Ancient philosophy a new history of western philosophy volume 1 (new history of western philosophy) ( PDFDrive ) 144

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 do 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. 2. 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.
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