80-150 The Nature of Reason
Summer Two 2001, Dirk Schlimm
Homework No. 4
Friday, July 6
Read TTT, pages 22-31.
Infinity and cardinality. (5 points)
- If you feel comfortable with the mathematics discussed on pages
25-30, explain Cantor's second proof (p.29-30) in your own words.
- If pages 25-30 don't make much sense to you, formulate 5-10 questions
that you would ask in order to understand the text better.
Category mistakes. (5 points)
In yesterday's lecture we have said that
it is not 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
- Read the Ryle handout. 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"?