To take a step back. the discussion is about mathematical Platonism, a theory of mathematical truth which is apparently motivated by the Correspondence theory of truth. That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts, not some special realm of immaterial entities. The relevance of my claim that there are unphysical mathematical truths is that is an argument against the second claim.
Lakoff and Nunez give an account of the origins and nature of mathematical thought that while firmly anti-Platonic doesn’t back a rival theory of mathematical truth, because that is not in fact their area of interest..their interest is in mathematical thinking.
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!
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.
To take a step back. the discussion is about mathematical Platonism, a theory of mathematical truth which is apparently motivated by the Correspondence theory of truth. That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts, not some special realm of immaterial entities. The relevance of my claim that there are unphysical mathematical truths is that is an argument against the second claim.
Lakoff and Nunez give an account of the origins and nature of mathematical thought that while firmly anti-Platonic doesn’t back a rival theory of mathematical truth, because that is not in fact their area of interest..their interest is in mathematical thinking.
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!
Who said that CToT motivates mathematical Platonism, or who said that CToT is the outstanding theory of mathemtaical truth?
I couldn’t agree more that coherence is the best description of mathematical practice.
This one.
Or rather, who claimed that the truth-makers of mathematical statements are physical facts?