Essay topic suggestions

Below are some topic suggestions for an essay for 80-211 Arguments and Inquiry. Feel free to suggest an own topic that is related to the material presented in class. Any applications of formal logic are worth considering. Feel free to dicuss any ideas you have with your instructor.

The topic can be chosen by the student, but must be approved by the instructor.

The essay should be 3-5 pages long and include a short presentation and discussion on an application on history of logic.

An outline must be presented to the instructor no later thantwo weeks before classes finish (i.e., Friday April 18, 2003).

The essay is due one week before classes finish (i.e., Friday April 25 2003).

You must include citations of all the materials you use to write the essay. This includes books, articles, websites, etc. I have compiled a list of examples on how to make citations.

The essay provides you the opportunity to study in more detail a particular subject of the course that interests you. Further information regarding the essay will be provided in class. Starting early with the essay gives you the advantage of having more time to work on it, discuss it with the instructor, and allows you to avoid being cluttered with work at the end of the semester.

Note: You can get copies of the literature mentioned below from the instructor.
1. Discuss whether logic is an account of how people reason or of how people should reason. What are George Boole's views on this, as expressed in An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities (1854).

2. Explain and discuss the difference between classical and intuitionistic logic. (Use Arend Heyting's Intuitionism: an introduction, 1956.)

3. Three-valued logic: In 1921 Emil Post generalized the notion of truth values for logic and introduced 3-valued logic as well as m-valued logics. Present his paper Introduction to a general theory of elementary propositions (Am. J. Math:43(3), 163--185; available at JSTOR) in a clear and concise fashion.

4. Discuss the difference of direct and indirect proofs (by contradiction. What are reasons one could be against using proofs by contradiction in mathematics? (Mancosu, Philosophy of Mathematics and Mathematical Practice in the 17th Century, 4.3 "Proof by contradiction from Kant to the present", p.106-117).

5. In 1919 Cassius J. Keyser introduced the notion of axiom systems as "doctrinal functions" (JPPSM:15(10), 262-267; available at JSTOR) in analogy to propositional functions. Present and discuss Keyser's view on axiomatic systems.

6. Present W.v.O. Quine's use of logic to assess what things do exists in On what there is (1948).

7. Present the section on the completeness of propositional logic from the book in a clear and precise fashion, so that your friends could understand it (p.84-91)

8. In Chapter 1 The Science of Deduction" of The Sign of the Four, Sherlock Holmes deduces that Watson has been at the post office to dispatch a telegram. Present Sherlock Holmes's chain of reasoning in the language of predicate logic.

9. The psychologist Clark Hull has formulated his theory of rote learning completely in predicate calculus. An example derivation is printed as Appendix A of Mathematico-deductive theory of rote learning, 1940 (p.315-320). Present this proof in the symbolism used in this class, rather than in Hull's arcane one.

10. Is it possible to introduce a logical connective in any way you like? Summarize and discuss The runabout inference-ticket by A.N.Prior and Tonk, plonk and plink by Nuel D. Belnap. (In Philosophical Logic, P.F. Strawson (ed.), p.129-139.)

11. Are proofs generated by a computer really proofs? (1) Present and discuss DeMillo et al. Social processes and proofs of theorems and programs.

12. Are proofs generated by a computer really proofs? (2) Present and discuss Tymoczko The four-color problem and its philosophical significance.

13. Summarize and discuss Georg Kreisel's article Mathematical logic: what has it done for the philosophy of mathematics? (1967). (In The Philosophy of Mathematics, J. Hintikka (ed.), 147-152.) [Difficult]

14. Present in a clear and concise fashion one of the following sections from the textbook that have not been covered in class:
    4.4 The Syllogism
    App. A: Normal Forms
    App. B: The elementary theory of classes