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Saturday, April 09, 2016


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I don't want to spam thread but I have one suggestion, not comment: I think it is good idea to collect posts on Peter van Inwagen under specific category, there are maybe two dozens or so posts about his work.

Good suggestion, Milos -- if I can figure out how to do it.

That was an exhilaratingly lucid and cogent performance by the Mighty Metaphysician – one that I shall gratefully absorb and process. As an initial response, I can note the apparent similarity between (a) van Inwagen’s view (or non-view) of properties and(b) that of Reinhart Grossman (whom you frequently cite in PTE), as registered by Arda Denkal (1996).

Let us begin with two sentences from your entry: (a) “It is also hard to understand how van Inwagen, on his own assumptions, can maintain that we see that certain things have certain properties.” (b) (quoting van Inwagen: “We never see properties, although we see that certain things have certain properties”

Now let us consider Denkel’s response to Grossman:

Grossman will not be deterred by those who might point to particular colours or urge that they see them with their own eyes. He insists that the alleged fact of showing or seeing the property is nothing but seeing something that exemplifies the property. Properties are neither in space nor in time. They are not concrete; they are abstract existences. (1996, 172-73)

Like you, Denkel cannot understand where this kind of theory is coming from:

Consider a bolt screwed in a nut. How can it be there unless it has the precise shape it has exactly where it is? I must admit that I am not at all convinced by Grossmann’s view that there are no particular properties because properties are not located in space (1996, 173).

Thanks for the Denkel quotation. It appears that Denkel and I are on the same page.

The differences between PvI and Grossmann would make an interesting post.

With Denkel’s help, it is perhaps possible to construct another refutation of van Inwagen’s property doctrine – one that hinges on deconstruction of the notion of properties as “abstract particulars.” According to Denkel, properties are neither abstract nor concrete. They are certainly not abstract, because, as will be discussed in a moment, properties (properly bundled) are causally efficacious, whereas anything abstract is causally inert. Nor are properties concrete (particulars), because they lack existential independence. Instead, properties are aspects of concrete objects: “The particular entities of the physical world are either concretes or the inhering aspects of such concretes. Conversely, anything abstract is universal and, perhaps with the exception of entities such as sets and numbers, mind-dependent” (1996, 187).

With respect to the causal efficacy of properties, Denkel proclaims: “…when things act causally, they act in virtue of their properties” (1996, 185). Campbell provides a hot example: “It is not the stove, the whole stove, that burns you . . . . It is the temperature that does the damage.” (1990, pp. 2-3). According to Denkel, “…when things act causally, they act in virtue of their properties” (1996, 185). He elaborates: “On its own, a property has no causal efficacy, for it is interpenetrable, and this will yield to every other property whatsoever. It lacks the supportive resistance lent by a concrete entity bearing it, a condition that would enable it to affect a property of another substance causally, instead of interpenetrating with, and hence inhering in, that substance” (1996, 186). In contrast, abstract particulars are presumed to be “in the physical world without at the same time there being a possibility for them to interact with anything else in there” (1996, 186). Abstract particulars cannot interact with anything else precisely because they are abstract.

Well, PvI does not think of properties as particulars.

I invoked Denkel to address not the notion of properties as particulars, but instead the notion of properties as abstract. Denkel’s argument is that properties are not abstract, because they are aspects of concrete objects. This position approaches – and might even be compatible with – the conclusion of your own argument against van Inwagen: “They [properties] are either tropes or else universals wholly present in the things that have them.” In this context, I note that, according to Hoffman and Rosenkrantz, (2007), tropes (that is, particular properties) are “concrete entities.”

Your van Inwagen blog was supremely informative and wonderfully lucid. Below I provide two elaborations of the notion of the bare particular – the first from Denkel (1996) and the second from Maurin (2002). These excerpts clarify the provenance and purpose of the notion:

(1) Denkel (1996): Locke’s account of substance reflects the conception of the substratum as a particular devoid of any attribute apart from that of being a bearer of properties. The non-spatial interpretation of Aquinas’ individuator, the “materia signata,” acquired some popularity in the seventeenth century. In contemporary philosophy it is at times labelled the view of the “bare particular” or the “pincushion account” (50).

Maurin (2002): It is true that some philosophers who have taken an ordinary object to be constituted by universals and a substratum have posited the latter in order to ground the particularity of the object. However, there is another reason philosophers have postulated substrata: in order to provide an ultimate subject for properties, an entity that is characterized by properties. The idea here is that unless there is, in a complex, a non-property constituent that is non-derivatively or fundamentally charactered by the constituent properties in that complex, the complex itself cannot be even derivatively charactered in the ways specified by those constituent properties. A bare particular is supposed to play this role; in terms of the above property/object distinction, a bare particular is an object – it is a charactered non-property. The claim that a bare particular is charactered might sound surprising, if not contradictory, since it is widely assumed that a bare particular is supposed to be something that essentially has no properties. But this assumption is mistaken, and arguably traces back to a footnote (!) by Wilfred Sellars (1963a: 282, fn. 1) in which bare particulars are caricatured in this way.9 However, the bareness of a bare particular is supposed to lie in the fact that there is no property that it has essentially, not that it essentially has no property whatsoever. In addition, the bareness of a bare particular does not entail that a bare particular fails to satisfy any description. Rather, the predicates necessarily satisfied by a bare particular hold primitively, in that they do not name reified properties. Thus, the predicates ‘being a bare particular,’ ‘being such as to have no property essentially’ (etc.) do not name properties (147). There is another role that bare particulars are supposed to play – namely, that of the non-property haver of properties, which has properties in the sense of being characterized by them. The thought being that, for example, where the sphere is there is more than just sphericalness, there is also something that is spherical, something charactered in a spherical way. In sum, there are at least two roles which bare particulars have been employed to play: First, a bare particular in a bare particular-cum-universal complex is supposed to render the complex non-repeatable (I .e. non-shareable or non-multiply-instantiable). Second, a bare particular in a bare particular-cum-universal complex is supposed to be characterized by the universal in that complex (148, original emphasis).

Might I supplement my preceding comment with a question: Why are van Inwagen’s properties not particulars? You refer to them as “abstract objects.”

Does the answer to my question concern the distinction between kinds and things? Are van Inwagen’s properties not particulars because, as universals, they are kinds of things, not things – that is, each is a “such,” but not a “this”?

I might be able partially to answer my preceding question: “Why are van Inwagen’s properties not particulars?”

Does the answer involve the fact that his properties are universals? As Denkel point out, “‘being a particular’ is for something to be the case uniquely and without repetition. For to have this qualification is for it to be identical with itself as a single case only, i.e., for it to be just one in its entirety” (1996, 65-66). In contrast, in Aristotle’s schema, “being a universal” entails “something’s being the case multiply and repetitively, as for example, when something is said to exist or to apply multiply and repetitively. Thus being a universal entails being identical with oneself as a plurality” (1996, 65).

I assume, therefore, that, unlike Platonic Forms, van Inwagen’s universals are not “thises” (as Aristotle alleges Platonic Forms to be).

That's right: properties for PvI are universals. They are also abstract items: not in space or time. Nor do they ever enter into spatiotemporal particulars. So it would be misleading to speak of them as repeatable. Blueness is not repeated in each blue thing. Blueness is rather instantiated by every blue thing. We should therefore speak of multiple instantiablity rather than repeatability.

One caveat: some properties are not instantiable at all, e.g., the property of being both round and square.

See sec. 4 of the pdf I sent you.

Thank you very much, Bill, for your validation and guidance.

Ordinarily, universals are characterized as both “repeatable” and “shareable.” For example, Heil (2015) refers to them in these terms (114), as does Ujvári (2012): “repeatable entities shared and sharable by many things” (17). Moreover, in PTE, you refer to universals as “repeatables” (2002, 203), and refer to a universal as “a repeatable entity (2002, 209). Loux (2006) also refers to universals as “repeatable entities (19).

Are van Inwagen’s universals not repeatable, but only multiply instantiable?

To add to my preceding comment:

Yes, I see. It is more precise to say that universals are repeatably instantiable than to say that they are repeatable.

A nice refinement - une mise au point.

Bill, You characterise the instantiation connection between ordinary particulars like Max and his properties as, under PVI's scheme, an external and abstract relation. This worries me. Firstly, because this relation is cross-category. And secondly, because I think the notion of instantiation, as a connection between the concrete and the abstract, must be logically prior to the notion of relation. We use the cross-category notions of instantiation and extension to explicate abstract relations, not the other way about. For if we try the other way about we have to say that the extension of a relation is the set of its instances. And what are its instances? Well, they are (embedded in) the extension of the instantiation relation, and I think we have here the beginnings of an infinite regress.


The topic is very difficult because of terminological fluidity but also because of the metaphors in play.

Consider the predicate 'red' or '____ is red.' Predicates are linguistic items not to be confused with properties which are extralinguistic. Now does it make sense to say that 'red' is repeated in each red thing? No. This is because of the great 'ontological distance' between the predicates 'red'/'rot'/'rouge' and red things. Similarly, it makes no sense to say that the PvI-property redness is repeated in each red thing. This is because PvI-properties do not enter as constituents into the individuals that instantiate them in the way that an Armstrongian immanent universal enters into an individual. It thus makes good sense to say that such a universal is repeatable.

You may have noticed that in PTE and also in the Armstong pdf I sent you I distinguish between constituency-nonconstituency and immanence-transcendence.

An immanent universal is one that cannot exist unless exemplified. Armstrong, a naturalist, of course holds that all universals are immanent in this sense. A transcendent universal, then, is one that can exist unexemplified.

A constituent universal is one that is an ontological part of a thing that has it. A nonconstituent universal, then, is one that cannot be an ontological part of a thing that has it.

These two distinction pairs 'cut perpendicular' to each other generating four combinatorially possible views: Immanent universals that are constituents of particulars (Armstrong); immanent universals that are not constituents of particulars (Grossmann); transcendent universals that are not constituents of particulars (van Inwagen); transcendent universals that are constituents of particulars (Blanshard?)

Now please tell me whether this makes sense to you.

That was an astoundingly informative explication, its matter extremely compressed like the molecules of a diamond. Yes, it makes sense to me, but, for more complete comprehension, sense needs my further familiarity with the relevant reference(s). To invoke Jaspers' formulation concerning the nature and project of the Socratic epistemology, “knowledge is knowledge in nonknowledge under the guidance of the good” (1962, 19). That is, the more I learn about this subject, the more I confront an abysm of ignorance.

According to your taxonomy, are the Platonic Forms to be categorized as "transcendent universals that are constituents of particulars," since, in the Platonic ontology, to be what they are, particulars participate in these Forms?

As some wit once observed, "Brevity is the soul of blog." To which I add the gloss: the highest form of brevity is lapidary brevity.

I am a great fan of Karl Jaspers who among German 'existentialists' remains too much in the shadow of Martin Heidegger. To which work of the former does '1962' refer?

The answer to your question must be in the affirmative given my definitions. The Forms exist whether or not exemplified. This is what makes them transcendent. The familiar particulars of the *mundus sensibilis* share in their Being, or participate in them. This is what makes them constituent universals.

But I don't think it will be helpful to relate the current discussion to Plato and Aristotle. This is because contemporary analytic ontologists are not known for their knowledge of the actual views of the great founding Greeks. They toss around 'Platonic' and 'Aristotelian' in an historically irresponsible way. This is typical of analytic philosophers, or at least those in the Anglosphere.

This is a very large topic. I will make only two points and make them quickly.

First, Platonic Forms are exemplars and thus nothing like the 'platonic' properties of analysts like van Inwagen and so many others. (Thus Platonic exemplification is very unlike PvI's instantiation.) The Wisdom in which Socrates participates is itself wise; the PvI- property of being wise is not itself wise. It is nothing but the unsaturated assertible expressed by the predicate '____ is wise' and insofar forth very much like a Fregean sense (Sinn).

Second, talk of immanent universals as 'Aristotelian' makes little sense since Aristotle has no truck with universals.

David writes,

>>the instantiation connection between ordinary particulars like Max and his properties as, under PVI's scheme, an external and abstract relation. This worries me. Firstly, because this relation is cross-category. <<

Yes, it is cross-category. Why is this a problem?

>>And secondly, because I think the notion of instantiation, as a connection between the concrete and the abstract, must be logically prior to the notion of relation.<<

Now you are onto something troublesome. Suppose A is on top of B. We distinguish: A, B, the relation. These three items can exist without the relational fact existing/obtaining. So it seems we must add the instantiation 'relation.' We say: A, B, in that order instantiate the relation *on top of.* Now if instantiation is a relation on a par with *on top of,* then we seem to ignite Bradley's regress.

>> We use the cross-category notions of instantiation and extension to explicate abstract relations, not the other way about. For if we try the other way about we have to say that the extension of a relation is the set of its instances. And what are its instances? Well, they are (embedded in) the extension of the instantiation relation, and I think we have here the beginnings of an infinite regress.<<

The extension of an n-adic relation is a set of ordered n-tuples. Sets are abstract. So the extension of a relation is abstract. The extension of a relation is what instantiates it. Is your point that the notion of the abstract is used to elucidate that of instantiation, when we first need the notion of instantiation to elucidate that of abstract? If so, then it looks like we have a circle rather than a regress.

But I may not have understood your argument.

The reference: Karl Jaspers, Plato and Augustine, ed. Hannah Arendt, trans. Ralph Mannheim (Harcourt, Brace & World, 1962).

Yes, many contemporary analytic metaphysicians refer to Plato and Aristotle’s respective doctrines of the universal. But surely not all of these commentators don’t know what they are talking about. In any event, there appears to be a consensus that Aristotle did indeed have a doctrine of the universal. Let’s begin with three contemporary commentators, with the third being yourself. I am citing commentators who demonstrate, in their respective discussions, profound knowledge of their ancient subject:

(1) Denkel: “Aristotle followed Plato in believing that universals are identities in diverse particulars, but claimed that they exist in rebus, that is to say, within particular things, hence making them dependent upon objects” (1996, 155).

(2) Galuzzo: “Aristotle is of the opinion that the properties that characterize a certain kind in the hierarchy get transmitted to all the kinds occupying a lower level in the hierarchy: if the property being capable of motion is necessarily associated with or characterizes the kind animal it will also be a necessary property of all the lower-order kinds as well as of the members of such kinds, e.g. human beings, horses, mice, etc.” (2015, 91).

(3) Vallicella: “But an essence is a universal: whatever the essence of being human turns out to be, it will be common to Socrates and Plato, something they share, hence not something identical with either” (2002, 218).

I turn now to two Twentieth-Century commentators on Aristotle:

(1) Owens (1963): re: the Aristotelian form: “Apparently, though neither singular nor universal, it is the cause of both individuality in the singular thing, and universality in the definition” (374).

“Form as act, moreover, when pluralized in entirely potential matter, remains formally the same in all its instances, since the matter adds no new actuality and so no new formality whatsoever. This sameness is a sameness neither of universality nor of singularity. It is a sameness that, as the form itself, is prior to both universality and singularity” (14).

In reference to Metaphysics Z, 10, 1035b27-31: “The universal that is predicated of the singular thing is therefore not immediately the form as such, but the composite taken universally. The form is Entity. It is the primary instance of Entity within the sensible thing. The universal, which is not Entity, is predicated of the singular composite” (336).

“The Aristotelian universal, accordingly, is an individual form considered according to its possibility of being seen in many things, whether these things be χαθ εν or προς εν” (431).

(2) Ross (1949): “The universal for Aristotle is always something which though perfectly real and objective has no separate existence” (169).

Ross (1924): comment on Metaphysics Z, 16, 1041a3: “No universal, then, is a substance, and no substance is compounded out of a substance” (2.218).

Bill, With regard to the first point, I guess I'm so impressed by the enormity of the chasm between the concrete and the abstract that I can't conceive of some concrete thing and some abstract thing being in relation to one another, unless that 'relation' is instantiation.

>> then we seem to ignite Bradley's regress

Yes, or something very similar. I'm struggling to articulate what I think the issue is. Perhaps we could say something like this: The idea of instantiation is part and parcel with the concrete/abstract distinction. If a is abstracted from concrete c then c instantiates abstraction a. Abstraction and instantiation are inverses. Instantiation = concretisation. We need the concrete/abstract distinction fully to explicate the idea of 'relation'. Having established what relation is, it then seems otiose to go back and redefine instantiation in terms of something that succeeds it. Whether this 'pulling up the ladder' manifests in paradox or explanatory regress, I'm not certain. But it looks fishy!

For example, it seems to lead to the absurdity of your conclusion (B). On PVI's view all properties are relations. An 'intrinsic property' is a monadic relation, and a 'relational property' is a dyadic or higher arity relation, I think. The relation 'being black' is monadic and hence an intrinsic property. Nothing absurd here, PVI would say.

>>Perhaps we could say something like this: The idea of instantiation is part and parcel with the concrete/abstract distinction.<<

Abstract: not spatiotemporal. Concrete: spatiotemporal. So Socrates and Plato are each concrete, but {Socrates, Plato} is abstract. Would you agree with this? And yet Socrates, Plato are elements or members of the set. The membership relation is not instantiation. As a mathematician you can easily conceive of the membership relation as connecting a concrete item (e.g., Socrates) and an abstract item such as the set mentioned.

I conclude that the idea of instantiation is not essential to, is not 'part and parcel of,' abstract-concrete distinction.

Notational issue: I use the single forward slash to indicate inclusive disjunction, 'or.'


Good quotations. You are using 'universal' in a different sense than I am. More later. Owens supports my view.

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