80-110 The Nature of Mathematical Reasoning

Thursday, July 13 2000

Quiz 3

Name: _______________________________

1. When is an argument sound?

2. An argument is sound, if it is valid and its premises are true. (Handout #5).

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.   A
:
:
---------
not A

From the assumption A and the derivation of a contradiction you infer `not A'. (Lecture 7/12/00)

7. Give a short argument such that from the premises
a) God is, by definition, the most perfect being, and
b) It is more perfect to exist than not to exist,
the conclusion `God exists' follows.

8. Assume: God does not exist.
Then, there is something more perfect than God, by assumption (b).
In other words, God is not the most perfect being.
Therefore, by reductio ad absurdum, God does exist. (This argument is attributed to Descartes.)

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 7/11/00)