Handbook of the History of Logic: - Fordham University Faculty

290 Henrik Lagerlund
He notes further that in none of these figures does a conclusion follow from only
negative premises, from only particular premises, and from a combination of the
major negative and the minor particular. 24 The first figure is different from the
other two in primarily two ways: first of all, the syllogisms in it are not reduced to
any other syllogisms, and the conclusions in it are of four different kinds, namely
universal affirmative, universal negative, particular affirmative, and particular negative.
In the second figure there are no affirmative conclusions and in the third
figure there are no universal conclusions. 25
As Aristotle himself had maintained the first figure is perfect. He, however, says
very little about why it is perfect. Al-Ghazālī want to explain this by showing why
the first figure syllogisms are “certain”, as he says. He says that “when you posit
a true affirmative proposition, then whatever is said about all of its predicate the
same thing is said about its subject.” 26 In a true proposition like ‘A human being
is an animal’ one must think that the subject includes all of the predicate. He
thus assumes some kind of inclusive relation between the subject and the predicate
and this accounts for the certainty of the first figure syllogisms. 27 This becomes
more clear when one has a look at how he presents the four valid syllogisms. He
namely presents them with the minor premise first, since he wants to highlight the
inclusion relation between the terms. The examples he gives of the four syllogisms
are:
(3.1.13) ‘Every body is a composite, but every composite began, therefore
every body began.’
(3.1.14) ‘Every body is a composite, but no composite is eternal, therefore
no body is eternal.’
(3.1.15) ‘Some thing is a composite, but every composite began, therefore
some thing began.’
(3.1.16) ‘Some thing is a composite, but no composite is eternal, therefore
some thing is not eternal.’ 28
The first thing to notice is of course that each syllogism is lined up as a conditional
with the minor premise first. Putting the premises in this order lines up the
terms nicely as minor, middle and major. In the first figure, ‘body’ includes
‘composite’ and ‘composite’ in turn includes ‘began’, which makes it obvious that
‘body’ includes ‘began’ as well. The quantification of the propositions is just
expressing how many of the subjects have the predicates. In (3.1.13), all have.
In the second figure, Al-Ghazālī presents the following valid syllogisms:
(3.1.17) ‘Every body is divisible, but no animal is divisible, therefore
no body is an animal.’
24Al-Ghazālī, Tractatus de logica, 260, 61-3.
25Al-Ghazālī, Tractatus de logica, 260, 64-70.
26Al-Ghazālī, Tractatus de logica, 260, 76-8.
27This was called taking the terms universally in Latin logic. See the discussion about this
below.
28Al-Ghazālī, Tractatus de logica, 261, 88-110.