Take Note

1
Take Note

• We will not be looking at the Aristotelian
  approach to Venn diagrams and rulesall Boole
  from here on out
• Read through the rest of the chapter for Thursday
• Goal date for first midterm two weeks from today
  (it will cover everything through chapter 5)

2
Venn Diagrams and Validity

• Remember if the argument contains one universal
  premise and one particular premise, diagram the
  universal premise first. Otherwise, it does not
  matter in which order you diagram premises

3
Examples

• P1 Some cats are pets
• P2Some pets are animals loved by humans
• C1 Some cats are animals loved by humans
• P1 All astronauts are men
• P2 No men are cowards
• C1 No astronauts are cowards

4
More examples

• P1 All students are citizens
• P2 Some citizens are not patriots
• C1 Some students are not patriots
• P1 No children are voters
• P2 No voters are democrats
• C1 No children are democrats

5
More!

• P1 All whales are mammals
• P2 All whales are animals that live in the sea
• C1 Some mammals are animals that live in the sea
• P1 No chickens are animals that weigh over 10
  pounds
• P2 All animals that weigh over 10 pounds are
  mammals
• C1 No chickens are mammals

6
Rules

• We can evaluate the validity of categorical
  syllogisms by determining whether they conform to
  5 rules
• Rule 1 The middle term must be distributed at
  least once
• Why?

7
Rules Continued

• Rule 2 If a term is distributed in the
  conclusion, then it must be distributed in a
  premise
• Why?
• Rule 3 Two negative premises are not allowed
• Why?

8
More Rules

• Rule 4 A negative premise requires a negative
  conclusion, and a negative conclusion requires
  are negative premise
• Why?
• Rule 5 If both premises are universal, the
  conclusion cannot be particular
• Why?

9
Reducing the Number of Terms

• Consider this argument
• Everything thats not a mammal is not a dog, and
  since any mammal is warm-blooded, dogs are
  warm-blooded.
• This argument is about warm-blooded things, dogs,
  and mammals. But it is also about non-dogs and
  non-mammals

10
We Might Translate Like This

• P1 All non-mammals are non-dogs
• P2 All mammals are warm-blooded creatures
• C1 All dogs are warm-blooded creatures
• Problem Five terms!
• Solution Contrapose P1

11
We Get

• P1 All dogs are mammals
• P2 All mammals are warm-blooded creatures
• C1 All dogs are warm-blooded creatures
• We can use the operations of conversion,
  obversion, and contraposition to reduce the
  number of terms to three, and then use Venn
  diagrams or rules to test validity

12
But Remember!

• You can only use these operations when they
  produce logically equivalent claims
• Conversion E and I
• Contraposition A and O
• Obversion All forms