Summary |
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. |