Thanks again to Professor Levy to getting me 'fired up' over this topic.
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Is the notion of a trope intelligible?
If not, then we can pack it in right here and dispense with discussion of the subsidiary difficulties. Peter van Inwagen confesses, "I do not understand much of what B-ontologists write." (Ontology, Identity, and Modality, Cambridge UP, 2001, p. 2) 'B' is short for 'Bergmann' where the reference is to Gustav Bergmann, the founder of the Iowa School. B-ontology is what I call constituent ontology. I will refer to it, and not just out of perversity, as C-ontology and I will contrast it with NC-ontology. Van Inwagen is a premier example of an NC-ontologist, a non-constituent ontologist.
The fundamental idea of C-ontology is that concreta have ontological parts in addition to their spatial parts if the concreta in question are material things. To invoke a nice simple 'Iowa' example, consider a couple of round red spots on a white piece of paper. Each spot has spatial parts. On C-ontology, however, each spot also has ontological parts, among them the properties of the spots. For a C-ontologist, then, the properties of a thing are parts of it. But of course they are not spatial or mereological parts of it. A spot can be cut in two, and an avocado can be disembarrassed of its seed and exocarp, but one cannot physically separate the roundness and the redness of the spot or the dark green of the exocarp from the exocarp. So if the properties of a thing are parts thereof, then these parts are 'ontological' parts, parts that figure in the ontological structure of the thing in question.
Examples of C-ontologies: a) trope bundle theory, b) universals bundle theory, c) tropes + substratum theory, d) Castaneda's Guise Theory, e) Butchvarov's object-entity theory, f) the ontological theories of Bergmann, Armstrong, and Vallicella according to which ordinary particulars are concrete facts, g) Aristotelian and Scholastic hylomorphic doctrines according to which form and matter are 'principles' (in the Scholastic not the sentential sense) ingredient in primary substances.
If van Inwagen is right, then all of the above are unintelligible. Van Inwagen claims not to understand such terms as 'trope,' 'bare particular,' 'immanent universal' and 'bundle' as these terms are used in C-ontologies. He professes not to understand how a thing could have what I am calling an ontological structure. "What I cannot see is how a chair could have any sort of structure but a spatial or mereological structure." (Ibid.) He cannot see how something like a chair could have parts other than smaller and smaller spatial parts such as legs made of wood which are composed of cellulose molecules along with other organic compounds, and so on down. If this is right, then there is no room for what I call ontological analysis as opposed to chemical analysis and physical analysis. There can be no such intelligible project as an ontological factor analysis that breaks an ordinary particular down into thin particular, immanent universals, nexus of exemplification, and the like, or into tropes and a compresence relation, etc.
In sum: trope theory stands and falls with C-ontology; the project of C-ontology is unintelligible; ergo, trope theory is unintelligible resting as it does on such unintelligible notions as trope, and bundle of tropes. Van Inwagen delivers his unkindest cut with the quip that he has never been able to understand tropes as "anything but idealized coats of paint." (Ibid.) Ouch!
Let's assume that van Inwagen is right and that the properties of concrete particulars cannot be construed as parts of them in any intelligible sense of 'part.' If so, this puts paid to every C-ontology I am familiar with. But can van Inwagen do better? Is his NC-ontology free of difficulties? I don't think so. It bristles with them no less than C-ontology does. I refer the interested reader to my "Van Inwagen on Fiction, Existence, Properties, Particulars, and Method" in Studia Neoaristotelica, vol, 12, no. 2 (2015), pp. 99-125. Here is a pre-print version. I will now reproduce some of it so that you can see how a C-ontologist can go on the attack:
Van Inwagen's Ostrich Realism and Commitment to Bare Particulars
Van Inwagen rejects both extreme and moderate nominalism. So he can't possibly be an ostrich nominalist. He is, however, as he himself appreciates, an ostrich realist or ostrich platonist. (214-15)
Suppose Max is black. What explains the predicate's being true of Max? According to the ostrich nominalist, nothing does. It is just true of him. There is nothing in or about Max that serves as the ontological ground of the correctness of his satisfying the predicate. Now 'F' is true of a if and only if 'a is F' is true. So we may also ask: what is the ontological ground of the truth of 'Max is black'? The ostrich reply will be: nothing. The sentence is just true. There is no need for a truth-maker.
The ostrich realist/platonist says something very similar except that in place of predicates he puts abstract properties, and in place of sentences he puts abstract propositions. In virtue of what does Max instantiate blackness? In virtue of nothing. He just instantiates it. Nothing explains why the unsaturated assertible expressed by 'x is black' is instantiated by Max. Nothing explains it because there is nothing to explain. And nothing explains why the saturated assertible expressed by 'Max is black' is true. Thus there is nothing concrete here below that could be called a state of affairs in anything like Armstrong's sense. There is in the realm of concreta no such item as Max-instantiating-blackness, or the concrete fact of Max's being black. Here below there is just Max, and up yonder in a topos ouranos are 'his' properties (the abstract unsaturated assertibles that he, but not he alone, instantiates). But then Max is a bare particular in one sense of this phrase. In what sense, then?
Four Senses of 'Bare Particular'
1. A bare particular is an ordinary concrete particular that lacks properties. I mention this foolish view only to set it aside. No proponent of bare particulars that I am aware of ever intended the phrase in this way. And of course, van Inwagen is not committed to bare particulars in this sense. Indeed, he rejects an equivalent view. “A bare particular would be a thing of which nothing could be said truly, an obviously incoherent notion.” (179)
2. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that has no properties. To my knowledge, no proponent of bare particulars ever intended the phrase in this way. In any case, the view is untenable and may be dismissed. Van Inwagen is of course not committed to this view. He is a 'relation' ontologist, not a 'constituent' ontologist.
3. A bare particular is an ontological constituent of an ordinary concrete particular, a constituent that does have properties, namely, the properties associated with the ordinary particular in question, and has them by instantiating (exemplifying) them. This view is held by Gustav Bergmann and by David Armstrong in his middle period. Armstrong, however, speaks of thin particulars rather than bare particulars, contrasting them with thick particulars (what I am calling ordinary concrete particulars). When he does uses 'bare particular,' he uses the phrase incorrectly and idiosyncratically to refer to something like (1) or (2). For example, in Universals and Scientific Realism, Cambridge UP, 1978, vol. I, p. 213, he affirms something he calls the "Strong Principle of the Rejection of Bare Particulars":
For each particular, x, there exists at least one non-relational property, P, such that x is P.
This principle of Armstrong is plausibly read as a rejection of (1) and (2). It is plainly consistent with (3). But of course I do not claim that van Inwagen is committed to bare or thin particulars in the sense of (3). For again, van Inwagen is not a constituent ontologist.
4. A bare particular is an ordinary concrete particular that has properties by instantiating them, where instantiation is a full-fledged external asymmetrical relation (not a non-relational tie whatever that might come to) that connects concrete objects to abstract objects, where abstract objects are objects that are not in space, not in time, and are neither causally active nor causally passive. What is common to (3) and (4) is the idea that bare particulars have properties all right, but they have them in a certain way, by being externally related to them. A bare particular, then, is nothing like an Aristotelian primary substance which has, or rather is, its essence or nature. The bareness of a bare particular, then, consists in its lacking an Aristotle-type nature, not it its lacking properties. My claim is that van Inwagen is committed to bare particulars in sense (4). Let me explain.
Van Inwagen's Bare Particulars
Consider my cat Max. Van Inwagen is committed to saying that Max is a bare particular in sense (4). For while Max has properties, these properties are in no sense constituents of him, but lie (stand?) outside him in a realm apart. These properties are in no sense at him or in him or on him, not even such properties as being black or being furry, properties that are plausibly held to be sense-perceivable. After all, one can see black where he is and feel furriness where he is. None of Max's properties, on van Inwagen's construal of properties, are where he is or when he is. None of them has anything to do with the concrete being of Max himself. As I made clear earlier, the realms of the concrete and the abstract are radically disjoint for van Inwagen. They are jointly exhaustive and mutually exclusive realms: for all x, x is either concrete or abstract, but not both and not neither. So Max is here below in the realm of space, time, change, and causality while his properties exist in splendid isolation up yonder in the realm of abstracta. They are far, far away, not spatially and not temporally, but ontologically.
Max and his properties are of course connected by instantiation which is a relation that is both external and abstract. In what sense is the relation external? X and y are externally related just in case there is nothing intrinsic about the relata that entails their being related. Max is two feet from me at the moment. This relation of being two feet from is external in that there are no intrinsic properties of me or Max or both that entail our being two feet from each other. Our intrinsic properties would be just the same if we were three feet from each other. But Max and his brother Manny are both black. In virtue of their both being intrinsically black, they stand in the same color as relation. Hence the latter relation is not external but internal. Internal relatedness is supervenient upon the intrinsic features of the relata; external relatedness is not.
Suppose I want to bring it about that two balls have the same color. I need do only two things: paint the one ball red, say, and then paint the other ball red. But if I want to bring it about that there are two balls having the same color ten feet from each other, I have to do three things: paint the one ball red, say; paint the other ball red; place them ten feet from each other. The external relatedness does not supervene upon the intrinsic properties of the relata. Given that concrete particulars are externally related to their properties, these particulars are bare particulars in the sense defined in #4 above.
And What is Wrong with That?
Suppose you agree with me that van Inwagen's concrete particulars are bare, not in any old sense, but in the precise sense I defined, a sense that comports well with what the actual proponents of bare/thin particulars had in mind. So what? What's wrong with being committed to bare particulars? Well, the consequences seem unpalatable if not absurd.
A. One consequence is that all properties are accidental and none are essential. For if Max is bare, then there is nothing in him or at him or about him that dictates the properties he must instantiate or limits the properties he can instantiate. He can have any old set of properties so long as he has some set or other. Bare particulars are 'promiscuous' in their connection with properties. The connection between particular and property is then contingent and all properties are accidental. It is metaphysically (broadly logically) possible that Max combine with any property. He happens to be a cat, but he could have been a poached egg or a valve lifter. He could have had the shape of a cube. Or he might have been a dimensionless point. He might have been an act of thinking (temporal and causally efficacious, but not spatial).
B. A second consequence is that all properties are relational and none are intrinsic. For if Max is black in virtue of standing in an external instantiation relation to the abstract object, blackness, then his being black is a relational property and not an intrinsic one.
C. A third consequence is that none of Max's properties are sense-perceivable. Van Inwagen-properties are abstract objects and none of them are perceivable. But if I cup my hands around a ball, don't I literally feel its sphericalness or spheroidness? Or am I merely being appeared to spheroidally?
D. Finally, given what van Inwagen himself says about the radical difference between the abstract and the concrete, a difference so abysmal (my word) that it would be better if we could avoid commitment to abstracta, it is highly counter-intuitive that there should be this abymal difference between a cucumber, say, and its greenness. It is strange that the difference between God and a cucumber should “pale into insignificance” (156) compared to the difference between a cucumber and the property of being green. After all, the properties of a thing articulate its very being. How can they be so ontologically distant from the thing?
If you deny that concrete things as van Inwagen understands them are bare in the sense I have explained, then you seem to be committed to saying that there are two sorts of properties, van Inwagen properties in Plato's heaven and 'sublunary' properties at the particulars here below. But then I will ask two questions. First, what is the point of introducing such properties if they merely duplicate at the abstract intensional level the 'real' properties in the sublunary sphere? Second, what justifies calling such properties properties given that you still are going to need sublunary properties to avoid saying that van Inwagen's concreta are bare particulars?
Perceivability of Properties
Let us pursue point C above a bit further. "We never see properties, although we see that certain things have certain properties." (179) I honestly don't know what to make of the second clause of the quoted sentence. I am now, with a brain properly caffeinated, staring at my blue coffee cup in good light. Van Inwagen's claim is that I do not see the blueness of the cup, though I do see that the cup is blue. Here I balk. If I don't see blueness, or blue, when I look at the cup, how can I literally see that the cup is blue? 'That it is blue' is a thing that can be said of the cup, and said with truth. This thing that can be said is an unsaturated assertible, a property in van Inwagen's sense. Van Inwagen is telling us that it cannot be seen. 'That the cup is blue' is a thing that can be said, full stop. It is a saturated assertible, a proposition, and a true one at that. Both assertibles are abstract objects. Both are invisible, and not because of any limitation in my visual power or in human visual power in general, but because abstract objects cannot be terms of causal relations, and perception involves causation. Both types of assertible are categorially disbarred from visibility. But if both the property and the proposition are invisible, then how can van Inwagen say that "we see that certain things have certain properties"? If van Inwagen says that we don't see the proposition, then what do we see when we see that the cup is blue? A colorless cup? A cup that is blue but is blue in a way different from the way the cup is blue by instantiatiating the abstract unsaturated assertible expressed by 'that it is blue'? But then one has duplicated at the level of abstracta the property that one sees at the concrete cup. If there is blueness at the cup and abstract blueness in Plato's heaven, why do we need the latter? Just what is going on here?
To van Inwagen's view one could reasonably oppose the following view. I see the cup. I see blueness or blue at the cup. I don't see a colorless cup. To deny the three foregoing sentences would be to deny what is phenomenologically given. What I don't literally see, however, is that the cup is blue. (Thus I don't literally see what van Inwagen says we literally see.) For to see that the cup is blue is to see the instantiation of blueness by the cup. And I don't see that. The correlate of the 'is' in 'The cup is blue' is not an object of sensation. If you think it is, tell me how I can single it out, how I can isolate it. Where in the visual field is it? The blueness is spread out over the visible surfaces of the cup. The cup is singled out as a particular thing on the desk, next to the cat, beneath the lamp, etc. Now where is the instantiation relation? Point it out to me! You won't be able to do it. I see the cup, and I see blue/blueness where the cup is. I don't see the cup's BEING blue.
It is also hard to understand how van Inwagen, on his own assumptions, can maintain that we see that certain things have certain properties. Suppose I see that Max, a cat of my acquaintance, is black. Do I see a proposition? Not on van Inwagen's understanding of 'proposition.' His propositions are Fregean, not Russellian: they are not resident in the physical world. Do I see a proposition-like entity such as an Armstrongian state of affairs? Again, no. What do I see? Van Inwagen claims that properties are not objects of sensation; no properties are, not even perceptual properties. I should think that some properties are objects of sensation, or better, of perception: I perceive blueness at the cup by sight; I perceive smoothness and hardness and heat at the cup by touch. If so, then (some) properties are not abstract objects residing in a domain unto themselves.
Van Inwagen's view appears to have the absurd consequence that things like coffee cups are colorless. For if colors are properties (179) and properties are abstract objects, and abstract objects are colorless (as they obviously are), then colors are colorless, and whiteness is not white and blueness is not blue. Van Inwagen bites the bullet and accepts the consequence. But we can easily run the argument in reverse: Blueness is blue; colors are properties; abstract objects are colorless; ergo, perceptual properties are not abstract objects. They are either tropes or else universals wholly present in the things that have them. Van Inwagen, a 'relation ontologist' cannot of course allow this move into 'constituent ontology.'
There is a long footnote on p. 242 that may amount to a response to something like my objection. In the main text, van Inwagen speaks of "such properties as are presented to our senses as belonging to the objects we sense . . . ." How does this square with the claim on p. 179 that properties are not objects of sensation? Can a property such as blueness be presented to our senses without being an object of sensation? Apparently yes, "In a noncausal sense of 'presented.'" (243, fn 3) How does this solve the problem? It is phenomenologically evident that (a definite shade of) blue appears to my senses when I stare at my blue coffee cup. Now if this blueness is an abstract object as van Inwagen claims then it cannot be presented to my senses any more than it can be something with which I causally interact.
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.
Posted by: Milos | Saturday, April 09, 2016 at 01:05 PM
Good suggestion, Milos -- if I can figure out how to do it.
Posted by: BV | Saturday, April 09, 2016 at 01:18 PM
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).
Posted by: Eric Levy | Saturday, April 09, 2016 at 02:57 PM
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.
Posted by: BV | Saturday, April 09, 2016 at 05:21 PM
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.
Posted by: Eric Levy | Saturday, April 09, 2016 at 06:21 PM
Well, PvI does not think of properties as particulars.
Posted by: BV | Sunday, April 10, 2016 at 05:27 AM
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).
Posted by: Eric Levy | Sunday, April 10, 2016 at 07:46 AM
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”?
Posted by: Eric Levy | Sunday, April 10, 2016 at 08:46 AM
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).
Posted by: Eric Levy | Sunday, April 10, 2016 at 02:59 PM
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.
Posted by: BV | Sunday, April 10, 2016 at 05:10 PM
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?
Posted by: Eric Levy | Sunday, April 10, 2016 at 10:25 PM
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.
Posted by: Eric Levy | Sunday, April 10, 2016 at 10:56 PM
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.
Posted by: David Brightly | Monday, April 11, 2016 at 04:57 AM
Eric,
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.
Posted by: BV | Monday, April 11, 2016 at 06:24 AM
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?
Posted by: Eric Levy | Monday, April 11, 2016 at 08:25 AM
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.
Posted by: BV | Monday, April 11, 2016 at 01:19 PM
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.
Posted by: BV | Monday, April 11, 2016 at 01:53 PM
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).
Posted by: Eric Levy | Monday, April 11, 2016 at 06:22 PM
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.
Posted by: David Brightly | Tuesday, April 12, 2016 at 01:54 AM
>>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.'
Posted by: BV | Tuesday, April 12, 2016 at 05:55 AM
Eric,
Good quotations. You are using 'universal' in a different sense than I am. More later. Owens supports my view.
Posted by: BV | Tuesday, April 12, 2016 at 07:14 AM