The topic of mathematical truth is importantly tied to the ontology of mathematics. In particular, a central question is what kinds of objects we commit ourselves to when we endorse the truth of ordinary mathematical sentences, like ‘4 is even’ and ‘There are infinitely many prime numbers.’ But there are other important philosophical questions about mathematical truth as well. For instance: Is there any plausible way to maintain that mathematical truths are analytic, i.e., true solely in virtue of meaning? And given that most ordinary mathematical sentences (e.g., the two sentences listed above) follow from the axioms of our various mathematical theories (e.g., from sentences like ‘0 is a number’), how can we account for the truth of the axioms? And how can we account for the objectivity of mathematics (i.e., for the fact that some mathematical sentences are objectively correct and others are objectively incorrect)? Can we do this without endorsing the existence of mathematical objects? Do mathematical objects even help? And so on.
Analyticity in Mathematics
Objectivity Of Mathematics
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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