Handbook of the History of Logic: - Fordham University Faculty

292 Henrik Lagerlund
(3.1.21) ‘Every human being is an animal, and every human being is
rational, therefore some animal is rational.’
(3.1.22) ‘Every human being is an animal, and no human being is a
horse, therefore some animal is not a horse.’
(3.1.23) ‘Some human being is white, and ever human being is an
animal, therefore some white thing is a human being.’
(3.1.24) ‘Every human being is an animal, and some human being is a
writer, therefore some animal is a writer.’
(3.1.25) ‘Every human being is rational, and some human being is not
a writer, therefore some rational thing is not a writer.’
(3.1.26) ‘Some animal is white, no animal is snow, therefore some white
thing is not snow.’
(3.1.21) is proved by conversion of the minor premise to get (3.1.15). The next
is proved in the same way by this time to get (3.1.16), and also (3.1.23) to get
(3.1.15). (3.1.24) is proved by conversion of the major premise and conversion
of the conclusion. He does not mention that he must transpose the premises as
well, but perhaps he takes this to be obvious given his conditional reading of the
syllogisms. The last syllogism in this figure is proved by converting the minor
premise to get (3.1.16).
(3.1.25) is claimed to be proven by supposition again, but no proof is this time
given. A proof in the line of the one given above might look like this:
Take a human being that is not a writer in ‘Some human being is not a
writer’ and call it H. Hence ‘No H is a writer’ is true. We have posited
that ‘Every human being is rational’ and since H is a human being,
it follows that ‘Some H is a human being’, which together by (3.1.15)
becomes ‘Some H is rational’. Given this and ‘No H is a writer’ it
follows by (3.1.26) that ‘Some rational thing is not a writer’. Q.E.D.
This proof method is very powerful and in fact Al-Ghazālī would need no other
to prove the valid syllogisms. It is somewhat reminiscent of Aristotle’s proof by
echtesis.
Al-Ghazālī ends his discussion of the categorical syllogisms at this point and
it is quite strange that he does not mention the other ten valid syllogisms of
the Aristotelian system. Avicenna’s discussion in the Danesh-name is equally
incomplete so Al-Ghazālī seems here only to follow his lead.
He then eventually turns the discussion towards the doctrine of the matter of
the syllogism. The matter of a syllogism is its propositions or premises. If they
are credible and true, then the conclusion will be credible and true, but if the
premises are false, then the conclusion will not be credible. 32 He tries to explain
what he means by the distinction between the matter and form of a syllogism by
an analogy with a coin. The matter of the coin is the gold it is made of and its
form is its roundness. If the form is destroyed or falsified in some way, we will
32 Al-Ghazālī, Tractatus de logica, 273, 495-8.