half-baked ideas about philosophy of math
introduction
I. orientation: explaining a practice rather than interpreting mathematical statements
1) Burgess'
dilemma and Wittgenstein's point
about philosophical interpretation of math
2)difference between assertability conditions and truth conditions (Goldfarb's problem
about p or ~p)
II. the theory
3) Language -> produces trivial necessary truths of logic as artifacts \-> pretend
there is a domain of mathematical objects and we know certain things about them
(which things we pretend depends on our various empirical needs, these are often
chosen to be abstractions of useful things)
4)why this isn't standard deductivism
III. some apparent problems
5) the compelling force of logic/quine's argument
that logic can't be conventional
6) necessary applications of math
7) contingent scientific applications: quine's
indispencibility argument; the in-the-story test and the project of giving a
causally/counterfactually complete account of reality ,
mathematical simplicity and a priori probability
IV. normativity and epistemology
8)how we know things about our own linguistic practices,
math's a priority, a radical proposal,
grasping in a flash ,
and E. Chudnoff's content objection
9) normativity with respect to special criteria, not some
amount of general normativity
Extra Stuff:
the problem of logical omniscience
learning mathematical facts from physics and physical facts from math
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