80-110   The Nature of Mathematical Reasoning

Spring 2001

Dirk Schlimm

Homework No.9

Thursday, March 22, 2001
Due Tuesday, April 3, 2001

1. Logical equivalence (1 point)

Read FOL, pages 44-46 (Section 3.5). Do the following problem:

2. Satisfiability and logical truth (3 points)

Read FOL, pages 51-64 (Sections 3.7-3.8). Do the following problems:

3. Alternative notation (1 point)

Read FOL, pages 88-90 (Section 3.12). The "Polish notation" should remind you of the axiomatization of sentential logic in Handout #16!
Do the following problem:

4. Reflections (5 points)

Imagine you ware at home over spring break and you met your older sister who is a graduate student of physics at MIT. After you told her that you are attending a course on the nature of mathematical reasoning, she says: "Well, I know what the nature of mathematical reasoning is - it's calculating. The Greeks started it 500 years ago with simple equations, and now we have differential equations and computer programs like Maple or Mathematica to solve them. It has become a zillion times more complex, but basically it's still the same thing." What would you reply to her? Write a few paragraphs.