Added by: Fenner Stanley TanswellAbstract:
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 formatExport text citationView this text on PhilPapersExport citation in Reference Manager formatExport citation in EndNote formatExport citation in Zotero format
Added by: Franci MangravitiAbstract:
Logical nihilism can be understood as the view that there are no laws of logic. This paper presents both a counterexample-based argument in favor of logical nihilism, and a way to resist it by using Lakatos' method of lemma incorporation. The price to pay is the loss of absolute generality.
Comment: The paper is appropriate for any course discussing the monism vs pluralism vs nihilism debate in logic (or maybe even focusing on varieties of logical nihilism). On a technical level it requires no more than an introduction to formal logic; some familiarity with monist and pluralist positions is helpful for context.Export citation in BibTeX formatExport text citationView this text on PhilPapersExport citation in Reference Manager formatExport citation in EndNote formatExport citation in Zotero format