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Strevens on Confirmation Theory

Submitted by Richard Zach on Thu, 12/21/2006 - 8:55am

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

Leon Henkin, 1921-2006

Submitted by Richard Zach on Fri, 11/03/2006 - 2:26am

I just heard that Leon Henkin passed away earlier this week. He was a terrific logician and a terrific teacher. He will be missed.

First-order Gödel Logics

Submitted by Richard Zach on Sat, 10/14/2006 - 11:40pm

Ok, this is hopefully my last paper ever on many-valued logics. Well, maybe not. In any case, it's done and will come out in APAL.

Primitive Recursion

Submitted by Richard Zach on Sat, 09/30/2006 - 10:42pm

In an interesting thread titled "Recursive" on FOM last week there was a discussion on the history of primitive recursive functions. Of course, already Grassmann, Dedekind, and Peano gave primitive recursive definitions of individual functions such as addition and multiplication, and Skolem's 1923 article

Independence of Goodstein's Theorem from PA

Submitted by Richard Zach on Mon, 09/25/2006 - 3:25pm

I was asked in email about a good source about Goodstein sequences and the independence of Goodstein's Theorem from Peano Arithmetic. The independence result is due to Kirby and Paris in a 1983 paper in the Proceedings of the London Mathematical Society (vol. 14), using the method of indicators. Georg Moser suggested the following paper by Cichon, which appeals to the characterization of provably recursive functions in PA only:

E. A. Cichon, A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods. Proceedings of the American Mathematical Society 87/4 (1983), 704-706. JSTOR

Cichon's proof can also be found in Fairtlough and Wainer's chapter on "Hierarchies of Provably Recursive Functions" in the Handbook of Proof Theory, S. Buss, ed. (Elsevier, 1998).

Philosophy of Language Texts?

Submitted by Richard Zach on Sun, 09/24/2006 - 6:03am

I'm going to be teaching philosophy of language next term. It's the first time--if you can believe that--we're offering a course with that title. We used to have a course called "Analytical Philosophy", which served that purpose, but it was also a history of analytic philosophy course. Anyway. I'd like to give my students a textbook, and was wondering if something new and good has shown up at the APA book exhibits in the last two years. Otherwise I'd probably use Ken Taylor's Meaning and Truth.

SSHRC Grants in Philosophy for 2006

Submitted by Richard Zach on Sun, 09/24/2006 - 3:14am

The Social Sciences and Humanities Research Council of Canada has posted a list of new Standard Research Grants for 2006. This year's stats: 85 applications (2005: 96, 2004: 92), 32 grants, for a success rate of 37% (2005: 38%, 2004: 48%). This year, new scholars (? 5 years beyond PhD) had a 29% success rate (2005: 38%, 2004: 29%). Full stats here.

A list of successful proposals follows. I've included the dollar figure (in CAD), but these shouldn't be taken as an indication of the quality of the project. The funding rate depends on the requirements of the project (travel, research support) and on the amount of graduate student funding, not just on the ranking of the proposal. I've certainly missed quite a few: I went by the titles in the full list (not broken down by subject area) and included grants that I guessed to be philosophy projects from the title and/or where I could ascertain that the applicant was in a philosophy department. Email me if you think I should include a grant not on here.

  1. Bartha, Paul , The University of British Columbia. Infinite Decision Theory. $31,500
  2. Campbell, Neil , Wilfrid Laurier University. Explanatory epiphenomenalism: at the crossroads of mental causation and consciousness. $57,106
  3. Davies, David A., McGill University. How making matters: provenance and the epistemology, ontology, and axiology of art. $49,469
  4. Duchesneau, François , Université de Montréal. Leibniz: système de la nature et organisation vitale. $78,948
  5. Joy, Morny M., University of Calgary. The confluence of head and heart: religion, ethics and the feminine in Hannah Arendt, Simone de Beauvoir and Edith Stein. $75,780
  6. Gauthier, Yvon , Université de Montréal. Logique arithmétique et philosophie de l'arithmétique. $49,542
  7. Griffin, Nicholas J., McMaster University. The collected letters of Bertrand Russell. $92,691
  8. Hacking, Ian , University of Toronto. Philosophical illustrations from the ultracold. $54,240
  9. Heath, Joseph M., University of Toronto. An adversarial approach to business ethics. $51,000
  10. Hudson, Robert G., University of Saskatchewan. The epistemology and metaphysics of dark matter research. $53,698
  11. Lin, Martin T., University of Toronto. Spinoza's conatus doctrine. $38,621
  12. King, Peter , University of Toronto. Mediaeval souls and modern minds. $57,148
  13. Miller, Jon A., Queen's University. Happiness in early modern philosophy. $48,423
  14. Norman, Wayne J., Université de Montréal. A skeptical business ethics. $41,381
  15. Moran, Brendan P., University of Calgary. Prose, myth, and time in late works of Walter Benjamin. $26,471
  16. Pickavé, Martin , University of Toronto. Medieval theories of the emotions (passions of the soul). $53,271
  17. Raffman, Diana , University of Toronto. Vagueness without paradox. $39,650
  18. Ripstein, Arthur S., University of Toronto. Authority and coercion: Kant's doctrine of right. $49,813
  19. Russell, Paul , The University of British Columbia. The limits of free will. $37,502
  20. Schmitter, Amy M., University of Alberta, Representation in Early Modern philosophy: the 17th century. $62,540
  21. Seymour, Michel , Université de Montréal. Les droits collectifs linguistiques et le droit à l'autodétermination. $50,617
  22. Speaks, Jeffrey J., McGill University. The role of mental states in the philosophies of action and language. $54,506
  23. Sullivan, Arthur M., Memorial University of Newfoundland. The externalism/individualism debates. $55,093
  24. Sumner, Wayne L., University of Toronto. Matters of life and death. $41,503

Martin Löb, 1921-2006

Submitted by Richard Zach on Wed, 09/20/2006 - 2:20pm

Martin Löb has passed away on August 28. Obituary here.

Notions of Logical Independence

Submitted by Richard Zach on Sun, 09/10/2006 - 2:49pm

In Prague this past week, David Miller gave a talk in which (among many other interesting things) he distinguished two notions of logical independence. One he credits to Moore (the mathematician, not the philosopher) and Wittgenstein, and that's the notion of independence at work when we say, e.g., that an axiom system is independent. A set ? is independent if for each A ? ?, ?\A is consistent with ¬A. Moore's notion of complete independence is a generalization of that, where we require that for each ? ? ?, ?\? is consistent with ¬?.

The other notion he credits to H. M. Sheffer, and that's the notion of maximal independence: ? is maximally independent if any two A, B ? ? have no consequences in common, other than tautologies.

{p, q}, for instance, is (completely) independent in the first sense, but not maximally independent (p and q have the non-tautological consequence p ? q in common).

I think these are interesting concepts, and I should find out more about them. David makes use of them in comparing (false) theories in a 1974 paper. I hadn't heard of Sheffer's notion before; maybe that's because the paper he defines it in is unpublished. But from David's paper I see that Tarski uses it as well.

David Miller, 1974. On the comparison of false theories by their bases. The British Journal for the Philosophy of Science 25(2) 178–188.

Eliakim Hastings Moore, 1910. Introduction to a form of general analysis. The New Haven Mathematical Colloquium 1–150.

Henry Maurice Sheffer, 1921. The general theory of notational relativity. (Mimeograph)

Dear Matt

Submitted by Richard Zach on Mon, 09/04/2006 - 12:50am

I am very sorry. There will be more logic blogging very soon, I promise. I'm off to Prague for the Vagueness and Uncertainty workshop, and if the Academy of Sciences also has internet access in the villa they're putting me up in, I will liveblog it. Rosanna Keefe! Stewart Shapiro (who has a new book, which y'all should check out)! Peter Milne! Roy Sorensen! And my man Chris Fermüller.
(And UPDATE: Patrick Greenough! Sorry.)

Grue Forever!

Submitted by Richard Zach on Mon, 08/07/2006 - 11:11am

The Austrian newspaper Der Standard, of all things, reminded me of another centenary: Nelson Goodman would have turned 100 today.

PhD Student Position in Logic at Bristol

Submitted by Richard Zach on Thu, 08/03/2006 - 8:07am

PhD Student Position in Logic and Cognitive Science, Department of
Philosophy, University of Bristol (UK):

A newly established research group headed by Hannes Leitgeb at the Department of Philosophy, University of Bristol, has an open position for a PhD student. The group, which will be part of an international EUROCORES Collaborative Research Project on Metacognition, will be funded by the AHRC and the European Science Foundation (as should be confirmed officially in the first half of August 2006). The Bristol group will be dealing with:

Logical Constraints on Conditionals and Introspection in Systems of Belief Revision and Non-Monotonic Reasoning.

The doctoral student will have an undergraduate background in philosophy, logic, and cognitive science, and will be expected to work on a suitable PhD thesis topic within the project. The group will be able to fund three years of tuition fees and maintenance (funds will also be available for computer equipment, conference fees, and travel costs).

There is no official deadline, but since the student's doctoral studies have to be taken up in the beginning of October 2006, we strongly recommend applications for this position to be submitted as early as possible.

Applications (including a CV and references) should be sent electronically to

Informal enquiries may be directed to: