Beyond Logic

Before I was introduced to the world of academic philosophy, I used to entertain the following idea quite often: there are always things in this world that we don't know about or cannot understand, given our limited capacities. From that, I skipped carelessly to the conclusion: anything is possible. For how can you say for sure that a certain phenomenon (e.g. that ghosts exist) is impossible, when it could just be a case where you failed to know enough?

When I began venturing into 'professional' philosophy, the answer to my question seemed immediately obvious: logic. Anything is possible, except for that which is forbidden by logic. For example, a ball cannot be black or white all over, we can never draw a square circle, and a triangle can never have four sides.

I admit that I wasn't a rigorous thinker. I couldn't think of examples such as these at the time. But for some reason, I was not 'psychologically' convinced. For instance, I would hesitate if someone asked me to bet me and my family's life (say for a million dollars) that it is impossible to draw a square circle, or that it is impossible to find a married bachelor. I wouldn't take that action. If it is as William James says - that belief is measured by action - then you can certainly come to the absurd conclusion that I don't believe in logic.

You may say that it is irrational not to place such a bet, or that I suffer from an extreme inferiority complex with respect to my intellect. After all, it does seem more of a psychological issue that I am so unconfident in my ability to reason. But let me just push this a little further:

Why can't we have ideas or existing things which are beyond what logic permits? What makes us always right? If it is possible for us to get a mathematical proof wrong, why is it not possible for us to get the more basic bits wrong? In other words, why must we have certain things which are necessary?

To solve this problem, I find it useful to see logic as as a model.

If logic, like mathematics, is a tool to model the universe around us, then the results it generates are fallible. Just like how classical macroeconomics models have failed to predict stagflation, logic - as a model - can fail to predict about facts of the universe. And when logic (as a language) fails, we get paradoxes, such as the Liar Paradox*. So maybe within logic, there are things which are necessary, and not everything is possible. But we shouldn't expect that if something is forbidden by logic, it cannot exist in any form in real life. (there's this famous demonstration where someone 'showed' that a triangle can have three right angles by drawing it on a non-Euclidean space - e.g. a basketball)

I certainly don't mean that we should be expecting to be able to find a married bachelor anytime soon. But I'm still sceptical as meanings of the words 'bachelor' and 'married' can shift in real life. Also, it needs to be said that all reasoning (including my train-of-thought as I write this entry) is captured by logic - if not logic, then grammar, or syntax. Anything illogical is very likely going to be meaningless, since logic plays a very important part in our thoughts (not everything illogical is meaningless - just think of how comedy often makes use of logical contradictions).

Hence, it's not crazy to be sceptical about whether logic tells us everything about possibility and necessity. But if we reject logic altogether, none of what I've just written should make hold any force since it relies on reasoning.

*'This sentence is false.' - as Tarski has shown, this paradox remains as long as we use our natural language which contains self-referring terms.

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