Hypothetical Syllogisms

We often use pure hypothetical syllogisms in describing chains of events in which each event causes the next. At no point do we assert anything as being the case. However, there is another sort of inference that allows us to derive a nonhypothetical conclusion. In an argument of this form, the first premise is hypothetical and the second premise is categorical.

There are two valid mixed hypothetical syllogisms. The medieval logicians called the first one modus ponens, the method of affirming the antecedent. They called the second one modus tollens, the method of denying the consequent. Both are valid for the same reason -- they spell out the implications of the hypothetical premise.


Comprehension Questions
1 Determine whether the following hypothetical syllogism is valid or invalid.

If she walks, then she moves.
She moves.


She walks.
a) It is valid.
b) It is is invalid.
2 Determine whether the following hypothetical syllogism is valid or invalid.

If she walks, then she moves.
She walks.


She moves.
a) It is valid.
b) It is is invalid.
3 Determine whether the following hypothetical syllogism is valid or invalid.

If she walks, then she moves.
She does not move.


She does not walk.
a) It is valid.
b) It is is invalid.
4 Determine whether the following hypothetical syllogism is valid or invalid.

If she walks, then she moves.
She does not walk.


She does not move.
a) It is valid.
b) It is is invalid.
5 Determine whether the following hypothetical syllogism is valid or invalid.

I will go skiing only if you will teach me, but since you are unwilling to teach me, I won't go.

a) It is valid.
b) It is is invalid.
6 Determine whether the following hypothetical syllogism is valid or invalid.

I will not go swimming unless a lifeguard is on duty. I didn't go swimming. Thus, you can conclude that there wasn't a lifeguard on duty.

a) It is valid.
b) It is is invalid.
7 Determine whether the following hypothetical syllogism is valid or invalid.

I will be able to travel to Europe if and only if the exchange rate remains favorable. I won't be able to go to Europe. Therefore, the exchange rate did not remain favorable.

a) It is valid.
b) It is is invalid.

Affirming the antecedent | Denying the consequent
Invalid forms | Finding missing premises

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