For Wednesday, read chapter 2, sections 3 and 4. As nongraded homework, do the problems at the end each section.

1

• For Wednesday, read chapter 2, sections 3 and 4.
  As nongraded homework, do the problems at the end
  each section.
• Also try exercises 7.1, C, D, and E on the Power
  of Logic web tutor
• http//www.poweroflogic.com/cgi/menu.cgi
• It uses a dot in place of the ampersand. Also,
  look at the help link to see how to enter the
  symbols.

2

• Soundness
• If possible, we would like our arguments to be
  valid and to have all true premises. An argument
  with both characteristics (valid, with all true
  premises) is sound.
• Any argument that is not sound is unsound. An
  unsound argument is either invalid or has at
  least one false premise (or both).

3

• All whales are fish.
• No fish live in trees.
• Therefore, no whales live in trees.
• Valid? Sound?
• Answer Valid, but unsound one false premise is
  enough to make the argument unsound.

4

• Some fruits are green.
• Some fruits are apples.
• Therefore, some fruits are green apples.
• Answer Invalid, and unsoundeven though all
  three statements in the argument are true.
• A note about some For our purposes, some
  means at least one.

5

• These arguments involve category relations all
  humans are said to be in the category of
  reptiles.
• But for the next few weeks, well be studying
  sentential logic we will treat entire simple
  sentences as single units
• If I win the lottery, then Ill be rich.
• I just won the lottery.
• Therefore, Im rich

6

• Sentential Logic
• The system contains three kinds of symbol, each
  playing a different role
• 1. The five sentential connectives (tilde),
  (ampersand), v (vee), ? (arrow), and ?
  (double-arrow).
• These connect smaller formulae together (or
  preface them, in the case of the tilde).
• 2. Capital letters A-Z abbreviate simple (or
  atomic) statements. These are grammatically
  simple sentences that have no words corresponding
  to sentential connectives in them.

7

• abbreviates not and equivalent phrases,
  such as it is not the case that
• Joanne is not tall. (J Joanne is tall)
• J
• It is not the case that Tom is a lawyer. (T Tom
  is a lawyer)
• T

8

• abbreviates and and equivalent terms
• José is a doctor and Martin is a lawyer. (J José
  is a doctor M Martin is a lawyer)
• J M
• Theresa is poor, even though she is a doctor. (P
  Theresa is poor D Theresa is a doctor)
• P D

9

• v abbreviates the inclusive either...or...
  and equivalent phrases (inclusive or is
  and/or)
• Either Jane is over four years old or over forty
  pounds. (F Jane is over four years old P Jane
  is over forty pounds)
• F v P
• We often use or to mean either...or...but not
  both this is the exclusive or. We can
  symbolize it if need be, but the formula is
  somewhat complex.

10

• 3. Parentheses are used for grouping.
• Either Tom is a doctor or Jill is a doctor, but
  not both. (T Tom is a doctor J Jill is a
  doctor)
• (T v J) (T J)
• This expresses the exclusive or.