PHL309 Logic, Language, and Thought
Professor: Craig DeLancey
For the next several days we'll be discussing Kant. I'll post our
class notes soon.
A quick homework. Give an example of a sentence for each of
Kant's four kinds: a priori, a posteriori, synthetic, analytic.
Each sentence example must be your own (no credit for an example
we used in class). Then, can you give an example of an analytic
a proiri sentence; an example of a synthetic a posteriori
sentence; and a synthetic a priori sentence. (If you disagree
with Kant's notions, consider yourself as trying to find
examples that he would accept.)
Start reading Logicomix, if you got it. It is also on
reserve in the library, so you can read it there! It's fun and a
quick read, and the glossary is really quite good also. (The
glossary is a comic also.)
Midterm. Possible questions include:
- Reconstruct one of Galileo's arguments that we cannot have an
actual infinity or that we cannot have actual infinitesimals.
Make your reconstruction an explicit reductio ad absurdum
argument, in which you make clear the contradiction, and the
premise we reject because of the contradiction.
- Answer some basic questions about set membership, subsets, powersets,
the definition of cardinality.
- What is Cantor's Claim (about some proper subsets of infinite
sets)? How we can use Cantor's Claim (assuming it works) to
answer some of Galileo's arguments?
- Reconstruct Cantor's Diagonal Argument to prove that the cardinality
of the reals is greater than the cardinality of the natural numbers.
- What is Cantor's Theorem?
- How does Cantor's Theorem, and the claim that a set exists if we
can determine its members, result in Cantor's Antinomy.
- Give an example of a sentence for each of Kant's four kinds:
a priori, a posteriori, synthetic, analytic.
Tentative Assignments (subject to revision)
Final exam, in class, 10:30 a.m. -- 12:30 p.m.