Teaching
I am posting two things here: Syllabi for some of the courses I've taught in the past, and copies of 'handouts' I've used in teaching these courses. A very old statement concerning my grading policies is also available.
Students should be able to use the syllabi as the beginnings of reading lists, should they find themselves interested in a topic that is not currently being taught. The handouts will be described below: Typically, these are fairly elementary presentations of technical material. Anyone who would like to use them (or modified versions of them) in their own teaching is welcome to do so: I'd appreciate credit, where it may be due, though (and will accept blame, where that is due).
Courses taught before Fall 2005 were given at Harvard. Those after that date were given at Brown.
Note: All of these files should open in a new window.
Syllabi
For many years now, my courses have all had websites of their own where one can find syllabi and related material. These are all hosted at frege.org. An up-to-date list of the sites can always be found there.
What follow are generally older syllabi, mostly from my courses at Harvard.
- Logic and Truth
- Philosophy 1880: Advanced Deductive Logic (from Fall 2007)
- Philosophy 188: Truth (from Spring 2006)
- Philosophy 143z: Truth (from Fall 2001)
- Philosophy 161: Metaphysics (Truth) (from Spring 1995)
- Realism and Anti-realism
- Meaning and Communication
- Sense and Reference
- Vagueness
- Other Courses
- Origins of Analytic Philosophy (from Fall 1993)
- Undergraduate Seminar: The Structure of Scientific Revolutions (from Fall 2007)
Handouts
Frege
- Begriffsschrift
An exposition of the central results, theorem 98 (the transitivity of the ancestral) and theorem 133 (the connectedness of the ancestral), of Gottlob Frege's Begriffsschrift. Available in PDF and Postscript. - Frege's Proofs
A simple sketch of Frege's proofs of the axioms of arithmetic in Die Grundlagen and Grundgesetze. Available in PDF and Postscript.
Logic
- Formal Background for the Incompleteness and Undefinability Theorems
As its name indicates, this note discusses the logical machinery one needs for the incompleteness and undefinability results due to Gödel and Tarski. It assumes nothing beyond a good understanding of the material that is covered in an introductory logic course: It assumes knowledge of some system of deduction; of the notions implication and interpretation; and at least a familiarity with the completeness theorem. Topics covered include the notion of a theory; properties of theories (for example, consistency and completeness); representability and definability; and Gödel numbering. To make things accessible to a wide audience, I just assume, rather than prove, that all recursive functions are representable and Q and argue that things are recursive by appeal to Church's Thesis. But, with such things assumed, the proof of the diagonal lemma, and of Tarski's Theorem from it, are then rigorous.
Available as PDF. - The Diagonal Lemma: An Informal Exposition
This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".)
Availble as PDF.
Truth
- Tarski's Theory of Truth
An elementary (but reasonably rigorous) exposition of a Tarski-style theory of truth for the language of arithmetic, together with a proof of its consistency (relative, of course, to that of a sufficient fragment of arithmetic).
Available as PDF. - Truth-theories for Fragments
A somewhat more sophisticated presentation of truth-theories for fragments (namely, the sigma-n fragments) of the language of arithmetic, themselves developed within weak theories (namely, sigma-n fragments). The presentation is based upon that in Petr Hájek and Pavel Pudlák, Metamathematics of First-order Arithmetic.
Available as PDF and as Postscript. - Kripke's Theory of Truth
An elementary, but again reasonably rigorous, exposition of a Kripke-style theory of truth for the language of arithmetic, together with a proof of its consistency. The proof given here is similar to that given by Martin and Woodruff. I discovered it while taking a course on this material with George Boolos; the version of the proof given here is based upon one published by Melvin Fitting.
The proof differs from Kripke's in that we do not use ordinals but Zorn's Lemma (so it is, in that sense, closer to Martin and Woodruff's proof). That makes it more suitable for beginners. My proof improves upon previous ones, in so far as we prove the existence not just of maximal fixed points but also of the minimal fixed-point (which is not just the intersection of all fixed points). No such proof, however, can be given of the existence of the maximal intrinsic fixed point, so the benefits come to an end here.
Available as PDF. - Truth and Inductive Definability
A much more sophisticated presentation of truth-theories for the language of arithmetic, developed within the general framework of the theory of inductive definitions on abstract structures (as first developed by Moschovakis). First, needed parts of the general theory of inductive definition are presented, together with proofs of basic results; then it is shown how both Tarski- and Kripke-style theories of truth can be developed on that basis (and some of their elementary properties thus established). Also contains remarks on, and a derivation of, the Kripke-Feferman axioms, and some suggestions about the importance of the notion of level.
Available as PDF.
