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Best Anglophone philosophers of mathematics post-1945: some help sought in compiling the list

Brian Leiter

Next up in our series of poll is philosophy of mathematics.  As before, what are wanted are philosophers of mathematics whose major contributions were post-1945 and written in English; among living philosophers, they must be at least 60 in 2016.  Here's an initial list:

Paul Benacerraf

George Boolos

John P. Burgess

Rudolf Carnap

Charles Chihara

Michael Detlefsen

Michael Dummett

Solomon Feferman

Hartry Field

Kit Fine

Michael Hallett

Geoffrey Hellman

Carl Hempel

Georg Kreisel

Penelope Maddy

D. Anthony (Tony) Martin

Charles Parsons

Hilary Putnam

W.V.O. Quine

Michael Resnik

Stewart Shapiro

Wilfrid Sieg

William Tait

Hao Wang

Hugh Woodin

Crispin Wright

I'd welcome additions (or corrections).  Thanks.

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43 responses to “Best Anglophone philosophers of mathematics post-1945: some help sought in compiling the list”

  1. Sean Matthews

    Saul Kripke, Kit Fine?

    BL COMMENT: Kit Fine is on the list. Do others consider Kripke a philosopher of mathematics?

    Reply
  2. Sean Matthews

    Per Martin-Löf?

    Reply
  3. Daryl J Sidle

    Mark Steiner
    Imre Lakatos
    Arend Heyting
    Eric Reck
    Ken Manders
    Van McGee
    Dan Isaacson
    Harold Hodes
    Mark Balauger

    Are you sure the living philosophers on this list are all over 60?

    Reply
  4. Oliver

    Saul Kripke, Haim Gaifman, Mark Steiner, Dan Isaacson

    Reply
  5. Christopher Hitchcock

    Kurt Godel
    Arend Heyting
    Haskell Curry
    Mark Steiner
    Philip Kitcher
    David Lewis
    Eugene Wigner
    Ken Manders
    Emily Grosholz

    Reply
  6. Daryl J Sidle

    Woops
    Reck and Belauger are under 60.
    Sorry

    Reply
  7. Aaron Thomas-Bolduc

    Do you want to include people in maths departments who do lots of work with philosophers/philosophical work on foundations? If so,
    Hugh Woodin and Philip Welsh are both over 60.

    BL COMMENT: Hugh Woodin is already on the list, and he is also appointed in philosophy at Harvard. I certainly want to include folks in mathematics departments as long as they are recognized by philosophers as contributors to philosophy of math. It's the border between philosophy of math and logic and mathematics generally that I'm not very good at gauging.

    Reply
  8. Aaron Thomas-Bolduc

    Then certainly Philip Welsh, and maybe also Joel David Hampkins, though he may be too young – I can't tell.

    Additionally, Ed Zalta seems to qualify.

    BL COMMENT: Thanks, what do others think? Also, anyone know about the ages?

    Reply
  9. Oliver

    Some published works by Kripke in the philosophy of mathematics:

    Free choice sequences: A temporal interpretation compatible with acceptance of non-constructive mathematical proofs (forthcoming issue of Indagationes Mathematicae devoted to Brouwer's work).
    The Road to Gödel (2014).
    The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Incompleteness Theorem (2013).
    The Collapse of the Hilbert Program” (abstract 2009, full paper forthcoming).
    Wittgenstein on Rules and Private Language (1981).

    Kripke has also given lectures on our concept of number (recently at Oxford) and of the ordered pair.

    Reply
  10. RPC

    Bob Hale

    Reply
  11. Sean Matthews

    Peter Aczel

    Reply
  12. Lisa Warenski

    Joel David Hamkins is not over the age of 60. There is a celebratory conference in honor of his 50th birthday on March 11. Here is a link: http://nylogic.org/set-theory-day

    Reply
  13. Daniel Nagase

    Mary Tiles and Craig Smorynski

    Reply
  14. Brian Leiter

    Let me note that if others disagree that some of the prior suggestions really count as philosophers of math, please feel free to note that, though explain why. Thanks.

    Reply
  15. Curtis Franks

    Some others:

    William Lawvere
    Colin McClarty
    Dana Scott
    Alanzo Church
    William Thurston
    Yehuda Rav
    Harvey Friedman
    Jeremy Gray
    Warren Goldfarb
    Judith Grabiner
    Reuben Hersh
    Edward Nelson
    Martin Gardner

    Reply
  16. Felipe

    Michael Resnik?

    BL COMMENT: He's already on the list!

    Reply
  17. Matt

    The line between mathematical logic, philosophy of logic, and philosophy of mathematics isn't always completely clear, but I'd think that Burton Dreben should be on the list. Goldfarb is over 60, so should be on the list for sure. Though I suppose he's unlikely to rank _very_ high, Bill Ewald is a very good philosopher of Mathematics and is, I think, over 60. (At least, he graduated from college in 1976, which probably makes him over 60.) I'm pretty sure that Scott Weinstein is over 60 as well. (At least, he published a paper in Nous in 1974, so unless he did that when he was 17 years old, he must be over 60.) (Maybe even more so than with Dreben, the line here between philosophy of mathematics and mathematical logic is a close one, where others can make a better judgement call, but I'd put him in.)

    Reply
  18. cat theory

    John Conway and William Craig

    A shoutout to category Theorists might also deserve mention, Saunders Mac Lane, Steve Awodey, Hans Halvorson (and almost surely others).

    BL COMMENT: Living philosophers must be at least 60 in 2016 to be eligible, some of these folks are plainly not.

    Reply
  19. Prabhu (math)

    If logicians and set theorists (like Woodin) are permitted, then we should include:

    Alonzo Church
    Kurt Godel
    Paul Cohen
    Saharan Shelah

    Reply
  20. JamieM

    Neil Tennant

    Reply
  21. moses88

    Saul Kripke
    Kurt Gödel
    Mark Belaguer

    Reply
  22. David

    These are more mathematicians than philosophers, but:

    Alfred Tarski (he was doing significant work well past 1945, even if his major contributions in foundations were earlier)
    Stephen Kleene
    Raymond Smullyan
    Martin Davis

    Reply
  23. Daniel Nagase

    A couple of others I haven't seen mentioned:

    William Demopoulos
    Evert Beth
    Jaakko Hintikka
    Neil Tennant
    Hourya Benis Sinaceur
    Akihiro Kanamori
    Göran Sundholm

    Is José Feirrós over 60? If so, he would certainly qualify.

    Reply
  24. Juliette

    It is spelled Philip Welch. Also, Penelope Maddy, Bill Tait, Tony Martin, John Steel, Menachem Magidor.

    BL COMMENT: Maddy, Tait and Martin are already on the list! Folks, please look at the list before posting names! And are folks like Steel really philosophers of math as distinct from logicians? Thanks.

    Reply
  25. Ed

    Arguably, Ian Hacking.

    BL COMMENT: What's the argument? That would help me decide, thanks.

    Reply
  26. Pablo Stafforini

    Mark Balaguer, which two people nominated, is only 52.

    http://lmgtfy.com/?q=Mark+Balaguer

    Reply
  27. Prabhu (math)

    It seems to me that it would be beneficial to distinguish philosophers of mathematics from those working in mathematical logic and set theory. For example, Woodin's work on set theory is so technical that few people, even within mathematics, would have a chance at understanding it. His courtesy appointment in philosophy notwithstanding, to my mind, his work falls squarely within technical mathematics. Kurt Godel and Paul Cohen both proved highly technical results (the incompleteness theorems and the independence of the continuum hypothesis via forcing, respectively), but their results have more direct and enormous implications for the philosophy of mathematics. So, while Godel and Cohen fall at the intersection of logic & set theory and the philosophy of mathematics, the inclusion of Woodin feels strange. Same with Edward Nelson, John Steel, and Saharon Shelah (who, along with Woodin, is considered among mathematicians to be one of the greatest living set theorists).

    Also, some of the logicians on the list above are more well-known (Smullyan, Martin Gardner), especially with the many books they have written for a popular audience, but if "major contributions" is to be interpreted in a technical sense, then they are not (in my view) in the same category as Godel, Church, Cohen, etc. And William Thurston, listed above, was a geometer and topologist, not a logician; indeed, his Fields Medal was awarded for contributions to geometry and topology.

    I guess I'm suggesting that it might be better to have a poll on philosophers of mathematics while (to the extent possible) excluding mathematical logicians and set theorists whose work is too technical to be appreciated, except by a very few others in logic and set theory.

    One way to capture the distinction I'm making is to ask if the researcher's work is likely to be understood by those working within the philosophy of mathematics whose primary appointment is in philosophy departments. So, while Paul Bencerraf's work would be accessible to other researchers in the philosophy of math, perhaps Woodin's work would largely not be so accessible except to those working in set theory within math departments.

    Reply
  28. Matt

    On Hacking, he recently published a book on the philosophy of mathematics called _Why Is there Philosophy of Mathematics at All?_. It looked interesting but I haven't read it. The one short review I've seen (can't remember where) was luke-warm. Depending on how broad a reach one wants to give to "philosophy of mathematics", I suppose that his work on probability chance could fit. I'm not sure what experts in the field would say.

    Reply
  29. Kyle Walker

    I think people are only seeing the partial list in the blog preview on your main page. That is why they are naming people already on the list.

    Reply
  30. Brian Leiter

    I guess if they click straight to the comments, that's right.

    Reply
  31. David Gordon

    Here are some suggestions, with links to what each has written:
    Ian Hacking wrote The Logic of Statistical Inference, which I think has been influential. Also, he has written a book on phil of math http://www.amazon.com/Why-There-Philosophy-Mathematics-All/dp/1107658152/ref=sr_1_10?s=books&ie=UTF8&qid=1457107238&sr=1-10&keywords=ian+hacking

    J.R. Lucas has written this; http://www.amazon.com/Conceptual-Mathematics-International-Library-Philosophy/dp/0415513723/ref=sr_1_8?s=books&ie=UTF8&qid=1457107642&sr=1-8&keywords=j.r.+lucas

    Judson Webb has written http://www.amazon.com/Mechanism-Mentalism-Metamathematics-Finitism-Synthese/dp/904818357X/ref=sr_1_1?s=books&ie=UTF8&qid=1457107776&sr=1-1&keywords=judson+webb+mechanism

    James Franklin has written http://www.amazon.com/Aristotelian-Realist-Philosophy-Mathematics-Structure/dp/1137400722/ref=sr_1_4?s=books&ie=UTF8&qid=1457107847&sr=1-4&keywords=james+franklin

    James Robert Brown has written http://www.amazon.com/Philosophy-Mathematics-Contemporary-Introduction-Introductions/dp/0415960479/ref=sr_1_1?s=books&ie=UTF8&qid=1457108079&sr=1-1&keywords=james+ andhttp://www.amazon.com/Platonism-Naturalism-Mathematical-Knowledge-Robert/dp/1138809772/ref=la_B001H6SAOO_1_1?s=books&ie=UTF8&qid=1457108142&sr=1-1

    Reply
  32. Ed

    Re Hacking: His work on probability and statistical inference is mostly historical but of philosophical interest. His latest book about philosophy of mathematics (a fun read), is concerned with why and how math raises philosophical responses rather than with defending views about hard core issues in philosophy of mathematics.

    Reply
  33. David

    Probably any mathematicians whose work did not appeal to, or was known by, philosophers, should not appear on the list of nominees, but I don't think that is true for most of those listed. In any event, ultimately Brian will be conducting a poll, and presumably most of those polled will fall on the "philosophy" side of the line, and so the final ranking should provide the distinction you seek.

    Oh, another name, which I add kind of reluctantly: Errett Bishop

    Reply
  34. Anon Graduate Student

    I'm not a specialist myself but I've heard specialists in philosophy of math highly recommend the work of John Bell at Western. I believe he qualifies as over 60, but much of his work is in mathematical logic.

    Reply
  35. KY

    Grigori Mints?

    Reply
  36. KM

    Really Surprised Stephen Yablo hasn't come up!

    BL COMMENT: I do not believe he's 60 yet, but am happy to be corrected. I also would not have thought of him as a philosopher of math.

    Reply
  37. LEJ

    Emily Grosholz
    Paolo Mancosu
    Marco Panza

    BL COMMENT: Are any of these folks over 60?

    Reply
  38. anonymous grad student

    I have no idea how he would do in the poll, but Jody Azzouni should probably be added to the list…

    BL COMMENT: He's not over 60. There is an age cut-off for living philosophers!!!

    Reply
  39. Juliette

    Woodin, Steel and Shelah are doing fundamental work that will/has completely changed our view of, e.g., mathematical existence, through the investigation of questions like whether there is an intended model of set theory—just the question that Goedel was concerned with. In model theory Shelah has vastly deepened our understanding of fundamental notions like completeness and categoricity. His Main Gap theorem is a monumental achievement, that can be viewed as a fulfillment (arguably) of the Hilbert Program.

    The Main Gap theorem presents the following dichotomy: countable first order theories are either "classifiable", which means that they have relatively few models and admit geometric invariants like the dimension of the basis of a vector space. Or in the nonclassifiable case they have the maximum number of models possible, and these models are very entangled, i.e. they are very hard to distinguish the one from the other.

    The work of Steel and Woodin is of course very technical, though the time will come when an emphasis on exposition rather than breaking new ground will make these results accessible where now they are beyond the grasp of most of us. Asa Hirvonen gave a proof of the Main Gap on last summer's Scandinavian Logic Society Summer School in Logic, in Helsinki. (Ok, leaving out some details!)

    Reply
  40. anon

    um. https://en.wikipedia.org/wiki/Jody_Azzouni

    BL COMMENT: Thanks, assuming that's correct.

    Reply
  41. Juliette

    Typo in the above: The work of Steel and Woodin is beyond the grasp of MANY of us.

    Reply
  42. Matt

    I had somehow thought he was on the original list, or I would have mentioned him before, but I'd think that Imre Lakatos should be included, for his book _Proofs and Refutations_. I'm certainly not an expert in the field, and I'm not sure how much influence it has had, but it always struck me as very interesting and rich.

    Reply
  43. Allen Hazen

    Maybe not at the VERY top od the list, but somewhere on it, W.D.Hart?

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