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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:

Logic Matters: Gödel at long last

Submitted by Richard Zach on Tue, 08/01/2006 - 7:45am

Dots as Brackets in Formulas

Submitted by Richard Zach on Wed, 07/19/2006 - 7:49am

Ever tried reading logical texts from the 20s or before (e.g., C. I. Lewis's Symbolic Logic)? Confused by the absence of parentheses and all the dots and colons? Here's Carnap's explanation of the notation (from Abriss der Logistik):

4 c. The Dot Rules

The dot symbols (. : :. :: etc.) replace the bracketing of propositions. The dot signs fall into three distinct levels, depending on whether they occur

  1. between two propositions in a conjunction,
  2. after an operator (x), (? x), [(?x)(?x)],
  3. after |-, before and after the sign ?, ? ?, |, =Df.

Dot rules for reading: The scope of a dot symbol (for 1, to the left and to the right, for 2 to the right, for 3 to left or right, depending) extends either to the end of the proposition or to a dot symbol with more dots or to a symbol of the same or a higher level with the same number of dots.

Dot rules for writing: If the scope of a dot sybol is to extend beyond that of another, it must, if it is of a higher level than the latter, contain at least as many dots, and otherwise more dots.


p ? . q . r means p ? (q . r)
|- : (p, q) : p ? q . ? . q ? p " |- {(p, q) . [(p ? q) ? (q ? p)]}
p : ? : q . ? . q ? p " p ? [q ? (q ? p)]
(x) . ?x . ? . p ? q " [(x) . ?x] ? (p ? q)
(x) : ?x . ? . p ? q " (x) . [?x ? (p ? q)]
(x) : ?x ? p . ? q " (x) . [(?x ? p) ? q]
(x) : ?x ? p : ? q " [(x) . (?x ? p)] ? q

Dartmouth AI Conference 50 Years Ago

Submitted by Richard Zach on Wed, 07/19/2006 - 7:41am

50 years ago this summer, McCarthy, Minsky, Rochester, and Shannon organized a summer conference at Dartmouth which turned out to be a milestone in Artificial Intelligence research. For the logically minded, this item in the funding proposal to the Rockefeller Foundation is perhaps most interesting:

4. Theory of the Size of a Calculation

If we are given a well-defined problem (one for which it is possible to test mechanically whether or not a proposed answer is a valid answer) one way of solving it is to try all possible answers in order. This method is inefficient, and to exclude it one must have some criterion for efficiency of calculation. Some consideration will show that to get a measure of the efficiency of a calculation it is necessary to have on hand a method of measuring the complexity of calculating devices which in turn can be done if one has a theory of the complexity of functions. Some partial results on this problem have been obtained by Shannon, and also by McCarthy.

Computability in Swansea

Submitted by Richard Zach on Mon, 07/10/2006 - 2:25pm

Last week I had the pleasure of attending the Computability in Europe conference in the lovely seaside town of Swansea, Wales. Lots of interesting talks on all kinds of aspects of computation, including a number of talks on the (limits of) hypercomputation, a tutorial on proof complexity by Sam Buss, and special sessions on Gödel's legacy for computability theory with talks by Arnon Avron, John Dawson, Andrew Hodges, and Wilfried Sieg. I won't talk about the details--the abstracts are up on the website, the slides for many of the talks should be up very soon, and the proceedings volumes (invited, contributed [big PDF!] talks) are online as well.

Oh, and this guy stopped by to visit the building across from the conference site:

HRH The Prince of Wales

I also had an enjoyable bus ride back to Heathrow with Bob Meyer, talking about relevant logic and the epsilon calculus.

A Sequitur of Logicians?

Submitted by Richard Zach on Thu, 06/29/2006 - 12:46pm

Reading over my previous post, I was wondering if a group of scholars can be referred to as a "gaggle". So I did some research (i.e., I asked google) and happened upon this wiki page, which lists the appropriate collective noun for logicians as "sequitur", and attributes this to Bertrand Russell. Anyone got a reference for this? (It doesn't list a special collective noun for scholars, though--maybe "a school of scholars" would be appropriate?)

UPDATE: The wikipedia page for Quine has him saying it, but maybe he got it from Russell?

Online Collaboration for Scholars Follow-up

Submitted by Richard Zach on Thu, 06/29/2006 - 6:34am

I mentioned it in comments on the other post already, but I thought of a few solutions to my question: how do you keep a gaggle of scholars jointly working on a publication project organized? They are outlined in a wiki page. Comments welcome (you can edit the wiki, of course, or write something on the talk page).

Conference Blogging

Submitted by Richard Zach on Thu, 06/29/2006 - 6:28am

Greg is reporting from the Realism/Anti-Realism Workshop in Nancy, and Yarden from the CMU Summer School in Logic. Stay tuned for reports from Computability in Europe next week from yours truly.

It's Alan's Birthday!

Submitted by Richard Zach on Fri, 06/23/2006 - 12:58pm

Friendster reminded me that today is Alan Turing's birthday.

Online Multi-Author Collaboration?

Submitted by Richard Zach on Thu, 06/22/2006 - 12:59pm

If you've ever coauthored a paper, you know what a hassle it is to send versions back and forth, keep track of changes, avoid conflicts when you're simultaneously changing things, and so on. Now software engineers have the same problems when working on large development projects and have developed very sophisticated Revision Control Systems. I've used the most well-known of these, CVS, for collaborating on a couple of papers. But CVS is not exactly easy to use, and for a larger project with more people who all use different systems (Linux, Mac, Windows) and who aren't as geeky as I, CVS is not a good choice. So: I'm looking for an easy way to collaborate on editing text documents. It should work cross-platform, it should have version control (keeping track of changes, ways of telling what parts of a document were edited by whom and when, reverting to previous versions), it should be easy to use (graphical user interface), it should be easy to install (preferably it should be completely distributed with the client programs doing all the work). It doesn't have to have fancy security, support for branching and merging projects, include a build environment, and all the other stuff that's important to programmers. I also don't want to have to set up a server or persuade my university's IT people to give accounts to my collaborators. Anyone have any ideas?