juggernaut
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- Joined
- Mar 22, 2009
- Messages
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And why am I thinking true mathematics and logic? Both maths and logic are axiom-based. Chock fulla tautologies. Everything true in maths and logic is true by definition. Innit? (I should be thinking semantics, I guess you mean.)
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Actually I do mean mathematics and logic. The first and second order differences. I'm thinking specifically of Goedel (the incompleteness theorem), Tarski (the undecidability theorem) and Peano arithmetic. There's also Cantor's theorem, and the problem Russell presented to Frege...which ultimately forced Frege to abandon his position. There's nothing relativistic in any of these systems or even semantically ambiguous. Truth is, nevertheless, a bit of a problem for all of them. So tautologies are in there, but the systems also present us with paradoxes and contradictions as we move from one to the next if we assume there is an absolute truth. Is everything true by definition in mathematics and logic? Only if you narrowly restrict the system in which you're working...and even then it's a little iffy.