Lesson 31: Hypothetical Syllogisms

Question 1

What is a hypothetical syllogism?

Answer 1

A syllogism that uses hypothetical statements.

Question 2

What is a pure hypothetical syllogism?

Answer 2

A pure hypothetical syllogism uses only if…then statement. That means that all three statements in a pure hypothetical syllogism are going to be in if…then form. A pure hypothetical syllogism is valid when it is in the form “If P then Q. If Q then R. Therefore, if P then R.”

Question 3

What is an antecedent?

Answer 3

An antecedent of a hypothetical statement is the condition, the part following the “if.”

Question 4

What is a consequent?

Answer 4

The consequent is the result of the condition, the part after the “then.”

Question 5

What is a mixed hypothetical syllogism?

Answer 5

A mixed hypothetical syllogism uses some categorical statements and some if…then statements to draw conclusions.

Question 6

What are the two basic, valid mixed hypothetical syllogisms?

Answer 6

1. Modus ponens: Putting the limit: If P, then Q. P. Therefore, Q.
2. Modus tollens: Taking the limit: If P, then Q. Not Q. Therefore, not P.

Question 7

What are the two basic, invalid, mixed hypothetical syllogisms?

Answer 7

1. The fallacy of affirming the consequent: The second premise affirms the consequent of the hypothetical statement
2. Denying the antecedent: The second premise denies the antecedent of the hypothetical statement.

Question 8

What does the latin phrase “non sequitur” mean?

Answer 8

It means “it does not follow,” meaning the argument is invalid.

Question 9

What is the form “affirming the consequent”?

Answer 9

The second premise affirms the consequent of the hypothetical statement. “If P, then Q. Q. Therefore, P.” This is the invalid form of Modus Ponens

Question 10

What is the form “denying the antecedent”?

Answer 10

The antecedent of the hypothetical statement is denied in the second premise. “If P, then Q. Not P. Therefore, not Q.” This is the invalid form of Modus Tollens