Full textRead freeBlue print
Müller-Hill, Eva. Formalizability and Knowledge Ascriptions in Mathematical Practice
2009, Philosophia Scientiæ. Travaux d'histoire et de philosophie des sciences, (13-2): 21-43.
Added by: Fenner Stanley Tanswell
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 is true 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 (*) are not necessarily employed 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 (*).

Comment (from this Blueprint): Müller-Hill is interested in the question of when mathematicians have mathematical knowledge and to what extent it relies on the formalisability of proofs. In this paper, she undertakes an empirical investigation of mathematicians’ views of when mathematicians know a theorem is true. Amazingly, while they say that they believe proofs have an exact definition and that the standards of knowledge are invariant, when presented with various toy scenarios, their judgements seem to suggest systematic context-sensitivity of a number of factors.

Export citation in BibTeX format
Export text citation
View this text on PhilPapers
Export citation in Reference Manager format
Export citation in EndNote format
Export citation in Zotero format
Share on Facebook Share on LinkedIn Share by Email

Leave a Reply

Your email address will not be published.