Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 541
32a29-b1). This was taken for granted in mid-thirteenth-century logical treatises.
It was noted that while the converted propositions of indefinite contingency propositions
are of the same type of contingency, the conversion of natural contingency
propositions or of those of the minor part contingency, whether with respect to
quality or terms, result in different modal propositions. 119 There were extensive
discussions of the kinds of contingency in the commentaries by Robert Kilwardby
and Albert the Great and in other treatises by their contemporaries based on
various philosophical ideas of contingency. 120 Following Aristotle’s remark in An.
pr. I.13, 32b23-32, according to which ‘A contingently belongs to B’ may mean
either ‘to that to which B belongs’ or ‘to that to which B contingently belongs’,
Kilwardby argues that the major premise in uniform first figure contingency syllogisms
is read in the second way, having the form ‘Everything/something that
is contingently B is contingently A’. 121 Contingency premises are ampliated, if
syllogistic relations do not demand restrictions. 122 In explaining the difference
between necessity propositions and contingency propositions in this respect, Kilwardby
teaches that syllogistic terms are substantial or accidental. Substantial
terms necessarily stand for the things they signify, while accidental terms contingently
stand for them. Since the terms in per se necessity propositions are
substantial, ‘Every A is necessarily B’ and ‘Whatever is necessarily A is necessarily
B’ mean the same. 123
Averroes did not have much to add to what Aristotle says about the convertibility
of contingent propositions, except that the subject terms of syllogistic contingency
propositions are always meant to be read with the prefix
‘Everything/something which is or is contingently’. 124 As distinct from the mid-
119 In Pr. an. (Orléans), 186b; Lambert of Auxerre, Logica, 42.26-49.43; Robert Kilwardby,
In Pr. An. 8rb-va; Peter of Spain, Syncategoreumata, ed. with an introduction by L.M. de
Rijk, with an English translation by J. Spruyt, Studien und Texte zur Geistesgeschichte des
Mittelalters 30 (Leiden: Brill, 1992), VII.6, 284-7: 17-19, 294-7; Albert the Great, Pr. an. I.13,
477a-480b; 14, 482b; Roger Bacon, Summulae III.1.2, 61-6; Jacobi 1980, 83-4, 382. For the kinds
of contingency, see also Averroes, Media expsitio in libros Priorun Resolutoriorum 35vb-36ra.
120 According to Aristotle, universal negative possibility proper propositions are simply convertible
into universal negative possibility propositions (An. pr. 1.3, 25b3-14). It was concluded
from this that a universal negative contingency proposition is convertible into a universal negative
possibility proposition; see Lambert of Auxerre, Logica, 47.14-48.7; Robert Kilwardby, In
Pr. an. 9ra; Roger Bacon, Summulae, III.1.2, 64; albert the Great, In Pr.an. I.14, 480a-482b.
121 Kilwardby, In Pr. an. .
122 In Pr. an. 19vb; 21ra-b; Kilwardby says later that the subject term of the minor premise
of a universal first-figure syllogism may also be actual (22rb).
123 In In Pr. an. 21ra-b; 22ra-b. See also Thom 2007, 22-3. These considerations did not
influence conversion rules. Kilwardby did not find it problematic that the contingency premises
in various mixed third-figure moods, which he did not treat as ampliated, were converted in
Aristotle’s modal syllogistic.
124 Media expositio in libros Priorum Resolutoriorum, 38rb; 44ra-b. According to Averroes,
Alfarabi mistakenly argued that the subject-term ampliates to the possible in all syllogistic
premises. In fact this is true only of contingency propositions (28vb). Alfarabi’s lost commentary
on the Prior Analytics may be the source of Avicenna’s view of ampliation (note 117 above).
See also T. Street, “‘The Eminent Later Scholar” in Avicenna’s Book of the Syllogism’, Arabic
Science and Philosophy 11 (2001), 205-18.