Sunday, February 26, 2006

I'm sure a real philosopher would just kick my nuts

bringing us inevitably around and around to coginitive dissonance. The brain jockeys say that cognitive dissonance occurs when our beliefs contradict each other. Since we depend on our beliefs for our sense of self, the rightness of our surroundings, our mental equilibrium, we strive to avoid and discredit these sensations.

Here's Godel again. There are a lot of simple explanations of Godel's Proof. Here's the simplest: Take a piece of paper. On one side of it write the sentence =the sentence on the other side of this piece of paper is true.= On the other side, write =the sentence on the other side of this piece of paper is not true.= no sit with it for a while and try to figure out what's going on. It's actually more complicated than it looks. This is not Godel's proof: what Godel's proof does is to demonstrate that no matter what you system of symbolic representation, it will always be possible to construct this kind of statement: it follows the appropriate logic of statements but cannot be logically parsed. There's no point going much further with explaining Godel's Proof. There are plenty of books that address the topic, at least one of which has won the Pullitzer Prize. I don't think it's that important: it's just a systematic demonstration of paradox. The paper trick illustrates the principle just as well if you accept text as as self-consistent a system of symblic representation as any. If the first side is true the other side cannot, by definition, be true, and yet if the first side is false then the other side is true, making the first side true after all, but if the first side is true... And repeat and repeat and repeat. Your basic logical positivist will say that any statement like that is simply meaningless, and most of us consciously or not go along with that theory. It is not logic but cognitive dissonance which leads us to this conclusion. The paradox is in fact an indictment of logic, making logical positivism positively illogical.

klik if you demand tedious explanations of every little thing.

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