Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 547
As distinct from his forerunners, Campsall comments separately on Aristotelian
modal syllogisms with premises in the compound and divided senses. Uniform
necessity syllogisms are valid on both readings. Syllogisms in the compound sense
are reduced to the principle
(20) If the premises are necessary, the consequent is necessary.
Syllogisms in the divided sense are valid because they are regulated by the same
principles as the assertoric syllogisms, i.e., dici de omni et nullo. 152 Mixed necessityassertoric
moods are valid in the compound sense on the basis of (20), when the
assertoric premise (de inesse proposition) is of the de inesse simpliciter type, i.e.,
necessarily true. These consequences are not syllogistic, however, and the same
holds of mixed assertoric-necessity moods with a necessary conclusion. Mixed
necessity-assertoric syllogisms in the divided sense are valid when the assertoric
premise is de inesse simpliciter or ut nunc primo modo, i.e., a proposition which
express a necessary relation between actual things. Propositions de inesse secundo
modo express accidental relations and assertoric minor premises of this kind do
not make valid syllogisms. Campsall describes the validity of the perfect necessityassertoric
syllogisms by referring, like Kilwardby, to the principle that the whole
syllogism is implicitly included in the first premise. The middle term is said to
be sufficiently the same in both premises only when the minor premise is in fact
necessary. 153
If syllogistic premises are contingent in the compound sense, it does not follow
that the consequent is contingent in the compound sense. Aristotelian uniform
contingency syllogisms are valid for divided modals when the middle term is ampliated
with respect to contingency. 154 Aristotelian first-figure mixed contingencyassertoric
syllogisms are said to be valid for divided modals provided that the
contingency premise is not ampliated and the assertoric premise is assertoric simpliciter
or ut nunc primo modo. 155 Because affirmative and negative contingency
propositions with terms standing for actual things imply affirmative assertoric
propositions and the contingent premises in mixed necessary and contingent syllogisms
are of this type, the conclusions are assertoric. Aristotle seemingly denied
this, but in fact he wanted to say that the assertoric conclusion was evident in
negative moods and less apparent in affirmative moods. 156 The conclusions are
to itself a natural contingency minor; op. cit. 27va-b. For Kilwardby’s discussion of contingency
syllogisms, see also Thom 2007, ch. 6.
152Campsall 11.58-9 (194); see also Lagerlund 2000, 74.
15312.33-5 (205). Campsall states that mixed assertoric-necessity Baroco and mixed necessityassertoric
Bocardo with necessary conclusions are syllogistically valid. When Aristotle did not
accept these, he did not mean that they were not acceptable — it was only because the indirect
proof involved a possibility proper syllogism which was presented later in the Prior Analytics.
The corresponding mixed necessity-assertoric Baroco and mixed assertoric-necessity Bocardo are
valid consequences, but not syllogistic (14.16-19 (221-2)).
15417.48-9, 17.70 (268-9, 274).
15518.36-8 (283-4).
15620.14-17 (304). Campsall does not deal with Aristotelian mixed contingency-necessity moods,
apparently regarding them immediately obvious when the contingency premises are not ampli-