eli_sennesh comments on Deliberate Grad School - Less Wrong

22 Post author: Academian 04 October 2015 10:11AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (153)

You are viewing a single comment's thread. Show more comments above.

Comment author: [deleted] 11 November 2015 03:03:32AM 0 points [-]

That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts

Who said that? Actual formal systems run on a coherence theory of truth: if the theory is consistent (and I do mean consistent according to a meta-system, so Goedel and Loeb aren't involved right now), then it's a theory. It may also be a totally uninteresting theory, or a very interesting theory. The truth-maker for a mathematical statement is just whether it has a model (and if you really wanted to, you could probably compile that into something about computation via the Curry-Howard Correspondence and some amount of Turing oracles). But the mere truth of a statement within a formal system is not the interesting thing about the statement!

Comment author: TheAncientGeek 14 November 2015 03:27:15PM 1 point [-]

Who said that?

Who said that CToT motivates mathematical Platonism, or who said that CToT is the outstanding theory of mathemtaical truth?

Actual formal systems run on a coherence theory of truth: if the theory is consistent (and I do mean consistent according to a meta-system, so Goedel and Loeb aren't involved right now), then it's a theory. It may also be a totally uninteresting theory, or a very interesting theory. The truth-maker for a mathematical statement is just whether it has a model (and if you really wanted to, you could probably compile that into something about computation via the Curry-Howard Correspondence and some amount of Turing oracles). But the mere truth of a statement within a formal system is not the interesting thing about the statement!

I couldn't agree more that coherence is the best description of mathematical practice.

Comment author: [deleted] 15 November 2015 09:53:09PM *  1 point [-]

who said that CToT is the outstanding theory of mathemtaical truth?

This one.

Or rather, who claimed that the truth-makers of mathematical statements are physical facts?