Formalizability and Knowledge Ascriptions in Mathematical Practice
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 ro...
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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2009-10-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/231 |
| Summary: | 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 (*). |
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| ISSN: | 1281-2463 1775-4283 |