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It's cool that "Alex Knapp, a science writer at Forbes" has solved one of the major issues in the philosophy of mathematics by, erm, just asserting that Platoni

by voyou 13y ago

It's cool that "Alex Knapp, a science writer at Forbes" has solved one of the major issues in the philosophy of mathematics by, erm, just asserting that Platonism is false. Of course, maths is a tool, but that doesn't mean that it is just a tool, and Knapp doesn't provide any arguments for that conclusion. I can use a rock as a tool, but that doesn't mean the rock has no existence independent of my mind. In fact, the only reason the rock works as a tool is because it has an independent existence (I can hit things with it); the same might be true of maths. Now, there are arguments for positions like Knapp's, but they're more complicated and contested than Knapp's facile post suggests. See, for instance, this Stanford Encyclopedia of Philosophy article: http://plato.stanford.edu/entries/fictionalism-mathematics/ http://plato.stanford.edu/entries/fictionalism-mathematics/

magicalist 13y ago
Seriously. At least Leah Libresco had the intellectual clarity to declare herself a Platonist, as in, literally, a believer in or adherent to some part of Plato's philosophy. Knapp latches onto a lack of empirical evidence for a Platonist viewpoint (though narrowly defines evidence as apparently needing to be extra-human to be valid, which isn't a well founded definition, but, then again, definitions are the fundamental problem here), and so he concludes that it must therefore be false, completely missing his own point. Sorry. While there is a wealth of interesting discussion to be had on philosophy of mathematics, and even more discussion (and certainly more concrete discussion) to be had on the difference between how mathematics is actually created and how it is then defined in proofs and literature, this passage misses the boat. Also, spitx: while fair use covers quoting from and discussing articles quite well, quoting the full article, even with discussion, could be problematic and certainly should be considered poor form. Take some quotes and then link to the rest.
jules 13y ago
I find what's written on that page much more naive than Knapp's view. Knapp is not advocating fictionalism, i.e. that math has no meaning. He is advocating the opposite: math has meaning, but the reason is not some metaphysical mystery, it has meaning because it was constructed for that purpose. Knapp's view is much closer to what that page describes as physicalism, with the caveat that humans are not perfect so our math is not necessarily the same as alien math. That is also one of the instances where that page is so naive. It dismisses physicalism in a just a couple of words on the grounds that physicalism cannot explain infinities, especially very large infinities. But mathematicians themselves are divided on whether those are "real" or just an artifact of the axioms (see constructivism and more radically finitism). Another view that fits perfectly within physicalism is that infinities are just an approximation, a reasoning tool to simplify things.
sedachv 13y ago
> It's cool that "Alex Knapp, a science writer at Forbes" has solved one of the major issues in the philosophy of mathematics by, erm, just asserting that Platonism is false. And what is wrong with saying that? The burden of proof is on Platonists, just like it is on theists. I don't see any reason not to think that Platonism has been a huge waste of time.

by voyou 13y ago

magicalist 13y ago

Seriously. At least Leah Libresco had the intellectual clarity to declare herself a Platonist, as in, literally, a believer in or adherent to some part of Plato's philosophy. Knapp latches onto a lack of empirical evidence for a Platonist viewpoint (though narrowly defines evidence as apparently needing to be extra-human to be valid, which isn't a well founded definition, but, then again, definitions are the fundamental problem here), and so he concludes that it must therefore be false, completely missing his own point. Sorry. While there is a wealth of interesting discussion to be had on philosophy of mathematics, and even more discussion (and certainly more concrete discussion) to be had on the difference between how mathematics is actually created and how it is then defined in proofs and literature, this passage misses the boat. Also, spitx: while fair use covers quoting from and discussing articles quite well, quoting the full article, even with discussion, could be problematic and certainly should be considered poor form. Take some quotes and then link to the rest.

jules 13y ago

I find what's written on that page much more naive than Knapp's view. Knapp is not advocating fictionalism, i.e. that math has no meaning. He is advocating the opposite: math has meaning, but the reason is not some metaphysical mystery, it has meaning because it was constructed for that purpose. Knapp's view is much closer to what that page describes as physicalism, with the caveat that humans are not perfect so our math is not necessarily the same as alien math. That is also one of the instances where that page is so naive. It dismisses physicalism in a just a couple of words on the grounds that physicalism cannot explain infinities, especially very large infinities. But mathematicians themselves are divided on whether those are "real" or just an artifact of the axioms (see constructivism and more radically finitism). Another view that fits perfectly within physicalism is that infinities are just an approximation, a reasoning tool to simplify things.

sedachv 13y ago

> It's cool that "Alex Knapp, a science writer at Forbes" has solved one of the major issues in the philosophy of mathematics by, erm, just asserting that Platonism is false. And what is wrong with saying that? The burden of proof is on Platonists, just like it is on theists. I don't see any reason not to think that Platonism has been a huge waste of time.