[FOM] query on the history of the philosophy of mathematics: mathematics as formal
cdutilhnovaes at yahoo.com
Sun Mar 2 13:20:08 EST 2008
A while ago, we had a very interesting discussion within this list concerning the formalizable character of mathematics (which was meant to be captured by Chow's Formalization Thesis). Among other things, one interesting fact that emerged from the discussion was that some took being formal -- and thus formalizable -- as an essential feature of mathematics, while others insisted that actual mathematical practice goes much beyond what can be formalized into mechanically checkable proofs.
In this context, I now have a historical query: since when is it widely (even if not unanimously) held that what is distinctive about mathematics is its *formal* character? Who were the first people to hold such a thesis, and what were their underlying motivations? What was the 'pedigree' of the notion of formal in question: was it the Aristotelian form vs. matter distinction or the Platonic idea of Forms (or perhaps neither)?
Just to give an idea of what I'm after: in his excellent PhD dissertation, 'What does it mean to say that logic is formal?', John MacFarlane argues that the source of the idea that what is distinctive about *logic* is its formal character is to be found in Kant. I'm looking for a similar analysis concerning mathematics, so basically this is a query concerning the history of the philosophy of mathematics.
At the moment, I am working on the history of the notion of 'formal', in particular but not exclusively with respect to logic. So even though mathematics is not my main concern, I feel that my story would be missing an important piece if I did not at least mention the history of the attribution of formality to mathematics. So your help on this matter would be much appreciated!
Many thanks in advance,
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