I was thinking a little about logic today. I’ve never understood the use of formal logic. That probably has a lot to do with my unfamiliarity with it; in spite of my interests in philosophy, I’ve never been taken with the explicitly analytical aspects of that field. But my recent thoughts have turned up some interesting (if not terribly Earth-shattering, or even original) observations. For example, consider this prototypical syllogism:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal

That’s air-tight logic, right there. You can argue with either of the premises (maybe some men aren’t mortal, or maybe Socrates isn’t really a man), but if you accept them then you’re essentially bound to accept the consequent as well. But so what? If you know that all men are mortal, and you know that Socrates is a man, then you already know that Socrates is a mortal. You’ve learned nothing at all. No new information is derived from these statements. They don’t give you any knowledge of men, mortality, or even Socrates, apart from that which you already possessed. In fact, you can use the same logic to show this:

I know that all men are mortal
I know that Socrates is a man
Therefore, I know that Socrates is mortal

So what is the point? If these are just arrangements and rearrangements of symbols, why do we value them so much? Why are there twenty types of syllogism, dozens of fallacies, and various (complicated) systems of formal logic? To answer that, consider another, slightly modified version of our overworked syllogism:

I believe that all men are mortal
I believe that Socrates is a man
Therefore, I believe that Socrates is mortal

Given the simplicity of the statements this is probably true, but it’s not at all guaranteed to be. It’s possible–even quite ordinary–for people to believe each premise of an argument, and yet still deftly deny its consequent. Call it cognitive dissonance, or even just confusion. The nature of the human brain is such that it can hold beliefs which are mutually exclusive, provided (it seems) that it keeps them logically separate. That is, it’s rare for a person to explicitly claim both P and Not P at the same time, but it’s commonplace to hold beliefs which, through a more circuitous path, lead to the same situation.

What this example demonstrates is not that the syllogism is faulty, but that our understanding of “belief” is. We generally consider them to be discrete things that reside in our brains somewhere, waiting to be recalled. But the neurology doesn’t really support this. It turns out that the organization of information and behavior in our brains is quite complex. It’s possible for different parts of our brains to believe and behave in entirely different ways. You can see extreme cases of this in split brain syndrome, but it happens in different parts of our brains, in all sorts of different ways. The positions and statements that we finally come to are just the product of all this, as it manifests in our consciousness. What sort of convoluted neurological gymnastics took place on the road to consciousness is anyone’s guess, however.

The value of formal logic, as I see it, is that it allows us to articulate many different propositions, in a linear manner, and establish a synthesis of further belief from them. In a sense, it’s a means of communications–not just with other people (though it’s certainly that as well), but with ourselves. Considering how much of our everyday thinking is a muddle of emotion and assumption, having a methodology for rigorous thought would seem to be quite helpful. Maybe I should think of formal logic like the scientific method of belief.