Essay topic suggestions
Last updated: 4/7/03
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.
- 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).
- Explain and discuss the difference between classical and
intuitionistic logic. (Use Arend Heyting's Intuitionism: an
introduction, 1956.)
- 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.
- 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).
- 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.
- Present W.v.O. Quine's use of logic to assess what things do
exists in On what there is (1948).
- 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)
- 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.
- 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.
- 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.)
- Are proofs generated by a computer really proofs? (1) Present and
discuss DeMillo et al. Social processes and proofs of theorems and
programs.
- Are proofs generated by a computer really proofs? (2) Present and
discuss Tymoczko The four-color problem and its philosophical
significance.
- 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]
- Present in a clear and concise fashion one of the following
sections from the textbook that have not been covered in
class:
© Dirk Schlimm, Last
modified: 4/7/03