Philosophy 1880: Syllabus

The syllabus is somewhat approximate and subject to change.

29 January Introductory Meeting, Chapter 1
1 February Chapter 2
Problem Set #1 due 8 February
3–12 February Chapter 3; Section 4.1
It's still worth reading Turing's original paper "On Computable Numbers", Proceedings of the London Mathematical Society s2-42 (1937), pp. 230-65 (Oxford Journals Archive). Section 9 of that paper contains a fascinating justification of his definition of computability in terms of a "conceptual analysis" of the intuitive notion. It's also worth looking at his paper "Computing Machinery and Intelligence", Mind 59 (1950), pp. 433-60 (JSTOR).
Problem Set #2 due 19 February
15–19 February Chapters 5–6
22 February

No Class: Long Weekend

24 February Chapters 6
Problem Set #3 due 2 March7 March
26 February–4 March Chapter 7, Section 8.1
There is a handout, "Coding Turing Machine Computations", that contains the definitions of a lot of the functions we need to do that.
Problem Set #4 due 11 March
7–11 March Chapters 9–10
A somewhat less formal presentation of Tarski's definition of truth can be found in the handout "Tarski's Theory of Truth", which I use in other classes. Note that this definition is given for the language of arithmetic, and only for the standard interpretation of that language. But it might nonetheless prove helpful.
Problem Set #5 due 18 March
14–18 March Section 11.1; Chapter 13
There is a handout that summarizes some of the important definitions and lemmas in the proof of the Compactness Theorem.
21 March

No Class: Snow Day

23 March Chapter 13
There is a handout that summarizes some of the important definitions and lemmas in the proof of the Compactness Theorem. There is another handout that contains the proof of the Closure Lemma that was presented in class.
Problem Set #6 due 6 April
25 March Chapter 14
You should have a look also at the handout on the simplified sequent calculus, which is the formal system we will actually discuss.
28 March–1 April

No Class: Spring Break

4–13 April Chapters 14-15
You should have a look also at the handout on the simplified sequent calculus, which is the formal system we will actually discuss.
There is also a handout containing the revised definition of "theory", and related notions, that we'll use in class.
Problem Set #7 due 20 April
15–27 April Chapter 16
There is a handout that lists the axioms of the various theories we will discuss and sumamrizes the important results we will prove.
Problem Set #8 due 4 May
29 April–4 May Chapter 17
You can find a very informal exposition of one form of the diagonal lemma here. You may also find it helpful to read the only slightly more formal exposition in §10 of this document.
Problem Set #9 due 11 May
19 May, 2pm Final Examination

Richard Heck Department of Philosophy Brown University