[HN Gopher] Philosophy of Mathematics - A Reading List (2020) ___________________________________________________________________ Philosophy of Mathematics - A Reading List (2020) Author : keiferski Score : 89 points Date : 2022-09-20 20:00 UTC (2 hours ago) (HTM) web link (www.logicmatters.net) (TXT) w3m dump (www.logicmatters.net) | steve_john wrote: | Koshkin wrote: | Why just quote Wikipedia? | Jtsummers wrote: | That's pretty much all their comments. Direct quotes from | something like Wikipedia, the article, or a paraphrased | version of a statement from the article. | mberning wrote: | It's kind of disappointing that history, philosophy, and | mathematics are not taught together. When you try to piece these | things together yourself you start to realize how much context | you miss out on when studying them in isolation. | Koshkin wrote: | It's not unusual for math books to include historical notes. | For example, _Elements de mathematique_ by N.Bourbaki includes | an entire companion volume, _Elements d 'histoire des | mathematiques_. | ouid wrote: | bourbaki is unusual among math textbooks, to say the least. | openfuture wrote: | The Dialogical Roots of Deduction[0] is an excellent book that I | was recommended by my math professor after making a comment about | how mathematics are a form of persuasion, not a religious truth. | It was refreshing to read something I could agree with so easily. | That being said, I think a lot of philosophy of mathematics is | not as insightful unless you also study mathematics. It is easy | to misunderstand or try to apply theorems incorrectly. | | 0: https://www.cambridge.org/core/books/dialogical-roots-of- | ded... | throwaway81523 wrote: | 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 | | Philosophy as an MO search keyword also finds interesting posts: | https://mathoverflow.net/search?q=philosophy | steppi wrote: | 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, many under the section on contemporary | developments. Smith's list also contains more recent works that | do not appear in Avigad's list. | zmgsabst wrote: | 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 | adamnemecek wrote: | Koshkin wrote: | There goes my evening... | morelisp wrote: | Smells like [?] to me. | adamnemecek wrote: | Which part? | morelisp wrote: | The part where you take a basic mathematical concept and | claim it solves all "meaning". | adamnemecek wrote: | It's not a basic concept. If you think it is you legit | don't understand it. | openfuture wrote: | Consider matrix bridge for those of us who will never use | discord? | Koshkin wrote: | This is great, this shows that philosophy of mathematics has a | long history and continues to be an active area of analytical | thought. (Judging by recent discussions, I believe that much of | the HN community desperately needs some education in this area.) | joe_the_user wrote: | _Modern philosophy of mathematics is still in part shaped by | debates starting well over a century ago, springing from the work | of Frege and Russell, from Hilbert's alternative response to the | "crisis in foundations", and from the impact of Godel's work on | the logicist and Hibertian programmes._ | | I wonder what the author thinks of Van Plato, The Great Formal | Machinery Works and other works on the history of the | foundational mathematics. | | One of the things that stands out in the book is that when | notions of mathematical logic and foundations of arithmetic were | being formulated by Frege and Grassman in the 19th century, | neither the notation nor the concept of proof as a mechanical | process existed and the process of creating theories about proof | processes also involved laying down the concept of proof and | creating tractable notations for it (Frege's original notation | quickly becomes incomprehensible as expressions grow, for | example). Principia Mathematica is notable for creating modern | notation despite it's failure to be a complete foundation of | mathematics. | valyagolev wrote: | Synthetic Philosophy of Contemporary Mathematics by Fernando | Zalamea | | for something very lively, contemporary and more continental in | spirit | fan_of_yoinked wrote: | This is great - I don't know if a full survey is in the cards for | me, but The Search for Certainty grabbed my eye. | | This reminds me of this guide | https://www.susanrigetti.com/physics for physics, and she has one | for self teaching math and philosophy as well. | | It makes me curious to see a similar reading list put together | for computer science - the history and theory of computing, or | the kinds of things you might generally study in a Comp Sci | program (as opposed to practical skills/how to types of reading) | dr_dshiv wrote: | Meh. No mention of Pythagoras or any Platonism. | | Max Tegmark, Karl Popper and Roger Penrose are the three best | known for promoting the Pythagorean-Platonic idea that | mathematics precedes matter. Because that seriously freaks some | people out--they can't even deal with the idea. But, fairly | basic, that triangles are transcendent and would exist in any | civilization, in any galaxy? Matter has never produced a perfect | sphere, but spheres are nevertheless truly real--- right? | silent_cal wrote: | Transcendent triangles... hm... | criddell wrote: | > Matter has never produced a perfect sphere, but spheres are | nevertheless truly real--- right? | | But doesn't Tegmark say matter _is_ mathematics? Or is that | your point? | chestervonwinch wrote: | parent is saying mathematics is the abstract base class. | they're in the source, but you never see instances of them at | runtime. | sbdaman wrote: | Edit: nevermind, this was overly critical. | goatlover wrote: | Platonism is a major school of thought in the philosophy of | mathematics. | virissimo wrote: | Not only that, but most philosophers who specialize in the | philosophy of mathematics are Platonists: https://philpaper | s.org/surveys/results.pl?affil=Target+facul.... IME, this | is also true of working mathematicians, but much less true | of physicists. | [deleted] | EpiMath wrote: | good comment. This seems to come up more in number theory than | in foundations/philosophy of mathematics, but I agree is has an | important place. Not just triangles, but natural numbers having | a fundamental place in reality ( e.g. integral numbers of | dimensions, degrees of equations at the foundations of physics, | etc., etc. Daniel Shanks has a list of about 60 of these | "arguments" for Pythagorean interpretation of numbers ) | anthk wrote: | Triangles' concept yes, in any of them, as long as you have two | dimensions. | tomrod wrote: | You can have triangles in higher dimensions, embedded in | manifolds or subspaces. | | You can have super pathological triangles in 1 and 0 | dimensions. Those aren't terribly interesting though. | steppi wrote: | There's an entire chapter devoted to Plato in Stewart Shapiro's | _Thinking About Mathematics_ , the first book the author | recommends. I think it's pretty reasonable to recommend people | start with an accessible contemporary survey rather than diving | directly into Plato's dialogues or any other particular primary | source. As far as I'm aware, Pythagoras left no written works | and would thus be unlikely to appear on a reading list. | Koshkin wrote: | Indeed! Abstractions deal with commonalities, and those do | exist. ("There _exists_ something in common between the three | horses and the three apples you want to treat the horses with. | ") | Barrin92 wrote: | the _notion of commonality_ exists in the head of the | observer because it 's a useful fiction. (even 'the horse' | itself is). But that is a subjective form of existence, what | Jakob von Uexkull called one's _" Umwelt"_ (the world as it | presents itself to you). There's no reason to believe it | precedes matter, or that triangles exist in a world without | anyone to conceive of them. | colechristensen wrote: | So much of it comes down to what exactly you mean by _exist_. | Which ultimately ends up being a boring disagreement. People | can have bigger or smaller definitions of what it means and | then have passionate disagreements with each other about what | fits inside which are ultimately about nothing but how big a | person prefers their definition. | Koshkin wrote: | Sure, there are many ways in which something may not exist; | but the _existence_ usually demonstrates itself in a pretty | straightforward way, like with the horse who bites you if | you show her that you have no more apples left. | colechristensen wrote: | Then you're painting yourself as one who has a certain | definition of _exist_ and can 't imagine other | definitions who would participate in such discussions | unwittingly about differences in definition rather than | the subject matter. | Koshkin wrote: | But it is _existence_ that is _the_ subject matter. | jonnybgood wrote: | As another comment said. What do you mean by exist? It | requires a little more rigour here. Using your example: What | does it mean for three horses and three apples to exist? | | The better question: What does it mean for three (of | anything) to exist? Why not one thing, one thing, one thing? | | The definition of existence you appear to be using is the | physical proximity of those objects. But even that can get | quite hairy. If there is two apples within inches of each | other and another apple 100 feet away, are there three apples | or two? The answer to this question depends on what you mean | by the existence of three apples. | sbdaman wrote: | Edit: replies are right! | mjh2539 wrote: | This would be considered an incredibly opaque | (and...particular?) introduction to the philosophy of | mathematics. | sbdaman wrote: | Fair enough. | silent_cal wrote: | I would venture to say that one of the most difficult | philosophy books of all time is not a good intro to anything, | lol | Koshkin wrote: | Not if you read it in German | [deleted] ___________________________________________________________________ (page generated 2022-09-20 23:00 UTC)