Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 539
the divided sense. One of the problems of his modal syllogistics is that reading
these conversion rules in the divided sense leads to obvious difficulties: the actuality
of subjects changes into necessity and possibility into actuality. Contrary to
what one might expect, the relationship between compound and divided modalities
was not dealt with in mid-thirteenth-century discussions of Aristotle’s rules,
these being associated with various philosophical ideas of the nature of necessity
and contingency. Many authors tried to redefine syllogistic necessity propositions
in a way which would match the conversion rules. This took place in treating some
often repeated counter-examples, such as
(17) Everything literate is necessarily a human being
(18) Everything healthy (or awake) is necessarily an animal
or
(19) Everything white is necessarily a body.
It was considered an obvious fact that no animal is necessarily healthy or that
‘some animal is healthy’ is not a necessary truth. Some authors argued that in
examples like (17)–(19) the denominative subject terms refer to things which are
qualified by non-essential forms and that these terms should be treated in the same
way when they are predicates. 114 ‘An animal is necessarily healthy’ is taken to
mean that an animal is necessarily that which is healthy. Accordingly, (17) could
be read: ‘Every literate being is necessarily a member of the class of human beings’,
but even then the conversion ‘Some human beings are necessarily members of the
class of literate beings’ is false, if this is not understood, as Lambert of Auxerre
suggests, to mean that some human beings are necessarily those who are literate,
that is, human beings.
Robert Kilwardby, after mentioning this pretty artificial idea, moves to a ‘more
probable’ interpretation which is based on the view that convertible necessity
premises in modal syllogistic are necessity propositions per se and not per accidens,
like (17)–(19), which are not convertible. In affirmative necessity propositions
per se, the subject is per se connected to the predicate. In negative necessity
propositions per se, the subject is apparently per se incompatible with the predicate.
In accidental necessity propositions, the connection is not based on a per se
inherence or repugnance. 115 In explaining the notion of per se later in his work,
114 See Lambert of Auxerre, Logica 39.1-41; Robert Kilwardby, In Pr. an. 7ra; Roger Bacon,
Summulae dialectices III.1.2, 58, 60; cf. In Pr. an. (Orléans) f. 180b.
115 In Pr. an. 7ra-b; cf. 45rb for essential negative propositions. Kilwardby’s concludes in 7rb:
‘Therefore, when Aristotle teaches that necessity propositions are convertible, he means that
only per se necessity propositions are convertible’. Aristotle did not say this; Kilwardby followed
the medieval commentator habit of maintaining that what commentators found reasonable was
what Aristotle said or meant. Kilwardby seems to assume that syllogistic necessity propositions
should be taken in the divided sense or at least not in the composite sense (27va). For per se
necessity in Kilwardby, see also Lagerlund 2000, 25-42; Thom 2003, 93-6; P. Thom, Logic and
Ontology in the Syllogistic of Robert Kilwardby, Studien und Texte zur Geistesgeschichte des
Mittelalters 92 (Leiden: Brill, 2007), 19-28.