PulpLit.net

Logic Problems

I've always been kind of puzzled by the way that logic works.

Take statistics. Say you have a six sided die. Presumably, then, your odds of rolling a six in one roll are one in six. You do this by counting the sides, and assuming each side has an equal chance of coming up.

Now say you roll the die a whole bunch of times. You get a random distribution, presumably, over the whole each of the six sides. And if you rolled three sixs in a row (or six sixs), it would be fair to say that that was unlikely to happen, right?

But if you rolled ten sixs in a row, or twenty, you'd probably start to assume that something was wrong with your premise. You'd conclude that the dice were loaded, which would again, be logical.

But the thing is, then, that you're reasoning backwards. Your premise was proven wrong by the conclusion, and then experience informs a new premise. So "logic", in so far as it works, isn't very useful. It is just an attempt to clarify the reasoning behind a guess.

That example doesn't make immediately clear exactly what I'm trying to say. Let's take another example.

A logical proposition that is self evidently true could be something like "something cannot both exist, and not exist." This is pretty self-evidently true, right? Logically, both A and NOT A cannot both exist in a universe, because the two statements are mutually exclusive. The neural calculator in our heads goes "nope."

But, of course, in the real world, thing can both exist and not exist. Electrons in an atom do not really "exist" in the strictest form. Oh, sure they may hang around. But in terms of what philosophers seem to define as corporeal existence, that is, staying in one place for a certain breadth of time, they don't. Like a guy hitting on a pretty bartender, they sort of appear and disapper around the object of their attaction. Technically, an atom in your body can appear near the moon in one instant, and be right back next to your earlobe the next.

Do they "exist"? Maybe. But they certainly challenge the concept that something can "exist" and "not exist".

Or particle wave duality. That fact that someting can be a particle and a wave depending on which test you expose it to challenges my notion of what it means for something to be something. Posed this problem, someone once confidently told me that what happened in this case was that we simply said to ourselves that we were mistaken in the first place, and that instead of there being two distinct objects, there was actually one, and our whole principle of distinction of objects lived on intact.

But this seems to me to be ducking the question, which is, if the logic which seemed to infallible and clean just a second ago can run into such readily available problems in the real world, why then should we relie upon it? If the soundest premise and syllogism still lands you on shakey ground, why is logic any better than merely being persuasively sexy?

I suppose the answer is that it is not. Of course, paradoxically, I've used logic to get myself here. Which is like painting oneself into a corner in a room; you have to step all over the paint and make a mess to get out.