News and views about philosophy, the academic profession, academic freedom, intellectual culture, and other topics. The world’s most popular philosophy blog, since 2003.
“Freedom’s just another word for Je est un autre.”
Touché. And given the present thread, Rimbaud may have arrived rather more punctually than either of us had any right…
Correction to my post: it should have read “when I went to her home last summer”.
I first met Gabriele Taylor when I was a graduate student in philosophy at St. Anne’s, studying for the B.Phil.…
Dear Roger of Invisible America, Your remarks towards the end of this comment about Nat Goldhaber (I’ve got a friend…
A remembered Dreyfus remark on the Maharishi: I recall hearing Dreyfus say in a recorded lecture, perhaps twenty-five years ago,…
I just published in the new PPA and can say it was one of the most difficult, rigorous R&R’s of…
Professor Benacerraf, who was emeritus at Princeton (where he was educated and spent his entire career), was a leading figure in philosophy of mathematics, and also supervised many of Princeton's best-known PhD graduates over a half-century on the faculty. Comments are open for remembrances from those who knew Professor Benacerraf or for those who wish to comment on the significance of his work.
(Thanks to Stephen Stich for the information).
Paul was the informal second member of my dissertation committee at Princeton. He was absolutely invaluable, a relentless critic, but always kind and hilarious. Once, early on, I sent him a draft of a paper and received back one so covered with red ink that you couldn't read the text. Embarrassed — part of an ongoing feeling that I was class-wise out of place in philosophy — I fixed all the typos (that I could find) within a couple of hours and sent it back to him with 'Hey Paul, here's a version with hopefully less typos''. He wrote back immediately 'Fewer. It's a count noun.' What a banger of a crack.
We spent a lot of time together, talking philosophy, cooking, and gabbing. His art collection (and knowledge) was outstanding, though a delightful mix of incredible museum pieces and stuff he'd picked up at an art fair by some kid that he had just taken a fancy to. I couldn't imagine graduate school or where I am now without him. He'll be sorely missed, by me and by those who knew him.
His thesis Logicism: Some Considerations was never published, apparently because it contains a formal system that is inconsistent. But it remains one of the best things ever written on the topic.
I am interested that you say that. I took the seminar based on it in the Spring of 1961 and thought it was wonderful. It was am amazing seminar, officially an undergradute course, Philosophy 314, but containing some great graduate students such as Bob Nozick and Alvin Goldman, along with other undergrads such as George Boolos. That course led me to write a senior thesis with Paul the next year, where I got just the kind of criticism that Jack Woods describes. That experience changed my life. Had it not been for Paul's encouragement and insistence, and criticism, I never would have gone into academic life. He was a remarkable person, brilliant and tough, and caring.
He was a great guy, very kind to the grad students. I remember giving a presentation in his Frege seminar my first year, which was frankly a pretty poor quality performance from me. He acknowledged the work I'd put in in a supportive way, without trying to paper over the weaknesses in the finished product. It meant a lot to know that I'd be held to high standards and at the same time that not everything needed to be perfect in order for my professor to be "on my side." This was emblematic of how he was with students, in my experience.
I had the good fortune to be placed in Paul's first-year Frege seminar with Dave Baker, Lara Buchak, and Phil Rutherford. That window into Paul's long-lived grappling with logicism and the nature of math showed me what a worthwhile career in philosophy could be. It was an inspiration to see him still in the grip of problems that had gripped him as a student, immersed in untold sophistication, aware of so many false starts and missteps that lay before any of us who followed his lead, frank about his frustrations with the subject, wry enough to keep us honest, yet still kind and charming and good-humored, able to set it all out with a light heart while living a rich and cultured life. He was a mensch and a caring advisor, and I'll continue to remember him fondly for leading me gently down the rabbit hole.
Professor Benacerraf had such a profound influence on me that I included the following story verbatim on the public website of the company I founded in 1986:
“If you think back to the teachers who have had the most lasting influence on you, you may recognize that they were the ones who spoke to you as an individual and challenged you. In so doing, such teachers inspire not only the hard work necessary to succeed, but also its attendant long-term rewards of academic and personal development.
Decades ago, as a sophomore at Princeton University, a conflict in my class schedule prevented me from taking a graduate-level seminar that interested me deeply. The seminar, “Philosophy of mathematics,” was to be taught by the chair of the philosophy department, a legendary academic in the field. I approached the professor nervously and asked whether he would consider teaching me the course material one on one through weekly independent tutorials.
He startled me by agreeing immediately. Without question or hesitation, the chair of one of Princeton‘s most renowned departments had agreed to a semester’s worth of private tutoring for a 19-year-old he had only just met. I appreciated that this opportunity was special, but I did not realize how extraordinary it would prove to be.
A month later, when I handed in my first assignment, I thought it was quite good. “This paper won’t do,” I was told.
It won’t do? These are hard words for any student to hear, much less for one as devoted to academics as I was. But when my professor explained the paper’s major weakness — its tendency to survey technical material rather than to interpret it — I saw that he was right. It wouldn’t do.
My professor had challenged me. That challenge served as a catalyst for significant intellectual and emotional growth. While offering invaluable advice, clear instruction, and warm encouragement, he set a high bar for acceptable work. I worked harder on my three remaining papers than I had on any assignments in my academic career until that point. These later papers did, thankfully, meet with my mentor’s approval. In the years since then, this professor‘s personal and professional model has profoundly influenced the high standards I set for myself and for others.”
We stayed in touch over the years. I once asked him why he had agreed to teach me weekly one on one in the second semester of my sophomore year. His response was “3/4 of the students at Princeton are undergraduates so 3/4 of the reason I am here is you.”
Rest in Peace, Professor. I will think of you often, with ineffable respect and admiration, and always with fondness.
Paul was a wonderful friend and colleague. We overlapped for a few years on the faculty when I first arrived at Princeton, although it seemed like longer, because he was still very much a presence around the department for some years after he officially retired. I didn’t know Paul personally when I showed up, although I certainly knew his papers “Mathematical Truth” and “What Numbers Could Not Be,” two of the great papers of 20th century philosophy of mathematics, along with his co-edited and co-introduced (the introduction alone is well worth the cover price) collection with Hilary Putnam, _Philosophy of Mathematics: Selected Readings _. For decades, the latter was _the_ anthology for phil math (is it still? At any rate, it’s still in print, 60 years after the first edition appeared in 1964..).
I expected Paul to be a great philosopher, and he was. What I wasn’t expecting was how unbelievably kind he was to me, as well as to others. I arrived without tenure and was far from certain that I would be around for long, while Paul had been a central part of Princeton philosophy for many decades. But he went out of his way to make me feel welcome, both around the department and by inviting me over to his home for dinners (Paul was a great cook and once he realized how much I liked eating his steaks that was always the main course).
Paul came to Princeton as a younger than typical undergraduate in the late 1940s (!) and never left, doing his PhD here and then joining the faculty in 1960. He also served in the administration, at one point rising to the level of Provost. (Once we were walking by Princeton's “Class of 1952 Stadium’ and he casually said: “That’s the building that my class donated to PU.”) Paul loved Princeton, although he was not oblivious to its shortcomings, either past or present. Among philosophers that I know of, only David Kaplan at UCLA has had a longer continuous association with a single department. Warren Goldfarb who just retired from Harvard had a similar career to Paul’s in this respect.
Paul used to come to my graduate seminars and participate, which I found both very flattering and very helpful. His comments were always penetrating, as one would expect, but this many years later I only remember one particular reaction. I was talking about Paul Boghossian’s book _Fear of Knowledge_, and somewhat to my surprise, I found myself defending Richard Rorty against some of Boghossian’s criticisms. My thought was that B’s criticisms were in fact decisive against the position that he attributed to Rorty, but that there was a much more attractive and defensible relativist view in the neighborhood. Benacerraf had of course been colleagues with Rorty the entire time RR had been at Princeton, and so had experienced firsthand RR’s growing alienation from and ultimate break with analytic philosophy. Afterwards Paul came up to me to tell me that the view that I had sketched was in fact Rorty’s view, and that during the seminar “the whole thing started coming back to me all over again, like a bad nightmare!”
A final thought: most people who have read some of Paul’s work have read the two papers that I mentioned above, but the other ones are worth reading as well. There are no bad or even mediocre Paul Benacerraf papers. RIP.
Paul also chaired one of the committees that from time to time evaluate the Harvard Philosophy Department . He was deeply thoughtful about what this involved and what the committee should be trying to find out; he was deeply conscientious as we carried out our investigations, and then later as we worked over drafts of a report. He wanted the time and energy going into the evaluation to make a serious difference to how well the department functioned, especially for the students. One great pleasure of my academic career was being able to work with Paul on this and being able to see how much he cared not just about philosophy the subject but also about what mattered in the lives of those engaged with it.
Paul was one my two advisors. Dick Jeffrey was the other one, and that both of them would be central to my time at Princeton (1995-2000) was clear quickly. At the time, Dick was getting increasingly interested in collective decision theory, and I arrived with a background in game theory and social choice. I had never looked into one-person decision theory, which of course was Dick’s area, but that we both thereby took an interest in something the other was more knowledgeable about created a wonderful starting point for an incoming grad student. I was assigned to Paul’s first-year seminar on Frege. At the end of that seminar, he said to me “Whatever you do for your dissertation project, I want to be the second advisor,” in a humorous ambiguity that was so typical of Paul. But thereby my team was complete, and in fact, it was quite the dream team. Many years of observing other dissertation experiences have taught me how lucky I was with this combination of Dick Jeffrey and Paul Benacerraf. Dick wasn’t good at the routine craftwork of pushing someone through the process of writing a dissertation. I would not be surprised if there were parts of my dissertation that he never read because they didn’t interest him. But to those bits that he did relate, he connected with great intensity and passion. Sometimes I would wake up and find several emails on a dissertation chapter that I had given to him, emails he had written at different times during the night because he just couldn’t let go. For those chapters he was almost a co-author in the end (which we had been on several projects by that time anyway, so this felt like a natural experience). Paul was very different. There was never a sense that he and I would write anything together: Paul’s perfectionism wouldn’t allow for that, even if it had been a match otherwise, but at that stage much of his energy really was spent on working with grad students.(It was in the 60s that he revolutionized the philosophy of mathematics.) And he was just amazing at that. It didn’t always feel like that at the time, though, since he drove me crazy with demands for revisions, sometimes to such an extent that Dick intervened to tell him to leave me alone. But the intellectual growth that came through all his insistence that I really needed to write the best dissertation I could was one of the best things that ever happened to me. For a while a complex tree of squares and circles symbolizing my real and envisaged dissertation chapters was on Paul’s office blackboard. And a moment of enormous relief and plain joy came when he pointed out how some subset of those squares and circles would do for a PhD, which for the first time brought the end in sight very clearly. Ultimately this dissertation generated five publications in good journals, with far more limited revisions than I would routinely have to do later when I needed to learn how to write new projects without the Benacerraf-treatment. None of this would have happened without the Dick&Paul dream team.
I interacted with Paul in many other capacities: I was the TF for his the famous (or notorious?) Princeton grad student logic course 312, and sometimes in intense dreams I return to sitting somewhere in Firestone Library figuring out the Turing machines of students in this course. Paul also was a very broadly cultured person with many interests, ranging from art, architecture, and dance to cooking and good wines. A map of central Parise hung proudly in his kitchen, anchoring his French heritage. A small metal structure about the Frères Benacerraf that sat on Paul’s desk went back to a business these ancestral brothers once had there, before moving to Tetouan, before moving to Caracas, before sending young Paul and his olde brother Baruch to the US (Baruch, who would end up winning the Nobel Prize in Medicine). Paul carried around a Venezuelan driver’s license.
He was a philosophers’ philosopher, and then he was so much more. I was also the grad rep when Paul stepped down as chair, a role in which he was beloved to the grad student population. It was a great honor for me to be asked to give a speech on behalf on the grad students at his retirement. I’ve rarely gotten so invested in an occasion of that sort. But he deserved so much gratitude from all of us, and from me in particular – no effort would have been enough, but spending time on putting something together to express gratitude to someone to whom one owes so much is the best way of spending time. My feelings of gratitude are still what they were then. Paul truly has been one of the most important people in my life. It was a privilege to play a small role in his life.
I opened my contribution to the 1996 Benacerraf Festschrift of Adam Morton and Stephen Stich with,
“In early 1973 I had the chance to hear Paul Benacerraf speak on “Mathematical Truth” at Berkeley, where I was a senior. Although I already knew that his “What Numbers Could not Be” was an important paper, I also knew that his next article had offered an inconsistent set of axioms. Despite the distinguished company this put him in, I was unimpressed and stayed home.
Soon after arriving in Princeton that fall I started thinking about "Mathematical Truth" and have not yet stopped. It is one of the few deeply illuminating articles about Platonism of the past fifty years …”
I would now write: of the past eighty years.
In January 1976 I took my generals on Quine, with Paul, Gil Harman, and David Lewis as examiners. I had studied across philosophy of language, epistemology, metaphysics, philosophy of mind, also with a serious (though non-logician’s) interest in logic. Though I had audited Paul’s philosophy of mathematics seminar, and was of course taken, I did not aim to write in that area (though then some philosophy of mathematics did enter the dissertation). I had asked Paul to be my advisor not due to his specialization. Rather I felt Paul more than anyone else wanted to see to the bottom of things.
Paul was also exactly and uniquely the Doktorvater I needed for steps toward growing up as a writer, as a person. Of course I had not the least idea what I lacked, but perhaps I sensed something about Paul on this score too.
That summer he sent me a postcard from Paris. An artwork showing a hand (just a hand) holding a pen, writing the word 'ecrire'. On the back,
Dear Steve,
The message should be clear!
Paul
I am still trying.
Some years back I remarked to Paul that the modish skeptical (or, worse, “debunking”) invocations and applications of “Mathematical Truth” looked to me to have little to do with what was going on there, with its interest. Paul shrugged: “They can say what they like as long as they spell my name correctly.”
Any bottom we can find in philosophy is provisional and narrow, as Paul knew. Himself a gifted writer, he held T. S. Eliot in particular regard.
There is, it seems to us,
At best, only a limited value
In the knowledge derived from experience.
The knowledge imposes a pattern, and falsifies,
For the pattern is new in every moment
And every moment is a new and shocking
Valuation of all we have been. We are only undeceived
Of that which, deceiving, could no longer harm.
In the middle, not only in the middle of the way
But all the way, in a dark wood, in a bramble,
On the edge of a grimpen, where is no secure foothold,
And menaced by monsters, fancy lights,
Risking enchantment …
In a note in late 1976, while trying to understand something about set theory (that’s gotten no easier … ) I echoed the common view, “for any universe we describe we can always imagine a larger one.” Paul’s response in my margin: “Why? Or is that what it’s like to have your nose pressed against the candy store window?”
Vaya con Dios, fellow rationalist.
Your description rang familiar, Jack. I had no career goals and no dissertation to defend yet he was the same with me, with every idea I shared. I believe it was an intellectual reflex of his — to find from whatever angle an idea was vulnerable, and to get me (or you or us) to think critically about my own proposals. (Feel free to correct my grammar, Jack, it'll make me feel better.) Meeting him was kind of like stepping into the ring to wrestle the bear, (if you get the reference). Nobody ever wins the $50.
Your list of activities also sounds familiar. We laughed alot. & kind of like my Jewish grandma, he'd be disappointed if he couldn't cook for me. While he could still get around we'd meet at the Frick or Neue (in the neighborhood where he grew up), admire (or not, as the case may be) some piece, and what I remember was that he was knowledgable about art history but also very easy to be quiet around. We fixated on a piece of Delft: he knew and I knew how to shut up and wordlessly love something beautiful.
Good luck to you, Jack.
The article by Paul in the Festschrift you mentioned, "What Mathematical Truth Could Not Be – 1" was my (chronologically assbackwards) introduction to his work. It was the first work of philosophy of mathematics I'd tackled, as a matter of fact. I had a lot of trouble with it, as you can imagine, but the contours of profound ideas take shape there. He was, in retrospect, extremely patient with the overlong emails I sent, parsing out some fine points for me at a stage while I was missing some very big references. He was professional at directing my reading: the second thing I read was the 2nd edition of the Benacerraf/Putnam "Selections." Our more focused conversations were sprinkled in with a lot of schmoozing and pastrami and after a few years I probably got the rudiments of what you got in 1 seminar.
What makes my eyes water right now is his kindness, and the clarity in those exchanges. I had been used to being the smartest boy in the room, and found at 40 I was a disorganized, barely competent journeyman thinker, and his good humor and encouragement helped guide me into my deepest and perhaps best thinking. I underscore that there was no class, no department, no degrees involved – he did this for nothing, on his own time, out of love for the subject and generosity to me.
Maybe I shouldn't thank him: I spent almost 20 years contemplating Benacerraf's dilemma, trying from various directions to resolve the problem, or expose it as a pseudoproblem. I've banged my head against the identification problem (where "banging" means "will positive outer domain free logic or mereology help? Let me try…" "Will category theory help? Let me try…") off and on for years. I have no product to show for the effort. So is "true" philosophy — knotty, irritating questions that remain questions — a waste of time? (You may be able to read the hypocrisy between the lines. Of course I'm grateful.) "See to the bottom of things" is a fine way to express it, as well as acknowledging how narrow that solid bottom is. Maybe the human mind wasn't designed to stand there for any length of time.
It seems you and he had some similar conversations as he and I did on the critical reception of his articles. My assessments were similar. It's far easier to "disprove" Paul when you miss his point. (It's related to what HBloom called "misprision" in poetry, I think.) The difficulties his most influential work tries to get us to face head on are, I believe, part of the reason his work is not more widely known: by fighting a more tractable famous thinker (let's say Rorty, eg) some young academic could aspire to make a name for him- or herself. Or perhaps it was because Paul had zero interest in self-promotion. He never wrote 'the Book' that could build a brand and was insulated by tenure, self-confidence, etc from the need to. He just wrote when he had something to say. (What academic now can afford to do that?) I asked him where I could find his work online. (In those days nowhere.) He got out his cane, drove to the office, found his hand-typed pages and photocopied them one page at a time, put them in a manilla folder with stamps, drove to the post office, etc… for me to read some of his articles. Every single one of those essays was valuable; has something specific and a modality of thinking to teach; taught me something.
I hope we meet someday, Steven. There's always more to say.
For now: I'll miss him, too.
Marco –
You got it! "Mensch"! That was the word I was looking for!
& thank you for your description — quite astute.
You have the same impulse, I see, from your posting of the link. Paul's work is rewarding and speaks for itself.
The difficulty of finding his work prompted me to make a website, Paul Benacerraf dot com which, due to lack of significant file sizes (just word document versions of his articles) and lack of ad traffic did not meet the "well-made" criteria for SEOs. I was old-school, trying to share the essays for some abstract ideal, and thinking that his writings deserved accessibility.
I still think so.
Why is there no "Complete Works of Paul Benacerraf"? I can only think of bad reasons for the lack.
—–
KEYWORDS:
Primary Blog
Leave a Reply