Homework No. 5

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?