The Nature of Logic.

So I was sitting in class and the prof was going on and on about probability. Mostly because that’s basically what we’re learning in the class. Somehow, my mind wandered to something more interesting, that I’ve been meaning to look at. Yes, as the title says, the nature of logic.

I think it was spurred because the prof randomly mentioned The Law of Excluded Middle. Without that law, there is no logic. At least in a concrete and defined sense. So I thought to myself, “Okay, well, what is logic?” I considered exactly what the Law of Excluded Middle does. Consider the world linearly. (I won’t even try to get into more than two dimensions.) Think of A being on one end, and ~A being at the other end. (If you don’t know, the ‘~’ is one notation for negation.) The world is not such where A and ~A covers all possible states. Example time.

We vote, right? Well, some of us. Okay, very few of us. But, when we vote, we give our entire support to one candidate. There is no, “Well, 60% of me wants to vote for him, but 40% of me doesn’t like some of his policies.” You can’t vote for and against somebody at the same time. (See Law of Contradiction.) This is the nature of voting. As I said, you either give all or none of your support to somebody, regardless of how you really feel. That’s the nature of the human construct of voting. Another example.

Consider the concept of a “flood”. Fxy will be, “Place x is flooded at time y.” ~Fxy would be the negation, “It is not the case that place x is flooded at time y.” Of course, this arbitrarily defines a certain water level. When is a place flooded? Common sense would say a place is flooded when there is excess water, typically caused by rain. It’s suppose it rains. If it’s a small drizzle, I doubt anybody will say it’s flooded. If a foot of water just falls out of the sky, I think there would be some amount of flooding. PHOOOM. *KABOOM* Anyway, there are infinitely many water levels between a drizzle and a foot of water. (If you think it’s finite, I can prove otherwise.) If an inch of rain falls, is it still not flooded? Two different states, but with the same logical assignment.

I suppose the point of logic is to cut out the fuzziness of the world. (Don’t even start on fuzzy logic, I’m not even sure what it is.) If you think of the world as black and white, logic essentially cuts out the gray area. It brings in a level of certainty. If someone says, “It is the case that place x is flooded at time y”, I would assume there’s a lot of fucking water!” I forget if I said this previously, but there are certain water levels that would be hard to guage.

This is the case of the heap. Let’s suppose you have tiny pebbles. If you start with one, and add another tiny pebble, it is not a heap. It is clear that if you add enough, it becomes a heap. But, as I said before, if you add one pebble to something that isn’t a heap, it doesn’t become a heap. Same principal can be applied to the flood scenario. Would a micron of water added to an area that isn’t flooded cause it to be flooded? (Don’t even think about scenarios where there’s a dam that breaks. I’m just thinking about rivers going over their banks.)

Part of the problem here is English. English is not logical. I can’t think of a language that is. (Don’t say math, we can’t talk to each other exclusively in math. Well, as far as I know.) English is imperfect. Well, how many other ways can I say it? It’s arbitrary. If I say, “Go over there”, well, where is there? It’s not one fixed point in space-time. I mean, hell, we’re flying around the sun at however-many miles per hour. “Here.” Is constantly changing, as well, relative to some static concept of space-time.

I don’t see too many absolute things in the world. This desk seems static to me. But, on an atomic level, it’s almost chaotic. Humans call things “chaotic” when we can not find some sort of pattern or order to it. But, I digress. This desk is static in that I will always know where “the desK” will “be”. And when I return, this desk will continue to be “the desk”. It won’t randomly morph into THEDOUBLEDONGOFJUSTICE.

Maybe the world is absolutely relative. …*laughs* I won’t even try to explain that one.

Logic introduces preciseness where there might not be one. What does it mean for something to be “true”? It’s VERY hard to think of a non-circular definition, assuming one exists. Logic invents this notion of absolute trueness. Well, relatively absolute trueness. “It can be true, it can be false, depends on what logical operators are applied.” Logic invents true and false, then applies logical operators to them. If I remember correctly, you can define any statement in or statements and negations. But, uh, that’s a pain in the ass. I also remember that nor can define any statement. Hmm. I’m rambling. This sounded so much better in my head.

Logic invents true and false. Then invents ways for them to interact. All really need is And, Or, and Implication. (A&B, AvB, A->B, respectively, though notation can differ.) OH. Oh yeah, that’s why I was going down this line of thought. There’s one really bad thing people do a lot when arguing. What’s it called, inferring the antecedent? I believe so. New paragraph.

Let’s suppose there’s ol` A->B. (Or A implies B.) What a lot of people do is, if they find B to be true, they’ll infer A. Examples show what I’m talking about. Suppose A is “John is human” and B is “John is a mammal”. A->B is true. (Why? There is only one way implication can be false: If you have A and you don’t have B. Implication means that if you have the antecedent, you MUST have the predicate.”) Now, as I said, the mistake people make is if they know B to be true, they’ll infer A. Suppose John is a monkey. B obviously true. But, from B, you can not infer A.

Also, to clarify another misconception, implication does not mean causation. I won’t even go into that one, I can’t think of a good example.

I’ve completely lost my train of thought. Maybe I’ll stop before I start thinking about things out of my league. By the way, the problem of inferring the antecedent is one reason I discount almost all “proofs” for the existence of Big G. You diddleys. I’m content to just say you can’t know. PUNY HUMANS. *cackles*

I dare somebody to prove that I’m not God. I mean, come on, BRING`EM ON. If you want to use skewed logic, you can prove that I am God rather easily. I mean, hell, Ray Charles is God. Reminds me, I was going to pose that as a general question. To refresh everybody’s memory:

God is love.
Love is blind.
Ray Charles is blind.
Therefore, Ray Charles is God.
And therefore, God exists.

I know why these statements aren’t consistent. Well, I don’t remember off the top of my head, but I’m sure I can derive the explanation again.