Win Gardner Book by Solving Puzzle

CUP is giving away copies of Martin Gardner’s New Mathematical Library if you can solve a logic puzzle–any reader of this blog should be able to solve this one!

N.B. The rules that say: These books represent new editions of Gardner’s massive Scientific American corpus. Many people know these puzzles by heart. If you do, please encourage a Gardner neophyte to take a crack at it. Tell your local high school math club. [UPDATE]: If you know the puzzle, but pull off an awesome answer for it (see the next rule), by all means, enter.

Speaking of awesome answers to Gardner’s logic puzzles, which really are Smullyan logic puzzles (I think?), please put XOR’s Hammer into your feed readers! Michael O’Connor has set the bar very high for awesome answers to logic puzzles. And generally writes very interesting logic/math posts.

Calgary Peripatetic Research Group in Logic and Category Theory

My colleague Robin Cockett and I have been running a research group here at Calgary where the various computer scientists, mathematicians, and philosophers interested in logic, theory, foundations, etc. meet and present work. For a long time we’ve had weekly meetings and everything went great, but then both Robin and I went on leave and almost nothing happened the past year or so. But we’re starting up again! We have a fancy new website to prove it! So if you’re in the area, please come to our talks, and if you’re not in the area ordinarily but plan to come through, let me know because then we’d love you to be one of the outside speakers.

We start today at 12:30 in ICT 616, and I’m giving a history of logic talk.

Kripke on Hilbert’s Program

The ASL Newsletter went out today, and it looks like the Winter Meeting will be very exciting:

2008-09 ASL Winter Meeting (with APA) Philadelphia, Pennsylvania
December 27–30, 2008

This meeting will be held jointly with the Annual Meeting of the Eastern Division of the American Philosophical Association. The program includes three invited sessions. For the first, a panel on Historical Ideals of Rigor in Mathematics, the invited speakers are: J. Folina, D. Jesseph, and D. Schlimm. The second invited panel, on Diagrammatic Reasoning in Mathematics, includes the following speakers: E. Grosholz, K. Manders, and S.-J. Shin. The speaker for the third invited session is S. Kripke, whose talk is entitled, The Collapse of the Hilbert Program.

I want to see every one of these talks! But I can’t go! I want to know especially what Kripke has to say about Hilbert’s Program. Can someone tape it for me? Or write a guest post about it? Pretty please? Maybe someone already knows what he will say because they attended the lecture of the same title at Indiana University a year ago, or this year at the Truth Values workshop in Dresden, or took his course at CUNY in 2005?

Vienna International Summer University 2009: The Culture of Science and Its Philosophy

The Vienna International Summer University next year (July 13-24, 2009) will be on the topic “The Culture of Science and Its Philosophy”. Call for Participation just came in. Stupid framed website: to apply, go to the website, then click on “Application” in the navigation bar on the left.

Call for Application
Application deadline: January 30, 2009

VISU Vienna International Summer University
SWC Scientific World Conceptions

Since 2001 the University of Vienna and the Institute Vienna Circle have been holding an annual two-week summer program dedicated to major current issues in the natural and social sciences, their history and philosophy. The title of the program reflects the heritage of the Vienna Circle which promoted interdisciplinary and philosophical investigations based on solid disciplinary knowledge.

As an international interdisciplinary program, VISU-SWC will bring graduate students in close contact with world-renowned scholars. It will operate under the academic supervision of an International Program Committee of distinguished philosophers, historians, and scientists. The program is directed primarily to graduate students and junior researchers in fields related to the annual topic, but the organizers also encourage applications from gifted undergraduates and from people in all stages of their career who wish to broaden their horizon through crossdisciplinary studies of methodological and foundational issues in science.

The summer course consists of morning sessions, chaired by distinguished lecturers which focus on readings assigned to students in advance. Afternoon sessions are made up of tutorials by assistant professors for junior students and of smaller groups which offer senior students the opportunity to discuss their own research papers with one of the main lecturers.

The Culture of Science and Its Philosophy
Vienna, July 13 – 24, 2009
organized by the University of Vienna and the Institute Vienna Circle.

A two-week high-level summer course on three main themes: aspects of the philosophical debates from about 1870 to 1950; the idea that scientific knowledge is perspectival and issues related to the social responsibilities of science, the social dimensions of science and the truth of scientific claims.

There are three main overlapping themes in the course. One theme concerns crucial aspects of philosophical debates from roughly 1870 to 1950, the alternatives offered, and some lingering consequences for analytic philosophy that arise from its historical relations to scientific philosophy. A second theme concerns the possible replacement of the Enlightenment idea that science delivers the absolutely objective truth by the view that scientific knowledge is perspectival, and the consequences of this view for how contemporary scientists confront religion. A third theme concerns twentieth-century scientists and philosophers of science who sought to sort out questions of the social responsibilities of science, the social dimensions of science, and the truth of scientific claims.

The lectures will deal with the following topics:

  • Scientific Perspectivism: An Alternative to Objectivist Realism
  • Scientific Neo-Kantianism and Positivism in Germany from 1870 to 1914
  • Naturalism, Pragmatism, and Experimentalism in American Philosophy of Science, 1870–1950
  • Scientific Realism and Scientific Socialism in France from Belle Epoque to Cold War
  • Bernalism and Approaches to the History and Philosophy of Science in Great Britain
  • Hierarchy and Intention in Scientific Representation
  • “Die wissenschaftliche Weltauffassung”: Logical Positivism from Austria and Germany to North America, 1920–1950
  • Weimar Berlin and Historical Sources of the View of Science as Social Practice
  • Politics and Values in the Philosophy of Science of Polanyi, Popper, and Kuhn
  • Science without Laws, Realism w/o Truth, Judgment w/o Rationality
  • Analytic Philosophy as Marginal Science
  • Contemporary Scientists Confront Religion

Main Lecturers:
Ronald Giere (University of Minnesota, USA)
Mary Jo Nye (Oregon State University, USA)
Alan Richardson (University of British Columbia, Canada)

International Program Committee
John Beatty (Vancouver), Maria Luisa Dalla Chiara (Florence), Maria Carla Galavotti (Bologna), Malachi Hacohen (Durham/Raleigh), Rainer Hegselmann (Bayreuth), Michael Heidelberger (Tübingen), Elisabeth Leinfellner (Vienna), Paolo Mancosu (Berkeley), Paolo Parrini (Florence), Friedrich Stadler (Vienna), Michael Stöltzner (Columbia), Roger Stuewer (Minneapolis), Thomas Uebel (Manchester), Jan Wolenski (Cracow), Anton Zeilinger (Vienna).

Karoly Kokai (Secretary of the VISU, Vienna)
ivc@univie.ac.at

The Main Lecturers

Ronald N. Giere is Professor of Philosophy Emeritus as well as a member and former Director of the Center for Philosophy of Science at the University of Minnesota. He is the author of Understanding Scientific Reasoning (5th ed., 2006), Explaining Science: A Cognitive Approach (1988), Science Without Laws (1999), Scientific Perspectivism (2006), and editor of Cognitive Models of Science (1992) and Origins of Logical Empiricism (1996). Prof. Giere is a Past President of the Philosophy of Science Association and a member of the editorial board of the journal Philosophy of Science. His current research focuses on agent-based accounts of models and scientific representation, and on connections between naturalism and secularism.

Mary Jo Nye is Emeritus Horning Professor of the Humanities and Professor of History at Oregon State University. She is a former president of the History of Science Society and received the Society’s 2006 Sarton Medal for Lifetime Scholarly Achievement. Her research focuses on the history of the modern physical and chemical sciences, science and politics, and the philosophy of science. She is editor of the volume on Modern Physical and Mathematical Sciences (2003) in The Cambridge History of Science series, and her most recent book is Blackett: Physics, War, and Politics in the 20th Century (2004). She is completing a book on scientific life and the philosophy of science in the 20th century, with a focus on Michael Polanyi (1891–1976) and his era.

Alan Richardson is Professor of Philosophy and Distinguished University Scholar at the University of British Columbia. His research examines the relations between the history of science and the history of philosophy in the era since Kant. He is currently President of the International Society for History of Philosophy of Science (HOPOS). His publications include the monograph, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism (1998) and the anthologies, Origins of Logical Empiricism (1996, co-edited with Ronald N. Giere), Logical Empiricism in North America (2003, co-edited with Gary L. Hardcastle), and The Cambridge Companion to Logical Empiricism (2007, co-edited with Thomas Uebel). His current book project is tentatively entitled, Logical Positivism as Scientific Philosophy.

Thank You, Internet

I’m going to pretend I’m not in the timezone I’m in, and that it’s still OneWebDay. And sing the praises of the internet. Specifically, “today,” I realized again how much I depend on the availability of information on the internet and the communication possibilities it opens up. As examples, two things:

  • Hotel room, 3am, preparing talk for the next morning’s session. I need to look up a quote or a result or whatever. It’s in the Nachrichten von der Königlichen Akademie der Wissenschaften zu Göttingen. That’s not on JSTOR or in the Springer Historical Archives. Where do I go? To the Göttinger Digitalisierungs-Zentrum! It has saved my ass so many times!
  • Working on a book with a bunch of other people. Everyone’s tracking down references for the bibliography, proofreading, making changes. Thank god we don’t have to send all the files back-and-forth every time we fix a typo—we have Subversion!

Thank you, Internet. But mainly thank you to all the people who make stuff available (for free!) on the internet.

2008 Rolf Schock Prizes to Nagel, Szemeredi

The “Nobel of philosophy and logic” was awarded this year to Thomas Nagel. And the Schock Prize in mathematics goes to Endre Szemerédi. Full citations here (PDF).

Update: I forgot that these were actually announced back in May. There’s a symposium at the Swedisch Academy in honor of Nagel tomorrow.

Mathematical Methods in Philosophy is Out!

In February of last year, BIRS had an amazing workshop on “Mathematical Methods in Philosophy”. We (i.e., Aldo Antonelli, Alasdair Urquhart, and I) collected some of the very exciting contributions from that workshop in a Special Issue of the new Review of Symbolic Logic, and that issue is now online! We even managed to get a nice picture of the participants into the Introduction.

Contents:

  • Editor’s Introduction, by Aldo Antonelli, Alasdair Urquhart, and Richard Zach
  • Topology and Modality: The Topological Interpretation of First-order Modal Logic, by Steve Awodey and Kohei Kishida

    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.

  • Relative-sameness Counterpart Theory, by Delia Graff Fara

    Just as set theory can be divorced from Ernst Zermelo’s original axiomatization of it, counterpart theory can be divorced from the eight postulates that were originally stipulated by David Lewis (1968, p. 114) to constitute it. These were postulates governing some of the properties and relations holding among possible worlds and their inhabitants. In particular, counterpart theory can be divorced from Lewis’s postulate P2, the stipulation that individuals are ‘world bound’—that none exists in more than one possible world.

  • Many-valued Modal Logics: A Simple Approach, by Graham Priest

    In standard modal logics, the worlds are 2-valued in the following sense: there are 2 values (true and false) that a sentence may take at a world. Technically, however, there is no reason why this has to be the case. The worlds could be many-valued. This paper presents one simple approach to a major family of many-valued modal logics, together with an illustration of why this family is philosophically interesting.

  • Axioms for Determinateness and Truth, by Sol Feferman

    A new formal theory DT of truth extending PA is introduced, whose language is that of PA together with one new unary predicate symbol T (x), for truth applied to Gödel numbers of suitable sentences in the extended language. Falsity of x, F(x), is defined as truth of the negation of x; then, the formula D(x) expressing that x is the number of a determinate meaningful sentence is defined as the disjunction of T(x) and F(x). The axioms of DT are those of PA extended by (I) full induction, (II) strong compositionality axioms for D, and (III) the recursive defining axioms for T relative to D. By (II) is meant that a sentence satisfies D if and only if all its parts satisfy D; this holds in a slightly modified form for conditional sentences. The main result is that DT has a standard model. As an improvement over earlier systems developed by the author, DT meets a number of leading criteria for formal theories of truth that have been proposed in the recent literature and comes closer to realizing the informal view that the domain of the truth predicate consists exactly of the determinate meaningful sentences.

  • On the Probabilistic Convention T, by Hannes Leitgeb

    We introduce an epistemic theory of truth according to which the same rational degree of belief is assigned to Tr(┌α┐) and α. It is shown that if epistemic probability measures are only demanded to be finitely additive (but not necessarily σ-additive), then such a theory is consistent even for object languages that contain their own truth predicate. As the proof of this result indicates, the theory can also be interpreted as deriving from a quantitative version of the Revision Theory of Truth.

  • Modal Models for Bradwardine’s Theory of Truth, by Greg Restall

    Stephen Read (2002, 2006) has recently discussed Bradwardine’s theory of truth and defended it as an appropriate way to treat paradoxes such as the liar. In this paper, I discuss Read’s formalisation of Bradwardine’s theory of truth and provide a class of models for this theory. The models facilitate comparison of Bradwardine’s theory with contemporary theories of truth.

  • Frege meets Zermelo: A Perspective on Ineffability and Reflection, by Stewart Shapiro and Gabriel Uzquiano

    There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, first-order Zermelo–Fraenkel set theory with the axiom of choice (ZFC): the iterative conception and limitation of size (see Boolos, 1989). Each strand provides a rather hospitable environment for the hypothesis that the set-theoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case.

There are two more papers submitted (and accepted) for the special issue which for boring reasons aren’t included here, but they’re coming out in the Journal of Philosophical Logic instead. They are:

  • Goodman’s “New Riddle”, by Branden Fitelson

    First, a brief historical trace of the developments in confirmation theory leading up to Goodman’s infamous “grue” paradox is presented. Then, Goodman’s argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman’s “grue” argument against classical inductive logic. The upshot of this analogy is that the “New Riddle” is not as vexing as many commentators have claimed (especially, from a Bayesian inductive-logical point of view). Specifically, the analogy reveals an intimate connection between Goodman’s problem, and the “problem of old evidence”. Several other novel aspects of Goodman’s argument are also discussed (mainly, from a Bayesian perspective).

  • One True Logic?, by Gillian Russell

    This is a paper about the constituents of arguments. It argues that several different kinds of truth-bearer may be taken to compose arguments, but that none of the obvious candidates—sentences, propositions, sentence/truth-value pairs etc.—make sense of logic as it is actually practiced. The paper goes on to argue that by answering the question in different ways, we can generate different logics, thus ensuring a kind of logical pluralism that is different from that of J. C. Beall and Greg Restall.

From the Introduction:

Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and mathematically trained philosophers continue to contribute to the literature in logic. For instance, modal logics were first investigated by philosophers and now have important applications in computer science and mathematical linguistics. The theory and meta-theory of formal systems were pioneered by philosophers and philosophically minded mathematicians (Frege, Russell, Hilbert, Gödel, Tarski, among many others), and philosophers have continued to be significantly involved in the technical development of proof theory and to a certain degree also in the development of model theory and set theory. On the other hand, philosophers use formal models to test the implications of their theories in tractable cases. Philosophical inquiry can also uncover new mathematical structures and problems, as with recent work on paradoxes about truth. Areas outside mathematical logic have also been important in recent philosophical work, for example, probability and game theory in inductive logic, epistemology, and the philosophy of science. Formal epistemology is an emerging field of research in philosophy, encompassing formal approaches to ampliative inference (including inductive logic), game theory, decision theory, computational learning theory, and the foundations of probability theory.

It in fact seems that technical mathematical work is currently enjoying something of a renaissance in philosophy. And so the idea of a workshop on just such topics held at a conference center for the mathematical sciences was developed. From February 18–23, 2007, 40 researchers who apply mathematical methods to current issues in philosophy congregated at the Banff International Research Station (BIRS) in the Canadian Rockies for a workshop on ‘Mathematical Methods in Philosophy’.

These mathematical methods come mainly from the fields of mathematical logic and probability theory, and the areas of application include philosophical logic, metaphysics, epistemology, philosophy of mathematics, and philosophy of science. It is a fortuitous coincidence that the Association of Symbolic Logic now has a third journal, The Review of Symbolic Logic, the scope of which more or less covers the topics of the BIRS Workshop, and so it is only fitting that this special issue of the Review collects some of the papers presented at the workshop.

Bloglines Problems

In Bloglines, the atom feed for LogBlog shows up as “does not exist”, and it has so for a couple of days. Is that just me? Maybe I should just switch to Google Reader, but Google is almost taking on a Microsoft-ish quality in my mind. Plus, not sure it can do the blogroll the same way with the categories and all.

Arché Project on Logical Consequence

This just came in over the wire:

A new project on the Foundations of Logical Consequence will start at the University of St Andrews in January 2009. Details of the project can be found at:

http://www.st-andrews.ac.uk/~arche/projects/logic/

The project will run for three and a half years from January 2009 until June 2012. There are two post-doctoral posts running for the entire period of the project, and there are two studentships (restricted by the Research Council rules to EU residents) running for three years (paying fees, and also maintenance for UK residents).

Details of the Post-Doctoral Research Fellowships can be found at:

http://www.jobs.ac.uk/jobs/QQ513/2_Research_Fellows_in_the_Foundations_of_Logical_Consequence/

and

http://www.st-andrews.ac.uk/employment/Code,23739,en.html

and of the Postgraduate Studentships at:

http://www.jobs.ac.uk/jobs/QQ470/Two_PhD_Studentships_in_Foundations_of_Logical_Consequence/

Can I be a grad student again?