Day 3: mat385

Today:

• Note: the book's been placed on reserve at the library.

• Class notes are on-line

• Collect homework 1.1 (grace period?)

• Finish and Review section 1.2 (propositional logic)

• Questions on homework/old stuff?

• 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, problem 11).

  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."