Escaping the Liar’s Paradox

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The liar’s paradox, regardless of whatever label it is given, can be reduced to either of these two forms:

1. The next statement is true. The previous statement is false.
2. This statement is false.

If you attempt to seek some solution to this as though it were a problem, then any attempt to restrain yourself to the prescribed confines of language will leave you baffled. In short, don’t try to “solve” it. If you want to make a conjecture about the “truth” or “validity” of any such statement, you first must understand the entirety of the setup.

First of all, the spontaneous approach relies on a few underlying false assumptions. The first false assumption is that the words of a language directly correlate to some real idea. They do not. A word is nothing more than associated sounds and letters that are used to call to mind a particular idea or ideas. The sounds for “no”, for example, mean two different things depending on the language of reference. There is no reason why “no” cannot have multiple associations because “no” isn’t bound to any one of them. Likewise, words “truth” and “false” are not bound to the the ideas they reference, nor are those ideas bound to the words. To phrase this in more practical terms: “You can’t make something true by saying so.” However, even knowing this, we cannot yet make a conjecture about the truth or validity of the paradox in question (even though this explanation does explain many other paradoxes).

The next false assumption is that the statement must make some kind of statement about truth. I am not disregarding this: That if the paradox is declared false, it then makes itself true, and if it is declared true, it then makes itself false. Instead, it is false to assume that any conjecture of the truth or validity of the paradox can be made at all! There is no reason why the statement must be recognized as true or false.

To better understand why this is the correct answer, a third false assumption must also be addressed. This assumption is that the paradox actually gives a real idea. The truth or validity of a statement is completely meaningless. For example, in English, “Red is blue” is naturally false based on the ideas associated with “red” and “blue”. However, if “blue” were to be “red” in some hypothetical language, then in such a language, “Red is blue” would be a perfectly true expression of reality. Therefore, the statement alone (“Red is blue”) has no particular inherent measure of truth. Analysis of truthfulness or validity can only be made when the statements as a whole invoke an idea. “Red” invokes the idea of a color, a comprehensible reality (a reality that can be imagined). But since the paradox in question (the Liar’s Paradox) invokes no comprehensible idea of reality, there is no sense in discussing whether that idea even applies to reality.

All lies share the common aspect that something about them does not apply to reality. If we knew all the facts, then the claim by the lie would be inconceivable. Thus all lies in some way relate back to the same issue with the Liar’s Paradox that I have discussed here. The difference is that usually things involved are more complex and thus allow for some modification or distortion of their definitions that makes it seem as though they would apply to reality.

For example, consider the following claim: “A banana is orange”. The concept of “banana” entails both a shape and a color. Since the shape is usually the primary association with “banana”, it is possible to conceive of both the banana shape enveloped in the color of orange. However, if the definition (and, in turn, the concept) of “banana” required that the “banana” have the color of yellow, then it would be inconceivable for a “banana” to be “orange”. The statement “A banana is orange” would be false – that is, inapplicable to reality.

From this analysis, we could say for certain that in the first structure of Liar’s Paradox (“The next statement is true. The previous statement is false.”), the entire claim as a whole is meaningless and should not be analyzed as two separate components. That says nothing about its applicability to reality. In fact, if we are to say anything about the system, we can say the entire system is “false”, or in other words, inapplicable to reality.

We could try to associate some fact with one of the statements. For example, we could say “The sun shines and the second statement is true. The first statement is false.” But even here, we can treat the parts (“the sun shines” and “the second statement is true”) separately and come to the conclusion that the latter part is still inapplicable to reality.

Paradoxical and ironic as it may seem, if we say that the system as a whole is false, then we should certainly admit that both statements in the system are false. “The second statement is true” and “The first statement is false” are both false. Neither is applicable to reality.

The important fact is that words and statements themselves don’t make something valid or true. They are merely supposed to be descriptors of reality.

If you try to find where such a problem might exist in reality, then the problem might be analogous to two mirrors reflecting the image of each other. Tracing the image back to the first mirror seems impossible, but the fact is, one mirror was hit with light first. Just because there is an apparent dependency does not mean there was no beginning.

If we are to take this analogy literally, we might (incorrectly) conclude that the statements alternate in their truthfulness and falseness as each is analyzed. In the case of the basic system – “This statement is false” – we could say that it is not false until completed, in which case it becomes true about itself and then goes back to being false in alternating manner. But this is what drives people crazy with this problem, and it’s better to stick with the truth: that the paradox is inapplicable to reality and therefore false.

On a related note, there may arise a situation in which (when reduced to its fundamental argument) one person claims a certain other person is always a liar and the other person claims that the first person is always honest. I’ve discussed the definition of a lie, and it hopefully it is evident that the liar is still a liar. Since lying is aimed at providing an idea other than the truth, it is clear that such a claim of “all honesty” is meant to counter the claim of “always a liar” and therefore distort the truth, which is an indirect way of providing an idea that is wrong. I say this as a hypothetical situation, assuming that one person is always honest and the other person is always lying, but the analysis is applicable regardless and could also be used to in the scenario where both people have lied or both people have always (before this point) been honest. The purpose in my pointing this out is that such scenarios, while related to the topic of the liar’s paradox, are not entirely the same.