Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 321
Impossibly not
Necessary
Given these it is not difficult to present the square of opposition for singular modal
propositions. It is the following:
Figure 3. The Modal Square
Notice that the modal square is only for singular propositions. No one at this
time presented a square of opposition for quantified modal propositions, which, of
course, made is completely useless for modal syllogistics. 86 A theory for quantified
modal propositions was not developed until the mid-fourteenth century. 87
86 None of the textbooks contain any discussion of modal syllgistics; except a discussion of
the modal conversion rules in Roger Bacon and Lambert of Auxerre’s books. They, however,
closely follow Kilwardby’s treatment discussed above (section 4.3). Roger Bacon follows the
first of Kilwardby’s solutions to the conversion of necessity propositions, while Lambeert of
Auxerre presents both solutions. Bacon’s continued discussion of contingency propositions is
rather confusing, since he uses contingency for what is usually calls possibility. He therefore
divides contingency into that which is necessary, possible and non-necessary. It is contingency
in the last sense that is usually calls contingency. He then proceeds to make a two fold division
of contingeency in this sense into contingency ad utrumlibet and contingency natum (compare
Aquinas threefold distinction above). Propositions taken in none of these senses of contingency
convert as necessity or possibility propositions. See Roger Bacon, Summulae Dialectices, III,
199-200.
87 See [Lagerlund, 2000, Chapter 5 and Appendix IX.3].