80-110 The Nature of Mathematical Reasoning

Thursday, February 8, 2001

Quiz 3

Name: _______________________________

1. When is a judgment objective (within a certain community)?

2. A judgment is objective if its outcome does not depend on the judge; taste of coffee vs. validity of argument. (Lecture).

3. What is a formal argument?

4. An argument is formal if the validity of the argument does not depend on the meaning of the symbols employed. (Handout #5).

5. What is the structure of an argument of the form reductio ad absurdum?

6.   not A
:
:
---------
A

From the assumption `not A' and the derivation of a contradiction you infer `A'. (Lecture)

7. If you know that the premises of an argument are true, and the conclusion is true, what do you know about the argument? (Is is valid?)

8. You know nothing, the argument could as well be invalid. (Lecture)

9. Consider the following argument:
If taxes are lowered, my income rises.
My income rises.
Therefore, my taxes are lowered.
Assuming that all three statements are true, is this a valid argument? Justify your answer in one sentence.

10. The argument is not valid. Because it is possible for the premises to be true, but the conclusion to be false, for example, if my income rises because of a raise and not because of the lowering of my taxes. (Lecture)