*Dirk Schlimm*

Due Friday, July 14, 2000

1. What is the meaning of
`a priori'? (Look it up in a dictionary).

Questions 2.-5. refer to Handout #9, *Proofs by
contradiction from Kant to present*. Answer each of them in a
paragraph or two.

2. What distinguishes mathematical from
transcendental proofs, according to Kant?

3. Why does Kant allow proofs by
contradiction in mathematics, but not in philosophy?

4. What does Kant consider to be `grounded
knowledge'?

5. What is Bolzano's view on apagogical
proofs in mathematics?

6. Discuss proofs by
contradiction: are they on the same level as direct proofs? What are
the advantages and disadvantages? If you could prove a theorem
directly or using an indirect argument, which one would you choose,
and why?