3 ms·

I think everything starting with the below paragraph of Smith’s article tries to give a decent answer to your question. As I said, I have surely provided more

by steppi 4y ago

I think everything starting with the below paragraph of Smith’s article tries to give a decent answer to your question. As I said, I have surely provided more than enough introductory reading! Still, let’s ask: what has been published since around the time of the Handbook which is both of note and is also reasonably accessible? There was a short collection edited by Otávio Bueno and Øystein Linnebo called New Waves in the Philosophy of Mathematics (Palgrave, 2009), which has moderate interest. Some of the papers collected in Paolo Mancosu (ed.) The Philosophy of Mathematical Practice (OUP, 2008) are worth reading. And of course, the journal Philosophia Mathematica continues to publish many good articles. But what of books? I’m not really up on the latest stuff myself, but like other fields, typically current research is published in journal articles and it takes time for developments to be synthesized into survey books. Then again, Smith seems to believe there’s been a lull in activity lately. My sense, though, is that after a period in which the philosophy of mathematics really flourished, there has perhaps been something of a lull more recently. However let me finish by mentioning a stand-out recent achievement, a little more wide-ranging than just philosophy of mathematics (though a considerably bumpier ride than perhaps the authors intended, so only just squeezing into what started out as an introductory list!) — namely Tim Button & Sean Walsh, Philosophy and Model Theory (OUP, 2018). The final version of Avigad’s article was published in The Edinburgh Companion to Twentieth-Century Philosophies in 2007. Based on the content I would place the version in your link to sometime in 2006.

throwaway81523 4y ago
Thanks. I'm pretty ignorant of the whole field beyond some old basic stuff. But there are contemporary issues that certainly must have drawn attention. E.g.: * natural language, cognition, and math. There is a book by Ganesalingam about this based on his PhD thesis, that was online a while back but was later taken down. * Philsophical aspects of complexity theory. Scott Aaronson and Avi Wigderson have both written about this. * Nonhuman cognition, AI being the closest to available. But would sufficiently smart fish or birds develop mathematics different from human math, given that their sensory systems must be a lot different from ours? * There is an article by Mirco Manucci that I thought was cool, but might be considered bogus by professionals, about ultrafinitistic model theory. I'd like to know if there is any other work in this area. * Other nontraditional logic like deep inference (http://alessio.guglielmi.name/res/cos/index.html http://alessio.guglielmi.name/res/cos/index.html) * I've looked at some stuff by J-Y Girard and can't tell what the heck it is about, but some of it has turned out to be important. Some more comprehensible treatments or criticism of his more recent works would help.

by steppi 4y ago

throwaway81523 4y ago

Thanks. I'm pretty ignorant of the whole field beyond some old basic stuff. But there are contemporary issues that certainly must have drawn attention. E.g.: * natural language, cognition, and math. There is a book by Ganesalingam about this based on his PhD thesis, that was online a while back but was later taken down. * Philsophical aspects of complexity theory. Scott Aaronson and Avi Wigderson have both written about this. * Nonhuman cognition, AI being the closest to available. But would sufficiently smart fish or birds develop mathematics different from human math, given that their sensory systems must be a lot different from ours? * There is an article by Mirco Manucci that I thought was cool, but might be considered bogus by professionals, about ultrafinitistic model theory. I'd like to know if there is any other work in this area. * Other nontraditional logic like deep inference (http://alessio.guglielmi.name/res/cos/index.html http://alessio.guglielmi.name/res/cos/index.html) * I've looked at some stuff by J-Y Girard and can't tell what the heck it is about, but some of it has turned out to be important. Some more comprehensible treatments or criticism of his more recent works would help.