Modality

The theory of modality has a long history going back to Aristotle. Within this work we will limit our attention to Kilwardby’s treatment of the modal syllogism as it is discussed in his Commentary on the Prior Analytics. The most natural place to start is with Kilwardby’s understanding of modes and the kinds of modal terms that result from them.

Kilwardby distinguishes between two kinds of necessary modal relationships that can hold between terms. Two terms can be related so as to be necessaryper se or be related so as to be necessaryper accidens. It should be noted that terms may fail to be related to each other in either way. This distinction betweenper se andper accidens is not unique to Kilwardby, but traces its origins to Aristotle. In Posterior Analytics I 4-6, Aristotle introduces four different ways that the termper secan be taken to function. The passage is known for being difficult in a number of ways. Thankfully, we only need to take away two things from Kilwardby’s treatment of Aristotle, which are nicely summed up by the following quotation from Henrik Lagerlund:

Aristotle discusses four different notions ofper se predication but Kilwardby . . . seems to only have the first two in mind when referring toper se. Aristotle says that the first type ofper sepredication (per se primo modo) occurs when the definition of the subject includes the predicate. The second type ofper se predication (per se secundo modo) occurs when the definition of the predicate includes the subject. . . to complete the picture of per se predication, one should discuss the concepts of genus, species, difference and proprium. This is not done by Kilwardby. . . who only very briefly states what [he] means by necessity per se. [35, p.30-31]

The first thing to take away is the unfortunate reality that, as far as I am aware, Kilwardby does not provide a sustained discussion of the notions of genus, species, 25. Recall that this is of the form: The stronger view would assert that, for all A, ‘It is not the case that

etc., in the commentary on the Prior Analytics. As such, this means that some of our reconstruction of Kilwardby’s logic will have to be somewhat speculative on these points. The second thing to observe is the distinction between per se primo modo and per se secundo modo. This distinction is very important and will be helpful to understand exactly how Kilwardby understands per se modalities. As was stated above, A is said to beper se primo modo B if the definition of A includes or makes use of the definition of B, while A isper se secundo modoB if the definition of B includes or makes use of A. For example, ‘Every man is an animal’ is true per se primo modo since the definition of ‘man’ makes use of the definition of ‘animal’. While ‘Every man is capable of laughter’ would be true per se secundo modo since ‘man’ is part of the definition of ‘capable of laughter’ because, according to the medievals, this a property unique to man alone.

One of the questions that we will need to answer is, byper se, does Kilwardby mean per se primo modo or per se secundo modo? From what we have already seen about natural consequences it is clear that what Kilwardby has in mind for these kinds of consequences are per se primo modo predications. To see this, recall that in a natural consequence it is the antecedent that posits the consequence, i.e. it is in virtue of the nature of the antecedent that the consequent is said to follow. In what follows when we speak of one term beingper se, we will meanper se primo modounless otherwise stated. The use of the distinction between being per se predicated of another term or per accidens predicated was employed to attempt to dissolve some purported counterexam- ples to conversion. In looking at these counterexamples, the relationship to essentialist modalities comes through clearly. The counterexample to conversion normally ran as follows: ‘Every man is necessarily literate’ therefore ‘Something literate is necessarily a man’. There are two challenges here. The first challenge is to understand why this inference may be problematic, and second, to explain how that problematic inference is to be dissolved.26

To address the first point, observe that the proposition ‘Every man is necessarily literate’ is true because every man has the potential to be literate.27 However, the converted proposition ‘Something literate is necessarily a man’ is, according to many authors of this time, not true. The exact reason for why this proposition is false is often unclear, but given an essentialist reading of the modality, we can easily make sense of the problem. It is part of the nature of being a man that they are able to be literate, since they are rational, and being rational includes the capacity for being literate. However, it is not part of the nature of being literate that one be a man.

Now, to explain why this inference does not work, the response by Kilwardby and others is to observe that man is per se literate, but that literate is not per se man. Again, it should be observed that this reading only makes sense if we readper se in the sense ofper se primo modo. Thus the solution adopted by Kilwardby was to distinguish the two senses of necessity mentioned above.

Kilwardby sums this up by saying:

26. The first point is an important one here. On a normal reading of the modal operators, reading them de dicto, the conversion is logically valid and unproblematic.

27. The term ‘literate’ here needs to be understood as, ‘has the ability or capacity to be literate’, not as saying that the person necessarily is able to read.

For a per se necessity-proposition requires the subject to be per se some of the predicate itself. But when it is said, “all who are literate are of necessity men”, the subject is not per se some of the predicate itself; but it is granted that it is necessary, because the literate are not separate from what is some man. But this is a per accidens necessity.[60, p.20]28

It should be observed here that Kilwardby is speaking not only of the relationship that exists between terms, but also of when a proposition (in this case ‘Every A is B’) can beper se necessary. As the quote illustrates, for Kilwardby a proposition is said to be per accidens necessary if a relationship of necessity per accidens holds between the subject and the predicate. Again, we see here that it is whether thesubject isper se the predicate that determines if a given proposition isper se or not.

So, it seems thatper se modalities do not always convert. This raises a very natural problem for Kilwardby’s interpretation of Aristotle, since Aristotle makes use of the conversion of modal propositions in various places in the Prior Analytics. What is Kilwardby to do about this? The answer is that Kilwardby sees a kind of symmetry within the terms that are essentially predicated.[60, p.21] This is very much in keeping with modern treatments of Aristotle’s modal syllogism. For example, in his paper on Aristotle’s syllogistic, Malink writes:

By analogy, the particular affirmative necessity Niabcould be defined as (13) ∃zΥbz∧Eˆaz

However, using this definition, Niabfails to convert toNiba; in order to avoid this problem we follow Thom and Brenner in weakening (13) by disjunction as follows:

(14) ∃z((Υbz∧Eˆaz) ∨ (Υaz∧Eˆbz))

[37, p.109][38, p.179]29

What is important here is that we will need to find a way to weaken the reading of the particular necessary propositions to ensure that modal conversion remains valid for Kilwardby as long as the inference does not confuseper se andper accidens modalities. Up to this point, we have seen that the distinction between two kinds of necessity, necessity per se and necessity per accidens, is essential for understanding Kilwardby’s reading of the modal syllogism. This distinction presupposes a difference between the essence of a thing and the properties that are necessarily true of a thing. We have also seen that Kilwardby does not discuss how essences and some of the related notions (such 28. “Propositio enim per se de necessario exigit subiectum esse per se aliquid ipsius praedicati. Cum autem dicitur ‘Omne grammaticum de necessitate est homo’, ipsum subiectum non est aliquid per se ipsius praedicati, sed quia grammaticum non separatur ab eo quod est aliquid ipsius hominis, ideo conceditur esse necessaria. Sed quae sic est de necessario, per accidens est de necessario.”

29. We will make considerable use of Malink’s reconstruction of Aristotle in our formal reconstruction of Kilwardby in Chapter Three. As such, there will be a sustained discussion of his system there as well as definitions for all of the logical symbols.

as genus, species, etc.) function within his logical theorising. As such, it may be helpful to look at other authors’ views about essences around the time of Kilwardby.

How does this distinction function within the 13thcentury metaphysics of Kilwardby’s day? First, it is helpful to realise that there were two theories about how the term esse functions in sentences.

According to the inherence theory, the copula is a sign of the fact that the ‘nature’ or ‘form’ signified by the predicate term is present in the individual things (supposita) denoted by the subject term. The identity theory instead claims that the terms should be taken as denoting classes and that the affir- mative propositions state that all or some members of the subject class are simultaneously members of the predicate class.[35, p.29]

What is important is to note that Kilwardby held to the inherence theory of the copula and it is this theory that allows him to distinguish the per se andper accidens senses of the necessary propositions. Given that there can be a distinction between the necessary and the essential, this distinction makes sense within an inherence framework. But how are we to make sense of this distinction? When is it true to say that ‘A is essentially B’, and when is it false?

There were two main questions that drove the metaphysical debates around the con- ception of an essence in Kilwardby’s time. First, the medievals wanted to develop a theory of essence and existence that could account for the existence of non-physical en- tities like angels and demons (i.e. creatures that were non-physical, but not simple and whose existence was not necessary.)[68, p.662] Second, the medievals wanted a distinc- tion that would help explain the difference between God, whose existence was necessary and who depended on nothing, and everything, which depended on God for existence.[68, p.662] The development of these positions drew from a number of ancient sources, the most important authors being Aristotle, Boethius and Ibn Sina.

As we have already observed, so far as modern authors are aware, Kilwardby does not provide a sustained discussion of essences. However, what is clear is the following: First, the essence of a thing is to be separated from the existence of a thing, so that one can posit a thing’s essence without positing the existence of the thing.30 Second, when we are dealing with necessary per se propositions, the universal affirmative lacks existential import. To claim that ‘Every man is essentially an animal’ does not require that there be some man who instantiates the term. The reasons for this are, at least to some degree, connected to the relationship between the interpretation of Aristotle and Christian theology. According to Christian theology, humans, animals etc. did not always exist and were created by God. Now, if the subject of a proposition of necessity needs to necessarily exist in order for the proposition to be true, many of the propositions that Aristotle says are necessary turn out to be false, such as the ‘Every 30. For the medievals there is one obvious counter-example to this, namely God, who due to His simplicity, is the place where existence and essence are identical. Such considerations will not concern us at this point.

man is an animal’ example cited above. According to Christian theology, there was some time when men did not exist, and so, it follows that men did not necessarily exist. Hence, ‘Every man is an animal’ would come out false if the subject had to necessarily exist. In fact, Kilwardby had this proposition, namely, that necessary truth depends on persistence of the subject, condemned in 1277! According to Kilwardby, “That necessary truth depends on persistence of the subject31” is to be condemned.32 As an interesting corollary to this, we should note here that if, for Kilwardby, the truth of the universal affirmative proposition requires the existence of the subject, then necessary universal affirmative propositions do not entail the corresponding assertoric proposition. As we shall see later on this is one way of providing an interpretation of Aristotle’s modal logic that does not run afoul of theological issues, while also preserving the inferences Aristotle takes to be valid. Another interpretation, consistent with Kilwardby’s condemnation, is to widen the class of objects under consideration. This interpretation, which Buridan uses, requires only that there be an object that can fall under the subject, regardless of whether that object exists or not. This approach yields a different theory of the modal syllogism that is weaker then Aristotle’s.33

Now, given the way that Kilwardby employs the term per se, it seems that it is best to think of this as concerning essential relationships that hold between the various terms under discussion. What we then need to develop is a logic that can relate the conceptual grounds of various terms to the objects that they pick out, and is fine-grained enough to be able to separate outper se from per accidens modalities.34 Before looking for such a formal model, we need to discuss how Kilwardby brings these results together in his treatment of the syllogism.