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There are a few challenges that are present if we want to compare and contrast Buri- dan and Kilwardby’s accounts of modality. First, and perhaps most glaringly, while Kilwardby offers us some explanation and motivation for the different sorts of modal op- erators that he is using (those that areper se and per accidens), Buridan does not offer us a similar sort of distinction for the sorts of modal operations that he is using.7 This entire chapter is intended to help us better compare these two theories. A second, and related problem comes from both the historical and philosophical distance between Kil- wardby and Buridan. Kilwardby’s metaphysics and ontology are fundamentally realist in nature, while Buridan is a chief defender of nominalism.

On the metaphysical front, things are not as grim as they appear. As has been pointed out by Klima (see [27],[28]), while seeking to be a nominalist, Buridan also wants to 6. As we have already noted, this was in the context of the validity of the syllogism as it relates to the presence of Trinitarian terms. Buridan remarks that: “Now whether according to another way of speaking syllogisms in divine terms are formally valid and what that form is, I leave to the theologians. And it should be noted and always kept in mind that, because it is not for me, an Arts man, to decide regarding the foregoing beyond what was said. . . ”[51]Book Three, Conclusion 1

7. So far as I am aware, the closest we get to this in the Treatise on Consequences is the difference between divided and composite modalities. However, in neither case are these modal operations reduced to simpler notions nor are we given explicit motivation for how they should be analysed.

‘affirm’ the ‘existence’ of essences and admit them into his theories. This has been coined Buridan’s “essentialist nominalism”. In order to better discuss the relationship between Kilwardby and Buridan’s analysis of modality, it will prove helpful to start with this natural touchstone. While (so far as I am aware) Buridan does not use per se to provide a distinction between different sorts of modalities, Buridan does have quite a bit to say about essences and essential properties, which we will review below.

6.3.1 Buridan’s Essentialist Nominalism

When speaking of an ‘essentialist nominalism’ it is very important that we be clear on exactly what such a position amounts to.8

Before we venture into this directly, it may be helpful to set aside a few possible misconceptions. First, the debate between medieval realists and nominalists was not a debate between those who accepted the existence of ‘platonic’ or ‘abstract objects’ (the realists) and those who denied their existence (the nominalists). Both camps took Aristotle to have soundly refuted such a position, to the point that some found the ‘platonic’ view so absurd that they doubted if Plato really subscribed to it.9 Hence both parties to this debate took the objects in question to be just as individual and temporal as any other object would be.[26, p.476]

So then, what is the difference between nominalists like Buridan and realists? At this point it is helpful to distinguish between ‘pre-Ockham’ realists, like Giles of Rome and Kilwardby, and ‘post-Ockham’ realists such as Burley, Scotus, etc.10 The main difference between ‘pre-Ockham’ realists and both nominalists and ‘post-Ockham’ realists was that:

while the former [‘pre-Ockham’ realists] would consider abstract terms in the accidental categories to be essential predicates of their particulars, the latter would reject this assumption. . .

What seems to be at the bottom of the “older realist” commitment, then, in interpreting abstract accidental terms as the genera and species, that is, essential predicates of their particulars. To be sure, even those authors who can justifiably be regarded as “older realists” in the sense of working within the semantic framework outlined above plus endorsing the view that abstract terms in the accidental categories are essential predicates of their supposita. . . were prepared to regard several abstract terms as non-essential predicates of their supposita. [26, p.483, ft 18]

What then makes Buridan an essentialist nominalist? In [27, p.740] Klima suggests that we can draw a distinction between ‘predicate-essentialism’ and ‘realist essentialism’. The view attributed to Buridan here is that Buridan wants to be able to attribute essential predicates to things, but in doing so, he is not committed to positing some 8. As is pointed out in [27, p.739], on many contemporary conceptions, nominalism and essentialism

turn out to be in strong tension or are flat out incompatible.

9. See [26, p.476] and the references in ft.7 to Giles of Rome and John Wyclif.

10. The terms ‘pre-Ockham’ and ‘post-Ockham’ are not ideal terms, since, for example, Burley is con- temporaneous with Ockham. However, they are better then using terms such as ‘older’ and ‘newer’.

shared common essence. The challenge, of course, is to see if it is actually possible to pull these two notions apart in a way that is coherent.

So then, how does Buridan conceive of essential predication? The following quote offers some insight:

Since something is called a predicable because it is apt to be predicated of many things, it is reasonable to distinguish the species or modes contained under the term ‘predicable’ according to the different modes of predication. Therefore, everything that is predicated of something is either predicated essentially, so that neither term adds some extraneous connotation to the signification of the other; or it is predicated denominatively, so that one term does add some extrinsic connotation to the signification of the other. This division is clearly exhaustive, for it is given in terms of opposites. [5, p.106]

What is interesting here is how Buridan goes about defining essential and denominative predication. The definition of essential predication is cashed out in terms of what is ‘added’ to the connotation of a term. This is, at least at first glance, different from Kilwardby’s conception of aper se necessity, where the consequent of the predication is understood in the antecedent. However, things become more interesting when we try to flesh out Buridan’s definition. In order to do this, we need to look at the connotation of a term. So far as I am aware, Buridan does not explicitly define connotation, how- ever, there are numerous examples that make it clear how Buridan sees the relationship working. For example:

The terms ‘white’ and ‘black’ connote qualities of the substances for which they supposit, and it is on account of these [qualities] that [the substances] are said to be such and such; again, the terms ‘two cubits long’ and ‘three cubits long’ [connote] the quantities [of substances] by which they are measurable. But it is in accordance with another mode of pertaining to [adiacentia], or relation [habitudo], that terms from the category of time [quando When?], such as ‘today’ or ‘tomorrow’, appellate the motion of the heavens around the things of which we say that they are today or will be tomorrow, and so on for the other cases. [5, p.880]

The point is that a term like ‘black’ or ‘two cubits long’ supposits for the particular object in question (the thing that is black, the thing that is two cubits long etc.) but it also connotes additional information about the thing for which it supposits. For example, in the proposition ‘Socrates is black’ both ‘Socrates’ and ‘black’ supposit for the same object, namely Socrates, but in this case the term ‘black’ provides additional information about Socrates. From this definition we can see how predicates get many of the properties they are usually taken to have. For example, on Buridan’s account, accidental (denominative) predicates can cease to be true about an object, even if the

object still exists. For example, ‘Socrates is walking’ will be true as long as Socrates is walking, but when he stops walking, the proposition becomes false. Likewise, the only way that an object can cease to have an essential property is if that object ceases to exist. For example, in the proposition ‘Socrates is a human’, both ‘Socrates’ and human supposit for Socrates, and since ‘humanity’ does not connote anything extraneous about Socrates, the only way this proposition could be false, is if Socrates ceased to exist. For this interpretation to work, we need to place quite a bit of emphasis on the connotation of the particular words and the way they constrain when a term can and cannot be truly predicated of a thing.

The role of connotation is also closely connected with Buridan’s analysis of appellative terms, and some discussion of this will help us get clearer on what is going on with connotation and essential terms.

First, translation of the term ‘appellatio’ varies from author to author and situation to situation. For example, in many authors other then Buridan, ‘appellatio’ is best trans- lated by ‘connotative’ or similar expressions. This is because Buridan’s understanding of appellative terms is an idiosyncratic one. According to Lambert of Auxerre (Lagny) there are four possible ways that ‘appellatio’ can be understood:

Because appellation is a kind of supposition, supposition was considered first. Now we must discuss appellation.. . . Now it is essential to know that ‘appel- lation’ is used in four ways. In one way, proper names, or the proper name of any person, is called appellation. In this connection it is said that some- one has the appellation ‘Peter’ or ‘William’. Taken in this way, appellation is nothing other than the establishment of an utterance for signifying some complex or noncomplex thing; and ‘appellation’ is often used this way in obligations, in connection with which it is said that ‘A’ appellates Socrates or appellates that a man is running. ‘Appellation’ used in the second way is a property of names in according with which names are called appellative. In this sense appellation is nothing other than the positing of a common nature containing more than one suppositum under it. (Appellation is something common when it belongs to more than one but something proper when it belongs to one.)

‘Appellation’ used in the third way is the acceptance of a term for a sup- positum or {212} for supposita contained under its thing signified, whether or not those supposita are existing things. ‘Appellation’ taken in this way applies to terms having supposita under them either actually or potentially, and also to names of things signified. Used in the fourth way, ‘appellation’ is the acceptance of a term for a suppositum or for suppositia actually existing. [34, pp. 113-114]

As Lambert goes on to observe, every instance of appellation requires an instance of supposition, while the converse does not hold.[34][p.114] The first sense of appellation is the one that is most closely connected with the dictionary definition of ‘appellare’,

meaning to name. This sense is just the usual action of giving something a name. The second sense of appellation is an extension of this, where a particular name supposits for something that is common (here called a common nature) to multiple supposita. This is further subdivided into common appellation if the name supposits for multiple objects, and proper appellation if it supposits for only one name. The third sense of appellation is when a term is taken for a particular suppositum, regardless of whether or not the thing exists. In this sense, the name ‘Socrates’ (referring to the historical philosopher) appellates a philosopher, even though Socrates does not currently exist. The final sense of appellation imposes the condition that the suppositum of the appellated term must actually exist.

Buridan distinguishes appellative and non-appellative terms in the following way:

Now we turn to appellation. Some terms are appellative and others are not. For substantial terms in the nominative case or terms not connoting anything at all beyond the things for which they supposit are not appellative terms properly speaking. But every term connoting something other than what it supposits for is called ‘appellative’ and appellates that which it connotes as pertaining to [adiacens] that which it supposits for, as when ‘white’ [album] appellates whiteness as pertaining to that which the term ‘white’ [album] is apt to supposit for.[5, p.291]

As is clear from this definition, appellation is defined in terms of connotation. As in the case of essential terms, non-appellative terms do not connote anything more then they supposit for. However, what an appellative term does is “always appellates its form, whether it is placed on the side of the subject, i.e., before the verb, or on the side of the predicate, i.e., after the verb” [5, p.291]. Buridan’s take on this classical expression is the following:

So I say that, conventionally, by the ‘matter’ of a term we usually understand that for which the term is apt to supposit. . . But by the ‘form’ of a term we usually understand whatever the term appellates, whether it is an accident or a substance and whether it is matter or form, a composite of matter and form, or an aggregate of many things. For example, the term ‘wealthy’ supposits for a man, and so the man is called its ‘matter’, and it appellates houses, lands, and money, and other things he possesses as pertaining to him as to their possessor, and so such things, insofar as [ea ratione qua] they are possessed, are called the ‘form’ of the term ‘wealthy’ [5, p.292]

So, on Buridan’s account of essences, a property is essential to an object if that object is among the supposita of the property in question, and the property does not connote anything additional to what the object is.

What are we to make of the difference between Buridan and Kilwardby on Essences? In one sense, there is not much of interest to say here that has not already been said

in connection with other debates between realists and nominalists in the Middle Ages. Buridan’s approaches to essences is cast in terms of the individuals and the connotation of terms, while Kilwardby grounds the essences of things in the meaning of the terms, which are things do not simply reduce down to the objects that fall under a particular term. It is, however, helpful to see the two theories in some detail to appreciate just how different they are.