Handbook of the History of Logic: - Fordham University Faculty

308 Henrik Lagerlund
from the early thirteenth century, but there are no major commentaries until the
1240’s when Kilwardby writes a commentary called, in Latin, In libros Priorum
Analyticorum expositio.
Kilwardby has nothing of substance to add to the theory of assertoric syllogism 66
(see my outline below of the textbook presentations of logic for a description
of the theory of the assertoric syllogisms), but his interpretation of the modal
syllogistic is quite remarkable and highly interesting. It was also very influential
in the thirteenth century, for example, Albert the Great, Simon of Faversham
and Radulphus Brito all follow him in their interpretations, which means that all
the major commentators of the Prior Analytics in the thirteenth century followed
Kilwardby.
He assumes from the beginning that Aristotle’s theory is correct and makes it
his project to find the interpretation that shows this. He begins by considering a
counter-example to the accidental conversion of necessity propositions, namely:
(4.3.1) ‘Every literate being is necessarily a human being’.
According to the conversion rules accepted by Kilwardby and Aristotle (1) should
convert to:
(4.3.2) ‘Some human being is necessarily literate’,
(4.3.1) is obviously true while (4.3.2) is false.
Kilwardby seems to assumes that Aristotle’s modal syllogistics is a logic for de
re propositions. 67 He proceeds, however, and gives two separate solutions to this
puzzle. The first is based on a distinction between different readings of (4.3.1).
Kilwardby explains, that the subject term of a sentence can stand for the subject of
the inherence (the suppositum), or for the qualification through which the subject
is specified (qualitas/forma). If the term ‘white’ stands for suppositum, it refers to
a thing that is white, or to ‘that which is white’, but if it stands for the quality (or
form), it refers to the whiteness that inheres in that which is white and not to the
thing in which it inheres. Kilwardby says that in (4.3.1), ‘literate being’ stands
66 See [Thom, 2007] for a different view.
67 Kilwardby here falls back on a distinction introduced by Peter Abelard (1079-1142). According
to Abelard, modal terms are, properly speaking, adverbs, expressing the way in which
the decisive thing said of the subject is actual, for example, ‘well’ or ‘quickly’ or ‘necessarily’.
Adverbs which do not modify an actual inherence, such as ‘possibly’, are secondary modal terms,
due to their position in a proposition. Abelard also noticed that in De interpretatione 12-13,
Aristotle does not operate with adverbial modes, but with nominal modes, such as ‘it is necessary
that’ or ‘it is possible that’. He seems to have assumed that Aristotle did this because the nominal
modes involve many more problems than simple adverbial modes. According to Abelard, this
is more clearly seen from the fact that propositions including nominal modes, such as ‘Necesse
est Socratem currere’, can be understood either adverbially, ‘Socrates runs necessarily’, or, as
suggested by the grammar, ‘That Socrates runs is necessary’. He calls these two alternatives de
re necessity propositions and de sensu (or de dicto) necessity propositions, respectively. Abelard
seems to be the first to employ this terminology. A de re modal proposition expresses the mode
in which a predicate belongs to a subject. The mode is, therefore, associated with a thing, while
the mode in the de dicto or de sensu case, as he also calls it, is said of that which is expressed
by a non-modal proposition. See further [Knuuttila, 1993, 82-96], and [Lagerlund, 2000, 35-39].