LOGIC If we apply these rules we Wnd that there are four, and only four, valid moods of syllogism in the Wrst Wgure Every S is M Every M is P Every S is P Every S is M No M is P No S is P Some S is M Every M is P Some S is P Some S is M Every M is not P Some S is not P Aristotle also oVers rules to determine the validity of moods in the second and third Wgures, but we not need to go into these since he is able to show that all second- and third-Wgure syllogisms are equivalent to Wrst-Wgure syllogisms In general, syllogisms in these Wgures can be transformed into Wrst-Wgure syllogisms by a process he calls ‘conversion’ (antistrophe) Conversion depends on a set of relations between propositions of diVerent forms that Aristotle sets out early in the treatise When we have particular afWrmative and universal negative propositions, the order of the terms can be reversed without alteration of sense: Some S is P if and only if some P is S, and no S is P if and only if no P is S (1 25a5–10) (By contrast, ‘Every S is P’ may be true without ‘Every P is S’ being true.) Consider the following syllogism in the third Wgure: ‘No Greek is a bird; but all ravens are birds; therefore no Greek is a raven’ If we convert the minor premiss into its equivalent ‘No bird is a Greek’ we have a Wrst-Wgure syllogism in the second of the moods tabulated above Aristotle shows in the course of his treatise that almost all second- and third-Wgure syllogisms can be reduced to Wrst-Wgure ones by conversion in this manner In the rare cases where this is not possible he transforms the second- and thirdWgure syllogisms by a process of reductio ad absurdum, showing that if one premiss of the syllogism is taken in conjunction with the negation of its conclusion as a second premiss, it will yield (by a deduction in the Wrst Wgure) the negation of the original second premiss as a conclusion (1 23 41a21 V.) Aristotle’s syllogistic was a remarkable achievement: it is a systematic formulation of an important part of logic Some of his followers in later times—though not in antiquity or the Middle Ages—thought that syllogistic was the whole of logic Immanuel Kant, for instance, in the preface to the second edition of his Critique of Pure Reason, said that since Aristotle logic had neither advanced a single step nor been required to retrace a single step 121