Paradox: Simply Invalid Argument

Unpeer-reviewed paper (Philpapers)

https://philpapers.org/rec/HORPSI

Abstract

This paper demonstrates that paradoxes are simply invalid arguments. A paradox arises from an invalid theory, the inappropriate application of a theory, or a misunderstanding by the person arguing. The cause of these is a lack of understanding of the preconditions. As examples of paradoxes, this paper cites Achilles and the Tortoise, the Monty Hall problem, the paradox of tolerance, the paradox of diversity, and natural rights. There is an aspect where paradoxes point out flaws in arguments and deepen the discussion. However, it remains true that paradoxes are invalid arguments caused by a lack of understanding of the preconditions. \end{abstract}

1. Classification of Paradoxes

A paradox is an unacceptable argument. The appearance of a paradox simply indicates an invalid argument. There are three cases.

One is the case of an invalid theory where an event occurs that cannot be explained within the preconditions of that theory.

One is the case of inappropriate application where a theory is applied outside its preconditions.

Alternatively, it is the case where the person arguing lacks understanding of the theory or event and mistakenly believes a paradox is occurring when it is not.

The third case refers to what is called a paradox as an unacceptable yet valid argument. This simply means the construction of the argument is invalid. It means making assertions based on superficial similarities and lacking a structural understanding.

When the preconditions of a theory or event are unclear, unexplainable events can inevitably occur. It merely means the preconditions were unclear, and it was an invalid description to begin with. The lack of understanding of the preconditions of a theory or event is the cause of paradoxes.

2. Concrete Examples of Paradoxes

2.1. Achilles and the Tortoise

This paradox is as follows.

Achilles, who is fast, and a tortoise, who is slow, race. The tortoise leads. In the time it takes Achilles to reach the tortoise’s location, the tortoise moves ahead. In the time Achilles moves to that location, the tortoise moves further ahead. Achilles, who is fast, cannot catch up with the tortoise, who is slow.

As a precondition of this argument, Achilles must be behind the tortoise. As this argument, he will never catch up from the beginning. People who apply this to cases of catching up or overtaking are just mistakenly believing it to be a paradox on their own. Regarding this, the discussion leaps to the infinite division of time and space, but its validity is a separate discussion.

2.2. Monty Hall Problem

There are three doors, one is a winner and the other two are losers. The respondent first chooses one. Next, the host excludes one of the remaining two. It is shown that one is a loser. At this time, the respondent is given another opportunity to choose. The probability of winning for the door not chosen by the first respondent becomes 2/3. Even though choosing from two doors, it is not 1/2.

This arises simply from the misunderstanding that the concept of ``equally likely’’ in probability always holds true. In the beginning, the winning probabilities of all doors are equally likely. However, the winning probability of the remaining two doors after the choice is 2/3. The host’s exclusion merely consolidated it into one door. Because attention was paid only to the superficial event of choosing from two doors and its formation process was ignored, a sense of discomfort arises. Discomfort is an argument with an invalid construction.

2.3. Paradox of Tolerance

If a society is unlimitedly tolerant, that society will ultimately have its tolerance taken away by intolerant people, or tolerance will be destroyed. In order to maintain a tolerant society, the tolerant society must be intolerant of intolerance.

There are academic theories about tolerance prior to this. Need to mention is that, the definition of tolerance is unclear. And tolerance is a restriction on a person’s freedom, in that the person must not restrict the freedom of others. A tolerant society means forcing this upon the members in a community. It is a broken concept.

After that, it is not worth talking about. But I will mention it anyway. In this argument, a description appears stating that if counteracted by rational argument, it should not be suppressed, but if violence such as fists or pistols is used, it should be suppressed. However, these cannot be derived from the initial preconditions. Arbitrary judgment intervenes. The criteria for rational argument or violence are unclear, and there is no validity to those criteria. This is a typical case where development of a broken argument needs to add even more broken descriptions.

This paradox can be said to be a childish argument that lacks understanding of preconditions, freedom, and community.

2.4. Paradox of Diversity

This is an example of similarity to the paradox of tolerance.\

Not recognizing diversity is also a form of diversity. However, if you recognize people who do not recognize diversity, diversity will be destroyed.

This, too, has an unclear definition of diversity. Proceeding with the argument assuming diversity refers to the diversity of structures. A structure holding a perception that does not recognize that concept can also appear. It is precisely a diversity of structures. If a specific structure is excluded, it is nothing but an arbitrary judgment.

And if there is a perception consisting of such a structure, there is a considerable leap in logic in the argument that diversity is destroyed. Destruction does not happen by perception alone. Destruction needs action. There is room for consideration whether perception and action are directly linked. However, that is not necessarily the case. Also, if one does not act harm, one is harmed. The action can be justified even from the perspective of the reduction of diversity. Even from the perspective of preventing the reduction of diversity, the validity of the action should be questioned, not the perception.

Also, the validity of respecting diversity should be questioned. The reason why priority should be given to respecting diversity is unclear.

That cannot be derived from the initial preconditions. In the end, both the preconditions and the theoretical development are childish, and it is an invalid argument.

2.5. Natural Law and Natural Rights

Regarding natural law and natural rights as well, a paradox arises. The restriction of natural rights is invalid, but the unjustifiability of actions restricting natural rights cannot be explained. Natural law and natural rights, within their framework, become a description that must not be restricted but can be restricted. This arises because natural rights fail to describe the characteristic of freedom where one’s freedom restricts the freedom of others.

In social contract theory, Mill’s harm principle, and etc, attempts were made to resolve that contradiction. However, the definition of harming others is unclear. It cannot help but be arbitrary. Those argument ignore the characteristic that freedom restricts others. In the end, this invalid argument arises because of an invalid precondition.

Conclusion

Paradoxes are invalid arguments. Unclear preconditions make them. There is an aspect where discussions deepen as pointing out flaws in preconditions. However, excessively praising paradoxes as intellectual is proof of not understanding paradoxes.

The ambiguity of definitions in arguments is partly the fault of the side arguing. However, it is not uncommon that the cause is that the proponent did not limit the interpretation.

This is not need that preconditions should simply be made detailed. Depending on the preconditions of the argument, words and concepts used in the argument, those level of preconditions must be grasped. Making it excessively detailed is useless.

The appearance of paradoxes arises from a lack of understanding of preconditions.