Breaking the Law of Non-Contradiction

Although I bear little respect for theologians, I’ve become terribly annoyed by the insistence of analytic philosophers lately. My annoyance stems from their arrogance, an arrogance that was once the realm of those whom they seek now to overthrow, theologians. To ad-lib from the Law of Non-Contradiction before I break it, let’s say that two wrongs do not make a right.

Analytic philosophers and logicians love the Law of Non-Contradiction (the LNC), maybe because they think Aristotle was so great. Or maybe they think it tells us something about the world, the Problem of Substance be damned. I’m not sure. I certainly don’t think Aristotle’s contributions to moral philosophy in particular were contributions at all and his formulation of physics certainly impeded progress in that field of study (seeing how he didn’t bother to test any of his hypotheses). Sorry, I'm already getting off track…What is this law analytic philosophers and logicians love? As blogger Bill Pratt puts it (via Leibniz via Aristotle), “There are at least three ways to state it:

1. A thing cannot both be A and not-A at the same time and in the same context.
2. A thing cannot both exist and not exist at the same time and in the same context.
3. A statement cannot both be true and not true at the same time and in the same context.” [Note: I exchanged his original word ‘sense’ for the more suitable word in this context, ‘context.’]

Bill Pratt goes on to say that he is amazed that people still try to deny this law. Never underestimate people, Bill; I am amazed how often analytic philosophers ignore underdetermination and other flaws in analytic and scientific reasoning. But I think that in part, my problem with The LNC stems from not liking being told what to do. So, if you tell me The LNC is a law, I’m going to find a way to refute it because, well, I can, at least some of the time. (And because I think Aristotle sucks.) What that means, kids, is that The LNC isn’t a law at all. Oooo, I can just feel the intense hatred of some analytic philosopher reading this right now…

My problem with the LNC comes via its linguistic analysis. Bill Pratt attempts to score one for his team by pointing out that you cannot negate the law without using the law itself to defeat it. He writes: “If you have any doubts about this fundamental law of rationality, try and deny it, but then write out your denial in a sentence – ‘The law of non-contradiction is false’ – and ask whether your statement is both true and false at the same time and in the same sense. If the law of non-contradiction is false, then your statement of denial must be both true and false.  But if your denial is false, then the law of non-contradiction is true! By denying the law of non-contradiction, you have just affirmed it.  The more you try to deny the law, the more you will affirm it.’

Typical; someone convinced they are right playing word games to prove their point. Pratt wants to put words in your mouth by claiming your denial of the law can only be structurally sentenced as ‘The law of non-contradiction is false.’ No, Bill, linguistically, all I have to do to deny the law is assert ‘A thing can be both A and not-A at the same time.’ (I do have to prove it, though.) Pratt continues to say that if you try to say the law is both true and false, the falseness of the statement makes the statement true, and if you say the law is true it’s both true and false and..that…doesn’t make much sense. Let us not forget that this word play just a mind-game, a paradox of language that is completely dependent upon what each word in the statement means. Aristotle engaged in this same word-play, insisting that a statement must have only one meaning if we’re to understand each other and gives the example of the word ‘man’ meaning ‘two-legged animal.’ Only, we do not have to consent to Aristotle’s definition and still understand what he means when he uses the word ‘man,’ though his definition may be more narrow than our own. I’d like to remark here that by way of his argument, Aristotle has proved the law to himself and only himself; the LNC doesn’t hold in the presence of two or more people.

By the way, Pratt suspiciously fails to point out that in order to prove the law, he has to use the law to prove itself. I’m not sure how he forgot such a minor detail.

To further illustrate the LNC is a contrivance of language, let me use this example: Pi is 3.14. Okay, so what are we saying here, that Pi is 3.14 (A)? Well, that can’t be since Pi and 3.14 are two different things, at least to my eyes. So, to say Pi is 3.14 would violate the LNC. Oh, or are we saying that Pi (A) is 3.14 (not-A)? Well, it can’t be A is not-A because that would violate the LNC, too! The way I see it, if Pi is 3.14, then two things are both A and not-A at the same time in the same context being that their meanings are synonymous. If we say Pi (A) is 3.14 (not-A), we’ve still refuted the LNC. If – in a desperate attempt to save the LNC – you’re thinking that ‘Pi’ is the written expression of 3.14 and ‘3.14’ is the numerical expression of Pi and this means the synonymous symbols make for two different contexts, I would strongly disagree; we’ve already agreed their meanings are synonymous and therefore the context is preserved. In fact, you can do this with almost any ‘is’ statement. This enigmatic vortex of the philosophy of language is academically referred to as a SNAFU.

I’m not the first to deny the LNC. The ancient Greek philosopher Heraclitus, Graham Priest and ‘inconsistency-tolerant’ logicians have also challenged the validity of the law, although in a manner unlike I have done here. And I’m not saying the LNC can always be refuted; in instances that are self-evident truths, of course you can’t refute the LNC. That is, when you see blue, of course you’re seeing blue. But ask a color-blind person what they see and you’ll get a different answer. Thus the LAW of Non-Contradiction isn’t a law at all. If it is, well, you know that old saying: Some laws were meant to be broken.