Rupert wrote: > > As I said, Nam Nguyen seems to be using "absolute truth" to mean > "something that is true independently of which semantics we use".
Imho, formally, it's near impossible to *directly* define "absolute truth". On the other hand, if we *indirectly* define it as: anything that is relative is not absolute, then we have a good chance to indirectly understand "absolute truth". And relativity is something we could easily define up-and-down the ladder of mathematical introspection. For instance, the truth of 1 + 1 = 0 is relative to what formal system we choose, hence it can't be an absolute truth. Or the truth of (x=x) would depend on what logical system that's being assumed, hence it's not an absolute truth. etc...
Imho, mathematical relativity could be grouped into 2 groups:
a) interpretation/semantic-based relativity: this is when a truth value would depend on a reasoning being's (model) interpretation, or (semantic) interpretation.
b) knowledge-based relativity: this is when knownability of the truth value would depend on the knowledge on the reasoning being. For instance, without loss of generality, let's k be a number so big that Prime(k) is unknown to human being, then Prime(k) is knowledge- relative. (If the theory is PA, then it's possible that PA can be inconsistent and in which case Prime(k), for there would be no model. But PA's shortest inconsistency-proof might be even longer than proof of Prime(k). Hence "Prime(k) is true" is a knowledge-based relative truth.)
And again, the truth that is relative is not an absolute truth.