Conditional Syllogism

2.Conditional Syllogism – a syllogism whose major premise is a conditional proposition. It is a mixed conditional syllogism if the minor premise is a conditional proposition or a pure conditional syllogism if both premises are conditional propositions.

a.The mixed conditional syllogism is governed by the two laws that governed relationship between the antecedent and the consequent.

1.If the antecedent is true and the sequence valid, the consequent

is true.

2. If the consequent is false and the sequence valid, the antecedent

Is false.

When applied to the mixed conditional syllogism, these general rules are

expressed thus:

If the antecedent is posited or affirmed in the minnow premise, then the consequent is also posited or affirmed in the conclusion.
VALID If A then B But A Therefore B	INVALID If A then B But not A Therefore not B
If the consequent is sublated or denied in the minor premise then the antecedent is sublated or denied in the conclusion.
VALID If A then B But not B Therefore not A	INVALID If A then B But not B Therefore not A

b.The purely conditional syllogism, which has conditional syllogism, which has conditional propositions for both its premises, has exactly the same forms and the same rules as the mixed conditional syllogism except that the condition expressed in the minor premise must be retained in the conclusion.

If A is B, then C is D; But if X is Y, then A is B; Therefore if X is Y, then C is D. If A is B, then C is D; But if X is Y, then C is not D; Therefore if X is Y, then A is not B.

If he has terminal cancer, then he is seriously ill. But if he is undergoing chemotherapy, then he has terminal cancer. Therefore if he is undergoing chemotherapy, then he is seriously ill. If he has terminal cancer, then he is seriously ill. But if he can go about his daily work, then he is not seriously ill. Therefore if he can go about his daily work, he has no terminal cancer.