Modal Syllogisms

Kilwardby’s discussion of the modal syllogism is divided according to the kinds of propo- sitions that occur within the syllogism. The LLL50 syllogisms are treated in P8, the mixed necessary/assertoric proposition in A9-11 respectively. Contingency syllogisms are treated in P14, P17, and P20. The mixed contingency/assertoric propositions are treated in P15, P18, and P21. Finally, the contingency/necessity propositions are treated in P16, P19, and P22. [60][p.147, p.180]

As has already been mentioned, necessary propositions must be per se necessary. When considering LL pairs, Kilwardby says that the valid syllogisms in the first figure are the same as the ones that are valid in the assertoric case (i.e. aa, ea, ai, ei all yield valid syllogisms). This uniformity continues in his treatment of the second and third figures.[60][p.150] Kilwardby then goes on to show how the second and third figure can be reduced to the first figure. The reductions are quite straightforward. The only cases worth commenting on are the proofs of LLL Baroco and Bocardo. In both cases, 49. Strictly speaking this needs to be sharpened to rule out cases where one of the terms is implicitly

negative or entails a negative proposition.

50. In what follows we use the letter L to denote a premise of necessity, M to denote a premise of one way contingency/possibility, X to denote an assertoric premise and Q to denote a premise of two way contingency.

Kilwardby makes use of expository syllogisms.51 The use of an expository syllogism here could be because Kilwardby is following Aristotle’s exposition of the text, and when Aristotle proves that these syllogisms are valid, he makes use of an expository syllogism, because he has not yet treated syllogisms with possibilities.

In the LX case, Kilwardby adds an additional principle to describe the valid syllogisms in this mood. He gives us the following principle:

P8 In First Figure assertoric/necessity syllogisms, the necessity-proposition must be the major.

From this, together with the principles P1-P4 Kilwardby is able to derive the same syllogistic validities as Aristotle, namely LXL Barbara, Celarent, Darii and Ferio. In interpreting this, what is important is to look at Kilwardby’s justification for P8. P8 can be used (with a bit of extra work) to rule out the XLL syllogisms that have traditionally been seen as problematic.52 Kilwardby justifies P8 as follows:

The conclusion is part of the Major, and mostly in regard to the predicate, which they share. With regard to the subject, it is part of the Minor. And so it follows the Minor in features affecting the subject (such as universality and particularity) and the major in features affecting the predicate (such as affirmative and negative, assertoric and modal). 53[60][p.154]

Kilwardby’s point pertains to the question of what sorts of properties are transmitted by which parts of the syllogism. Here, Kilwardby claims that it is the major premise that conveys the mode and the quality of the syllogistic conclusion, whereas the minor term determines if the conclusion is universal or particular. Kilwardby then proceeds to sketch how useless premise pairs can be excluded using these principles. Kilwardby’s justification for P8, in some sense, seems a little thin. The feature that he points to is clearly true of the LXL syllogisms that Aristotle takes to be valid. However, what is missing is an explanation of why exactly this is the case.

In Thom’s presentation of Kilwardby it does not seem that Kilwardby has a principled reason for requiring that P8 be true. Thom says “As I read him, Kilwardby holds that since the assertoric Major in the first Figure XLL moods may be true merely as-of-now, those moods are invalid.”[60][p.161] This would be sufficient to generate counterexamples to the various XLL syllogisms, however it is unclear how this could be justified in a way that is not ad hoc. This is particularly problematic given that Kilwardby takes 51. We will discuss the expository syllogism in more detail when we talk about Buridan’s theory of the syllogism. At this point it suffices to know that an expository syllogism is a syllogism where the two premises are linked by a common singular term, i.e. a term that refers to an individual. We will discuss how Kilwardby uses the expository syllogism in Chapter Six, pg. 158.

52. The most famous of these being XLL Barbara, but any first figure XLL syllogism will do.

53. Et dicendum quod conclusion est pars maioris et maxime secundum praedicatum in quo communicat cum ipsa et quantum ad subiectum pars minoris. Et ideo sequitur minorem in dispositionibus ac- cidentibus subiecto eius quae sunt universalitas et particularitas, maiorem autem in dispositionibus accidentibus praedicato eius quae sunt affirmativum et negativum de inesse et de modo.

the assertoric propositions in such syllogisms to be unrestricted.54 This leads to one natural question: If Kilwardby wants to try and preserve Aristotle’s reading of the modal syllogism, how is he going to be able to justify the rejection of various XLL syllogisms (most importantly XLL Barbara)?

First, observe that if we require that the assertoric premise in an XLL syllogism be unrestricted, then we can generate a counterexample to P8. For example, consider the syllogism:

Every animal is a substance. (true and necessary in Aristotelian ontology.) Every man is necessarily an animal.

Every man is necessarily a substance.

Kilwardby gives additional principles that explain the validity of the syllogisms in the other figures. As these principles hold if a syllogism is to produce a valid conclusion and as we will be making use of them in the next chapter, we restate them here:

P1 In every syllogism, at least one premise must be universal. P2 In every syllogism, at least one premise must be affirmative.55 P3 In first figure syllogisms, the major must be universal.56 P4 In first figure syllogisms, the minor must be affirmative.57 P5 In second figure syllogisms, the major must be universal.58

P6 In second figure syllogisms, at least one of the premises must be negative.

54. “He[Kilwardby] holds that the Minor in the LXL moods must be an unrestricted assertoric which is the same in reality as a necessary proposition, even if it is not the same in mode and he deals with the issue by stating that despite the syntactic differences, there is no difference ‘in reality’ between the minor premises in the LLL and the LXL case”[60][p.158]

55. See [24, p.ad A4 Part 2 Dub. 8 10vb].

56. Kilwardby writes: “Alternatively, it can also be said that if the Major were particular, the Middle could be more common than the Major Extreme. For, an inferior is predicated of a superior in part, affirmatively and negatively. And if this were so, it could happen similarly that the Major was negative and the Extremes convertible, or exceeding and exceeded. And a negative conclusion couldnt follow unless it was false as it clear from the terms man, animal, ass.”[60, p.120], [24, ad A4 Part 2 dub.11 (IIra)]

57. Kilwardby writes: Now, of the remaining principle, namely that the Minor is affirmative, it is to be said that if the Minor were negative, either the Major would be negative (and then a syllogism would not be produced– for the stated reason), or the Major would be affirmative (and then there would be a fallacy of the consequent), because from the negation of a things inferior there doesnt follow the negation of the same things superior.[60, pp.119-120], [24, ad A4 Part 2 dub.11 (IIra)].

58. Kilwardby affirms P5 and P6 is given in the following passage: “Next, someone will enquire concerning the sufficiency of the moods in this Figure, why when there are premise-pairs, only are useful. This is to be solved by supposing the common principles we had before, and two that are proper to this Figure, of which one is that the Major is universal, and the second is that one of the propositions is negative.”[60, p.131]. [24, ad A5 dub.2 12ra-b]

P7 In third figure syllogisms, the minor must be affirmative.59

P8 In first figure assertoric/necessity syllogisms, the necessity-proposition must be major.60

P9 In second figure assertoric/necessity syllogisms, one premise must be a universal negative necessity proposition.61

P10 In affirmative third figure assertoric/necessity syllogisms, the necessity premise must be a universal affirmative.62

P11 In negative third figure assertoric/necessity syllogisms, the necessity premise must be a universal negative.63

In his book, Thom does not always provide quotations for each of these propositions. In cases where he does, where he provides additional arguments that Kilwardby offers for these propositions, or references to the Renaissance edition, they can be found in the footnotes.

For a full summary of these principles and the citations to the references see [60, pp.145,176—177,238].