This entry is a summary and critique of Peter van Inwagen's "A Theory of Properties," an article which first appeared in 2004 and now appears as Chapter 8 of his Existence: Essays in Ontology (Cambridge University Press, 2014, pp. 153-182.) Andrew Bailey has made it available on-line. (Thanks Andrew!) I will be quoting from the Existence volume. I will also be drawing upon material from other articles in this collection. This post is a warm-up for a review of the book by me commissioned by a European journal. The review wants completing by the end of February. Perhaps you can help me. Comments are enabled for those who know this subject.
Exposition
1. The Abstract and the Concrete.
Platonism is "the thesis that there are abstract objects." (153) Van Inwagen uses 'object' synonomously with 'thing,' 'item,' and 'entity.' (156) Everything is an object, which is to say: everything exists. Thus there are no nonexistent objects, pace Meinong. There are two categories of object, the abstract and the concrete. These categories are mutually exclusive and jointly exhaustive. Thus for any x, x is either abstract or concrete, but not both, and not neither. Van Inwagen is a bit coy when it comes to telling us what 'abstract' and concrete' mean; he prefers a roundabout way of introducing these terms. He stipulates that the terms and predicates of ordinary, scientific, and philosophical discourse can be divided into two mutually exclusive and jointly exhaustive classes. The denotata of the members of these two classes of terms and predicates, if they have denotata, are concrete and abstract objects. Thus 'table,' 'God,' and 'intelligent Martian,' if they pick out anything, pick out concreta, while 'number,' 'the lion,' (as in 'The lion is of the genus Felis') and 'sentence' (as in 'The same sentence can express different propositions in different contexts'), pick out abstracta. (154) (See footnote * below)
Van Inwagen holds that platonism is to be avoided if at all possible. On platonism, there are abstract objects. This characteristic thesis does not entail, but it is consistent with, the proposition that there are also concrete objects. Van Inwagen is a platonist who accepts both abstract and concrete objects but thinks we would be better of if we could avoid commitment to abstract objects. Why? Well, apart from considerations of parsimony, the difference between members of the two categories is abysmal (my word): "the differences between God and this pen pale into insignificance when they are compared with the differences between this pen and the number 4 . . . ." (156) Such a radical difference is puzzling. So it would be preferable if the category of abstracta were empty. That the category of concreta cannot be empty is obvious: we know ourselves to be concreta. (157) Van Inwagen goes on to belabor the point that the things we can say about concrete things are practically endless, while little can be said about abstracta.
In short, reality, unlike ancient Gaul, "is divided into two parts . . . ." (158, emphasis added). The two parts of reality are radically disjoint. Everything is either abstract or concrete, nothing is both, and nothing is neither. Among the abstracta are instantiated properties. Instantiation or 'having' would seem to forge a connection between the disjoint realms. But the instantiation relation is "abstract and external." (206, 242) So it too resides in the realm of abstracta and hence (as it seems to me) does nothing to mitigate the radical dualism or span the abyss that yawns between reality's two parts. So if we could eke by without abstracta, that would be preferable. But we cannot manage without them, says van Inwagen. (158)
2. Why We Need Abstract Objects.
The short reason is that we need them because we need properties, and properties are one sort of abstract object, along with propositions and "proper relations." (240) A proper relation is a relation whose adicity is two or more; van Inwagen thinks of properties as one-place relations and propositions as zero-place relations. Every abstract object is a relation (a relation-in-intension) in the broad or improper sense, and everything else is a substance, a concrete object. (239)
But why do we need properties? We need properties because things have common features. The class of humans, for example, has something in common. This appears to be an existential claim: there is something, humanity, that the members of this class share. Platonists take the appearance at face value while nominalists maintain that the appearance is a mere appearance such that in reality there are no properties. How do we decide the issue that divides the platonists and the nominalists? Here van Inwagen is referring to what he calls "austere" nominalists, the nominalists more standardly called extreme: those who deny that there are properties at all. There are also the nominalists van Inwagen calls "luxuriant" nominalists, the ones more standardly called moderate: those who admit the existence of tropes or individual accidents or particularized properties. (203, 203 fn 5) The extreme nominalist denies that there are properties at all -- a lunatic view if I may inject my opinion -- while the moderate nominalists admit properties but deny that they are universals. Platonists are not austere nominalists because they accept properties; they are not luxuriant nominalists because they accept universals.
3. Van Inwagen's Method.
The method derives from Quine. We start with the beliefs we already have, couched in the sentences we already accept. We then see if these sentences commit us to properties. We do this by translating these sentences into "the canonical language of quantification." (160) If we need to quantify over properties for the sentences we accept as true to count as true, then we are ontologically committed to the existence of properties. If, on the other hand, we can 'paraphrase away' the apparent reference to properties in the sentences we accept that appear to refer to properties, then the ontological commitment is merely apparent.
Van Inwagen's main idea here is that our discourse commits us to quantification over properties, and thus to the existence of properties. We deduce the existence of properties from certain sentences we accept. The argument is not epistemological: it does not seek to provide evidence for the existence of properties. Nor is it transcendental, or an inference to the best explanation. (167) The operative methodological principle, if there is one, is only this: "if one does not believe that things of a certain sort exist, one shouldn't say anything that demonstrably implies that things of that sort exist." (167)
Example. We accept 'Spiders share some of the anatomical features of insects.' (159) This says nothing different from 'There are anatomical features that insects have and spiders also have.' This then is translated into canonical English. I will spare you the rigmarole. The upshot is that there are anatomical features. Hence there are properties.
The most promising way of rebutting platonism so derived is by finding a paraphrase of the original sentence that says the same thing but does not even seem to commit its acceptor to properties. (The nominalists would of course have to do this for every sentence proposed by platonists that supposedly commits its users to abstracta.) Van Inwagen, predictably, argues against the paraphrastic way out. Nominalist paraphrases are not to be had. (164-167)
4. Van Inwagen's Theory of Properties.
Given that there are properties, what are they like? What are the properties of properties? To specify them is the task of a theory of properties. What follows is my list, not his, but gleaned from what he writes. Properties are
a. abstract objects, as we have already seen. As abstract, properties are non-spatiotemporal and causally inert. (207) Better: abstract objects are categorially such as to be neither causally active nor causally passive.
b. universals, as we have already gleaned, with the exception of haecceities such as the property of being identical to Plantinga. (180) Van Inwagen has no truck with tropes. (241) See my Peter van Inwagen's Trouble with Tropes.
c. the entities that play the property role. And what role would that be? This is the role "thing that can be said of something." It is a special case of the role "thing that can be said." (175) Properties are things that can be said of or about something. Propositions are things that can be said, period, or full stop.
d. unsaturated assertibles. Things that can be said are assertibles. They are either unsaturated, in which case they are properties, or saturated, in which case they are propositions.
e. necessary beings. (207)
f. not necessarily instantiated. Many properties exist uninstantiated.
g. not all of them instantiable. Some unsaturated assertibles are necessarily uninstantiated, e.g., what is said of x if one says 'x is both round and square.'
h. such that the usual logical operations apply to them. (176) Given any two assertibles, whether saturated or unsaturated, there is 'automatically' their conjunction and their disjunction. Given any one assertible, there is 'automatically' its negation.
i. abundant, not sparse. There is a property corresponding to almost every one-place open sentence with a precise meaning. The 'almost' alludes to a variant of Russell's paradox that van Inwagen is fully aware of but that cannot be discussed here. (243) Thus, contra David Armstrong, it is not the task of what the latter calls "total [empirical] science" to determine what properties there are. Perhaps we could say that properties for van Inwagen are logical fallout from one-place predicates. (My phrase) But since properties are necessary beings, there are all the properties there might have been; hence they 'outrun' actual one-place predicates. (My way of putting it.)
j. not parts or constituents in any sense of the concrete things that have them. Indeed, it makes no sense to say that an assertible is a part of a concrete object. And although properties or unsaturated assertibles are universals, it makes no sense that such an item is 'wholly present' in concrete objects. (178) Concrete things are 'blobs' in David Armstrong's sense. They lack ontological structure. "Their only constituents are their parts, their parts in the strict and mereological sense." (243)
k. not more basic ontologically than the things whose properties they are. A concrete thing is not a bundle or cluster of properties. The very suggestion is senseless on van Inwagen's scheme. A property is an unsaturated assertible. It is very much like a Fregean (objective) concept or Begriff, even though van Inwagen does not say this in so many words. (But his talk of unsaturatedness points us back to Frege.) Clearly it would be senseless to think of a dog as a bundle of Fregean concepts. That which can be truly said of a thing like a dog, that it is furry, for example, is no part of the critter. (178-79)
I should point out that while talk of saturated and unsaturated assertibles conjures the shade of Frege, van Inwagen has no truck with Frege's concept-object dichotomy according to which no concept is an object, no object is a concept, and the concept horse is not a concept. You could say, and I mean no disrespect, that he 'peters out' with respect to this dichotomy: "I do not understand the concept-object distinction. The objects I call properties are just that: objects." (206, fn 11)
l. are not objects of sensation. (179) To put it paradoxically, and this is my formulation, not van Inwagen's, such perceptual properties as being blue and being oval in shape are not perceptible properties. One can see that a coffee cup is blue, but one cannot literally see the blueness of the coffee cup.
Critique
My readers will know that almost everything (of a substantive and controversial nature) that van Inwagen maintains, I reject and for reasons that strike me as good. Ain't philosophy grand?
1. Perceivability
I'll begin the critique with the last point. "We never see properties, although we see that certain things have certain properties." (179) If van Inwagen can 'peter out,' so can I: 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 see (literally see, with the eyes of the head, not the eye of the mind) 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"? What am I missing?
How can he say that we don't see the property but we do see the proposition? Both are abstract and invisible. How is it that we can see the second but not the first? Either we see both or we see neither. 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 (obviously!) and I see blueness at the cup (obviously!) 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.
2. But Is This Ontology?
Why does van Inwagen think he is doing ontology at all? It looks more like semantics or philosophical logic or philosophy of language. I say this because van Inwagen's assertibles are very much like Fregean senses. They are intensional items. (As we noted, he reduces all his assertibles to relations-in-intension.) Taking his cue from Quine, he seeks an answer to the question, What is there? He wants an inventory, by category, of what there is. He wants to know, for example, whether in addition to concrete things there are also properties, as if properties could exist in sublime disconnection from concrete things in a separate sphere alongside this sublunary sphere. That no property is an object of sensation is just logical fallout from van Inwagen's decision to install them in Plato's heaven; but then their connection to things here below in space and time become unintelligible. It does no good, in alleviation of this unintelligibility, to say that abstract blueness -- the unsaturated assertible expressed by 'that it is blue' -- is instantiated by my blue cup. For instantiation is just another abstract object, a dyadic external relation, itself ensconced in Plato's heaven.
But not only the formulation of the question but also the method of attack come from Quine. Van Inwagen thinks he can answer what he and Quine idiosyncratically call the ontological question by examining the ontological commitments of our discourse. Starting with sentences we accept as true, he looks to see what these sentences entail as regards the types of entity there are when the sentences are properly regimented in accordance with the structures of modern predicate logic with identity.
The starting point is not things in their mind- and language-independent being, but beliefs we already have and sentences we already accept. The approach is oblique, not direct; subjective, not objective. Now to accept a sentence is to accept it as true; but a sentence accepted as true need not be true. Note also that if one sentence entails another, both can be false. So if sentences accepted as true entail the existence of properties in van Inwagen's sense, according to which properies are unsaturated assertibles, it is logically possible that there be no properties in reality. The following is not a contradiction: The sentences we accept as true entail that there are properties & There are no properties. For it may be -- it is narrowly-logically possible that -- the sentences we accept as true that entail that there are properties are all of them false. Not likely, of course, and there may be some retorsive argument against this possibility. But it cannot be ruled out by logic alone.
So there is something fishy about the whole method of 'ontological' commitment. One would have thought that ontology is concerned with the Being of beings, not with the presuppositions of sentences accepted as true by us. To put it vaguely, there is something 'transcendental' (in the Kantina sense) and 'subjective' and 'modern' about van Inwagen's Quinean method that unsuits it for for something that deserves to be called ontology.
This is connected with the point that van Inwagen's assertibles, saturated and unsaturated, are hard to distinguish from Fregean senses. They are denizens of Frege's Third Reich or Third World if you will, not his First Reich, the realm of primary reference. To illustrate: Venus is an item in the First World, while the senses of 'Morning Star' and 'Evening Star' and the sense of the sentence 'The Morning Star is the Evening Star' are three items all in the Third World. Senses, however, are logico-semantic items: their job is to mediate reference. Van Inwagen is arguably just hypostatizing items that are needed for us to secure reference -- whether thinking reference or linguistic reference -- to things that truly exist extramentally and extralinguistically.
Again, this is vague and sketchy. But good enough for a weblog entry! Is think my Czech scholastic friends will know what I am driving at.
3. 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 iff '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 solely, instantiates). But then Max is a bare particular in one sense of this phrase, though not in Gustav Bergmann's exact sense of the phrase. (Bergmann is a constituent ontologist.) In what sense, then?
A bare particular is not a particular that has no properties in any sense of 'having properties'; a bare particular is a particular that has properties, but has them in a certain way: by being externally related to them. Thus bare particulars, unlike Aristotelean substances, have neither natures nor essences. Indeed, the best way to understand what a bare particular is is by contrast with the primary substances of Aristotle. These concrete individuals have natures by being (identically) natures: they are not externally related to natures that exist serenely and necessarily in Plato's heaven.
In this sense, van Inwagen's concrete things are bare particulars. There are no properties 'in' or 'at' Max; there are no properties where he is and when he is. What's more, on van Inwagen's scheme -- one he shares with Chisholm, Plantinga, et al. -- Max can only be externally related to his properties. This has the consequence that all of Max's properties are accidental. For if x, y are externally related, then x can exist without y and y can exist without x. So Max can exist without being feline just as he can exist without being asleep.
Could Max have been a poached egg? It is narrowly-logically possible. For if he has all of his properties externally, then he has all of his properties accidentally. Even if it is necessary that he have some set of properties or other, there is no necessity that he have any particular set. If properties are externally related to particulars, then any particular can have any set of properties so long as it has some set or other.
If you deny that concrete things are bare in the sense I have explained, then you seem to be committed to saying that there are two sorts of properties, PvI-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 PvI-properties if they merely duplicate at the abstract intensional level the 'real' properties in the sublunary sphere? Second, what justifies calling PvI-properties properties given that you still are going to need 'sublunary' properties to avoid saying that van Inwagen's concreta are bare particulars?
4. Existence
One can say of a thing that it might not have existed. For example, I can say this of myself. If so, it must be possible to say of a thing that it exists. For example, it must be possible for me to say of myself that I exist. As van Inwagen remarks, "it is hard to see how there could be such an assertible as 'that it might not have existed' if there were no such assertible as 'that it exists.'" (180) Existence, then, is a property, says van Inwagen, for properties are unsaturated assertibles, and 'that it exists' is an assertible.
There are many problems with the notion that existence is a first-level property on a van Inwagen-type construal of properties. Instantiation for van Inwagen is a full-fledged dyadic relation. (It is not a non-relational tie or Bergmannian nexus). He further characterizes it as abstract and external as we have seen. Now it is perfectly obvious to me that the very existence of Socrates cannot consist in his instantiation of any PvI-type property, let alone the putative property, existence. For given the externality of the instantiation relation, both Socrates and the putative property must 'already' exist for said relation to hold between them. So one moves in an explanatory circle of embarrassingly short diameter if one tries to account for existence in this way.
This circularity objection which I have developed in painful detail elsewhere will, I expect, leave van Inwagen stone cold. One reason is that he sees no role for explanation in metaphysics whereas I think that metaphysics without explanation is not metaphysics at all in any serious sense. This is large topic that cannot be addressed here.
I'll mention one other problem for van Inwagen. I'll put it very briefly since this entry is already too long. Van Inwagen is a Fregean about existence; but on a Fregean view existence cannot be a first-level property. For Frege, 'x exists' where 'x' ranges over individuals is a senseless open sentence or predicate. There is no unsaturated assertible corresponding to it. I have a number of posts on van Inwagen and existence. Here is one. My latest published article on existence is "Existence: Two Dogmas of Analysis" in Novak and Novotny, eds., Neo-Aristotelian Perspectives in Metaphysics, Routledge 2014, 45-75.
5. Haecceities
Among the properties, van Inwagen counts haecceities. They are of course abstract objects like all properties. But they are not universals because, while they are instantiable, they are not multiply instantiable. The property of being identical with Alvin Plantinga is an example van Inwagen gives. (180) This property, if instantiated, is instantiated by Plantinga alone in the actual world and by nothing distinct from Plantinga in any possible world. Plantingitas -- to give it a name -- somehow involves Plantinga himself, that very concrete object. For this property is supposed to capture the nonqualitative thisness of Plantinga. (Haecceitas is Latin for 'thisness.')
I submit that these haecceity properties are metaphysical monstrosities. For given that they are properties, they are necessary beings. A necessary being exists at all times in all possible worlds that have time, and in all worlds, period. Plantinga, however, does not exist in all worlds since he is a contingent being; and he doesn't exist at all times in all worlds in which he exists, subject as he is to birth and death, generation and corruption. I conclude that before Plantinga came into being there could not have been any such property as the property of being identical to Plantinga. I conclude also that in worlds in which he does not exist there is no such haecceity property. For at pre-Plantingian times and non-Plantingian worlds, there is simply nothing to give content to the unsaturated assertible expressed by 'that it is Alvin Plantinga.' (Alvin Plantingas hung out at those times and in those worlds, but not our Alvin Plantinga.) Plantinga himself enters essentially into the very content of his haecceity property.
But this is absurd because PvI-properties are merely intensional entities. No such entity can have a concrete, flesh and blood man as a constituent. Just as a PvI-property cannot be a constituent of a concretum such as Plantinga, Plantinga cannot be a constituent in any sense of 'constituent' of a PvI-property.
But if Plantinga hadn't existed, might it nonetheless have been true that he might have existed? (180). Van Inwagen says yes and introduces haecceities. Plantingitas exists in every world; it is just that it is instantiated only in some. I say no, precisely because I take haecceities to be metaphysical monstrosities.
Conclusion
I am not out to refute van Inwagen or anyone. Philosophical theories, except for some sophomoric ones, cannot be refuted. At most I am out to neutralize van Inwagen's theory, or rather his type of theory, to explain why it is not compelling and how it is open to powerful objections, only some of which I have adduced in this entry. And of course I do not have a better theory. I incline toward constituent ontology myself, but it too is bristling with difficulties.
As I see it, the problems of philosophy are most of them genuine, some of them humanly important, but all of them insoluble.
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*At this point I should like to record a misgiving. If sentences (sentence types, not tokens) are abstract objects, and abstract objects are necessary beings as van Inwagen holds (cf., e.g., p. 242), then sentences are necessary beings. But sentences are tied to contingently existing languages and cannot exist apart from them. Thus 'I am hungry' is a sentence of English while 'Ich habe Hunger' is a sentence of German, and neither sentence can exist apart from its respective language. A natural language, however, would seem to be a contingent being: German came into existence, but it might never have come into existence. Given all this, a contradiction appears to follow: Sentences are and are not necessary beings.
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