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Very helpful answer, thank you! I suspected that it has something to do with "Tarski's definition of truth", but there seem to be different ideas around about w
by auggierose 5y ago
Very helpful answer, thank you! I suspected that it has something to do with "Tarski's definition of truth", but there seem to be different ideas around about what this means. While Wikipedia agrees with yours, I can point to at least one popular book ("An Introduction to Mathematical Logic" by Richard E. Hodel) that equates Tarski truth just with model theoretic truth.
I wouldn't fire the analyst in your example, by the way, because the fault would be mine: I should have just specified what complexity bound would be acceptable in a termination proof of the algorithm for it to be practical for my purposes.
- rssoconnor 5y agoI guess Tarski's definition of truth is relative to some interpretation, but the usual unqualified version of his definition is implicitly relative to the standard model of natural numbers. (Edit: or maybe it is me who is using the notion of Tarski's definition of truth incorrectly.)
- rssoconnor 5y ago> I wouldn't fire the analyst in your example, by the way, because the fault would be mine: I should have just specified what complexity bound would be acceptable in a termination proof of the algorithm for it to be practical for my purposes. I thought someone might say something like this. My counter is that if the analyst just used a normal proof system (i.e. one that doesn't assume false (in the standard model) axioms) then we could use Goedel's Dialectica [1] to mine the proof for some (probably crappy) complexity bound. That said, this is getting close to the edge of my knowledge on this subject. [1] http://math.stanford.edu/~feferman/papers/dialectica.pdf http://math.stanford.edu/~feferman/papers/dialectica.pdf