Handbook of the History of Logic: - Fordham University Faculty

310 Henrik Lagerlund
Kilwardby. Necessity per accidens belongs to all other necessity proposition that
do not have the intrinsic relation between subject and predicate.
He also stresses that in a per se necessity proposition, the subject must be ‘per se
aliquod ipsius predicati’. He seems to mean that in such a proposition, the subject
has the predicate as an essential property; in other words, the subject has the
predicate as a necessary property through itself and not through something else.
A syllogistic necessity proposition is then understood as a proposition expressing
essential properties of things located in a genus-species structure. He seems to
assume that in a necessity proposition per se, the subject term is not an accidental
term, but an essential or a necessary term, and that the subject is essentially (per
se), and not only through inseparability, linked to the predicate. Consequently, if
the subject term is necessary and the link is necessary, it follows that the predicate
term cannot be a contingent (accidental) term. It must be necessary as well.
The Aristotelian theory of necessity syllogistic is thus limited to a special class
of terms, which all stand for substances. The same terminology is also used to
explain the syllogistic for contingency propositions, which means that Kilwardby
is trying to develop a uniform and highly original interpretation. There are several
contemporary scholars that have developed a similar interpretation of Aristotle. 68
In interpreting Aristotle’s modal syllogistics, most medievals saw the need to
introduce a distinction between different kinds of assertoric proposition. In the
mixed syllogism L–L, the assertoric minor premise cannot be any kind of assertoric
sentence, since the terms could just be accidentally connected. Kilwardby
therefore introduces a distinction between simply (simpliciter) and as of now (ut
nunc) assertoric propositions. The seed of this distinction can already be found
in Aristotle (Prior Analytics I, 15, 34b7-18), but Kilwardby of course uses his
per se/per accidens distinction to spell out the difference. A simply assertoric
proposition involves a per se predication while an as of now assertoric proposition
involves a per accidens predication. In such a way he can ensure that an essential
connection between the terms in the valid L–L syllogisms are preserved to
the conclusion. This is not unproblematic, 69 but the distinction between different
assertoric propositions needed somehow to be made and it remained a problem all
the way through the Middle Ages.
In the end, however, Kilwardby does not quite succeed in getting just the moods
accepted by Aristotle. He for example accepts –LL for the first figure, which is not
accepted by Aristotle, and does not manage to get –CC and LCC for Disamis in
the third figure. 70 There are also some other moods that he does not succeed in
validating and some others which he get but which are not accepted by Aristotle,
but perhaps he gets as close as one possible can get to making Aristotle’s system
consistent. 71
68 [van Rijen, 1989; Patterson, 1995; Thom, 1996; Nortmann, 1996].
69 See [Lagerlund, 2000, 39-42].
70 For the explanation of these names see below.
71 See [Knuuttila, 1996; Lagerlund, 2000; Thom, 2004].