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1
Traditional Logic II
Martin Cothran
Instructor
Traditional Logic II
Chapter 8
2
Types of Hypotheticals
ConditionalDisjunctiveConjunctive
Types of Hypotheticals
ConditionalDisjunctiveConjunctive
3
Types of Hypotheticals
ConditionalDisjunctiveConjunctive
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
4
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
5
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
6
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
7
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
8
Disjunctive Syllogisms
Either Socrates is a philosopher, or Socrates is a
farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
Disjunctive Syllogisms
Either Socrates is a philosopher, or Socrates is a
farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
9
Disjunctive Syllogisms
Either Socrates is a philosopher, or Socrates is a
farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
Disjunctive Syllogisms
Either Socrates is a philosopher, or Socrates is a
farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
10
Disjunctive Statements
Either P or Q
~P
Therefore, Q
Disjunctive Syllogisms
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
11
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
12
Disjunctive Syllogisms
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is not a farmer
Therefore, Socrates is philosopher
Alternants
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is not a farmer
Therefore, Socrates is philosopher
13
Disjunctive Syllogisms
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is not a farmer
Therefore, Socrates is philosopher
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
14
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
Disjunctive Syllogisms
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is not a farmer
Therefore, Socrates is philosopher
15
Disjunctive Syllogisms
Either P, or Q
Not P
Therefore, Q
Denying the first alternant
Denying the second alternant
Affirming the first alternant
Affirming the second alternant
Four moods in disjunctive hypothetical syllogisms
16
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
17
Disjunctive Fallacies
Fallacy of Affirming the First Alternant
Either P, or Q
P
Therefore, not Q
18
Fallacy of Affirming the First Alternant
Either Jesus is God, or Jesus is a man
Jesus is God
Therefore, Jesus is not a man
Fallacy of Affirming the First Alternant
Either Socrates is a farmer, or Socrates is a
philosopher
Socrates is philosopher
Therefore, Socrates is not a farmer
19
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
20
Inclusive vs. Exclusive Disjunctions
Either Socrates is a farmer, or Socrates is a
philosopher
Inclusive vs. Exclusive Disjunctions
Either Socrates is a philosopher, or Socrates is not a
philosopher
21
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Hypothetical Syllogisms
22
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
23
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
24
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
25
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
26
Reduction of Disjunctive Syllogisms
If _______________________, then Socrates is a farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
27
Rules for ReductionRule #1: The minor premise and the conclusion must remain unchanged
Rule #2: The major premise is changed from a disjunctive statement to a conditional
statement by:Step #1: Placing the alternant denied in the
minor premise in the place of the consequent
Step #2: Placing the denial of the other alternant in the place of the antecedent
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
28
Reduction of Disjunctive Syllogisms
Either Socrates is a farmer or Socrates is a philosopher
Socrates is not a farmer
Therefore, Socrates is a philosopher
Reduction of Disjunctive Syllogisms
If _______________________, then Socrates is a farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
29
Reduction of Disjunctive Syllogisms
If Socrates is not a philosopher, then Socrates is a farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
Reduction of Disjunctive Syllogisms
If Socrates is not a philosopher, then Socrates is a farmer
Socrates is not a farmer
Therefore, Socrates is a philosopher
30
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
31
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
32
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
33
What is a disjunctive syllogism?The elements of disjunctive syllogisms
Two valid moods for disjunctive syllogismsTwo invalid moods for disjunctive syllogisms
Inclusive and exclusive disjunctionsReducing disjunctive syllogisms to conditional
syllogisms
Disjunctive Syllogisms
Exercises
34
Exercises
Exercise 25
Exercise 25
Either Frodo destroys the ring or evil will triumph
Frodo destroys the ring
Therefore, evil will not triumph
35
Exercise 25
Either P or Q
P
Therefore, not Q
Exercise 25
Either P or Q
Not P
Therefore, Q
36
Exercise 37
Exercise 37
Either abortion destroys a human being, or abortion only destroys a mass of tissue
Abortion does not only destroy a mass of tissue
Therefore, abortion destroys a human being
37
Exercise 37
Exercise 37
Either we stop the profitability of urban sprawl, or we will destroy green space
We have not stopped the profitability of urban sprawl
38
Exercise 37
Either we stop the profitability of urban sprawl, or we will destroy green space
We have not stopped the profitability of urban sprawl
Therefore, we will destroy green space
Traditional Logic II
Martin Cothran
Instructor
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