Day 27 in Mat115H

Today:

• Announcements:
  • Return of your one-page, typed, revised update on your project
  • Assignment due today: your write up (and resolution) of some syllogisms of Lewis Carroll. Let's look at some examples!
  • New assignment:
    • Please read the "Conclusion: Math and Aftermath" for next time (our last class discussion of new material!).
    • Test the trios of your handout (#1-26); for any that are not valid, demonstrate using the bi/tri-lateral diagrams of Carroll (due next Tuesday, 12/8).
  • Assignment of days for demonstrations: they're coming right up!

• Fit the Eighth
  • symbolic logic "as an entertainment for children to develop their powers of logical thought."
  • Elements of The Game of Logic
    • An example:
      1. Babies are crazy;
      2. Crazy people should be in an asylum.
    • Fundamentals
      • What's a syllogism? Give some examples. (p. 174)
      • What's a proposition? (p. 175)
      • Three types of propositions (p. 175)
      • What is negation?
      • The method: eliminating the common term (p. 173)
      • The board
        • Bilateral
        • Trilateral
        • Counters:

          Let us agree that a Red Counter, placed within a Cell, shall mean "This Cell is occupied" (i.e. "There is at least one Thing in it").

          Let us also agree that a Red Counter, placed on the partition between two Cells, shall mean "The Compartment, made up of these two Cells, is occupied; but it is not known whereabouts, in it, its occupants are." Hence it may be understood to mean "At least one of these two Cells is occupied: possibly both are."

          Our ingenious American cousins have invented a phrase to describe the condition of a man who has not yet made up his mind which of two political parties he will join: such a man is said to be "sitting on the fence." This phrase exactly describes the condition of the Red Counter.

          Let us also agree that a Grey Counter, placed within a Cell, shall mean "This Cell is empty" (i.e. "There is nothing in it").

      • The universe
    • Example: p. 186
    • Example: top of p. 174
      • Using Venn Diagrams (and their problems), and comparing
      • Carroll's method
    • Other Diagrams to help us solve these problems
      • e.g. your homework problem
    • Further examples:
      • "No son of mine is dishonest; People always treat an honest man with respect."
      • "All cats understand French; Some chickens are cats".
      • Trios of Concrete Propositions (and a selection of Trios of Concrete Propositions for homework)