For other examples it is enough to refer to the Critique of Pure Reason, where Kant sets out the Antinomies of Rational Cosmology. But even if we do not agree with Kant that the human understanding, in attempting to deal with certain subjects beyond its reach, inevitably falls into such contradictory reasonings; yet it can hardly be doubted that we not unfrequently hold opinions which, if logically developed, result in Antinomies. And, accordingly, the Antinomy, if it cannot be imputed to Reason herself, may be a very fair, and a very wholesome argumentum ad hominem. It was the favourite weapon of the Pyrrhonists against the dogmatic philosophies that flourished after the death of Aristotle.
CHAPTER XII
CONDITIONAL SYLLOGISMS
§ 1. Conditional Syllogisms may be generally described as those that contain conditional propositions. They are usually divided into two classes, Hypothetical and Disjunctive.
A Hypothetical Syllogism is one that consists of a Hypothetical Major Premise, a Categorical Minor Premise, and a Categorical Conclusion. Two Moods are usually recognised the Modus ponens, in which the antecedent of the hypothetical major premise is affirmed; and the Modus tollens, in which its consequent is denied.
(1) Modus ponens, or Constructive.
If A is B, C is D;
A is B:
∴ C is D.
If Aristotle's reasoning is conclusive, Plato's theory of Ideas is erroneous;