Formalizability and Knowledge Ascriptions in Mathematical Practice
Eva Wilhelmus

Abstract:
We investigate the truth conditions of knowledge ascriptions for the
case of mathematical knowledge. The availability of a formalizable
mathematical proof appears to be a natural criterion: (*) X knows that
p iff X has available a formalizable proof of p.  Yet, formalizability
plays no major role in actual mathematical practice. We present
results of an empirical study, which suggest that certain readings of
formalizability criteria like (*) are not necessarily applied by
mathematicians when ascribing knowledge. Further, we argue that the
concept of mathematical knowledge underlying the actual use of 'to
know' in mathematical practice is compatible with certain
philosophical intuitions, but seems to differ from philosophical
knowledge conceptions underlying (*).

Keywords: philosophy of mathematics;  epistemology;  mathematical knowledge