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Submitted by Richard Zach on Thu, 12/02/2004 - 10:52pm

1. Reminder: if you want a reason to go to the APA Pacific Division Meeting in San Francisco in March, and have something logical to present: The deadline for submission of contributed papers to the ASL Spring Meeting is a week away.

2. There will be a special session on logic and philosophy, especially, logic in philosophy graduate training at said APA/ASL Meeting. Here's the abstract; if you have suggestions for questions, comments, etc., please share! And come to the session, if you can.

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?

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## Comments

It's probably worth considering what kind of undergrads sign up for Logic courses. Beyond the basic definitions and an overview of formal material, they're probably better off leaving with a decent ability to mix formal and informal material that will allow them to identify faulty arguments and explain where the reasoning falls flat, either with regards to their own claims, or to counter anothers. Because a grounding in logic protects one from being abused by rhetorical gimmicks, teaching the practical value of logic should be a priority.For more advance courses, the best thing for academic logicians to grasp is that a fair number of your students will be engineers or computer scientists. If you send grad students who don't know any code down to teach kids who've already had to learn Von Neumann gates and boolean operators and C languages, you might as well feed your grads to a pack of hungry lions. So make sure all your grad students can pass EECS 101-201, and can handle C+ type basic programming. (Computer languages are ALL examples of formal symbolic systems of logic, and at their most basic reduce to binary machine languages of '0' and '1'). In truth, if philosophy departments subjected their doctoral candidates arguments to a computers standard of logic, as programmed and defined by its analytical philosophers, I think you'd find other branches of philosophy would view the suggestion with outright horror. Why, you'd put the philosophers who weren't proficient in logic out of work!

Richard -- there are actually two types of graduate programs even in analytic philosophy. One type requires some sort of basic metatheory course. The other type requires only an undergraduate formal logic (symbolization, derivations, counterexamples) course, even for graduate students (examples of good departments like this: Toronto, Chicago, Berkeley, Harvard, Arizona). Arguments can be given on both sides concerning what is an appropriate requirement for all philosophy graduate students.--Michael Kremer

Michael's comment brings up an important point about the distribution of formal requirements. To take examples from departments I have been in:Harvard's is indeed an undergraduate logic class--indeed the same course that Harvard undergraduates from across the college take to satisfy theirt "Quantitative Reasoning" requirment for the undergrad degree.Arizona's requirement cannot in the normal case be met by taking a standard undergraduate proficiency course. The standard way students fulfill it (this was true when I was there, and think it is still true) is by taking a one term of a year-long course titled "Symbolic Logic"--but this is a metatheory course, using Mendelson and covering completeness, incompleteness, undecidability, L\"ob's Theorem, etc. There is some flex in the requirment, in that it can also be fulfilled by taking Formal Semantics, or one of the more technical philosophy of physics courses, or by taking a seminar in logic, or (for that matter) by taking any grad course deemed by the Graduate Advisor to meet the requirement.And, at Texas, the requirement in logic is now treated *not* as a proficiency-type requirement (on a par with a foreign language requirement), but as a genuine area distribution requirement to be fulfilled in the way that distribution requirements are fulfilled. At Texas that means taking a graduate seminar in the area.--Thony Gillies

I actually have a survey up on the various ways US departments deal with a graduate logic requirement inhttps://www.ucalgary.ca/rzach/blog/2004/10/formal-logic-and-philosophy-i... .