Day 3: mat385

Today:

• Collect homework 1.1 (grace period?): grading #5 and 31/34

• Homework 1.2 due next time, in any event.

• Last time: Section 1.2 (pdf): propositional logic

• Questions over 1.2?

• section 1.3 (pdf) (Quantifiers, Predicates, and Validity)

Links:

• What does it mean when one says that "The domain is the whole world."? (e.g. p. 43/46, problem 11/16).

  On a set containing all sets: Russell's paradox.

  "Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.

  "Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves S. If S is a member of itself, then by definition it must not be a member of itself. Similarly, if S is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics."