Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 327
Given these combinations they present some general rules for the theory. First of
all there are five rules:
1. There are no syllogisms from only particular, indefinite or singular premises.
2. There are no syllogisms from only negative premises.
3. If one of the premises is particular then a particular conclusion follows, but
not its converse.
4. If one of the premises is negative then a negative conclusion follows, and also
its converse follows.
5. The middle term must not be part of the conclusion.
The first figure has nine valid moods or forms of syllogisms. Four of these have
direct conclusions and five are indirect. In a direct conclusion the major extreme is
predicated of the minor extreme and in an indirect conclusion the converse holds.
It became standard in the thirteenth century to treat the fourth figure introduced
by Galen as an indirect form of the first. The reason for this was to give a more
faithful interpretation of Aristotle who does not mention the fourth figure.
There are two rules that govern the first figure:
6. If the minor premise is negative, then no conclusion follows.
7. If the major premise is particular, then no conclusion follows.
The four first syllogisms with direct conclusions are not given proofs, since they
are perfect. Their validity is shown by reference to the dici de omni et nullo rules
mentioned above. Dictum de omni governs the first mood (Barbara): 89
I.
Every B is A
Every C is B
Every C is A
Dictum de nullo governs the second mood (Celarent):
II.
No B is A
Every C is B
No C is A
The two other moods (Darii and Ferio) are reduced to these two by the square of
opposition:
89 For an explantion of the names of the valid syllogisms see below in this section.