80-110   The Nature of Mathematical Reasoning

Spring 2001

Dirk Schlimm

Homework No.3

Thursday, February 1, 2001
Due Tuesday, February 6, 2001

1. Kinds of arguments (3 points)

Give an example of an argument (different than those mentioned in handout #6) for each the following forms: (i) modus ponens, (ii) modus tollens, (iii) hypothetical syllogism, (iv) disjunctive syllogism, (v) dilemma.

2. Deductive validity (3 points)

Answer the following question in a paragraph or two.

Is it possible to have a valid deductive argument with the conclusion that `The moon is made of green cheese'? Justify your answer. (See also FOL, p.24-25)

3. Hume on induction (4 points)

Answer the following questions in a paragraph or two.

a) What are `relations of ideas' and `matters of fact' according to Hume?

b) For Hume, Mathematics belongs to the `relations of ideas'. Why? Do you agree?

c) What would Hume reply to the claim `I know for sure that the sun will rise tomorrow'?


Please hand in your portfolio by Tuesday, February 6, before class. Do not bring the portfolio to class, but drop it off at Dirk's office in Baker Hall A 60 B.

Make sure to read in the syllabus what the portfolio should contain. All terms from the index list on the syllabus that have been mentioned in class or in the homework should appear in the index.