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The Mexican Multiplier Trounces Dr. Evil in Large Number Duel

Submitted by Richard Zach on Thu, 02/01/2007 - 7:04pm

Agustín Rayo wins over Adam Elga, uses "googol" and a variant of Berry's paradox in knock-out punch: see here.

Dr. Evil clutched his heart as though it had been pierced by an arrow. Trembling, he fell to his knees on the floor of the crowded stuffy room, all eyes watching him. The Mexican Multiplier threw up his hands in victory, smiling, as Dr. Evil whispered, “I’ve been crushed.” The battle was finally over.

HT: Henri Galinon/Kai von Fintel

Gödel quote

Submitted by Richard Zach on Thu, 02/01/2007 - 6:29pm

Varol Akman kindly sent a link to this picture of the poster advertising the Gödel exhibition in Vienna, with the nice quote: "Today philosophy has arrived, at best, at the point mathematics was at in Babylonian times."

Jason Stanley coming to Calgary

Submitted by Richard Zach on Wed, 01/31/2007 - 9:02pm

Unfortunately, only for a talk: this Friday at 4, "Knowledge and Action," in SS 1253. He hasn't told us what specifically he will be speaking about, but I'm sure it's going to be excellent.

Quantifiers and Claims about the Inferiority of Women

Submitted by Richard Zach on Tue, 01/30/2007 - 4:09am

My colleague Elizabeth Brake pointed out to me a wonderful passage in the "1706 Preface" to Mary Astell's Reflections upon Marriage, in which she's criticizing William Nicholls' claim (in The Duty of Inferiors towards their Superiors, in Five Practical Discourses (London 1701), Discourse IV: The Duty of Wives to their Husbands), that women are naturally inferior to men. Shorter Astell: "You're supressing your quantifiers. Once you make them explicit, you're either committing treason or are stating the obvious." (Note that in 1706 England was ruled by Queen Anne.)

'Tis true, thro' Want of Learning, and of that Superior Genius which Men as Men lay claim to, she [the author] was ignorant of the Natural Inferiority of our Sex, which our Masters lay down as a Self-Evident and Fundamental Truth. She saw nothing in the Reason of Things, to make this either a Principle or a Conclusion, but much to the contrary; it being Sedition at least, if not Treason to assert it in this Reign. For if by the Natural Superiority of their Sex, they mean that every Man is by Nature superior to every Woman, which is the obvious meaning, and that which must be stuck to if they would speak Sense, it wou'd be a Sin in any Woman to have Dominion over any Man, and the greatest Queen ought not to command but to obey her Footman, because no Municipal Laws can supersede or change the Law of Nature; so that if the Dominion of the Men be such, the Salique Law, as unjust as English Men have ever thought it, ought to take place over all the Earth, and the most glorious Reigns in the English, Danish, Castilian, and other Annals, were wicked Violations of the Law of Nature!

If they mean that some Men are superior to some Women this is no great Discovery; had they turn'd the Tables they might have seen that some Women are Superior to some Men. Or had they been pleased to remember their Oaths of Allegiance and Supremacy, they might have known that One Women is superior to All the Men in these Nations, or else they have sworn to very little purpose. And it must not be suppos'd, that their Reason and Religion wou'd suffer them to take Oaths, contrary to the Laws of Nature and Reason of things. (iii-iv, and Astell: Political Writings, ed. Patricia Springborg, Cambridge University Press, 1996, 9-10)

Bullshit and Philosophy

Submitted by Richard Zach on Tue, 01/30/2007 - 3:34am

Open Court sent a couple of volumes from their Popular Culture and Philosophy series a few weeks back, but I've only now had time to read the intro to Bullshit and Philosophy. It's about bullshit, in particular, about Frankfurt's On Bullshit, and it's edited by Gary Hardcastle and George Reisch. Like I said, I've only read the intro so far, but it promises to be really interesting. I'm particularly looking forward to Gary's chapter on the Vienna Circle as an anti-bullshit movement, "The Unity of Bullshit."

Helvetica: A Semicentennial

Submitted by Richard Zach on Wed, 01/24/2007 - 3:44pm

Ok, this has nothing to do with logic, but it's so awesome that I have to post about it. Thanks to Lillian Lovich for sending the link!

Helvetica, the best font of all time, is turning 50 this year. There's a movie about the font coming out, which I'm really excited about.

Carnegie Mellon Summer School in Logic and Formal Epistemology

Submitted by Richard Zach on Tue, 01/23/2007 - 4:55pm

In the summer of 2007, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, and other sciences.

The goals are to

  • introduce students to cross-disciplinary fields of research at an early stage in their career; and
  • forge lasting links between the various disciplines.

The summer school will be held from Monday, June 11 to Friday, June 29, 2007. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events.

The summer school is free. That is, we will provide

  • full tuition, and
  • dormitory accommodations on the Carnegie Mellon campus.

So students need only pay round trip travel to Pittsburgh and living expenses while there. There are no grades, and the courses do not provide formal course credit.

Instructions for applying can be found on the summer school web page,

Materials must be received by the Philosophy Department by March 15, 2007.

This year's topics are:

Causal and Statistical Inference
Monday, June 11 to Friday, June 15
Instructor: David Danks

Logic and Formal Verification
Monday, June 18 to Friday, June 22
Instructor: Jeremy Avigad

Decisions and Games
Monday, June 25 to Friday, June 29
Instructor: Teddy Seidenfeld

The summer school is open to undergraduates, as well as to students who will have just received their undergraduate degrees. Applicants need not be US citizens.

Inquiries may be directed to Jeremy Avigad (

Of Names

Submitted by Richard Zach on Mon, 01/22/2007 - 7:52pm

I just had the following interesting exchange with my colleague Jack MacIntosh, in which every question was asked sincerely, and I have every reason to believe that Jack's statements were true:

RZ: Zeno and Plato were contemporaries, right?
JM: Yes, for a while.
RZ: Did Plato retire before Aristotle began his studies?
JM: About Aristotle, I don't know.
RZ: But Aristotle was never Plato's student, right?
JM: No, he wasn't. But Plato's favorite historical figure--whom he worked on and gave classes on--was Plotinus.

Tarski in the SEP

Submitted by Richard Zach on Mon, 01/22/2007 - 4:16pm

I totally missed it, but the first entry on history of logic in the Stanford Encyclopedia to be published since Paolo Mancosu and I signed on as subject editors has been published over two months ago: Mario Gómez-Torrente on Tarski.

Special Issue of Studia Logica on Applied Logic in the Philosophy of Science

Submitted by Richard Zach on Sun, 01/21/2007 - 7:11pm
Special Issue of Studia Logica
on Applied Logic in the Philosophy of Science

Guest editors: Igor Douven and Leon Horsten

Studia Logica is extending its scope. In future the journal will not only cover pure logic but also applications of formal-logical methods in philosophy and cognitive science. To mark this change, the journal will have several special issues, of which this is one.

Theme of the Special Issue

When logical empiricism declined, logic seemed to lose its role as the primary tool for investigating the methodology of science. Recently, logical methods in the philosophy of science have been making a comeback.

Recent developments of logical methods in areas outside of logic as it was traditionally conceived have excited new interest in the application of logic to methodological questions. New logical tools and methods are gradually being absorbed by the philosophical community and are being applied to specific problems in the philosophy of science. The proposed Special Issue intends to illustrate this new trend in the philosophy of science on the basis of exemplary instances.

The proposed theme is fairly open-ended, but contributions of the following sort fall squarely within its scope:

  • Investigations of the interaction between logical and probabilistic methods in the methodology of the sciences;
  • Applications of specialized logical tools and modelling techniques to the methodology of particular sciences;
  • New ideas for using logical techniques in the development of rational reconstructions of scientific theories;

The application of novel logical modelling techniques to the process of the evolution of scientific theories in response to new empirical evidence.

Invited authors: Hannes Leitgeb (Bristol) and Gerhard Schurz (Düsseldorf); Sonja Smets (Free University of Brussels) and Alexandru Baltag (Oxford); Simon Huttegger (Konrad Lorenz Institute for Evolution and Cognition Research); Otavio Bueno (University of Miami).

The invited authors are kindly requested to limit their contribution to between 15 and 20 pages (including bibliography).

Submission of Papers

Submitted papers are should be between 15 and 20 pages long (including bibliography), and should be formatted according to the Studia Logica LaTex style (see Some contributions in Microsoft Word may also be accepted: authors should consult the guest editors about this possibility. Only electronic submissions will be accepted. The authors should send an email with subject "Studia Logica Submission" to the guest editors (Igor Douven, and / or Leon Horsten, ), with the file of the paper as an attachment, and the following information in the body of the email in plain text: paper title, author names, surface mail, email address of the contact author and a short abstract.

Deadline for submission of manuscripts: June 30th 2007

All papers will be refereed according to the standards of the journal. The refereeing process is expected to be finished by December 2007 and the issue published in Spring 2008.

Rosser Centennial Year

Submitted by Richard Zach on Sun, 01/21/2007 - 4:11pm

Hello, all. Sorry for not posting lately. Anyway. Happy New Year! I pronounce 2007 the

John Barkley Rosser, Sr. Centennial Year

Rosser was born December 6, 1907 and was one of the pioneers of modern mathematical logic, especially, of recursion theory and the ?-calculus. He also contributed to areas such as number theory and ballistics. As director of the Army Mathematics Research Center during the Vietnam War he was not an uncontroversial figure politically. He died September 5, 1989.

He is the (co-)author of three logic books:

J. Barkley Rosser and Atwell R. Turquette. Many-valued logic. Amsterdam, North-Holland, 1952.

J. Barkley Rosser. Logic for mathematicians. New York, McGraw-Hill, 1953.

J. Barkley Rosser. Simplified independence proofs: Boolean valued models of set theory. New York, Academic Press, 1969.

His two most famous papers are, no doubt:

J. Barkley Rosser. Extensions of some theorems of Gödel and Church. The Journal of Symbolic Logic 1 (1936) 87-91. doi:10.2307/2269028

Alonzo Church and J. Barkley Rosser. Some properties of conversion. Transactions of the American Mathematical Society 39 (1936) 472-482. doi:10.2307/1989762

(Theorem 2 in this paper is "the Church-Rosser Theorem")

Wisconsin Rosser memorial Resolution [PDF]
Interview with Kleene and Rosser from the Princeton Mathematics Oral History Project

Classic Logic Papers, pt. 1

Submitted by Richard Zach on Mon, 12/18/2006 - 8:18am

Nice of LtU to link to a classic paper that everyone should (re)read: Hoare's Axiomatic basis for computer programming.

Kurt Gödel Centenary Research Prize Fellowship

Submitted by Richard Zach on Sat, 12/02/2006 - 11:25am

(Organized by the Kurt Gödel Society with support from the John Templeton Foundation)

The Kurt Gödel Society is proud to announce the commencement of the research fellowship prize program in honor and celebration of Kurt Gödel's 100th birthday.

The research fellowship prize program sponsored by the John Templeton Foundation will offer:

  • two Ph.D. (pre-doctoral) fellowships of $ 60,000 US per annum for two years
  • two post-doctoral fellowships of $ 80,000 US per annum for two years
  • one senior fellowship of $ 120,000 US per annum for one year.

The selection will be made based upon an open, international competition. An international Board of Jurors chaired by Professor Harvey Friedman will oversee the process. The finalist papers will be published in a special issue of a premier journal in mathematical logic.

Goal and Criteria of Merit

The purpose of the fellowship is to support original research in mathematical logic, meta-mathematics, philosophy of mathematical logic, and the foundations of mathematics. This fellowship is to carry forward the legacy of Gödel, whose works exemplify deep insights and breakthrough discoveries in mathematical logic. In pursuit of similar insights and discoveries, we adopt the following criteria of merit for evaluating Fellowship applications:

  1. Intellectual merit, scientific rigor and originality of the submitted paper and work plan. The paper should combine visionary thinking with academic excellence.
  2. Potential for significant contribution to basic foundational understanding of logic and the likelihood for opening new, fruitful lines of inquiry.
  3. Impact of the grant on the project and likelihood that the grant will make this new line of research possible.
  4. The probability that the pursuit of this line of research is realistic and feasible for the applicant.
  5. Qualifications of the applicants evaluated via CV and recommendation letters (recommendation letters are not required for senior applications).



Original fellowship proposals from all fields of mathematical logic (such as Computability Theory, Model Theory, Proof Theory, Set Theory), meta-mathematics, the philosophy of mathematics, and the foundations of mathematics insofar as the research has strong relevance or resemblance to the Gödelian insights and originality.

Preliminary Timeline

1 December 2006 Pre-announcement
15 June 2007 Submissions deadline
October 2007 Jury decision due on papers to be published
15 December 2007 Final versions due
January 2008 Jury decision on winners due
February 2008 Award Ceremony
March-September 2008 Commencement of the Fellowships

Teaching Logic from Historical Sources

Submitted by Richard Zach on Thu, 11/23/2006 - 7:26pm

This is an interesting project: teach discrete mathematics not from a textbook, but using the historical papers that first dealt with the topics taught. A bunch of mathematicians and computer scientists at New Mexico State are doing that, and they're asking for your help: try it out in your courses, write them letters of support for NSF funding. They have two modules on logic: one on set theory (Cantor), and one on computability (Turing's 1936 paper). Here's their email that came over FOM yesterday.

A team of mathematicians and computer scientists at New Mexico State University and Colorado State University at Pueblo has developed an innovative pedagogical technique for teaching material in discrete mathematics, combinatorics, logic, and computer science, with National Science Foundation support for a pilot project. Topics are introduced and studied via primary historical sources, allowing students to participate in the sense of discovery, and to appreciate and gain motivation from the context in which concepts were developed.

For example, we have authored classroom modules in which students learn mathematical induction from Pascal's "Treatise on the Arithmetical Triangle," written in the 1660's. Another module develops the short recursion relation for the Catalan numbers from a seminal paper of G. Lame in 1838 (based on a start by Euler!!) We also have authored modules on binary arithmetic, based on the original historical sources by Leibniz and von Neumann; on infinite sets, based on original historical sources by Cantor; and on Turing machines, and Church's Thesis, based on original historical sources by Goedel, Church, Turing, and Kleene.

We have authored 18 modules so far; all these modules and more information can be found at The modules will appear in a chapter of a forthcoming MAA resource book for teaching discrete mathematics. We found that 65% of the students who completed a course with these historical projects performed equally well or better than the mean GPA in subsequent mathematics and computer science courses.

We are seeking to expand our pilot program with further major support from the National Science Foundation to create a full book with a comprehensive collection of classroom projects based on historical sources. We would like to invite any instructors of mathematics or computer science courses to agree to site test future projects in related courses in discrete mathematics, combinatorics, logic, or computer science, or perhaps even to design your own projects. We hope to be able to provide a little NSF support as travel and/or consulting for site testers.

If you think that you (or a colleague) would be interested in teaching with a project during 2008-2011, we would like to hear from you. We plan to finalize our new NSF proposal by mid-December, and would like to attach a brief letter of support from you if you are interested. It would be nice if it indicated the institution, the course, nature of students, rough timeframe, why you think it would be good for your students, and possible choice of projects for your testing.

Contact persons:
Guram Bezhanishvili (
Jerry Lodder (
David Pengelley (

Universal Logic in China

Submitted by Richard Zach on Thu, 11/23/2006 - 7:21pm
2nd World Congress and School on Universal Logic
Call for papers
Xi'an, China, August 16-22, 2007

This event is the second in a series of events whose objective is to gather logicians from all orientations (philosophy, mathematics, computer science, linguistics, artificial intelligence etc) - people not focusing only on some specific systems of logic or some particular problems, but inquiring the fundamental concepts of logic.

There will be a four days school with about 20 tutorials followed by a 3 days congress. Among the participants there will be Walter Carnielli, Hartry Field, Valentin Goranko, Vincent Hendricks, Wilfrid Hodges, Istvan Nmeti, Gabriel Sandu, Stan Surma, Heinrich Wansing and many others.

The deadline for submission of contributed papers is March 15, 2007. There will also be a contest with subject: How to translate a logic into another one?

This event will take place in Xi'an, the ancient capital of China, just after the 13th LMPS to happen in Beijing. For further information, please visit the website below:

Applied Logic Job in Darmstadt

Submitted by Richard Zach on Thu, 11/23/2006 - 7:18pm

The Department of Mathematics of the Darmstadt University of Technology (TUD) invites applications for a

Juniorprofessorship in Mathematics - Applied Logic (W1 B BesG)

to be filled 1.4.2007.

Applicants must be qualified in Applied Logic. Applications from candidates working in "Mathematical Proof Theory" (e.g. proof mining, proofs as programs, reverse mathematics, constructive formal systems) and/or "Computability in Mathematics" (e.g. effective algebra and analysis, symbolic computation) are particularly welcome.

Besides pedagogical skills the ability to conduct high quality scientific research must be proven by a PhD of exceptionally high quality and additional research papers. The duration of the PhD studies plus subsequent academic employment should in total not have exceeded 6 years.

Candidates should be willing to cooperate with colleagues from neighboring areas in the department as well as be open towards problems in other scientific areas such as Computer Science.

Duties of the successful candidate are to take part in the teaching provided by the department, to conduct original research in the area mentioned above and to further develop pedagogical skills. Willingness to take part in academic administrative issues is also expected.

The employment is initially for 3 years. After a successful evaluation as professor it will be extended for another 3 years.

Darmstadt University of Technology aims at increasing the number of women among the faculty and particularly encourages applications from women. Disabled candidates are considered -- given equal qualification -- with preference.

Applicants are asked to have 3 letters of recommendation sent to the Dekan of the Department of Mathematics of TUD.

Applications with the usual documents (CV, list of publications, teaching record) should be sent (referring to the Kenn-Nr. 337 of the position) by 31.12.2006 to: Dekan, Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany.

The official German version of this advertisement can be found at

Canadian PhD programs in the 2006-08 PGR

Submitted by Richard Zach on Sun, 11/12/2006 - 1:39pm

table.lines td { vertical-align: top; border: 1px dashed gray; empty-cells: show; padding: 2pxWith the kind permission of Brian Leiter, here's a breakout of the Canadian philosophy departments by specialty according to the Philosophical Gourmet Report 2006-08. The same programs are ranked in 2006-08 as in the 2004-06 edition. This year, only the rank ordering of the top four departments was given in the PGR. As two years ago, I'm providing the the rank ordering based on both the entire survey responses and the responses from Canadian evaluators (with mean scores in parentheses). The numbers following the specialties are: the peer group the program falls in and the rounded mean/median score. The "Notable" category (median of 3.0) is no longer included in the PGR (according to Brian Leiter, merely for reasons of time). See the overall rankings and the specialty rankings from the PGR for explanations.

PS: Because Canadian students wanting to study at a Canadian school don't exactly have many options for any given specialty, you might consider consulting last year's rankings as well. That still gives the "notable" category for the various specialties (ie, median scores of 3.0 that just barely didn't make the official rankings).

Program Ranked Specialties
University of Toronto
Overall rank: 1 (3.7)
Canada rank: 1 (4.1)
Philosophy of Language (4/24-36, 3/3)
Philosophy of Mind (3/13-25, 3.5/3.5)
Metaphysics (5/25-36, 3.0/3.0)
Philosophical Logic (3/13-21, 3.5/4)
Normative Ethics and Moral Psychology (3/6-12, 4.0/4)
Political Philosophy (2/4-13, 4.0/4)
Philosophy of Law (2/3-11, 4.0/4)
Applied Ethics (2/7-18, 3.5/3.5)
Philosophy of Science (4/13-29, 3.5/3.5)
Philosophy of Biology (3/8-16, 3.5/3)
Philosophy of Cognitive Science (4/12-27, 3.0/3.5)
Philosophy of Social Science (4/16-34, 3.0/3.25)
Philosophy of Mathematics (4/13-22, 3.5/3.5)
Mathematical Logic (3/10-19, 3.5/3.5)
Ancient Philosophy (2/2-4, 4.5/4.5)
Medieval Philosophy (1/1-3, 5.0/5.0)
Early Modern: 17th C (2/2-11, 4.0/4.0)
Early Modern: 18th C (1/1-7, 4.0/4.0)
Kant and German Idealism (4/9-18, 3.5/3.5)
19th C Continental Philosophy after Hegel (4/18-27, 3.0/3.25)
American Pragmatism (1/1-3, 4.0/4.0)
20th Century Continental (4/17-33, 3.0/3.5)
Feminist Philosophy (2/3-13, 4.0/4.0)
University of Western Ontario
Overall rank: 2 (2.7)
Canada rank: 2 (3.1)
Philosophy of Language (4/24-36, 3/3)
Applied Ethics (3/19-42, 3.0/3.25)
Philosophy of Science (3/4-12, 4.0/4)
Philosophy of Physics (3/4-10, 4.0/4.0)
Philosophy of Social Science (3/7-15, 3.5/3.75)
Decision, Rational Choice, and Game Theory (5/10-19, 3.0/3.0)
Philosophy of Mathematics (4/13-22, 3.5/3.5)
Mathematical Logic (4/20-24, 3.0/3.0)
Medieval Philosophy (5/15-25, 3.0/3.5)
Early Modern: 17th C (3/12-33, 3.5/4)
Early Modern: 18th C (2/8-14, 3.5/4.0)
Feminist Philosophy (4/23-27, 3.0/3.0)
McGill University
Overall rank: 3 (2.4)
Canada rank: 3 (2.8)
Philosophy of Art (3/7-13, 4.0/4.25)
Philosophy of Mathematics (5/23-32, 3.0/3.75)
Ancient Philosophy (5/13-21, 3.0/3.0)
Medieval Philosophy (5/15-25, 3.0/3.25)
Early Modern: 17th C (3/12-33, 3.5/3.5)
Early Modern: 18th C (3/15-39, 3.0/3.0)
Kant and German Idealism (5/19-32, 3.0/3.5)
University of British

Overall rank: 4 (2.2)
Canada rank: 4 (2.6)
Philosophy of Art (4/14-21, 3.5/4)
Philosophy of Science (4/13-29, 3.5/3.5)
Philosophy of Biology (3/8-16, 3.5/3.5)
Philosophy of Social Science (4/16-34, 3.0/3.0)
History of Analytic Philosophy (4/18-37, 3.0/3.25)
University of Alberta
Overall rank: 5 (2.1)
Canada rank: 4 (2.6)
Philosophy of Art (5/22-28, 3.0/2.75)
Feminist Philosophy (2/3-13, 4.0/4.0)

Overall rank: 6 (2.0)
Canada rank: 6 (2.5)
Political Philosophy (3/14-27, 3.5/3.75)
Applied Ethics (3/19-42, 3.0/3.25)
Feminist Philosophy (2/3-13, 4.0/4.0)
Simon Fraser University
Overall rank: 6 (2.0)
Canada rank: 7 (2.4)
Philosophical Logic (4/22-36, 3.0/3)
University of Calgary
Overall rank: 6 (2.0)
Canada rank: 7 (2.4)
Philosophical Logic (4/22-36, 3.0/3)
Philosophy of Action (incl. Free Will) (4/13-19, 3.0/3)
Philosophy of Biology (4/17-23, 3.0/3.0)
York University
Overall rank: 9 (1.8)
Canada rank: 10 (1.9)
Philosophy of Law (4/21-33, 3.0/3)
American Pragmatism (3/7-10, 3.0/2.75)
Tri-University (Guelph, McMaster, Laurier)
Overall rank: 9 (1.8)
Canada rank: 9 (2.1)
Philosophy of Law (4/21-33, 3.0/3)
Early Modern: 18th C (3/15-39, 3.0/3.0)
History of Analytic Philosophy (incl. Wittgenstein) (4/18-36, 3.0/3.0)
University of Waterloo
Overall rank: 11 (1.7)
Canada Rank: 10 (1.9)

Hilbert in Kyoto

Submitted by Richard Zach on Sun, 11/12/2006 - 1:00pm

I just spent a wonderful week in Kyoto at the invitation of Susumu Hayashi. Susumu's been working on Hilbert's notebooks, and he, Mariko Yasugi, Wilfried Sieg, Koji Nagatogawa, and I have had several days of interesting discussions about them. The last two days there was a workshop on Hilbert and computability, and it was a pleasure to see and talk to Yasuo Deguchi, Anton Setzer, Toshi Arai, and many others. Many thanks to Susumu and his students, and in particular to Koji, without whose help and translation services Wilfried and might have gotten lost, starved to death, and certainly wouldn't have had as good a time.

If you read German, check out Susumu's students' compilation of Hilbert's maxims from the notebooks.

Henkin Obituary

Submitted by Richard Zach on Sat, 11/11/2006 - 2:22pm