PutnamTalk060711 - 1 AN APPRECIATION OF HILARY'S...

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1 AN APPRECIATION OF HILARY'S MATHEMATICAL WORK philosophy in an age of science a conference in honor of Hilary Putnam's 85th birthday delivered June 1, 2011 revised June 7, 2011 1. Hilary 1964-65. 2. Hilary's work on Validity and Satisfiability. 3. Hilary's work on Integral Polynomials. 4. Hilary's other mathematical work. 5. Two controversial philosophy of mathematics papers by Hilary. 6. Evaluation of Hilary's work, and Hilary's new homework. 1. HILARY 1964-65. I met Hilary for the first time in Fall, 1964. At that time I was an entering 16 year old Freshman at MIT. I already “knew” Hilary from the MIT course catalog. Let me explain. I was deeply moved in high school by Bertrand Russell’s Introduction to Mathematical Philosophy, a book Russell wrote in jail in World War I. Hilary remarked that his productivity substantially increased after his retirement from Harvard as University Professor. Come to think of it, could it be that jail may also be a good environment for scholarly work? No teaching, no committee work, and no pressure to follow conventional academic wisdom! In the Russell book, the status of the Axiom of Choice relative to the other axioms of set theory was raised as a central open question. I decided then that I would work on this problem when I got to MIT. But I received the MIT course catalog, which contained the course description for an advanced course in the Spring 1965, mentioning “consistency and independence
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2 results of Paul J. Cohen concerning the Axiom of Choice and the Continuum Hypothesis”. Instructor: H. Putnam. So I realized that “my” problem was taken away. I wanted to meet this H. Putnam guy. I got an appointment with Hilary in the Fall of 1964 outside Walker Memorial, on the MIT campus. I had an “easy” question for Hilary. I told Hilary that I had read Bertrand Russell's Introduction to Mathematical Philosophy, and Inquiry into Meaning and Truth, and also Hilbert and Ackermann, Principles of Mathematical logic. I wanted to know how does logic start? I said logic appeared to be circular because of all this careful thinking involved in setting up logic. I.e., there seemed to be logic involved in starting logic - and I was confused by this. Hilary said I should look at the Rosenbloom and Smullyan books, and not be paralyzed by this circularity. He gave me the distinct impression that he was able to do logic even though it was circular! Of course, I did ask Hilary something really deep, and I hope no student comes to me with that question! I remember going home, I think, for Christmas vacation, and listening to a BBC interview with Bertrand Russell over the radio. It was a short interview, and I savored every word. I distinctly remember thinking - Hilary Putnam is going to
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This note was uploaded on 08/05/2011 for the course MATH 366 taught by Professor Joshua during the Fall '08 term at Ohio State.

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PutnamTalk060711 - 1 AN APPRECIATION OF HILARY'S...

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