Mathematical Truth

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.

Some key works on these topics include the following: Carnap 1950; Benacerraf 1973; Putnam 1980; Field 1993; Field 1998; Wright & Hale 1992; Gödel 1964; Maddy 1988; and Maddy 1988.

Introductory works include Shapiro 2000 and Colyvan 2012.