Aristotle's reasoning is conclusive:
∴ Plato's theory of Ideas is erroneous.
Rule of the Modus ponens: The antecedent of the major premise being affirmed in the minor premise, the consequent is also affirmed in the conclusion.
(2) Modus tollens, or Destructive.
If A is B, C is D;
C is not D:
∴ A is not B.
If Pythagoras is to be trusted, Justice is a number;
Justice is not a number:
∴ Pythagoras is not to be trusted.
Rule of the Modus tollens: The consequent of the major premise being denied in the minor premise, the antecedent is denied in the conclusion.
By using negative major premises two other forms are obtainable: then, either by affirming the antecedent or by denying the consequent, we draw a negative conclusion.
| Thus (Modus ponens): | (Modus tollens): |
| If A is B, C is not D; | If A is B, C is not D; |
| A is B: | C is D: |
| ∴ C is not D. | ∴ A is not B. |
Further, since the antecedent of the major premise, taken by itself, may be negative, it seems possible to obtain four more forms, two in each Mood, from the following major premises: