Syllogisms

Kilwardby’s discussion of the syllogism looks at three different readings of Aristotle’s text. One view appears to be based on that of Boethius. Another one is broadly Aris- totelian and based on comments Aristotle makes elsewhere in thePrior Analytics. The third and final reading, according to Thom, is advanced in theDialectica Monacensis.[60, p.40]35 The differences between these views can be seen in a number of places, but is perhaps clearest if we start with how the different views look at Aristotle’s opening def- inition of a syllogism in thePrior Analytics. Kilwardby quotes Aristotle saying that “A syllogism is a discourse in which, certain things being set out [positis] something else comes about [contingit] of necessity from their being so.”36 [60, p.42] The three different readings all try to address the following problem: why does Aristotle give discourse as the genus of the syllogism?[60, p.42] The Boethian reading sees the use of the term ‘dis- course’ as a way to preclude other classes of arguments such as induction, example, and 31. Item quod veritas cum necessitate tantum est cum constancia subjecti. [63, p.217]

32. See [63, p.217] and the reference to Lewry therein.

33. See Chapter Four, section 5 for Buridan’s ampliative account of modality.

34. Ideally, the logical system should also help us make sense of the distinction between natural and accidental consequence and so give rise to a connexive logic.

35. Hereafter, the Boethian, the Aristotelian and the Munichian readings. 36. The quote from Aristotle isPrior Analytics24b1820.

enthymeme.37 On this view the syllogism is a kind of complex argument that is used to create a belief in the soul of an individual.[60, pp.43-44] Kilwardby spends much less time on the Aristotelian exposition. On this view, the genus is not intended to exclude induction, enthymeme, or example since these can be reduced to syllogisms.[60, p.45] Instead, the reading focuses on the ‘necessity of the conclusion’ excluding syllogism pairs that do not produce a valid conclusion.38 This reading also excludespetito principii and non causa ut causa on the same grounds.

On the Munichian reading, the definition of the syllogism is intended to preclude all other kinds of reasoning. Accordingly, they state that:

The definition given can therefore make clear from what has been said that all other species of argumentation are excluded (namely Induction, Example, Enthymeme), and it also excludes the sophistical syllogism no matter what its cause (and this includes fallacies).[60, p.46]39

The first part of this definition is similar to the Boethian account, however the Mu- nichian account goes further, in that it also precludes so called ‘sophistical’ syllogisms. Unfortunately, after mentioning these sophisms, the Munichian author moves onto a dis- cussion of quid sit dici de omini and does not bother to tell us what the author means by sophistical syllogisms. However, given Kilwardby’s rejection of this view, it seems that Kilwardby took this to refer to arguments that have the form of a syllogism, but are deficient in matter, where the form of the syllogism refers to how the propositions and terms are arranged in the argument, while (at least part of) the matter of the syllogism is whether the propositions are true or false. Thom connects this view with William of Sherwood’s[60, p.47] [67, pp.57-58]. Kilwardby rejects the view because:

For Syllogism formally (as dealt with in this Book) is merely two propositions and three terms. Form and Figure and Mood can be saved in a sophistical syllogism, as is clear from this “Every dog runs, everything that barks is a dog, therefore etc.” and in many others.40[60, p.47]

Kilwardby is dissatisfied with this reading because he thinks it excludes too much. According to a view like the Munichian, it is only sound syllogistic arguments that 37. Thus the particular “certain things” excludes Enthymeme. By “set out” is understood arrangement in Mood and Figure and this excludes the useless premise-pairs and Induction. “Of necessity” excludes example, which possesses mere probability since it is a rhetorical argument. . . By “something other comes about” petito principii is excluded, not as a sophistical ground but as a fault in syllogism simpliciter. . . By “from their being so”non causa ut causa is excluded. [60, p.42]

38. Thom uses the term ‘useless premise pairs’ [60, p.45]

39. “Potest igitur manifestum esse ex predictis per diffinitionem datam, quod excluduntur omnes alie species argumentationis, scilicet inductio, exemplum, entimema, et preterea excluditur sophisticus sillogismus secundum omnes sui causas, et hoc quantum ad tredecim fallacias.” The quote is taken from [11, p.490:12-15]

40. Syllogismus enim formaliter, de quo determinatur in hoc libro, tantum modo sunt duae propositiones et tres termini. Forma autem et figura et modus potest salvari in syllogismo sophistico, sicut patet hic: Omnis canis currit, omne latrabile est canis, ergo etc., et in multis aliis.

count as syllogisms. Phrased slightly differently, this view entails that a syllogism which is faulty in its matter is not a syllogism.[60][p.47] This is a view that Kilwardby explicitly condemns in the condemnation of 1277 and he objects to in his commentary. The argument is of interest to us because it hinges on how the form and the matter of the syllogism are to be understood.

It is to be said that the material principles of the syllogism without qualifi- cation are two propositions (and if this is lacking there will be no syllogism); but of the ostensive syllogism [the material principles are] two true proposi- tions. So, even though a syllogism with false premises is lacking in matter, it is not lacking in the matter of a syllogism without qualification, but in the matter of an ostensive syllogism; and so, even though it has false premises, it does not follow that it is not a syllogism without qualification, but that it isn’t an ostensive syllogism.41[60][pp.47-48]

At the heart of Kilwardby’s point is that while a syllogism with false premises will fail to be an ostensive syllogism, it does not outright fail to be a syllogism. For Kilwardby an ostensive syllogism must have true premises, while a syllogism is only required to have two propositions. It should also be observed that here we see what Kilwardby thinks the matter of a syllogism is. Kilwardby takes the matter of a syllogism to be the two propositions that are used to make up the syllogism. For him it is simply the propositions. The truth value of the propositions is irrelevant, as long as they are not ruled out by the previous kinds of considerations given in the other two readings. For example, the propositions cannot be ambiguous.

Kilwardby goes on to analyse the syllogism in terms of its material, formal, and final causes. Kilwardby tells us that:

And it is to be said that there is an order in materials. For some are re- mote and unarranged, and some are proximate and arranged. And so it is in forms. Some are material forms, which are in potentiality to an ulterior form, and some are ultimate and completing forms. Thus we find an order in a syllogism’s materials and forms. For, in materials, the term is its remote and unarranged material, and the proposition is its proximate and arranged materials; and in forms, Figure is the incomplete form which is in poten- tiality to an ulterior form, and Mood is the ultimate form completing the syllogism.42[60][p.57]

41. Dicendum quod syllogismo simpliciter sunt principia materialia, quae sunt duae propositiones, et si in hoc sit defectus non erit syllogismus, syllogismi autem ostensivi sunt duae propositiones verae. Quamvis ergo syllogismus ex falsis deficiat in materia, non deficit in materia syllogismi simpliciter sed in materia syllogismi ostensivi, et ideo, quamvis ex falsis sit, non tamen sequitur quod non sit syllogismus sed quod non ostensivus simpliciter.

42. Et dicendum quod sicut ordo est in materiis, quaedam enim est remota et indisposita, quaedam autem propinqua et disposita, sic est in formis. Quaedam est forma materialis et in potentia ad formam

The above passage is one of the clearest summaries of Kilwardby’s view of the form and matter of the syllogism. The distinction between proximate and remote matter is a standard medieval distinction and is fairly straightforward. The idea is that the proximate matter is the matter that is closest to what the particular thing is made up of, while the remote matter is conceptually further away. Using modern biology as an example, the remote matter in a human would be the basic atomic components that make them up, while the proximate matter could be their various body parts (heart, arms, legs etc). In the case of the syllogism, the terms are the remote and most ‘basic’ part of it. The propositions that make up the syllogism are its proximate matter. As is standard, two of the necessary conditions for being a syllogism are that the argument be composed of a pair of propositions, composed of three terms from which a conclusion can be drawn. Since propositions are made up of terms together with the copula, they serve as the remote matter of the syllogism. Then the propositions themselves form the proximate matter of the syllogism.