## 80-110 The Nature of Mathematical Reasoning

**Spring 2001**

*Dirk Schlimm*
# Homework No.7

Tuesday, March 6, 2001

Due Tuesday, March 13, 2001

**1. Category mistakes** (6 points)
In one of the earlier lectures there has been some discussion whether
it is admissible to speak of a "valid statement" or a "true
argument", after *valid*, *statement*, and *argument*
had been introduced as in the lectures.
This discussion is related to what Gilbert Ryle calls a *category
mistake*.

- Read handout #19. In particular parts (2) and (3). The
other parts are an application of Ryle's analysis to the mind-body problem.
- Explain what Ryle means by
*category mistake*. Use some
examples to illustrate the point.
- Discuss whether Ryle's analysis applies also to "This argument is true"?

**2. Interpretations of probability** (4 points)

Summarize the main interpretations of probability discussed in the
entry **probability** of the Cambridge Dictionary of Philosophy
(Handout #18). Write a few (more than two) sentences for each interpretation.