One last plug for the Logic Instruction and Philosophy Graduate Training session at this week’s APA/ASL meeting in San Francisco: It will take place as scheduled in the evil St. Francis hotel. Nevertheless, we hope you can all come. Note that Delia Graff won’t be joining us, unfortunately; but Brian Weatherson has agreed to participate in her stead. An extended abstract follows, note the plan of the session at the end.
UPDATE: Materials from the session are online.
ANDREW ARANA (CO-CHAIR), MICHAEL GLANZBERG, BRIAN WEATHERSON, TED SIDER, AND RICHARD ZACH (CO-CHAIR), Special Session on Logic Instruction and Philosophy Graduate Training. Session X-K, Saturday, March 26, 2005, 2-5 pm.
Formal Logic in the Philosophy Curriculum. Over more than half a century, formal logic has held an important position in analytic philosophy and consequently in the philosophy curriculum at English-speaking philosophy programs, both at the undergraduate and graduate level. Typically, undergraduates are required to complete a first course in formal logic covering semantics and proof theory of classical first-order logic. A graduate course on metalogic dealing with completeness and Löwenheim-Skolem theorems, undecidability and often also Gödel’s Incompleteness Theorems is a standard requirement in Ph.D. programs.
The Special Session on Philosophy and Logic Education provides a forum for reflection on and evaluation of the form and content of such courses, and the place and role formal logic courses play or should play in training in philosophy, especially at the graduate level.
Logic and Philosophy. One issue explored at the session is the question of how formal logic relates to other areas of philosophy, and how logic courses and requirements should relate to other courses and requirements in Ph.D. programs. On the one hand, working in formal logic is certainly a different kind of enterprise than, say, working in metaphysics or ethics. At the introductory level, the main motivation to require courses in logic is simply that it trains students in reasoning and assessing arguments. Logic provides the tools (formalization, deductive proofs, truth tables and interpretations) to do this. At this level, logic courses are more in the business of imparting skills than of a body of knowledge. The situation is somewhat different regarding requirements at the graduate level, where logic training presupposes those skills to a large extent, and students are taught results, such as the completeness theorem, and their proofs. And as these are in the first instance mathematical results, the question might be raised, “Why burden philosophy Ph.D. students by requiring such courses?”
Methodology. There are undeniably similarities in the methodology of formal logic and philosophical methodology: often, the limitative results of metalogic have served as examples for how questions could be made precise so that they are amenable to a (often negative) solution, and how to give such solutions with mathematical rigor. One motivation for requiring metalogic in philosophy graduate training then is that it imparts to students an appreciation for limitative results, and how they can be proved.
Content. There are also connections between formal logic and other areas of philosophy in terms of content. This is most obviously so in the philosophy of logic (e.g., theories of truth), the philosophy of mathematics (e.g., Gödel’s theorems as refutation of logicism and formalism), and the philosophy of language (formal semantics), but also in other areas. One might think of Lucas’ argument against mechanism, Putnam’s model-theoretic argument, or the contributions of formal logic in illuminating modality, the logic of knowledge, mereology, etc. Philosophy Ph.D.’s arguably should be able to understand, appreciate, and apply such results, and acquire the foundation necessary for further training enabling them to contribute to this literature. A more specific question for the panel then is how a graduate logic course would best accomplish this. Which results should be taught? How should they be taught? What is the relative importance of the topics now standard in graduate logic courses and more recent developments such as formal theories of truth or intensional logics and possible worlds semantics? Which recent developments should be taught, in what form, and where (required courses, supplementary courses, or incorporated into subject-specific courses, e.g., possible worlds semantics in metaphysics courses)?
History of Analytic Philosophy. The history of philosophy is rightfully considered a central part of the philosophy curriculum. As the history of analytic philosophy matures as a recognizable field of study (and teaching), a background in logic and metalogic becomes increasingly important. For the major figures in early (Frege, Russell, Wittgenstein) and more recent (Carnap, Quine, Lewis) analytic philosophy, logic was a central tool in philosophy and an area to which they themselves contributed. On the one hand, this raises similar questions as above: What to include or emphasize in graduate logic courses so to enable graduate students to understand, e.g., Russell’s theory of types, or what Frege’s Axiom V says? On the other hand, perhaps graduate logic courses should incorporate the philosophical aspects of the development of logic in the 19th and 20th century?
Additional Questions. (1) Textbooks: To some extent, the form and content of courses is influenced by the available textbooks. In graduate level logic courses, the two most popular texts are probably Boolos, Burgess, and Jeffrey’s Computability and logic and Enderton’s A mathematical introduction to logic. In light of the issues outlined above, how do they and other texts serve the purpose? What would an ideal graduate level logic text for philosophy look like? (2) Logic in the Profession: One important aspect of graduate training is, of course, preparation to teach. How important is it to have received advanced training in logic in order to effectively teach an introductory course? How can graduate training in logic enhance the effectiveness of introductory logic teachers?
Plan of the Session. Richard Zach will introduce the panelists and the questions and discuss the role of logic in the history of analytic philosophy. Michael Glanzberg will address some of the “content” issues: areas of logic which are closely related to philosophical concerns where there are some relatively accessible results, but also, where the more you look, the more interesting logic there is to be found. This includes, in particular, theories of truth and quantifiers, and their relation to definability theory and finite model theory. Brian Weatherson will speak on the place of teaching modal logic and non-classical logics in graduate courses. Andy Arana will talk about the lasting importance of the traditional metalogical results (completeness, incompleteness, Löwenheim-Skolem), what philosophical application they have, as well as about the general significance of limitative results is, and what it takes to get to a point where one can prove them. Finally, Ted Sider will talk about a graduate course on “philosophically useful logic” he has been developing, and generally on what logic is useful in philosophy. The session will end in an open discussion with the audience.