[FOM] mathematics as formal

catarina dutilh cdutilhnovaes at yahoo.com
Thu Mar 6 08:21:12 EST 2008

Dear all,

Many thanks for the several informative and insightful replies to my query. At this point, my impression is that the attribution of formality to mathematics is a phenomenon much more recent than I had thought at first, apparently it only started with Hilbert and the formalist program. Kand did not think that math was formal, Bolzano did not think that math was formal, and (somewhat surprisingly) Frege did not think that math was formal. The first two authors explicitly attribute formality to logic but NOT to mathematics, but for different reasons.

And just a clarification, perhaps my original query was not sufficiently clear. There are two related but independent issues here: one issue is when mathematics became formal in OUR sense(s) of formal (e.g. mechanically checkable proofs, among others); the other issue, and the one I'm interested in at the moment, is when mathematics began to be seen as formal, in THEIR (i.e. past mathematicians and philosophers of mathematics) sense(s) of formal. The first issue concerns the philosophy and history of mathematics from the vantage point of OUR conceptual framework, while the second issue concerns the history of the philosophy of mathematics, i.e. how mathematics was viewed at different times from the vantage point of THEIR conceptual framework.

This being said, both issues are (equally) important, and can/should continue to be discussed here at FOM, if other FOM'ers are interested in them (and the moderator agrees, of course). I for one would be happy to hear more on both issues.



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