THOUGHTS ON TRUTH THE TWO QUESTIONS OF MATHEMATICAL PHILOSOPHY –“If you ask a p

https://www.dpmms.cam.ac.uk/~wtg10/philosophy.htmlMORE THOUGHTS ON TRUTH

THE TWO QUESTIONS OF MATHEMATICAL PHILOSOPHY

–“If you ask a philosopher what the main problems are in the philosophy of mathematics, then the following two are likely to come up: what is the status of mathematical truth, and what is the nature of mathematical objects? That is, what gives mathematical statements their aura of infallibility, and what on earth are these statements about ?” —

ON THE PAPER

Nothing new or interesting. I still can’t figure out if the problem of what mathematicians consider ‘arbitrary precision’ is one that they are conscious of or not. (Correspondence and utility in context. )

What I can tell you is that mathematicians do not define truth, that philosophers do. Conversely, the craft of math requires a language for the production of proofs that humans can manipulate symbolically. Just like we need language that humans can speak and use, not language which would be more ‘true’.

However, if at some point we want to test whether our mathematics or our language is in fact ‘true’ – in that whatever content we construct corresponds to reality – we must be able to express it in operational language. If we cannot, then it is not in fact ‘true’. I can tell a story about a fantasy world with a certain form of gravity. I can write a proof using certain assumptions. However, these cannot correspond to reality, and therefore, can be consistent with their definitions (internally consistent) but they cannot ever be ‘true’ (correspondent).

This is important otherwise truth has no meaning, and reality is indistinguishable from dream.

More later.