These two kinds of syllogism are synthesis and analysis in the ancient sense.
When Aristotle called syllogism X6yos, he meant that it is a combination of premises involving a conclusion of necessity.
Nevertheless, deduction or syllogism is not independent of the other processes of inference.
On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative.
Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the modus ponens and the second to the modus tollens of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions.