person who wants a job, is available, and has stopped applying because he believes nothing is available is not unemployed under the standard definition. He is outside the labour force. A person working ten hours a week who wants forty is employed. A person in a training programme may be either, depending on the programme.
This is not concealed. Statistical agencies publish alternative measures precisely because they know the headline is a convention. In the United States, the headline rate is one of six published measures, and the broadest one, which includes those who have given up searching and those working part-time who want full-time work, typically runs at roughly twice the headline. Both are correct. They are answers to different questions.
The solutions developed by statistical agencies are worth describing because they represent good practice under exactly the conditions this book analyses. The definitions are published in full. Multiple measures are computed and released simultaneously. The methodology is documented, revisions are announced, and breaks in series caused by definitional changes are flagged so that comparisons across the break are not made silently. The agencies do everything the declaration requirement in this book’s conclusion asks for.
The measurable result is that the professional users of the data are generally well informed and the public discussion is generally not. The headline number travels; the definitional apparatus does not. This is the degradation pattern described in the conclusion: the core proposition survives transmission and the contextual qualifiers are stripped first. A minister announcing that unemployment has fallen to a historic low is not lying, and the sentence has lost the information required to evaluate it, and no participant in the exchange has done anything wrong.
The consequences are not academic. During periods when labour force participation falls, the headline rate can decline while the number of people without work rises, because people leaving the search are removed from the denominator and from the numerator at once. Two people can therefore hold opposite views about whether the labour market is improving, both citing official statistics, both correct, and neither able to identify the source of the disagreement because it lies in a definition that neither has read.
The contemporary relevance extends across the whole apparatus of official statistics. Inflation depends on a declared basket of goods and on declared methods for handling quality improvements, and the choices measurably affect the reported rate and therefore every payment indexed to it. Poverty depends on a declared line, and the choice between an absolute and a relative line determines whether poverty falls when everyone gets richer. Crime statistics depend on declared recording practices, and a change in recording practice produces a change in the crime rate with no change in crime.
The general point is the one this book has made about scientific pipelines, transposed into public life. The numbers are honest. The definitions are published. The chain from definition to headline is long enough that the definition is invisible at the far end, and the invisibility is not the result of anybody hiding anything. It is what happens to boundary conditions in transmission, and the only remedy anyone has found is to restate them at every step, which is tedious, which is why it is not done.
Case Study Six — The Number That Runs the World and Was Never Meant To
In 1934 an economist delivered a report to the United States Congress presenting a new measure of national income. In the same report he warned that the welfare of a nation could scarcely be inferred from such a measure. The warning was ignored, the measure was adopted, and within a generation it had become the single most consequential number produced by any government, governing interest rates, election outcomes, credit ratings, and the allocation of trillions.
The background is a genuine problem that the measure solved. Governments planning a war economy needed to know the productive capacity of the nation, and there was no consistent way to add up an economy’s output. The apparatus developed during the following decade produced one: a systematic accounting of goods and services produced for exchange, valued at market prices, aggregated into a single figure.
The core challenge is that a great many things had to be declared in order for this to work, and each declaration excludes something.
Only transactions are counted, because prices are needed to add unlike things. Work performed without payment is therefore invisible: childcare within a family, care for elderly relatives, subsistence agriculture, cooking, cleaning, and the enormous volume of unpaid labour that keeps every society running. A country in which such work moves into the paid economy records growth without any increase in what is actually done.
Depletion is not subtracted. A forest cut down appears as output. The disappearance of the forest appears nowhere, because it was never on the books as an asset.
Damage is counted positively when it generates transactions. An oil spill raises measured output through the cleanup. Congestion raises it through fuel consumption. Illness raises it through treatment.
Government services, having no market price, are valued at what they cost to provide, which means a public sector that becomes more efficient records a fall in output.
And quality change is handled by adjustments that are unavoidable and consequential. A computer costing the same as one from a decade ago is vastly more capable, and the statistical treatment of that improvement materially affects the reported growth rate and the reported inflation rate.
Every one of these is a declared component, and every one was documented by the people who built the accounts. The literature is voluminous and candid. The declarations are public.
The solutions attempted over eighty years are instructive precisely because they have largely failed to displace the original. Satellite accounts were developed to measure household production, environmental depletion, and human capital alongside the main figure. Alternative indices were constructed, some adjusting for distribution, others for sustainability, others for reported wellbeing. A national government adopted a happiness index as an official goal. Commissions of distinguished economists have twice recommended a broader dashboard.
The measurable results are that the satellite accounts exist and are consulted by specialists, that the alternative indices are published and cited, and that the headline figure continues to govern policy exactly as before. The reason is not intellectual. It is that a single number can be compared across countries and quarters, can be forecast, can be targeted, and can be reported in a headline, and no dashboard has any of those properties. The convention survives because it is operationally superior, not because anyone believes it measures welfare.
This is the clearest available demonstration of a point made in the chapter on performativity. A measure that is used to allocate resources will be optimised, and optimisation does not respect the difference between the measure and the intention. Every government in the world is now steering by a quantity whose designer warned, in the document introducing it, that it should not be used for the purpose it is now used for.
The contemporary application is the design of any metric that will govern an institution. The relevant question at the design stage is not whether the metric captures what matters, since no single number does. It is what the metric excludes, who is disadvantaged by the exclusion, and what behaviour will emerge when people optimise against it. Those questions have answers, the answers are usually available in advance, and they are almost never asked, because the pressure at the moment of adoption is always to get a number into use.
The deeper lesson concerns the fate of declarations over time. Nothing about this case involves concealment. The exclusions were stated by the designer in the founding document, restated by every subsequent commission, and taught in every economics course. They are declared, and they are invisible, and the invisibility is a property of the transmission chain rather than of anybody’s intentions. A declaration that is made once and never repeated has the same practical effect as one that was never made at all.
Case Study Seven — The Two Weeks That Separated Grief From Illness
Until 2013 the diagnostic manual used by psychiatry across much of the world contained an instruction that a diagnosis of major depression should not be made if the symptoms were better accounted for by bereavement, unless they persisted beyond a stated interval. In the fifth edition, that exclusion was removed. No new disease appeared. A boundary moved, and with it moved the classification of a very large number of grieving people.
The background is the structure of psychiatric diagnosis. Unlike most of medicine, psychiatry generally lacks tests that identify a condition independently of its symptoms. A diagnosis is made when a specified number of specified symptoms have been present for a specified duration and cause specified impairment. Each of those specifications is declared. The manual is explicit about this and its authors have never claimed otherwise.
The core challenge in this instance was that the symptoms of ordinary grief and the symptoms of a depressive episode overlap almost completely. Sadness, disturbed sleep, loss of appetite, difficulty concentrating, withdrawal from activity, and a sense of worthlessness are the ordinary phenomenology of losing somebody. If the criteria are applied without qualification, a person two weeks into mourning meets them.
Two defensible positions were available, and both were held by serious clinicians.
The first says the exclusion should stay. Grief is not an illness, it is a normal response to loss, it resolves without treatment in most people, and classifying it as a disorder pathologises a universal human experience and exposes bereaved people to unnecessary medication.
The second says the exclusion should go. Bereavement is a common precipitant of genuine depressive episodes, an exclusion based on cause rather than presentation is inconsistent with the rest of the manual, which does not exclude depression triggered by job loss or divorce, and withholding a diagnosis from a suffering person because his suffering has an identifiable cause denies him treatment that works.
The solution adopted was removal of the exclusion, accompanied by an explanatory note advising clinicians to use judgement in distinguishing normal grief from a depressive episode. The note is the interesting part: having removed the rule, the manual instructed clinicians to make the distinction anyway, without a criterion. That is judging case by case, precisely as described in the chapter on paganism, and it is what happens when a field discovers that its boundary was doing work no rule can do.
The measurable results were contested and remain so. Studies attempting to detect a surge in diagnoses following the change produced mixed findings, complicated by the fact that many clinicians had never applied the exclusion consistently in the first place. Prescription trends moved, though other factors moved at the same time. What is not in dispute is that a definitional change altered the population classified as ill without any change in the population’s condition.
The contemporary relevance extends to every diagnostic threshold in medicine, and the pattern is consistent. In 2017 a revision to blood pressure guidelines lowered the level at which hypertension is diagnosed, and the arithmetic consequence was that tens of millions of people in one country became hypertensive overnight without a single blood vessel changing. The revision was made on the basis of trial evidence and was defended by serious people; it was also opposed by serious people on the grounds that it medicalises risk rather than disease and that the benefit at the margin is small while the harms of treatment are not. Similar shifts have occurred for diabetes, for obesity, for osteoporosis, and for the definition of who requires cholesterol-lowering treatment.
In each case there is a real underlying continuum, real evidence about outcomes at different points along it, and a declared cut that converts the continuum into a binary. The cut is not discoverable, because nature does not supply one. It is chosen, and the choice trades false positives against false negatives with real consequences in both directions.
What makes this a good case study for this book is the sharpness with which it separates the measured from the declared. The blood pressure is measured. The association between blood pressure and stroke risk is derived from data. The threshold at which a person becomes a patient is declared, by a committee, and could have been declared elsewhere. Everything downstream of the threshold, including the prevalence of the disease, the apparent effectiveness of screening programmes, and the size of the treated population, depends on it.
And the general failure to distinguish these is why public discussion of such changes is so unproductive. A person who says the prevalence of hypertension has risen is stating a fact about a definition. A person who hears it as a fact about the health of the population has been misinformed by a sentence that contained no falsehood.
Case Study Eight — The Day the Kilogram Stopped Being an Object
For one hundred and thirty years, the mass of a kilogram was the mass of a particular cylinder of platinum and iridium kept under three glass bells in a vault outside Paris. If the cylinder had gained mass, every kilogram in the world would have gained mass with it, by definition, and no measurement could have detected the change. In 2019 this arrangement was abolished, and the kilogram was redefined in terms of a fundamental constant of nature whose value was fixed by declaration.
The background is the awkwardness of defining a unit by an artefact. The cylinder, known as the international prototype, was made in 1879 and adopted as the standard in 1889. Official copies were distributed to member states, and every few decades the copies were brought back to Paris and compared with the original. The comparisons showed drift. Relative to the prototype, the copies appeared to gain roughly fifty micrograms over a century, or the prototype appeared to lose that much relative to them, and there was no way to distinguish these statements, because the prototype was the definition. There is no meaningful sense in which the standard kilogram could be wrong.
The core challenge was that all of modern metrology, and through it a large fraction of commerce and science, ultimately rested on a lump of metal in a basement whose stability could not be assessed, whose value could be destroyed by a fire or a clumsy technician, and which existed in exactly one copy.
The solution was to invert the logic. Rather than measuring a constant of nature in terms of an artefact, the constant would be declared to have an exact value, and the artefact would become unnecessary. A quantity that had been measured for a century, with steadily improving precision, was fixed by decision at the best available value, with no uncertainty whatever. The unit of mass then follows from that fixed number together with the already-fixed definitions of the second and the metre.
Implementing this required experiments of extraordinary difficulty. Two independent routes were developed. One balances mechanical against electromagnetic power in an instrument whose coil moves in a magnetic field, allowing mass to be related to electrical quantities that are themselves tied to fundamental constants. The other counts atoms: a sphere of isotopically pure silicon is manufactured to a roundness of a few tens of nanometres, its volume is measured by optical interferometry, its lattice spacing by X-ray methods, and the number of atoms it contains is thereby determined. The two routes had to agree, within their uncertainties, before the redefinition could proceed. After decades of work, they did.
The measurable results are that the unit of mass is now realisable in any suitably equipped laboratory in the world, that it cannot be lost or damaged, that it will not drift, and that the prototype in the vault has been demoted to an object of historical interest whose mass is now, for the first time in its existence, a quantity that can be measured and found to have changed.
This is the most instructive case in the collection, because it is a declared component functioning perfectly, and it shows what the distinction between measured and declared is actually for.
The value of the constant was measured, with great care, for a very long time. Then it was declared. The declaration was not a discovery and did not pretend to be; it was a decision to stop treating a particular number as an object of measurement and start treating it as a fixed point of the system. This is legitimate, it is enormously useful, and it is completely transparent. Everybody involved knows which numbers in the international system are now exact by definition and which are measured, because the list is published and short.
Compare this with the situation described elsewhere in this book, where a quantity is chosen, becomes a default in a piece of software, and is inherited by people who do not know a choice was made. The difference is not that one system contains declarations and the other does not. Both are full of them. The difference is that metrology maintains a public register of which of its numbers are declared, revisits the register on a schedule, and would regard the loss of that register as a catastrophe.
The contemporary application is straightforward and, I think, underappreciated. Metrology solved this problem. Any field that carries declared components, which is every field, could adopt the same practice: maintain a list of the quantities that are fixed by convention rather than determined by evidence, publish it, and review it periodically. The cost is a document. The benefit is that the declarations remain visible to the people who inherit them, which is the single failure mode that has done the most damage in every other case study here.
Case Study Nine — The Rubber Ring and the Missing Qualifier
On a cold morning in January 1986 a space shuttle broke apart shortly after launch, killing its crew of seven. The technical cause was established quickly: a rubber sealing ring in a solid rocket booster had failed to seal at low temperature, allowing hot gas to escape and burn through an adjacent tank. The organisational cause has been studied ever since, and it is a case study in the transmission of a claim without the conditions of its validity.
The background is that engineers at the booster manufacturer had been worried about the sealing rings for years. Evidence of erosion had appeared on recovered boosters from previous flights, and internal memoranda had described the situation in urgent terms. On the evening before the launch, with an unusually cold night forecast, engineers recommended against launching, on the grounds that the rings had never been tested at such temperatures and that resilience of rubber falls as it cools.
The core challenge, and the thing worth studying, is what happened to that recommendation as it moved through the organisation. The engineers’ concern was a conditional claim: the seals are qualified within a certain temperature range, the forecast lies outside it, and outside it we have no data. That is a statement about boundary conditions and about the absence of evidence. It is not a prediction of failure.
At the meeting that followed, management asked for evidence that the seals would fail. The engineers had none, because the point was that nobody had data in that regime at all. The absence of evidence of failure was then treated as evidence of safety, and the recommendation was reversed. What travelled upward was a decision that the launch was acceptable. What did not travel was the qualifier that the acceptability rested on an absence of data rather than on a body of it.
This is the stripped claim described in this book’s conclusion, and it is worth noting that the stripping went in the opposite direction from the usual one. Ordinarily a positive finding loses its qualifiers and becomes overconfident. Here a statement of ignorance lost its qualifiers and became a statement of safety.
There is a second mechanism in the same case which the subsequent investigation named and which deserves wider currency. Each previous flight that had shown ring erosion and returned safely had been treated as evidence that erosion was tolerable. Over time, an outcome that had originally been classified as an anomaly became normal, without anybody deciding that it should. The absence of catastrophe was read as a demonstration of margin, when in fact it was a sequence of narrow escapes whose narrowness was not visible from the outside.
The solutions implemented after the investigation were substantial. The booster joint was redesigned. Launch commit criteria were rewritten to include explicit temperature limits. The reporting structure was changed so that safety concerns could travel independently of programme management. A physicist on the investigating commission conducted a famous demonstration with a clamp and a glass of ice water at a public hearing, which had the effect of restoring the qualifier to the public record in a form that could not be stripped.
The measurable results include a return to flight after a thirty-two month pause, a redesigned joint that has not failed since, and a substantial literature on organisational risk that has influenced practice in aviation, nuclear power, and offshore drilling. It also produced a memorable formulation in the commission’s report, to the effect that reality must take precedence over public relations, since nature cannot be fooled.
Seventeen years later the same organisation lost a second orbiter, for a different technical reason, with an organisational pattern the investigating board described as strikingly similar.
The contemporary application is to any situation where a technical judgement passes through a decision-making layer that speaks a different language. The engineer’s statement is conditional, hedged, and specific about its domain of validity. The decision required is binary. In the translation, the conditions are what get lost, because they are the part that cannot be converted into a yes or a no.
The remedy is not better communication in the abstract, which is what such reports usually recommend and which never works. It is a structural requirement that the conditions travel with the claim: a standing rule that any technical recommendation reaching a decision meeting must state the domain in which the supporting evidence was gathered and whether the proposed action lies inside it. That is a form, not a virtue, and forms survive personnel changes in a way that virtues do not.
Case Study Ten — The Formula That Priced the Unpriceable
Between 2000 and 2007, a mathematical formula borrowed from actuarial science made it possible to assign a price to bundles of mortgages, and the price was accepted by rating agencies, regulators, and the buyers of several trillion dollars of securities. The formula required one declared input that could not be measured, and the collapse of the market in those securities is the most expensive demonstration in history of what happens when a declaration is loaded beyond its capacity.
The background is a genuine financial problem. If a bank holds a thousand mortgages, the risk of the whole is not the sum of the risks of the parts, because the defaults are not independent. A model of the bundle therefore needs a description of how the individual defaults move together. Without such a description, the bundle cannot be priced, and if it cannot be priced it cannot be sold.
The solution adopted came from a technique developed in insurance for a structurally similar question: the tendency of one spouse to die shortly after the other. The mathematical device involved, a copula, separates the individual probabilities from the structure of their dependence, allowing the dependence to be described by a single parameter. Applied to mortgages, it allowed the correlation among defaults across a pool to be summarised in one number.
The core challenge is that the number could not be measured. The relevant quantity is how mortgage defaults across regions and borrower types would behave together during a nationwide fall in house prices. There was no such episode in the available data, because national house prices in the relevant market had not fallen in the period for which records existed. The correlation was therefore estimated from other things: from the prices of credit default swaps, which are themselves the prices of instruments valued using the same model, and from historical periods that contained no analogue of the event that mattered.
The result was a circular and thinly grounded declaration presented, throughout the chain, as a technical input. Rating agencies applied the model to assign top grades to tranches of securities built from loans that individually would not have qualified for investment. Buyers relied on the ratings. Regulators permitted capital treatment based on the ratings. Every participant was looking at a number that had been derived from a declaration nobody had measured, and the number was displayed in the same typeface as the measured ones.
When house prices did fall nationally, defaults proved to be far more correlated than the declared parameter implied, tranches rated as extremely safe suffered losses, and the resulting cascade removed several trillion dollars of asset value and precipitated the deepest recession since the 1930s.
The measurable results, beyond the losses, include substantially revised capital rules, mandatory stress testing against scenarios chosen precisely because they are absent from the historical record, and a general requirement that models used for regulatory purposes be tested for sensitivity to their assumptions rather than merely calibrated to recent data.
Three points make this the most consequential case in the collection.
The mathematics was not wrong. The copula does what it claims. The failure was in the input, and the input was declared rather than measured, and the declaration was invisible by the time the output reached a decision maker.
The absence of relevant data was the reason the declaration was needed and also the reason it could not be checked. This is the structural situation of every model applied to a regime outside its calibration range, and it is why the second failure mode described in this book, deriving from a declaration and reporting in the voice of a measurement, is the dangerous one.
And the warnings existed. The originator of the technique published a paper noting the limitations of applying it in this way. Several analysts raised the correlation problem in print before the collapse. The warnings did not travel, for the reasons this book has described repeatedly: the qualifier is the part of a claim that does not survive transmission, and by the time the model reached the desks where it was used, it had become a function that returned a price.
Case Study Eleven — The Bridge That Nobody’s Model Contained
In June 2000 a new footbridge across the Thames opened to the public. Within minutes of the crowd stepping onto it, the deck began to sway from side to side with an amplitude that alarmed everybody on it. The bridge was closed after two days, remained closed for nearly two years, and was reopened after modifications costing a substantial fraction of its original price. The engineering was not incompetent. The behaviour that closed the bridge was absent from every model in use, and it was absent because it belonged to a domain that structural engineering did not describe.
The background is a design of considerable elegance. The bridge is a suspension structure with unusually shallow cables, chosen so that the deck would appear to be a thin blade across the river. The structure was analysed for the loads that bridges are analysed for: dead weight, live weight of a dense crowd, wind, and the vertical forces produced by walking. It satisfied every applicable standard by comfortable margins.
The core challenge was that walking produces a lateral force as well as a vertical one. Each step shifts the walker’s centre of mass sideways, and in a crowd of people walking randomly these sideways forces cancel, because the steps are uncorrelated. That is the assumption on which the analysis rested and it was a reasonable one.
What the analysis did not contain was the walker’s response to motion. A person on a laterally moving surface adjusts his gait to maintain balance, and the adjustment is not random: he steps in time with the motion, because that is what balance requires. A small initial sway, produced by the ordinary statistical variation in a large crowd, therefore causes a fraction of the walkers to synchronise with it. Synchronised walkers push in phase, which increases the sway, which recruits more walkers. The feedback is positive and the onset is sudden: below a critical number of pedestrians nothing happens, and above it the response grows rapidly.
The phenomenon has a name now, synchronous lateral excitation, and the name did not exist when the bridge was designed. Isolated instances had been recorded, in a footbridge in Japan and in a stadium, and the reports were scattered across literatures that did not communicate. The mechanism sits precisely between two disciplines: it involves structural dynamics, which engineers model, and human motor control, which they do not.
The solutions implemented were thorough and expensive. The response was reproduced experimentally by walking volunteers across the closed bridge in increasing numbers until the onset occurred, which established the critical count directly rather than by inference. Thirty-seven viscous dampers were fitted to absorb lateral energy, along with tuned mass dampers for the vertical modes. The bridge reopened and has behaved impeccably since, carrying far larger crowds than the ones that closed it.
The measurable results extend well beyond one river crossing. Design guidance for footbridges was rewritten internationally to include lateral pedestrian loading and the synchronisation effect. Existing bridges were assessed and several were modified. A body of research on crowd-structure interaction now exists where none did.
What makes this a case study for the present book is the location of the failure. Nothing was measured wrongly and nothing was calculated incorrectly. The model was internally valid and its domain of validity did not include the situation. The declared component was the assumption that pedestrian lateral forces are uncorrelated, and that assumption was so deeply embedded in practice that it was not experienced as an assumption at all. It appeared in no calculation, because it was the reason certain terms were absent from the calculation.
This is the most difficult category of declared component to audit, and I want to state it plainly because it recurs everywhere. The dangerous declaration is often not a number that was chosen. It is a term that was omitted, and an omitted term leaves no trace in the document. You cannot audit a quantity that does not appear.
The remedy that engineering adopted after this event is worth copying. The bridge was not reopened on the basis of a corrected model. It was reopened after the phenomenon had been produced deliberately, at scale, on the actual structure, with instruments attached. When a model’s domain of validity is in doubt, the productive move is not to refine the model but to go and find the boundary experimentally.
The contemporary application is to every complex system whose behaviour emerges from the interaction between an engineered component and a human one: traffic systems where drivers respond to congestion prediction, financial systems where participants respond to published risk measures, and recommendation systems where the audience responds to what it is shown. In each case the engineering model treats the human side as an external input with fixed statistics, and in each case the human side adjusts to the system’s own output. The bridge is the cleanest illustration available, because the feedback loop closes in seconds and the consequence is visible to everybody standing on it.
Case Study Twelve — Seven Countries Out of Twenty-Two
Beginning in the late 1950s, a physiologist organised a study that followed roughly twelve thousand men across seven countries, recording diet and cardiovascular outcomes over decades. The study was a landmark of epidemiology, produced a strong association between saturated fat intake and heart disease, and became the empirical foundation of dietary guidance in much of the world for half a century. It also became the most frequently cited example of a declared component determining a conclusion, and the dispute about it is unresolved.
The background is an urgent public health problem. Heart disease mortality in the industrialised world rose sharply in the middle of the twentieth century, and the causes were unknown. Comparative data existed for a growing number of countries, showing wide variation in both diet and outcomes.
The core challenge, and the origin of six decades of argument, is the selection of the seven countries. Data of varying quality were available for a larger number, and the study examined seven. The critics’ charge is that the seven were chosen because they exhibited the expected relationship, and that a graph including the full set available at the time shows a much weaker association. The defenders reply that the countries were selected for practical reasons, namely the availability of collaborating investigators and the feasibility of standardised measurement, and that the data excluded were of poor quality and would have introduced noise rather than signal.
Both accounts are defensible and the historical record does not decisively settle which is right. What is not in dispute is that the selection was a declared component, that it was consequential, and that the conclusion drawn from the study was very much louder than a study of that design can support.
The design point deserves emphasis because it is general. The study was observational and comparative across populations. Populations differ in a very large number of ways simultaneously: in fat intake, in sugar intake, in smoking, in physical activity, in the age at which cardiovascular disease was diagnosed, in the accuracy of death certification, and in the genetic composition of the population. An association observed across countries cannot distinguish among these, and the investigators knew it. The qualification appeared in the papers and did not survive the journey into policy.
The solutions attempted have been running for forty years and constitute a large part of the modern history of nutritional science. Randomised trials of dietary modification were conducted, at enormous expense, and produced results considerably weaker than the observational literature had implied. Meta-analyses of the trial evidence have reached conflicting conclusions depending on which trials are included and how the comparison diet is characterised, which is itself a definitional dispute of exactly the kind described in this book’s chapter on definition-dependent provability. Guidance has shifted repeatedly, with dietary cholesterol removed as a specific concern, with attention moving to the composition of what replaces saturated fat, and with a growing recognition that the original framing may have been asking a badly posed question.
The measurable results are difficult to state without taking sides, so I will state what is agreed. Population-level dietary guidance based on this line of research was adopted almost universally. During the same period, consumption of refined carbohydrate rose substantially, partly in response to the guidance, and obesity and type 2 diabetes rose steeply. Whether the guidance contributed to that outcome is disputed and probably not resolvable, since no control population exists.
The reason this belongs among the case studies is not to adjudicate the nutrition question, which I am not competent to adjudicate and which is not the point. It is that the case exhibits three of this book’s failure modes simultaneously.
A declared component, the country selection, carried a conclusion far heavier than it could bear.
The qualifiers attached to an observational design were stripped as the finding travelled from the journals to the guidelines to the public, so that a statement about an association across populations arrived as an instruction to individuals.
And the field lost its variance. Once the guidance was official, alternative hypotheses about the drivers of cardiovascular disease became difficult to fund and unrewarding to pursue, and the researchers who continued to press them were marginalised. When the guidance was eventually questioned, the field discovered that it had few well-developed alternatives ready, because they had not been maintained.
The contemporary relevance is any domain where an observational finding becomes the basis of universal advice before trial evidence exists, and where the advice then shapes the behaviour that subsequent studies observe. Nutrition is the leading example. It is not the only one.
Case Study Thirteen — What Heritability Does Not Mean
Few technical terms have caused more public damage through misunderstanding than heritability, and the misunderstanding is not the public’s fault. The word means something precise, its precise meaning is counterintuitive, and the intuitive meaning it appears to have is not merely a simplification but the negation of what the statistic actually reports.
The background is a statistical concept developed for agriculture and animal breeding. A breeder wants to know how much of the variation in a trait within a population, in a given environment, is associated with genetic variation in that population, because that determines how rapidly selective breeding will shift the average. The quantity that answers this is a ratio: the proportion of the observed variance in the trait that is attributable to variance in genes.
Every element of that definition matters and every element is routinely dropped.
It is a statement about variance, not about an individual. A heritability of eighty percent does not mean that eighty percent of any person’s height is due to genes and the rest to diet. It means that within the population studied, in the environments present in that population, four fifths of the differences among people are associated with genetic differences.
It is a statement about a specific population in a specific range of environments. The same trait can have a different heritability in a different population, and, crucially, heritability rises as environments become more uniform. If every child in a society receives adequate nutrition, then variation in adult height will be almost entirely genetic, and the heritability of height will approach one, precisely because the environmental contribution has been equalised. A high heritability can therefore be evidence of environmental equality rather than of environmental irrelevance.
It says nothing about the malleability of the trait. Eyesight is highly heritable and is corrected with spectacles. The heritability of a trait and the effectiveness of an intervention on it are separate questions, and the answer to one does not constrain the other.
And it says nothing whatever about differences between groups. A trait may be highly heritable within each of two populations while the difference between their averages is entirely environmental. This is a mathematical fact with a standard demonstration involving two pots of soil and one bag of seed, and it has been misunderstood, sometimes deliberately, in every public argument about group differences for a century.
The core challenge is that the word looks like it means the proportion of a trait that is inherited, and it does not. This is a definitional trap of the kind described in the chapter on definition-dependent provability, with the additional feature that the misleading reading is the one a competent English speaker would reach unaided.
The solutions attempted have been repetition, mostly by geneticists, mostly in vain. Textbooks state the qualifications. Review articles restate them. Public discussion proceeds regardless, because the qualifications are exactly the part that does not survive transmission.
The measurable results of the confusion are substantial. Educational policy debates have repeatedly invoked heritability estimates as evidence about the limits of intervention, which they are not. Public arguments about group differences have used within-group heritability as evidence about between-group causes, which is invalid. And a body of genuinely interesting science has become difficult to discuss in public, which harms the science as well as the discussion.
The contemporary relevance has increased rather than diminished with the arrival of methods that estimate genetic contributions directly from sequence data. These produce numbers that are more precisely estimated and no less liable to misreading, and they add a new trap: a score computed in one population frequently performs poorly in another, because it partly captures correlations specific to the population in which it was trained rather than causal relationships. A score built for a purpose and applied outside its domain of validity is the same failure this book has described in bridges, in financial models, and in cosmological pipelines.
What makes this a useful case study is that it is not a story about anyone’s bad faith. The statistic is correctly defined, correctly computed, and correctly reported in the technical literature, with all qualifications attached. The failure is entirely in transmission, and it is caused by a single feature: the technical meaning and the vernacular meaning of one word are not merely different but opposed on the point that matters. When that happens, no amount of care by the producers of the statistic will protect it, and the only remedy is to change the word, which nobody will do.
Case Study Fourteen — Three Instruments and Four Minutes
On a night in June 2009 an airliner crossing the Atlantic ran into a band of storms. Ice crystals blocked the tubes that measure airspeed. The autopilot disengaged, as designed, handing control to the crew. Four minutes and twenty-three seconds later the aircraft struck the ocean. Everybody aboard was killed. The investigation that followed, which required locating the recorders at nearly four thousand metres of depth two years afterwards, produced one of the most studied accounts in aviation of what happens when a person must act while the available descriptions of the situation disagree.
The background is that a modern airliner reports its state through several independent systems. Airspeed comes from pressure tubes. Attitude comes from inertial reference units. Altitude comes from a barometric system and from radio altimetry near the ground. Angle of attack, the angle between the wing and the oncoming air, is measured by vanes. Engine parameters are reported separately. In normal operation these agree, and the flight management system integrates them.
The core challenge began when the airspeed indications became unreliable for a period of somewhat under a minute. This is a known failure with a known procedure: maintain attitude and thrust, wait for the ice to clear, and the readings return. The tubes did clear. By then the situation had changed.
What the investigation established is that the crew was presented with a set of indications that supported more than one interpretation, and that the interpretation they acted on was internally coherent and wrong. Control inputs were made that raised the nose. The aircraft climbed, lost speed, and entered an aerodynamic stall, in which the wing no longer generates lift. The stall warning sounded. It then stopped, not because the condition had improved but because the angle of attack had become so extreme that the system treated the readings as invalid. On the occasions when the nose was lowered, the readings became valid again and the warning resumed. The instrument was therefore providing a signal that grew quieter as the situation worsened and louder as it improved.
The aircraft descended for three and a half minutes in a stall, nose high, at a very high rate of descent, with the engines running. The recorded exchanges show a crew constructing hypotheses about the situation that did not include the one that was occurring, and the reason is legible: an aircraft that is stalled at high altitude with the nose above the horizon does not resemble anything in a pilot’s training, where stalls are practised near the ground with the nose falling.
The solutions implemented were substantial and are the reason to include this case here. Pitot tube designs were replaced across the fleet. Stall training was reformed internationally: recovery at high altitude was added, and the emphasis shifted from minimising altitude loss to reducing angle of attack, which had been the reverse of what pilots were previously rewarded for. The behaviour of stall warnings at extreme angles was reviewed. Displays were modified so that the angle of attack is more directly available. Procedures for unreliable airspeed were simplified and made memory items.
The measurable results include a substantial change in how the industry trains for events in which the instruments disagree, and a body of research on how crews build and revise a model of the situation under time pressure.
The reason this belongs in this collection is that it is the negative image of the navigator described in the chapter on acting under incompatible descriptions. That navigator knew the error profile of each instrument, cross-checked deliberately, and treated disagreement as information. This crew, through no personal failing, was placed in a situation where one instrument had failed in a known way, another was providing a signal whose sign was inverted with respect to the danger, and the training that would have supplied the error profile for the resulting configuration did not exist because the configuration was not in the syllabus.
The general lesson is about the design of warning systems and generalises well beyond aviation. A signal that switches off when a parameter leaves its validity range is behaving correctly by its specification and pathologically in use, because the user experiences its absence as reassurance. Any monitoring system that declares data invalid rather than alarming, in a domain where invalidity is itself the danger signal, has the same defect. Clinical monitors, industrial control systems, and financial risk dashboards all contain instances, and they are found by asking a single question: what does this system do when its inputs go out of range, and does the user know the difference between silence and safety?
Case Study Fifteen — The Doctor Who Was Right Without an Idiom
In the 1840s, a Hungarian physician working in a Vienna maternity hospital observed that the mortality rate from puerperal fever in one of the two clinics was several times the rate in the other. He established the cause, implemented a remedy, reduced deaths by roughly ninety percent, and was ignored, dismissed, and eventually driven out of the profession. He died in an asylum. His finding was correct and it was rejected for reasons that had nothing to do with the evidence and everything to do with the absence of a language in which it could be stated.
The background is a horrifying statistic. The hospital had two clinics, one staffed by medical students and one by midwives. Mortality among mothers in the first ran at rates that in some months exceeded ten percent, while the second ran at a small fraction of that. Women were said to beg to be admitted to the midwives’ clinic, and some preferred to give birth in the street.
The core challenge was explanation. The physician eliminated candidate causes systematically: differences in crowding, in climate, in the birthing position used, in the route by which a priest passed through the ward. The decisive observation came when a colleague died after being cut with a scalpel during an autopsy, exhibiting the same pathology as the women. The medical students, unlike the midwives, performed autopsies and came directly from the dissection room to the delivery ward.
He proposed that some material from cadavers was being carried on the hands and that washing with a chlorinated solution would remove it. Mortality in the affected clinic fell immediately and dramatically.
Now the part that concerns this book. The finding was not rejected because the numbers were disputed. It was rejected because it could not be expressed within the framework the profession used. Disease in that period was understood in terms of imbalances in the individual patient and in terms of miasmas, foul air arising from decay. Both explanations locate the cause in the patient or in the atmosphere. Neither has a slot for an invisible material carried on the hands of a physician, because such a substance did not exist in the available ontology, and the germ theory that would supply one was two decades away.
The proposal therefore arrived at the tribunal in a language the tribunal did not speak. It also arrived carrying an accusation, since the mechanism implies that doctors were killing their patients, and the professional self-image of the period did not accommodate that either. The two obstacles are separable and both were operative.
This is a differend in the precise sense used in this book: a party with a valid claim, no available idiom in which to state it, and a tribunal that is not corrupt but deaf in a specific direction. The physician’s own response made matters worse rather than better; he wrote increasingly furious open letters accusing his colleagues of murder, which is what a person does when he is correct and cannot be heard, and which guaranteed the outcome.
The solution, when it came, came from elsewhere. The work on fermentation and on microorganisms in the following decades supplied the missing ontology, and once the idiom existed the observation became not merely acceptable but obvious. Antiseptic surgical practice was introduced on the basis of the new framework, and the practice this physician had established empirically was reintroduced with an explanation attached.
The measurable results are the ones that make the case unbearable. The intervention worked when it was first implemented, in the 1840s, and it was abandoned, and the mortality returned, and the interval before it was reinstated is measured in decades and in a number of preventable deaths that nobody has attempted to total.
The contemporary application is not the comfortable one that everyone draws, that we should listen to mavericks. Most mavericks are wrong, and a hospital that acted on every unorthodox proposal would be a hazard. The useful lesson is the diagnostic test proposed in this book’s chapter on institutional exclusion. When a claim is rejected, ask whether it is being rejected on the evidence or because it cannot be stated in the available framework. Those are different situations requiring different responses. The first is ordinary science working. The second is a signal that the framework, not the claimant, is what needs examining, and it is detectable in advance: the sign is that the claim’s opponents cannot state what evidence would persuade them, because no evidence would fit.
Case Study Sixteen — Two Systems That Both Predicted the Sky
For roughly fourteen centuries, European and Islamic astronomers used a model in which the Earth stands still and the heavens turn around it. In 1543 a book appeared proposing that the Earth moves. The usual account has the second model defeating the first because it was more accurate. The usual account is false, and the truth is a considerably better illustration of how incompatible descriptions actually get resolved.
The background is that the geocentric system was not a crude picture. Developed to its mature form in the second century and refined continuously afterwards, it accounted for the observed motions of the sun, moon, and planets by combining circular motions: a large circle carrying a smaller circle on which the planet rides, with the centre of the large circle displaced from the Earth, and with the motion uniform not about that centre but about a third point. The apparatus was intricate and it worked. It predicted planetary positions to within a degree or two over long periods, which was better than the observations of the period could easily check, and it supported the calculation of calendars, eclipses, and astrological tables across three civilisations.
The core challenge that the new proposal addressed was not accuracy. In its original form, the heliocentric model retained circular orbits and therefore required its own set of auxiliary circles to match the data, and it was not noticeably more accurate than the system it proposed to replace. Its author’s motivation was different: he objected to the third point, the one about which motion was uniform but which was not the centre, as a device that violated the principle that celestial motion should be genuinely uniform about a genuine centre. His complaint was aesthetic and metaphysical, and he was explicit about it.
What the new model did offer was explanation of features that the old one accommodated without explaining. The retrograde loops of the planets fall out of the arrangement automatically rather than requiring a circle for each. The ordering of the planets and the sizes of their orbits become determinate rather than adjustable. The fact that the inner planets are never seen far from the sun becomes a consequence rather than a coincidence.
Against it stood serious objections that were not stupid. If the Earth moves, the fixed stars should show an annual shift in position, and no such shift could be detected. The defenders answered that the stars must be enormously distant, which required the universe to be far larger than anyone had supposed and was, at the time, an unsupported declaration. It later turned out to be true, and the shift was finally measured in the nineteenth century.
The resolution, when it came, came from three developments that took a century. The invention of the telescope revealed that one planet shows a full cycle of phases, which the geocentric arrangement in its standard form cannot produce, and revealed moons orbiting another planet, which demonstrated that not everything circles the Earth. Improved observations, accumulated over decades with instruments of unprecedented precision, were fitted by an assistant who abandoned circles altogether and found that ellipses worked, at which point the auxiliary apparatus on both sides became unnecessary. And a physics was eventually supplied in which the motion of the planets and the fall of an apple are the same phenomenon, which gave the arrangement a cause rather than a description.
Three features of this history bear on the argument of this book.
The two systems were, for a long period, empirically equivalent in their predictions and incompatible in what they took as basic. That is precisely the situation described in the chapter on truths that will not combine, occurring in the discipline that is usually held up as the model of cumulative progress.
The choice between them was not made on the evidence available at the time of the proposal, because the evidence did not distinguish them. It was made on grounds of what each took as primitive, on which coincidences each converted into consequences, and on which one turned out to be extendable into a physics. Those are real criteria and none of them is a measurement.
And the objection that defeated the new system for two generations, the absence of stellar parallax, was correct as an objection and was answered by a declaration that happened to be true. The defenders of the moving Earth were, at that moment, doing exactly what this book criticises elsewhere: rescuing a theory by declaring an unmeasured quantity to have whatever value the theory required. They were right. That is worth remembering before anyone concludes that declared components are always a symptom of trouble. They are a symptom of a claim exceeding its evidence, which is sometimes the condition of being ahead of it.
Case Study Seventeen — The Continents That Could Not Move
In 1912 a German meteorologist proposed that the continents had once been joined and had since drifted apart. He assembled an impressive body of evidence: the fit of the coastlines on either side of the Atlantic, matching rock formations and mountain chains on opposite shores, identical fossil species on continents now separated by oceans, and evidence of ancient glaciation in places that are now tropical. The proposal was rejected by the geological establishment for half a century, and the rejection was, by the standards of the time, reasonable.
The background is that the evidence for the pattern was strong and the evidence for a mechanism was absent. Every element of the correspondence had been noticed before, and had been explained by land bridges: strips of continent that had subsided beneath the ocean, allowing species to cross and later removing the connection. The land-bridge account was clumsy but it fitted the data, and it did not require anything unprecedented.
The core challenge for the drift proposal was force. Continents are made of rock and rest on rock. To move one requires a mechanism capable of shifting a mass of that scale through a solid medium, and the mechanism proposed was inadequate: tidal forces and a supposed drift toward the equator, both of which physicists calculated to be several orders of magnitude too weak. One prominent geophysicist observed that if the forces were sufficient to move continents, they would have brought the Earth’s rotation to a halt.
This is a genuine and honourable objection, and it is worth being clear about that, because the case is usually told as a parable of establishment stupidity. The critics were not defending a comfortable position against evidence. They were pointing out that a proposed effect had no proposed cause and that the cause offered was demonstrably too small. That is what critics are for.
There was also a second objection of a different character, and it is the one this book is interested in. The proposer was a meteorologist. The evidence he assembled came from palaeontology, from structural geology, from climatology, and from geodesy, and no single discipline possessed all of it. Specialists in each field could see that the argument from their own domain was suggestive and not conclusive, and no one was positioned to weigh the accumulated force of arguments drawn from five domains at once. A claim assembled across disciplinary boundaries has no natural tribunal, which is the institutional situation described in the chapter on exclusion at the boundary.
The solution arrived from an unexpected direction and had nothing to do with continents. During and after the Second World War, ocean floors were surveyed at scale for military reasons, and the survey revealed a globe-spanning ridge system, sediment far thinner than an old ocean floor should carry, and a pattern of magnetic stripes on either side of the ridges that mirrored each other symmetrically. Rock records the direction of the Earth’s magnetic field as it solidifies, and the Earth’s field reverses at irregular intervals; the stripes were therefore a record of new floor being created at the ridge and spreading outward, printed with a timestamp.
The mechanism followed. The continents are not ploughing through the ocean floor; they are passengers on plates that are created at ridges and consumed at trenches, driven by convection in the mantle beneath. The objection about forces dissolved, because the proposed mechanism had been wrong while the pattern had been right.
The measurable results were a complete reorganisation of the earth sciences within about a decade, one of the fastest changes of framework in the history of any discipline. Once the mechanism existed, the previously scattered evidence became a single coherent body, and the land bridges vanished without anybody troubling to refute them.
Two lessons, and they point in opposite directions, which is why the case is worth including.
The first is that a correct pattern with a wrong mechanism looks, from the inside, exactly like a wrong pattern. There is no reliable way to tell them apart at the time, and demanding a mechanism is not obscurantism.
The second is that the field’s response to the ambiguity was to eliminate the variance rather than to maintain it. Drift was not merely doubted, it became professionally disreputable, and the small number of geologists who continued to work on it were treated as eccentrics. Had the field maintained a funded minority position, the mechanism would very likely have been found earlier, because the people looking for it would have been more numerous. The cost of eliminating an unpromising line is invisible until it turns out to have been the right one.
Case Study Eighteen — The Bacterium That Was Not Supposed to Be There
For most of the twentieth century, peptic ulcer disease was understood as a disorder of excess acid, caused by stress and diet, treated by neutralising the acid, and prone to recur for life. In the early 1980s two researchers in Western Australia proposed that most ulcers are caused by a bacterial infection and can be cured with antibiotics. They were correct. It took roughly a decade for the proposition to be accepted, and the delay is a well-documented example of an observation that could not be assimilated because it contradicted a framework proposition rather than a finding.
The background is a piece of received knowledge that was regarded as settled: the stomach is sterile. The reasoning was straightforward and had the form of a physical argument rather than an empirical one. Gastric acid is extremely corrosive, no organism could survive in it, and therefore reports of bacteria in gastric tissue must represent contamination. Such reports had in fact appeared periodically for a century and had been dismissed on precisely those grounds each time.
The core challenge, then, was not that the new claim lacked evidence. It was that the evidence was being filtered by a prior that assigned it essentially zero probability. This is the structure described in the chapter on definition-dependent provability, appearing in its Bayesian rather than its logical form: when the prior is sufficiently extreme, no realistic quantity of evidence moves the posterior, and the rejection of the evidence is a rational consequence of the prior rather than a failure of reasoning.
The organism was cultured, in the end, by accident. Plates were routinely discarded after two days, which was insufficient; over an Easter holiday a batch was left for five, and colonies grew.
Even with the organism in hand, the association could be dismissed as opportunistic colonisation of tissue already damaged by ulceration. Correlation was not going to settle it, and a randomised trial in humans would have required infecting healthy people, which no ethics committee would approve.
The solution was that one of the researchers drank a culture of the organism himself. He developed gastritis, the organism was recovered from his stomach, and the sequence from infection to inflammation was demonstrated in a single subject who had consented in the most direct manner available. This is not a method anyone should recommend, and it worked, and it worked specifically because it converted an argument about interpretation into an event with a date.
The measurable results are unusually clean for a medical case study. Ulcer disease moved from a chronic condition managed for life to an infection cured in a week or two by a course of antibiotics with an acid suppressant. Surgical procedures for ulcers, once common, became rare. Rates of gastric cancer, for which the infection is a risk factor, have declined in populations where the infection has been treated. The two researchers received a Nobel Prize in 2005.
The reasons for the delay are worth separating, because they were not all disreputable.
The prior was genuinely strong and had a physical basis, and strong priors with physical bases are usually a good thing.
The proponents were not established figures in gastroenterology, and their submissions were initially rejected by the relevant conferences and journals, which is the institutional filtering described earlier in this collection.
And there was a large industry supplying acid-suppressing drugs to a chronic population, which is a fact that should be stated without being made to carry more explanatory weight than it can bear. The financial interest did not create the resistance, since the resistance predated the drugs by decades, but it did not accelerate the resolution either.
The contemporary application is the recognition of a specific signature. When a claim is being rejected not on the strength of the evidence but because the evidence is being assigned to a category that disqualifies it in advance, the argument will have a characteristic shape: the opponents will explain why the observations must be artefactual rather than why the hypothesis is unlikely. That distinction is visible in the literature at the time and it is the most reliable early indicator available that a framework proposition rather than a finding is doing the work.
Case Study Nineteen — The Formula That Decides Cricket Matches
When rain interrupts a limited-overs cricket match, somebody has to decide who won. The two teams have batted for different lengths of time under different conditions, and there is no fact about which team was ahead, because the game was not completed. For decades the problem was handled by rules that everybody agreed were unsatisfactory, and since 1997 it has been handled by a mathematical method that everybody agrees is better and that nobody fully understands, including a large fraction of the professionals whose careers it affects.
The background is a genuine structural feature of the sport. In the limited-overs form, each side receives a fixed number of overs and has ten wickets to lose. A team batting second knows the target and can pace itself accordingly. If rain shortens the second innings, the target must be adjusted, and the adjustment must account for the fact that a team with all its wickets intact and few overs remaining will score much faster than one that has already lost most of them.
The core challenge is that the resource available to a batting side is two-dimensional. Overs remaining and wickets remaining are not interchangeable, and neither alone determines how many runs can still be scored. Early methods used one dimension and produced absurdities. A method based on average run rate produced, in a famous semi-final in 1992, a revised target that required a team to score twenty-two runs from one delivery, which is not possible, and the match ended in front of a stadium full of people who understood that they had watched an arithmetic error rather than a contest.
The solution was devised by two statisticians who modelled the combined resource directly. Their method treats a team’s remaining scoring capacity as a single quantity determined jointly by overs and wickets, computed from historical data on how much teams actually score from each combination. When an interruption occurs, the resources available to each side are computed, and the target is scaled by the ratio. The method was adopted internationally, refined over time as scoring patterns changed, and is now the standard.
The measurable results are that revised targets are no longer absurd, that the method handles interruptions in either innings and multiple interruptions in one match, and that its outputs are accepted as authoritative by players, officials, and audiences.
Three features make this an unusually clear case study.
The declared component is fully visible and openly acknowledged. The resource table is a model fitted to historical data, and everybody involved knows it is a model. Nobody claims that the revised target is the number of runs the team would have scored; it is the number the method assigns. The convention is understood as a convention, which is precisely what fails to happen in the other nineteen cases in this collection.
The model is updated when the world changes. Scoring rates in the sport rose substantially over two decades, the original table began to produce targets that favoured one side systematically, and the table was revised. A declared component with a maintenance schedule is a different kind of object from one that has been inherited.
And the acceptance rests on function rather than on truth. Nobody believes the method is correct in the sense of describing what would have happened. It is accepted because it is consistent, published, applied identically to both sides, and better than the alternatives, which is the only kind of legitimacy available for a rule that decides an unfinished contest.
The contemporary application is broad and mostly unrecognised. Any situation in which an incomplete process must be resolved requires a rule of this kind: the allocation of a contract when a tender is aborted, the settlement of a derivative when the underlying market fails to open, the calculation of a pension when a scheme is wound up early, the awarding of grades when examinations are cancelled. That last case is instructive by contrast. When an examination system was replaced by an algorithm in 2020, the algorithm was neither published in advance nor understood by those it affected, and the resulting outcry destroyed it within days. Cricket solved the same problem successfully, and the difference was not mathematical sophistication. It was that the sport declared its convention, explained it, applied it symmetrically, and revised it in public.
Case Study Twenty — The Baseline Question
In the spring of 2020, every government in the world needed to know how many people were dying. This appears to be a simple counting problem. It is not, and the way it was handled produced numbers differing by factors of two or three between equally competent sources, generated a large volume of public argument in which both sides cited official statistics, and provided the clearest recent demonstration of what a declared baseline does to a measurement.
The background is that deaths can be attributed to a cause in more than one way, and each way answers a different question.
A death can be counted when a test confirms the pathogen and the person subsequently dies, within some specified interval. This requires specifying the interval, and different jurisdictions specified twenty-eight days, sixty days, or no limit, producing systematically different totals from identical underlying events. It also depends entirely on testing capacity, so that a country with limited testing records fewer deaths regardless of how many people die.
A death can be counted when a physician records the disease on the certificate, either as the underlying cause or as a contributing one. This depends on certification practice, which varies by country and changed during the period, and on the physician’s judgement in cases where an elderly person with several conditions dies after an infection.
Or the total number of deaths from all causes can be compared with the number expected, and the difference reported as excess. This avoids attribution entirely and requires instead a declared expectation: what would have happened otherwise.
That declared expectation is the whole problem, and it repays examination.
The expected number is typically computed from the average of several preceding years, adjusted for population, for age structure, and often for seasonal patterns and for trend. Every one of those adjustments is a choice. Using a five-year average gives one answer; using a model with a linear trend gives another. Including or excluding a preceding severe influenza season shifts the baseline materially. Adjusting for the ageing of the population raises the expectation and lowers the excess. Some methods incorporate temperature, because heat and cold both kill.
Serious teams made different choices, published them, and produced excess estimates that differed substantially. The differences were not errors. They were the consequence of different declared baselines, and each estimate was correct given its own.
There is a further and deeper problem with excess mortality that was widely misunderstood in public discussion. It measures the deviation from expectation, not the deaths caused by the pathogen. During the period in question, deaths from road accidents fell because people travelled less, deaths from some infectious diseases fell because of distancing, and deaths from untreated conditions rose because health systems were disrupted. Excess mortality is the net of all of these. It is the right quantity for some questions, such as the total human cost of an entire episode including its policy response, and the wrong quantity for others, such as the lethality of a pathogen.
The solutions that emerged represent good practice under difficulty. Several teams published their methods in full, released their code, and reported results under multiple baseline choices so that the sensitivity was visible. International bodies convened technical groups to agree on comparable methods. Retrospective estimates, computed years later with better data and stable baselines, have converged considerably.
The measurable result is that the eventual global estimates of excess mortality substantially exceed the confirmed totals, by a factor that varies by region and is largest where testing was weakest, which is what the structure of the two measures predicts.
The contemporary application is any measurement of an effect against a counterfactual, which includes most of applied economics, most of programme evaluation, all of climate attribution, and every claim about lives saved by an intervention. In each case there is a real measurement, an honest derivation, and a declared statement of what would otherwise have happened. The third is where the argument actually is, and it is almost never where the argument is conducted.
Glossary
Abduction — Reasoning to the best available explanation of a set of observations, distinguished from deduction and induction.
Adaptive observer — A knower that is inside the system it studies, has limited capacity, holds several incompatible descriptions at once, must act, and improves by tracking where each of its descriptions fails.
Adaptive variance — The diversity of approaches maintained within a system, which functions as its instrument for detecting its own errors.
Admissible definition — A definition that preserves the inferences competent users of a term actually make, classifies the obvious cases correctly, and does not reduce the term to a triviality.
Aesthetic engagement — Sustained attention to an object that resists immediate categorisation and rewards continued looking with structure not apparent at first.
Affirmative reporting — The practice of stating explicitly what was assumed as well as what was found.
Algorithmic filtering — The selection of what a person sees by an automated system whose selection principles are not available to that person.
Anomaly — An observation that does not fit the expectations generated by the current description, and that may indicate noise, a local error, or a boundary.
Antirealism — The position that the success of a scientific theory does not warrant belief in the unobservable entities it postulates.
Approximate truth — The idea that a theory can be close to correct without being correct, whose several incompatible formal definitions produce different verdicts about scientific realism.
Argumentative scaffolding — The reasoning that supports a claim, one of the four components of a scientific statement, and among the first to be lost when the claim is transmitted.
Assumption — Anything taken as given for the purposes of an argument, whether or not the person making the argument is aware of taking it.
Asymmetry of totalizing ideals — The structural result that eliminating deviation from a chosen optimum causes more long-term damage than tolerating it, because the deviations were the system’s error detector.
Attention — The limiting resource in any environment where information is abundant, and the quantity that automated distribution systems are generally built to maximise.
Attribution — The assignment of an observed effect to a specified cause, which always requires a statement of what would otherwise have occurred.
Autopoiesis — The capacity of a system to maintain its own organisation, used here informally to describe how institutions preserve their operating assumptions.
Baseline — A declared statement of what would have happened otherwise, against which an effect is measured.
Bibliometrics — The measurement of scholarly activity by counting publications and citations, and the basis of most modern research evaluation.
Blinding — The concealment from analysts of which condition they are examining, so that their choices cannot be shaped by the result.
Boundary condition — A statement of the circumstances in which a claim holds, without which the claim cannot be verified at all.
Boundary-conditioned verification — The principle that a statement is capable of being true or false only relative to a specified domain, scale, and set of admissible checking procedures.
Bundling — The practice of selling access to many journals as a single package, so that a subscriber must buy what it does not want to obtain what it does.
Calibration epoch — The point in time chosen as a reference for a measurement chain, whose selection can alter the sign of a reported trend.
Case-by-case judgment — Deciding each situation on its own terms rather than by applying a general rule, which is possible without being arbitrary when the practitioner knows where each of his descriptions fails.
Catalogue — A list of individual verdicts with no organising principle, which cannot be disagreed with because it makes no general claim.
Category error — Treating something as a member of a class to which it does not belong, such as asking for the temperature of a single molecule.
Cerebral hygiene — Auguste Comte’s practice of refusing to read the work of contemporaries in order to keep his system free of outside influence.
Citation cartel — An arrangement, tacit or explicit, in which researchers cite one another in order to raise their measured standing.
Coarse-graining — The mapping of many distinct fine-scale configurations onto a single coarse-scale state, a process that destroys information and cannot be reversed.
Code of practice — A written procedure specifying what must be stated when a new entity is introduced into a field, so that declarations remain visible to later readers.
Compatibility — The relation between two descriptions when a single consistent account exists whose consequences include all the consequences of both.
Complexity threshold — The level of complication above which a domain requires more than one non-equivalent description and cannot be reduced to a single one.
Compression — The derivation of many particular results from a small number of commitments, which is what makes something a theory rather than a list.
Compression imperative — The requirement that a valid description be shorter than an enumeration of the cases it covers.
Conceptual degradation — The systematic loss of parts of a scientific claim as it passes through a chain of transmission, with qualifiers and structure lost before the core proposition.
Consensus — Agreement among the parties present, which is compatible with any degree of prior selection at the boundary of the group.
Constructive empiricism — The position that the aim of science is empirical adequacy rather than truth about unobservable things.
Context signal — Any indication of which situation an agent is currently in, without which contextual switching between descriptions cannot be performed.
Contextual qualifier — The part of a claim that states when and where it applies, and the part most likely to be stripped in transmission.
Contextual switching — The strategy of maintaining several incompatible descriptions and applying whichever is accurate in the current situation.
Convention — A choice adopted by a community for the sake of comparability, which is legitimate when acknowledged and dangerous when forgotten.
Copula — A mathematical device for separating individual probabilities from the structure of their dependence, used to price bundled mortgages before 2008.
Core proposition — The central factual assertion of a claim, the component most likely to survive transmission intact.
Cost vector — The combination of proof power, tractability, and ontological commitment that any formal configuration purchases and pays for.
Counterfactual — A statement about what would have happened under conditions that did not obtain, required by every measurement of an effect.
Critique — The evaluation of an institution or practice against a standard it does not itself supply.
Cross-check — The deliberate comparison of independent instruments or methods, in which disagreement beyond the known error profiles is treated as information.
Declared — Describing a quantity chosen by a person and written down, where nothing in the data forced the choice.
Declared component — Any element of an argument that was chosen rather than measured or derived, and on which the conclusion may depend.
Deep disagreement — A dispute in which the parties reason competently from different fundamental commitments and cannot be reconciled by further argument.
Default — A choice embedded in a procedure or a piece of software, inherited by users who were not present when it was made.
Deferred referent — A role in a theory whose occupant has not been observed but which the theory specifies well enough that an observation could in principle find it.
Definition-dependent provability — The principle that whether a claim can be proved may change with the definition assigned to its key terms.
Degradation audit — An examination of what has been lost from a scientific claim during its transmission into policy or public communication.
Delegitimation — The loss by a body of knowledge of the story that gave it standing, as distinct from the loss of confidence in its results.
Deliberation — The process by which a group examines a decision, whose required time may exceed the time available.
Dependency coefficient — A measure of how much of a system’s critical function relies on decisions and resources originating outside it.
Derived — Describing a quantity obtained from measured quantities by steps that can be written down and checked.
Description — A finitely specified account of a domain, with a language, a set of commitments, and a way of drawing consequences.
Descriptive completeness — The requirement that a valid description not remain entirely silent about the observables within its own domain.
Dialectic — In the older sense used by Lyotard, the discussion of opinions where certainty is unavailable, not the Hegelian process of thesis and synthesis.
Differend — A conflict in which no rule of judgment applies to both parties, so that resolving it in the language of one automatically wrongs the other.
Dissensus — Sustained disagreement, valued by Lyotard as a defence against settlements imposed under the appearance of agreement.
Domain — A region of reality with states, some dynamics relating them, and stable observables that behave reproducibly.
Domain overlap — The condition in which two domains share at least one observable, so that their descriptions make claims about the same feature.
Dwarf planet — A category created in 2006 for bodies that orbit the sun and are round but have not cleared their orbital neighbourhood.
Effective theory — A theory explicitly valid only up to a certain scale, with the influence of finer scales entering through a few parameters it cannot compute.
Emergence — The appearance at one scale of properties and regularities that are not present at, and not derivable from, the scale below.
Empirical adequacy — Correctness about the observable phenomena, whose meaning depends on where the line between observable and unobservable is drawn.
Epistemic architecture — The design of the structures through which a community produces, checks, and transmits knowledge.
Epistemological patience — The deliberate maintenance of an unresolved position on a specific question for as long as the evidence does not support resolution.
Error profile — Knowledge of where, in which direction, and by how much a given instrument or description goes wrong.
Excess mortality — The difference between observed deaths and the number expected under a declared baseline, which measures net deviation rather than deaths from a single cause.
Exit — The genuine availability of leaving an arrangement, without which participation cannot be voluntary and voice is not credible.
Exteriorisation — The separation of knowledge from the person who holds it, so that it can be stored, transmitted, and sold independently of any knower.
Fiducial cosmology — A model of the universe assumed in advance in order to convert observations into the quantities an analysis requires.
Fix — An estimated position produced by a procedure and carrying a known uncertainty, not to be confused with the position itself.
Foreclosed referent — A role in a theory whose occupant cannot be observed as a matter of the theory’s own structure, so that no future instrument will find it.
Foreground — Any signal from an intervening source that must be subtracted before the signal of interest can be claimed.
Formal reality — A complete specification of a logic, a set of commitments, and a set of definitions, within which claims acquire determinate status.
Formalisation — The translation of a phenomenon into a formal language under a set of constraints.
Formalization laws — Three results holding that formalisation is always possible for determinate structure, always bounded, and always plural.
Framework proposition — A structural assumption that governs somebody’s reasoning from within and is not itself defended in the course of that reasoning.
Free riding — Benefiting from a collective effort without contributing to it, the dominant strategy in any arrangement without exit or exclusion.
Gemeinschaft — Community grounded in personal bonds, distinguished by Tonnies from society organised through formal institutions.
Genre of discourse — A mode of speech with its own criteria for what counts as a successful move, such as narration, prescription, or demonstration.
Goodhart effect — The tendency of a measure to cease measuring what it measured once it is adopted as a target.
Grand narrative — A story that authorises a body of knowledge by placing it within a larger account of history, humanity, or the development of understanding.
Grey literature — Material circulated outside formal publication, including preliminary results presented in conference talks.
Heritability — The proportion of variation in a trait within a specific population and range of environments that is associated with genetic variation.
Hinge proposition — A commitment that is not itself an object of justification but that holds the framework within which justification operates.
Idiom — A language in which a particular kind of claim can be stated, whose absence converts a grievance into a differend.
Impact factor — A measure of the average citation rate of a journal, originally devised to help librarians decide which periodicals to buy.
Incommensurability — The condition of two frameworks that disagree not only about claims but about the standards by which claims are assessed.
Incompatible truths — Descriptions that are each valid within their domain and cannot be combined into a single consistent account.
Inevitability of choice — The result that no position of neutrality among formal configurations exists, so that declining to choose means adopting one’s community’s default.
Infrastructure — The layer of assumptions, defaults, and conventions that is executed rather than asserted, and that therefore presents nothing to contradict.
Internal observer — An observer that is a part of the system it observes, and is therefore subject to structural limits on what it can access.
Irony — The swap of the role attributed to a statement while its content is preserved, requiring a system that can hold a model and its failure at once.
Land bridge — A hypothesised submerged connection between continents, used to explain matching fossils before continental drift was accepted.
Laundering — Reporting a quantity derived from a declared component in the same voice as a measurement, with an uncertainty that describes only instrument noise.
Legibility — The property of a piece of work that allows a reader to reconstruct what was assumed, what was found, and which of the two the conclusion rests on.
Legitimation — The conferral of standing on a body of knowledge, as distinct from the establishment of its content.
Litigation — In Lyotard’s usage, a dispute for which a rule of judgment recognised by both parties exists.
Load-bearing — Describing any element on which a conclusion actually depends, as opposed to elements that could be removed without effect.
Measured — Describing a quantity produced by an instrument in a way that another party could in principle reproduce.
Metalanguage — A language standing above several others in which their disputes could be adjudicated, whose existence Lyotard denied.
Metanarrative — A story about stories whose function is to authorise knowledge rather than to add to it.
Micronarrative — A small local story that organises the life of a particular community without claiming general authority.
Model — A simplified representation built for a purpose, to be evaluated by its adequacy for that purpose rather than by its resemblance to everything.
Monoculture — A system in which one configuration has displaced the alternatives, efficient against current conditions and blind to its own errors.
Noise attack — The flooding of an information channel with material so that the cost of determining what is supported exceeds any individual’s budget.
Non-degeneracy — The requirement that two descriptions genuinely differ rather than being the same account in different vocabulary.
Non-uniqueness — The result that no sufficiently rich task determines a single formal configuration as the only adequate one.
Novel prediction — A prediction of something not already used in building the theory, whose several definitions admit different rosters of historical cases.
Observational asymmetry — The fact that successful deception is invisible while detected deception is prominent, which causes hostility to be systematically overestimated.
Ontological commitment — What a theory obliges its user to accept as existing, one of the currencies in which a formal configuration is paid for.
Open access — Publication arrangements in which the reader pays nothing, commonly funded by a charge levied on the author.
Overloading — Requiring a declared component to support a conclusion far heavier than its own evidence can justify.
Paganism — Lyotard’s term for judging without possessing the criterion by which one judges, deciding case by case in the situation.
Paradigm audit — A structured examination of the tacit assumptions embedded in a policy or research framework and of their adequacy to the present problem.
Parallax — The apparent shift in a star’s position caused by the Earth’s motion, absent from observation for two centuries after it was predicted.
Paralogy — Lyotard’s proposal that legitimation be sought in the invention of new moves and the cultivation of disagreement rather than in consensus.
Peer review — The evaluation of a submission by anonymous specialists, a ceremony whose function and whose drift are both real.
Performativity — Legitimation by the ratio of output to input, in which a claim or a programme earns standing by being efficient rather than by being justified.
Phrase regimen — A set of rules determining what counts as a well-formed and successful utterance of a given kind.
Plurality and incompleteness — The law that any determinate structure admits at least two adequate formalisations, each faithful to some features and blind to others.
Policy architecture — The design of institutional structures that reduce the consequences of translation errors, rather than attempting to eliminate the errors.
Positivism — Auguste Comte’s programme of confining inquiry to relations among observable phenomena and abandoning questions of ultimate cause.
Preregistration — The public deposit of an analysis plan before data are collected, which preserves the distinction between prediction and observation.
Primitive — A feature treated as basic within a description, from which the others are derived, and whose selection is a substantive commitment.
Prior — A statement of what was believed before the evidence was examined, which determines the conclusion precisely where the evidence is weakest.
Projection — A mapping of a structure onto a lower-dimensional representation, which necessarily preserves some features and distorts others.
Provability function — The mapping from admissible definitions of a term to the status of a claim expressed in that term.
Puerperal fever — The infection that killed women after childbirth in nineteenth-century hospitals and whose cause was identified before an idiom existed for it.
Ranking function — An automated rule determining the order in which material is presented, which suppresses without prohibiting and leaves no record of what it did not show.
Reference model — A specification of a system’s behaviour adopted before an analysis begins and used to make the analysis possible.
Registered report — A publication accepted on the basis of its design before its results exist, removing the incentive to produce a particular outcome.
Replication — The repetition of a study by independent investigators, and the mechanism by which a field detects the errors it has published.
Residue — The content that no observer inside a system can reach, established as necessary by the structure of embedding and empty of specified content.
Rigid adherence — The strategy of applying one description everywhere, which performs well within its domain and fails silently outside it.
Ritual — A prescribed sequence of actions whose correct performance confers a standing that the underlying facts do not confer by themselves.
Salami publication — The division of a body of work into the smallest publishable units in order to raise the count.
Satellite account — A supplementary set of national statistics measuring what the headline figure excludes.
Scale coupling — The condition in which two domains overlap, so that descriptions belonging to different scales make claims about the same feature.
Scale-specific principles — The law that principles governing one level of description need not extend to another, because the mapping between levels is not invertible.
Scientific realism — The position that the success of mature scientific theories provides reason to believe that they are approximately true.
Scope tracking — Maintaining, for each description one holds, an estimate of the region in which it performs, updated from its failures.
Selection at the boundary — The management of an institution’s coherence by controlling who is admitted rather than by suppressing dissent among those present.
Self-exclusion — The decision by a party not to bring a case to an institution because he has correctly concluded that it cannot succeed there.
Sensitivity analysis — The systematic examination of how a conclusion changes when its assumptions are varied across their admissible range.
Significance threshold — A conventional level of statistical improbability adopted as a criterion for publication, originally proposed as a convenience.
Silence — In Lyotard’s analysis, itself a phrase, which may deny that the hearer is the right one, that the situation is as described, that the speaker has standing, or that the matter can be formulated at all.
Stall — The condition of a wing that has exceeded its critical angle and no longer generates lift, recoverable only by reducing that angle.
Stigmatisation of doubt — The marking of certain questions in advance as the questions asked by a disreputable kind of person, which raises the cost of asking them.
Stripped claim — A true proposition severed from the conditions that determine when it applies, and dangerous for that reason.
Structural continuity — The preservation of mathematical form across a change of theory, secure but empty under permissive definitions and substantive but vulnerable under strict ones.
Structural cost — The price paid by any formal configuration in proof power, tractability, or ontological commitment.
Structural generality — The property of a result that survives every admissible variation of formal configuration, and the only available criterion of robustness across a disagreement.
Sublime — The experience of encountering something that cannot be assembled into a single presentation, given a structural address by the limits on internal observers.
Synchronous lateral excitation — The feedback in which walkers adjust their gait to a swaying surface and thereby amplify the sway, absent from every structural model before 2000.
Tacit assumption — A commitment that shapes reasoning without being stated, and that therefore cannot be examined until somebody names it.
Terror — Lyotard’s term for a criterion that removes an unproductive player rather than arguing with him, leaving no position from which to reply.
Testimony — An account offered by a witness, whose admissibility depends on a tribunal willing to receive it in the form in which it can be given.
Time density — A measure of how far the interval between the appearance of information and its assimilation has been compressed.
Tree-top meta-method — The procedure of generalising a claim upward until further generalisation would empty it of content, then descending with a map of everything the ascent passed through.
Triadic model — The account of hostile epistemic environments as the interaction of noise attack, stigmatisation of doubt, and algorithmic filtering in a self-reinforcing cycle.
Uncertainty interval — A statement of the range within which a quantity is believed to lie, which describes only the sources of error the analysis modelled.
Undecidability — The condition of a precisely defined claim that is neither provable nor refutable within a specified system, distinct from indeterminacy caused by definitional choice.
Universalism — The claim that a standard applies everywhere and to everyone, which grand narratives supplied and whose loss removes the footing for certain kinds of critique.
Use-novelty — A definition of novel prediction requiring only that the predicted phenomenon was not used in constructing the theory.
Validity — The property of a description that is internally consistent and correct about the observables it addresses within its scope.
Variance — The spread of configurations within a system, which functions as information about the part of the environment nobody has mapped.
Verisimilitude — A formal notion of closeness to truth, several incompatible versions of which have been proposed and none of which commands agreement.
Voluntariness — Formation by choice with a real option of exit, necessary but not sufficient for a communal arrangement to be sustainable.
Whole and part — The relation between a system and an observer inside it, which generates the structural limits on what any internal observer can access.
Timeline
c. 400 BCE — Greek medical and philosophical writers debate whether disease should be explained by humoral balance or by external agents, an early instance of two frameworks addressing the same phenomena from different primitives.
c. 380 BCE — Plato sets out the position that just action copies an Idea of justice available to those who have contemplated it, establishing the model of judgment by criterion that Lyotard will later reject.
c. 350 BCE — Aristotle develops practical wisdom and rhetoric as disciplines of reasoning where certainty is unavailable and a decision is nonetheless required.
c. 300 BCE — Euclid organises geometry from a small set of postulates, providing the model of compression from which later formal ideals descend.
c. 150 CE — Ptolemy completes a geocentric system that predicts planetary positions accurately for fourteen centuries using circles carrying circles.
c. 200–500 CE — Rabbinic compilations preserve minority legal opinions alongside the majority ruling, creating an institutional method for carrying incompatible valid positions in a single text.
c. 700–900 CE — Four schools of Islamic jurisprudence stabilise, each internally rigorous, differing in their rulings, and all regarded as legitimate.
1088 — The first European university is founded at Bologna, and the disputed question becomes the central format of instruction.
c. 1320 — William of Ockham advances the principle that entities should not be multiplied without necessity, the ancestor of every later argument about unearned additions to an ontology.
1543 — Copernicus publishes a heliocentric system that is not more accurate than its rival but converts several coincidences into consequences.
1609–1619 — Kepler abandons circles for ellipses, removing the auxiliary machinery from both competing systems.
1610 — Galileo observes the phases of Venus and the moons of Jupiter, providing the first observations that the standard geocentric arrangement cannot accommodate.
1687 — Newton supplies a physics in which planetary motion and terrestrial falling are the same phenomenon, converting a description into an explanation.
1717 — Leibniz and Clarke exchange letters on whether space is a container or a system of relations, each position internally coherent and neither settled by observation.
1739 — Hume observes that no statement of what ought to be follows from statements of what is, establishing the gap between genres that Lyotard will later formalise.
1781–1790 — Kant distinguishes judgment that applies a rule from judgment that must find one, and analyses the sublime as the experience of a magnitude the imagination cannot assemble.
1810 — The University of Berlin opens under a plan uniting teaching and research, embodying the story that the disciplines are organs of one developing intelligence.
1830–1842 — Comte publishes his course of positive philosophy, proposing the law of three stages and naming sociology.
1849 — Comte establishes the Religion of Humanity with a calendar of thirteen months, recognising that a legitimating story must be told rather than merely asserted.
1847 — Semmelweis reduces mortality from puerperal fever by roughly ninety percent through handwashing, and is rejected because his finding has no available idiom.
1859 — Darwin publishes an account of descent with modification, providing a second great narrative of development alongside the story of progress in knowledge.
1865–1876 — Pasteur and Lister supply the germ theory and antiseptic practice, furnishing the ontology within which the earlier finding becomes obvious.
1872 — Comte’s disciples split between those who want the science and those who want the church, and the scientific content separates cleanly from its legitimating apparatus.
1889 — The international prototype kilogram is adopted as the definition of mass, and the words order and progress appear on the flag of Brazil.
1900–1927 — The old quantum theory and then quantum mechanics develop, producing descriptions of matter that resist assimilation to the classical account.
1912 — Wegener proposes continental drift with strong evidence for the pattern and no adequate mechanism.
1920s — Fisher proposes a conventional threshold of one in twenty for treating a result as worth a second look, and states explicitly that it is a convenience.
1930 — Pluto is discovered while searching for a planet that does not exist.
1931 — Gödel establishes that a sufficiently rich consistent formal system contains statements neither provable nor refutable within it.
1934 — Kuznets presents national income accounts to Congress and warns that national welfare cannot be inferred from them.
1930s — The liquid drop model of the nucleus produces quantitative predictions from a metaphor with no liquid in it.
1936 — Turing establishes the limits of mechanical computation and the undecidability of the halting problem.
1945 — Vannevar Bush argues for public funding of basic research on frankly narrative grounds, creating the postwar research system.
1948 — Socialisme ou Barbarie is founded, arguing that the Soviet Union is a system of exploitation with a new ruling class.
1950 — Lyotard is posted to teach philosophy in Constantine, Algeria, where the gap between universal principles and their rationed application becomes visible to him.
1953 — Wittgenstein’s later work is published posthumously, replacing meaning as reference with meaning as use within an activity.
1954 — Lyotard joins Socialisme ou Barbarie and begins a decade of writing on Algeria, partly under a pseudonym.
1955 — Keys begins the seven-country study of diet and cardiovascular disease.
1960 — The Quiet Revolution transfers control of education in Quebec from the Church to the state, replacing one legitimating story with another.
1962 — Kuhn describes scientific revolutions and the incommensurability of successive paradigms.
1962 — Garfield’s citation index is established as a tool for librarians.
1963 — Lyotard leaves Socialisme ou Barbarie to found Pouvoir Ouvrier.
1963–1968 — The seafloor magnetic stripes are interpreted, the mechanism for drift is found, and the earth sciences reorganise within a decade.
1969 — Wittgenstein’s notes on certainty are published, introducing propositions that hold the framework in place without themselves being justified.
1971 — Lyotard defends a doctoral thesis on the quarrel between discourse and the visible.
1972 — Anderson argues that reduction to fundamental laws does not entail reconstruction from them, and that each level of complexity requires research as fundamental as any other.
1970s — The renormalisation group shows that most microscopic detail is irrelevant to large-scale behaviour, giving scale-specific principles a mathematical basis.
1978 — Nora and Minc report to the French president on the computerisation of society.
1979 — Lyotard delivers The Postmodern Condition to the Council of Universities of Quebec, and publishes Just Gaming in the same year.
1980 — Van Fraassen proposes that the aim of science is empirical adequacy rather than truth.
1981 — Laudan’s confutation of convergent realism sets out the historical record of abandoned theoretical entities.
1982 — Marshall and Warren culture the bacterium associated with gastric ulcers after a plate is left over a holiday.
1983 — Lyotard publishes The Differend, the book he considers his real work of philosophy.
1984 — Marshall drinks a culture of the organism and develops gastritis, converting an argument about interpretation into an event with a date.
1985 — Fogelin introduces the concept of deep disagreement into argumentation theory.
1985 — Lyotard curates an exhibition at the Pompidou Centre on immaterial technologies.
1986 — The Challenger accident demonstrates the loss of boundary conditions in the transmission of a technical recommendation.
1987 — Lyotard tells an Australian art magazine that The Postmodern Condition is the worst of his books and belongs to the satirical genre.
1989 — Worrall proposes structural realism as a response to the historical record.
1990s — Bibliometric evaluation spreads through national research assessment systems.
1997 — The Duckworth-Lewis method is adopted to resolve rain-affected cricket matches by a published and symmetric convention.
1998 — Lyotard dies in Paris of leukaemia while preparing a conference on postmodernity and the media.
2000 — The Millennium Bridge sways on opening day, revealing a feedback mechanism absent from every structural model.
2000–2007 — Copula methods are used to price bundled mortgages using a correlation parameter that could not be measured.
2005 — Hirsch proposes an index combining publication count and citation count to rank individual researchers.
2005 — Marshall and Warren receive the Nobel Prize.
2006 — The International Astronomical Union adopts a definition of planet, and Pluto is reclassified.
2008 — The correlation assumption fails, and the securities built on it precipitate the deepest recession since the 1930s.
2009 — Air France 447 is lost after airspeed instruments fail and the stall warning falls silent as the situation worsens.
2011–2012 — Analytic flexibility and the practice of forming hypotheses after seeing data are documented as systematic problems in psychology.
2013 — The bereavement exclusion is removed from the diagnostic criteria for major depression.
2014 — A claimed detection of primordial gravitational waves is announced and, within a year, attributed to galactic dust.
2015 — A large collaboration reports that fewer than half of a hundred psychology experiments replicate.
2017 — Revised guidelines lower the threshold for diagnosing hypertension, reclassifying tens of millions of people overnight.
2019 — The kilogram is redefined in terms of a fundamental constant whose value is fixed by declaration, and the prototype in the vault is demoted.
2020 — Excess mortality estimates diverge widely between competent teams according to the baseline each declares.
2020 — An algorithm replaces cancelled examinations, is neither published in advance nor explained, and is withdrawn within days.
2020s — The disagreement between two independent measurements of the expansion rate sharpens as both measurements improve.
2020s — Large corpora assembled from published text become capital assets, and disputes over the exteriorisation of knowledge reach the courts.
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