traditional logic ii - memoria presshypothetical syllogisms what is a disjunctive syllogism? the...

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Traditional Logic II

Martin Cothran

Instructor


Chapter 8

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Types of Hypotheticals

ConditionalDisjunctiveConjunctive



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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

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syllogisms





syllogisms


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syllogisms





syllogisms


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syllogisms





syllogisms


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syllogisms





syllogisms


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Disjunctive Syllogisms

Either Socrates is a philosopher, or Socrates is a

farmer

Socrates is not a farmer

Therefore, Socrates is a philosopher



farmer



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farmer





farmer



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Disjunctive Statements

Either P or Q

~P

Therefore, Q


Either Socrates is a farmer, or Socrates is a

philosopher



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syllogisms





syllogisms


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philosopher


Therefore, Socrates is philosopher

Alternants


philosopher



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philosopher






syllogisms


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syllogisms




philosopher



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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

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syllogisms





syllogisms


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Disjunctive Fallacies

Fallacy of Affirming the First Alternant

Either P, or Q

P

Therefore, not Q

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Either Jesus is God, or Jesus is a man

Jesus is God

Therefore, Jesus is not a man



philosopher

Socrates is philosopher

Therefore, Socrates is not a farmer

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syllogisms





syllogisms


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Inclusive vs. Exclusive Disjunctions


philosopher

Inclusive vs. Exclusive Disjunctions

Either Socrates is a philosopher, or Socrates is not a

philosopher

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syllogisms





syllogisms


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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






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Reduction of Disjunctive Syllogisms

Either Socrates is a farmer or Socrates is a philosopher







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25









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If _______________________, then Socrates is a farmer








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If _______________________, then Socrates is a farmer



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If Socrates is not a philosopher, then Socrates is a farmer




If Socrates is not a philosopher, then Socrates is a farmer



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syllogisms





syllogisms


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syllogisms





syllogisms


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syllogisms





syllogisms


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syllogisms


Exercises

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Exercises

Exercise 25

Exercise 25

Either Frodo destroys the ring or evil will triumph

Frodo destroys the ring

Therefore, evil will not triumph

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Exercise 25

Either P or Q

P

Therefore, not Q

Exercise 25

Either P or Q

Not P

Therefore, Q

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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

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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

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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


Martin Cothran

Instructor

traditional logic ii - memoria presshypothetical syllogisms what is a disjunctive syllogism? the...

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