Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 301
Chapter 3 of Quaesitum IV deals with the mixed necessity and assertoric syllogisms.
Averroes first states that the terms of necessity propositions in Aristotle’s
modal syllogistic are themselves necessary and that such a term is one by virtue
of itself (unus per se). What does this mean? A necessary term always stands for
its subject. It is a name of a thing which is continuously actualised in the world,
such as eternal individual beings, or natural species of substances and their essential
properties. Averroes also states that there are terms which are accidental.
An accidental term does not always stand for the same subject, that is, the term
sometimes stands for a certain subject and sometimes not.
Given this, Averroes explains what constitutes a necessity proposition and what
in general constitutes a assertoric proposition and a assertoric simpliciter proposition,
which he thinks is the right type of assertoric premise in a mixed Aristotelian
syllogism with necessity and assertoric premises. It is clear that if both terms in a
proposition are necessary and an essential predicate is predicated of a (necessary)
subject, then the proposition is necessary. According to Averroes, a proposition
can be considered necessary if it consists of a necessary subject and a necessary
predicate inhering in it ‘connexo ipsi subiecto’. This probably means that even if
the property is not essential, but an inseparable accident (accidens inseparabile),
such as the whiteness of swans, then the proposition is necessary.
If, on the other hand, both terms are accidental, and refer to properties which
are not always actual, then the proposition is an assertoric proposition. Averroes
is here interested in a special class of assertoric propositions, namely, in those
which are assertoric simpliciter. If they are true, they are true independently
of temporal restrictions whenever the subject is actual. His example of such an
assertoric proposition is ‘Every walking being is moving’. He adds that if the
subject is walking it is necessarily moving. One could say that such propositions
are conditionally necessary. 51
The third suggestion discussed by Averroes is the combination of necessary and
accidental terms. He first discusses the case in which the subject term is accidental
and the predicate term is necessary. His example is ‘Every walking being is an
animal’. This proposition can be understood in two ways: either the subject term
‘walking being’ is understood to stand for its supposita as walking, or it is taken
to stand for them as those which are walking. In the former case, the proposition
is assertoric, and in the latter case, it is necessary. Because the latter reading is
indirect, it can be said that the proposition is a assertoric proposition per se and a
necessity proposition per accidens. According to Averroes, in a mixed first figure
syllogism with necessity and assertoric premises, the assertoric premise should be
assertoric per se and necessary per accidens. One can ask, of course, why the minor
premise is called an assertoric premise and the conclusion necessary. Both are
assertoric per se and necessary per accidens. The second case with necessary and
accidental terms is that the subject term is necessary and the predicate accidental.
51 It was standard practice in Arabic logic after Avicenna to elaborate modal propositions
with all kinds of restrictions placed on the terms involved. See [Street, 2004] and [Lagerlund,
forthcoming b].