4 ms·

The stuff on that list all seems rather historical. I have no clue as to what is going on in the field in the current century, and the list doesn't seem to hel

The stuff on that list all seems rather historical. I have no clue as to what is going on in the field in the current century, and the list doesn't seem to help much. This was better: https://www.andrew.cmu.edu/user/avigad/Papers/PhilMath.pdf https://www.andrew.cmu.edu/user/avigad/Papers/PhilMath.pdf Philosophy as an MO search keyword also finds interesting posts: https://mathoverflow.net/search?q=philosophy https://mathoverflow.net/search?q=philosophy

zmgsabst 4y ago
I think the past 100 years are: “Algebra and geometry are the same?… Oh, our whole field is blind people describing elephants.” https://en.wikipedia.org/wiki/Blind_men_and_an_elephant https://en.wikipedia.org/wiki/Blind_men_and_an_elephant
- Koshkin 4y ago
  A.k.a. Algebraic Topology.
  - zmgsabst 4y ago
    Yeah — but we’re still digesting the impacts. Eg, you see that algebra and geometry “reappear” in things like computing — and the different perspectives of difference equations (geometry) versus typed statements (algebra). Or, in things like category theory giving a framework where we can “abstract” arguments from different (type) theories that are the same “shape” — which has connected a number of fields.
steppi 4y ago
Working through all of Peter Smith’s suggested books from the original post should give one a solid understanding of much of what’s been going on in field up until fairly recently. Every recommended book in Smith’s list from the original post up to and including Shapiro’s The Oxford Handbook of Philosophy of Mathematics and Logic also appears in Avigad’s suggested readings from your link, several under the section on contemporary developments. I think it’s a plus that Smiths list is more focused. Smith’s list also contains more recent works that do not appear in Avigad’s list.
- throwaway81523 4y ago
  Well, let's say I want purely to know what has been happening this century, i.e. from 2001 til today, treating anything earlier as general background knowledge (formalism vs platonism, etc.). I saw a few works in Smith's list that were published later than 2000, but didn't have any indication that they weren't primarily surveys of older work. The Oxford Handbook is from 2005 and it sounds like a survey. I don't see a date on Avigad's article but it does discuss some stuff that was contemporary at the time it was written, and some of the MO posts are quite recent and topical.
  - 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.
    - 4y ago

zmgsabst 4y ago

I think the past 100 years are: “Algebra and geometry are the same?… Oh, our whole field is blind people describing elephants.” https://en.wikipedia.org/wiki/Blind_men_and_an_elephant https://en.wikipedia.org/wiki/Blind_men_and_an_elephant

Koshkin 4y ago
A.k.a. Algebraic Topology.
- zmgsabst 4y ago
  Yeah — but we’re still digesting the impacts. Eg, you see that algebra and geometry “reappear” in things like computing — and the different perspectives of difference equations (geometry) versus typed statements (algebra). Or, in things like category theory giving a framework where we can “abstract” arguments from different (type) theories that are the same “shape” — which has connected a number of fields.

steppi 4y ago

Working through all of Peter Smith’s suggested books from the original post should give one a solid understanding of much of what’s been going on in field up until fairly recently. Every recommended book in Smith’s list from the original post up to and including Shapiro’s The Oxford Handbook of Philosophy of Mathematics and Logic also appears in Avigad’s suggested readings from your link, several under the section on contemporary developments. I think it’s a plus that Smiths list is more focused. Smith’s list also contains more recent works that do not appear in Avigad’s list.

throwaway81523 4y ago
Well, let's say I want purely to know what has been happening this century, i.e. from 2001 til today, treating anything earlier as general background knowledge (formalism vs platonism, etc.). I saw a few works in Smith's list that were published later than 2000, but didn't have any indication that they weren't primarily surveys of older work. The Oxford Handbook is from 2005 and it sounds like a survey. I don't see a date on Avigad's article but it does discuss some stuff that was contemporary at the time it was written, and some of the MO posts are quite recent and topical.
- 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.
  - 4y ago