Thanks again to Professor Levy to getting me 'fired up' over this topic.
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.