Day 2, Mat385: Welcome, Let's Go!

Last time

Next time

Announcements
- This session will be captured on Zoom, if I remember to turn it on, and record it. Please help me to remember.
  Here's the recording of the session from the first day, and here's today's.
- Roll (anyone need to fill out a card?)
- I still have two textbooks (Edition 5), if anyone wants a hardcopy.
Last time:
- We chatted about Lewis Carroll's The Game of Logic, and you tried your hands at playing the game.
  A couple of interesting observations:
  - Two types of "counters" -- grey (there's nothing in this cell) and red (there is -- or may be -- something in this -- or these -- cells). Frequently our goal is to force a red counter "off the fence" -- to make it choose sides.
  - It's important to keep the universe in mind: in the syllogisms that Carroll tackled on your handout, the first two involved animals (pigs and rabbits). In the first case, the universe was all creatures (say); in the second, the universe was rabbits! It makes a difference in how one treats a problem....
    We'll glance at those.
  Then let's look at an example in detail: one of those with multiple premises, found within this description of Lewis Carroll and his logic game:
  1. No birds, except ostriches, are 9 feet high.
  2. There are no birds in this aviary that belong to anyone but me.
  3. No ostrich lives on mince pies.
  4. I have no birds less than 9 feet high.
  Clearly the conclusion is that "No bird in this aviary lives on mince pies....":)
  How do we arrive at that, the Carroll way?
  (you can do it with "algebra", as we will in these next few sections, but it's far less amusing!:) And, as you can see in the comments to this attempt, if you make a mistake in your formulation of the algebra, you won't arrive at the correct conclusion (except by accident, perhaps).
Today we delve into section 1.1, and take a more "mundane" look at logic! That is, without the mince pies....
- Section 1.1 (Statements, Symbolic Representations, and Tautologies), which we'll examine using the highlight worksheet 1.1. If you have your copy, play along!
- There's a sheet for highlight worksheet 1.2, so you can prepare for next Tuesday (and get started on those homework problems in section 1.2). Remember that your homework problems for 1.1 will be due next Wednesday, Midnight.
Links:
- More "historical logic": this is a fun one (the dilemma of Protagoras and Eualthus)
  The story reminds me of a poem by A. E. Housman: The Laws of God, The Laws of Man. The reason that the story of Protagoras and Eualthus is a dilemma, a paradox, or a quandary, is that there are two different systems of laws operating.
- Some Fun, Motivating Examples from Propositional and Predicate Calculus
- Paradoxes are fun! Evidently Eubulides was the master of them.

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