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When I was a kid, I wanted to be like Mr. Spock on Star Trek. He was smart, he could kick ass, and he usually saved the day while Kirk was too busy pontificating or womanizing.
And since Spock loved logic, I tried to learn something about it myself. But by the time I was 13 or 14, grasping the basics of boolean algebra (from borrowed computer science textbooks), and propositional logic (through a game of "Wff'n'Proof" I picked up at a garage sale), I began to get a little dissatisfied with it.
Spock had made it seem like logic was some sort of "formidable" thing, with which you could do all kinds of awesomeness. But real logic didn't seem to work the same way.
I mean, sure, it was neat that you could apply all these algebraic transforms and dissect things in interesting ways, but none of it seemed to go anywhere.
Logic didn't say, "thou shalt perform this sequence of transformations and thereby produce an Answer". Instead, it said something more like, "do whatever you want, as long as it's well-formed"... and left the very real question of what it was you wanted, as an exercise for the logician.
And it was at that point that I realized something that Spock hadn't mentioned (yet): that logic was only the beginning of wisdom, not the end.
Of course, I didn't phrase it exactly that way myself... but I did see that logic could only be used to check things... not to generate them. The ideas to be checked, still had to come from somewhere.
When I was 17, in college philosophy class, I learned another limitation of logic: or more precisely, of the brains with which we do logic.