On Wed, Sep 12, 2012 at 7:50 AM, Paul Tanner <firstname.lastname@example.org> wrote:
<< snip >>
> I also said that this does not show that repeated addition is what > multiplication *is*, and that it actually shows the opposite, which is > that it is simply a property or model of multiplication. >
There is no showing what multiplication *is*. There is no one thing or essence of *isness* and none such is necessary for mathematics.
There are some inferior brands of philosophy that insist on "essences" and "isnesses" but they're not usually considered among the more refined flavors. They come across as too "dark ages".
Mathematics got a shot in the arm from the Vienna Circle, more than from Bourbaki I would hazard.
On other lists, were we look at the philosophy of mathematics in more depth, I still see Wittgenstein's star rising, after an early period where commentators needed to dismiss his contributions to that field (a defensive maneuver).
Without help from the philosophers, I don't think we'd be able to continue our efforts to crack open prison-infotainment complex (Haim's "mafia") and insert newer content. As it is, I'm seeing the infusion of new geometric ideas helping improve prospects for many student-prisoners.