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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 196465.
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 196465.
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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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
be the closest I will ever get to Bertrand Russell! This
turned out to be essentially true  I also met Kurt Gödel
in 1977.
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 Fall '08
 JOSHUA
 Math, Hilary Putnam, Hilary, HILARY'S

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