The topic of logic has really gotten me thinking over the past few weeks. Many debates have arisen in which the usage and application of logic has been questioned. I'm not just referring to the threads debating the infallibility of logic - the threads about God, omnipotence, free will, sin, etc all procure many questions regarding the nature of logic as well.

In this thread, I postulate that logic is founded upon and constrained by human language and understanding, and since both are fallible, logic by extension shares the same vulnerabilities. I shall demonstrate these assertions using examples, and conclude by saying that logic should not be treated as the be-all and end-all in verifying everything in this universe.

1) Logic is limited by language

Example 1:

"This statement is false."In this classic Liar Paradox, the paradox arises because the statement is self-referential. If we claim that this statement is true, then it must be false, because it describes itself to be false. Yet if we claim this statement to be false, then it has to be true.

Attempts to resolve this paradox have invariably contradicted the law of bivalence or resorted to attacking the language upon which this paradox is based. This example is not to demonstrate that logic is false, but that it is highly dependent on language.

Example 2:

The adjectives "autological" and "heterological" are defined as follows:

1. An adjective is autological if and only if it describes itself. For example "short" is autological, since the word "short" is short. "Pentasyllabic" is also autological.

2. An adjective is heterological if and only if it does not describe itself. Hence "long" is a heterological word, as is "monosyllabic".

"Heterological is not heterological."The Grelling-Nelson paradox arises when we attempt to find out the nature of the word "heterological". Is the word "heterological" heterological? On the one hand, if the word "heterological" is heterological, then it does not describe itself. Since the fact of it not describing itself does, in fact, describe it, it is autological, which means it isn't heterological. On the other hand, if the word "heterological" is not heterological, then it must be autological, which means it describes itself, and therefore it must be heterological. Either case leads to the contradiction that the word "heterological" is both heterological and not heterological, which is impossible.

Again, we see a case where logic is constrained by the limitations of language.

2) Logic is limited by the human framework of understanding

Example 1:

Suppose a point P is moving between points A and B (just like in the original Racetrack). And suppose also that we stipulate that P is in the state "even" for the first half of the journey, "odd" for the next 1/4, "even" for the next 1/8, and so on. That is, we simply decide to classify P based on where along the journey it is, such that it alternates between what we call an "even" and an "odd" state. We can in addition stipulate that once it is in one state it remains in that state unless it gets switched according to the above rule.Here is a paradox which arises when we attempt to use logic to deal with the concept of infinities. The question is: In what state is P at point B?

Critics of this paradox normally claim that it is physically impossible to divide distance into infinitely small units. While this may be true, that only demonstrates that logic cannot cope with matters out of our physical realm of understanding.

Example 2:

1. All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of 'infinite regression'.This is not a paradox. It is the Munchhausen Trilemma, which argues that all techniques to used to verify truth are fallible as they ultimately cannot justify themselves.

2. One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.

3. The third horn of the trilemma is the application of a circular and therefore invalid argument.

Many people have claimed that logic is infallible. But the interesting thing is, no one has ever attempted to justify logic as being an infallible system for the verification of knowledge. Instead, the onus is always shifted to the skeptic: "Prove logic is wrong", "Prove that any of the laws of logic are wrong", the defenders of logic say.

However, the claimant is usually hard-pressed to prove logic on its own. Most of the time one would appeal to empirical evidence and say that in all known cases of logic being utilised, it has never failed before (which is an unsatisfactory answer on its own). But when presented with paradoxes where logic produces contradictory/indeterminate results, the claimant usually produces a wide variety of reasons to justify why logic cannot deal with the said paradoxes. Hence, we see that the application of logic is in effect tautological, as anything that it cannot adequately deal with is cast to the realm of "illogical".

This then leads to the obvious question: We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?

Conclusions:

1) Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and imcomplete understanding of the world.

2) Since logic is based heavily on human language and understanding, and in fact,isa component of human understanding, it is a human construct rather than a human discovery. A concept cannot exist independently without a conceiver, and logic, as well, is a concept which does not exist on its own. It is a system of reasoning created by humans to understand our world.

3) Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence.

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