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Category: Predication
Trope Troubles: An Exercise in Aporetics
Elliot C. asked me about tropes. What follows is a re-post from 30 March 2016, slightly emended, which stands up well under current scrutiny. Perhaps Elliot will find the time to tell me whether he finds it clear and convincing and whether it answers his questions.
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A reader has been much exercised of late by trope theory and other questions in ontology. He has been sharing his enthusiasm with me. He espies
. . . an apparent antinomy at the heart of trope theory. On the one hand, tropes are logically prior to objects. But on the other hand, objects (or, more precisely, the trope-bundles constituting objects) are logically prior to tropes, because without objects tropes have nowhere to be – without objects (or the trope-bundles constituting objects) tropes cannot be. Moreover, as has I hope been shown, a trope cannot be in (or constitute) any object or trope-bundle other than that in which it already is.
How might a trope theorist plausibly respond to this? Can she? [My use of the feminine third-person singular pronoun does not signal my nonexistent political correctness, but is an anticipatory reference to Anna-Sofia Maurin whom I will discuss below. 'Anna-Sofia'! What a beautiful name, so aptronymic. Nomen est omen.)
What are tropes?
It is a 'Moorean fact,' a pre-analytic datum, that things have properties. This is a pre-philosophical observation. In making it we are not yet doing philosophy. If things have properties, then there are properties. This is a related pre-philosophical observation. We begin to do philosophy when we ask: given that there are properties, what exactly are they? What is their nature? How are we to understand them? This is not the question, what properties are there, but the question, what are properties? The philosophical question, then, is not whether there are properties, nor is it the question what properties there are, but the question what properties are.
On trope theory, properties are assayed not as universals but as particulars: the redness of a tomato is as particular, as unrepeatable, as the tomato. Thus a tomato is red, not in virtue of exemplifying a universal, but by having a redness trope as one of its constituents (on the standard bundle version of trope theory) or by being a substratum in which a redness trope inheres (on a nonstandard theory championed by C. B. Martin which I will not further discuss). A trope is a simple entity in that there is no distinction between it and the property it ‘has.’ 'Has' and cognates are words of ordinary English: they do not commit us to ontological theories of what the having consists in. So don't confuse 'a has F-ness' with 'a instantiates F-ness.' Instantiation is a term of art, a terminus technicus in ontology. Or at least that is what it is in my book. More on instantiation in a moment.
Thus a redness trope is red, but it is not red by instantiating redness, or by having redness as a constituent, but by being (a bit of) redness. So a trope is what it has. It has redness by being identical to (a bit of) redness.
It is therefore inaccurate to speak of tropes as property instances. A trope is not a property instance on one clear understanding of the latter. First-order instantiation is a dyadic asymmetrical relation: if a instantiates F-ness, then it is not the case that F-ness instantiates a. (Higher order instantiation is not asymmetrical but nonsymmetrical. Exercise for the reader: prove it!) Suppose the instantiation relation connects the individual Socrates here below to the universal wisdom in the realm of platonica. Then a further item comes into consideration, namely, the wisdom of Socrates. This is a property instance. It is a particular, an unrepeatable, since it is the wisdom of Socrates and of no one else. This distinguishes it from the universal, wisdom, which is repeated in each wise individual. On the other side, the wisdom of Socrates is distinct from Socrates since there is more to Socrates that his being wise. There is his being snub-nosed, etc. Now why do I maintain that a trope is not a property instance? Two arguments.
Tropes are simple, not complex. (See Maurin, here.) They are not further analyzable. Property instances, however, are complex, not simple. 'The F-ness of a' – 'the wisdom of Socrates,' e.g. — picks out a complex item that is analyzable into F-ness, a, and the referent of 'of.' Therefore, tropes are not property instances.
A second, related, argument. Tropes are in no way proposition-like. Property instances are proposition-like as can be gathered from the phrases we use to refer to them. Ergo, tropes are not property instances.
One can see from this that tropes on standard trope theory, as ably presented by Maurin in her Stanford Encyclopedia of Philosophy entry, are very strange items, so strange indeed that one can wonder whether they are coherently conceivable at all by minds of our discursive constitution. Here is one problem.
How could anything be both predicable and impredicable?
Properties are predicable items. So if tropes are properties, then tropes are predicable items. If the redness of my tomato, call it 'Tom,' is a trope, then this trope is predicable of Tom. Suppose I assertively utter a token of 'Tom is red.' On one way of parsing this we have a subject term 'Tom' and a predicate term '___ is red.' Thus the parsing: Tom/is red. But then the trope would appear to have a proposition-like structure, the structure of what Russell calls a propositional function. Clearly, '___ is red' does not pick out a proposition, but it does pick out something proposition-like and thus something complex. But now we have trouble since tropes are supposed to be simple. Expressed as an aporetic triad or antilogism:
a. Tropes are simple.
b. Tropes are predicable.
c. Predicable items are complex.
The limbs of the antilogism are each of them rationally supportable, but they cannot all be true. Individually plausible, collectively inconsistent. The conjunction of any two limbs entails the negation of the remaining one. Thus the conjunction of (b) and (c) entails ~(a).
We might try to get around this difficulty by parsing 'Tom is red' differently, as: Tom/is/red. On this scheme, 'Tom' and 'red' are both names. 'Tom' names a concrete particular whereas 'red' names an abstract particular. ('Abstract' is here being used in the classical, not the Quinean, sense.) As Maurin relates, D. C. Williams, who introduced the term 'trope' in its present usage back in the '50s, thinks of the designators of tropes as akin to names and demonstratives, not as definite descriptions. But then it becomes difficult to see how tropes could be predicable entities.
A tomato is not a predicable entity. One cannot predicate a tomato of anything. The same goes for the parts of a tomato; the seeds, e.g., are not predicable of anything. Now if a tomato is a bundle of tropes, then it is a whole of ontological parts, these latter being tropes. If we think of the tomato as a (full-fledged) substance, then the tropes constituting it are "junior substances." (See D. M. Armstrong, 1989, 115) But now the problem is: how can one and the same item — a trope – be both a substance and a property, both an object and a concept (in Fregean jargon), both impredicable and predicable? Expressed as an aporetic dyad or antinomy:
d. Tropes are predicable items.
e. Tropes are not predicable items.
Maurin seems to think that the limbs of the dyad can both be true: ". . . tropes are by their nature such that they can be adequately categorized both as a kind of property and as a kind of substance." If the limbs can both be true, then they are not contradictory despite appearances.
How can we defuse the apparent contradiction in the d-e dyad? Consider again Tom and the redness trope R. To say that R is predicable of Tom is to say that Tom is a trope bundle having R as an ontological (proper) part. To say that R is impredicable or a substance is to say that R is capable of independent existence. Recall that Armstrong plausibly defines a substance as anything logically capable of independent existence.
It looks as if we have just rid ourselves of the contradiction. The sense in which tropes are predicable is not the sense in which they are impredicable. They are predicable as constituents of trope bundles; they are impredicable in themselves. Equivalently, tropes are properties when they are compresent with sufficiently many other tropes to form trope bundles (concrete particulars); but they are substances in themselves apart from trope bundles as the 'building blocks' out of which such bundles are (logically or rather ontologically) constructed.
Which came first: the whole or the parts?
But wait! This solution appears to have all the advantages of jumping from the frying pan into the fire. For now we bang up against the above Antinomy, or something like it, to wit:
f. Tropes as substances, as ontological building blocks, are logically prior to concrete particulars.
g. Tropes as properties, as predicable items, are not logically prior to concrete particulars.
This looks like an aporia in the strict and narrow sense: an insoluble problem. The limbs cannot both be true. And yet each is an entailment of standard (bundle) trope theory. If tropes are the "alphabet of being" in a phrase from Williams, then they are logically prior to what they spell out. But if tropes are unrepeatable properties, properties as particulars, then a trope cannot exist except as a proper ontological part of a trope bundle, the very one of which it is a part. For if a trope were not tied to the very bundle of which it is a part, it would be a universal, perhaps only an immanent universal, but a universal all the same.
Furthermore, what makes a trope abstract in the classical (as opposed to Quinean) sense of the term is that it is abstracted from a concretum. But then the concretum comes first, ontologically speaking, and (g) is true.
Interim conclusion: Trope theory, pace Anna-Sofia Maurin, is incoherent. But of course we have only scratched the surface.
Pictured below, left-to-right: Anna-Sofia Maurin, your humble correspondent, Arianna Betti, Jan Willem Wieland. Geneva, Switzerland, December 2008. It was a cold night.
The Hatfields and the McCoys
Whether or not it is true, the following has a clear sense:
1. The Hatfields outnumber the McCoys.
(1) says that the number of Hatfields is strictly greater than the number of McCoys. It obviously does not say, of each Hatfield, that he outnumbers some McCoy. If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys.
It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates. In
2. The Hatfields are 100 strong
it cannot be any individual Hatfield that is 100 strong. This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'
So here is a challenge to Ed Buckner the nominalist. Provide truth-preserving analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.
Nominalists and realists alike agree that one must not "multiply entities beyond necessity." Entia non sunt multiplicanda praeter necessitatem! The question, of course, hinges on what's necessary for explanatory purposes. So the challenge for Buckner the nominalist is to provide analyses of (1) and (2) that capture the sense and preserve the truth of the analysanda and yet obviate the felt need to posit entities in addition to concrete particulars.
Now if such analyses could be provided, it would not follow that there are no 'collective entities.' But a reason for positing them would have been removed.
The Ramsey Problem and the Problem of the Intrinsically Unpropertied Particular
Here at Maverick Philosopher: Strictly Philosophical
Frege’s Horse Paradox, Bradley’s Regress, and the Problem of Predication
The concept horse is not a concept. Thus spoke Frege, paradoxically. Why does he say such a thing? Because the subject expression 'the concept horse' refers to an object. It names an object. Concepts and objects on his scheme are mutually exclusive. No concept is an object and conversely. Only objects can be named. No concept can be named. Predicates are not names. If you try to name a concept you will fail. You will succeed only in naming an object. You will not succeed in expressing the predicativity of the concept. Concepts are predicable while objects are not. It is clear that one cannot predicate Socrates of Socrates. We can, however, predicate wisdom of Socrates. It is just that wisdom is not an object.
But now we are smack in the middle of the paradox. For to explain Frege's view I need to be able to talk about the referent of the gappy predicate ' ___ is wise.' I need to be able to say that it is a predicable entity, a concept. But how can I do this without naming it, and thus objectifying it? Ineffability may be the wages of Frege's absolute object-concept distinction.
To savor the full flavor of the paradox, note that the sentence 'No concept can be named' contains the general name 'concept.' It seems we, or rather the Fregeans, cannot say what we or they mean. But if we cannot say what we mean, how do we know that we mean anything at all? Is an inexpressible meaning a meaning? Are there things that cannot be said but only shown? (Wittgenstein) Perhaps we cannot say that concepts are concepts; all we can do is show that they are by employing open sentences or predicates such as '___ is tall.' Unfortunately, this is also paradoxical. For I had to say what the gappy predicate shows. I had to say that concepts are concepts and that concepts are what gappy predicates (predicates that are not construed as names) express.
Why can't concepts be named? Why aren't they a kind of higher-order object? Why can't they be picked out using abstract substantives? Why can't we say that, in a sentence such as 'Tom is sad,' 'Tom' names an object while 'sad' names a different sort of object, a concept/property? Frege's thought seems to be that if concepts are objects, then they cannot exercise their predicative function. Concepts are essentially and irreducibly predicative, and if you objectify them — think or speak of them as objects — then you destroy their predicative function. A predicative proposition is not a juxtaposition of two objects. If there is Tom and there is sadness, it doesn't follow that sadness is true of Tom. What makes a property true of its subject? An obvious equivalence: if F-ness is true of a, then *a is F* is true. So we might ask the questions this way: What makes *a is F* true?
The Problem of the Unity of the Proposition and the Fregean Solution
We are brought back to the problem of the unity of the proposition. It's as old as Plato. It is a genuine problem, but no one has ever solved it. (Of course, I am using 'solve' as a verb of success.)
A collection of two objects is not a proposition. The mereological sum Tom + sadness is neither true nor false; propositions are either true or false. The unity of a proposition is a type of unity that attracts a truth value, whereas the unity of a sum does not attract a truth value. The unity of a proposition is mighty puzzling even in the simplest cases. It does no good to say that the copula 'is' in 'Tom is sad' refers to the instantiation relation R and that this relation connects the concept/property to the object, sadness to Tom, and in such a way as to make sadness true of Tom. For then you sire Mr Bradley's relation regress. It's infinite and it's vicious. Note that if the sum Tom + sadness can exist without it being true that Tom is sad, then the sum Tom + R + sadness can also exist without it being true that Tom is sad.
Enter Frege with his obscure talk of the unsaturatedness of concepts. Concepts exist whether or not they are instantiated, but they are 'gappy': if a first-level concept is instantiated by an object, there is no need for a tertium quid to connect concept and object. They fit together like plug and socket, where the plug is the object and the concept the socket. The female receptacle accepts the male plug without the need of anything to hold the two together.
On this approach no regress arises. For if there is no third thing that holds concept and object together, then no worries can arise as to how the third thing is related to the concept on the one side and the object on the other. But our problem about the unity of the proposition remains unsolved. For if the concept can exist uninstantiated, then both object and concept, Tom and sadness, can exist without it being true that Tom is sad.
The dialectic continues on and on. Philosophia longa, vita brevis. Life is brief; blog posts ought to be.
Against Ostrich Nominalism
As magnificent a subject as philosophy is, grappling as it does with the ultimate concerns of human existence, and thus surpassing in nobility any other human pursuit, it is also miserable in that nothing goes uncontested, and nothing ever gets established to the satisfaction of all competent practitioners. (This is true of other disciplines as well, but in philosophy it is true in excelsis.) Suppose I say, as I have in various places:
That things have properties and stand in relations I take to be a plain Moorean fact beyond the reach of reasonable controversy. After all, my cat is black and he is sleeping next to my blue coffee cup. ‘Black’ picks out a property, an extralinguistic feature of my cat.
Is that obvious? Not to some. Not to the ornery and recalcitrant critter known as the ostrich nominalist. My cat, Max Black, is black. That, surely, is a Moorean fact. Now consider the following biconditional and consider whether it too is a Moorean fact:
1. Max is black iff Max has the property of being black.
As I see it, there are three main ways of construing a biconditional such as (1):
A. Ostrich Nominalism. The right-hand side (RHS) says exactly what the left-hand side (LHS) says, but in a verbose and high-falutin' and dispensable way. Thus the use of 'property' on the RHS does not commit one ontologically to properties beyond predicates. (By definition, predicates are linguistic items while properties are extralinguistic and extramental.) Predication is primitive and in need of no philosophical explanation. On this approach, (1) is trivially true. One needn't posit properties, and in consequence one needn't worry about the nature of property-possession. (Is Max related to his blackness, or does Max have his blackness quasi-mereologically by having it as an ontological constituent of him?)
B. Ostrich Realism. The RHS commits one ontologically to properties, but in no sense does the RHS serve to ground or explain the LHS. On this approach, (1) is false if there are no properties. For the ostrich realist, (1) is true, indeed necessarily true, but it is not the case that the LHS is true because the RHS is true. Such notions as metaphysical grounding and philosophical explanation are foreign to the ostrich realist, but not in virtue of his being a realist, but in virtue of his being an ostrich.
C. Non-Ostrich Realism. On this approach, the RHS both commits one to properties, but also proffers a metaphysical ground of the truth of the LHS: the LHS is true because (ontologically or metaphysically speaking) the concrete particular Max has the property of being black, and not vice versa.
Note 1: Explanation is asymmetrical; biconditionality is symmetrical.
Note 2: Properties needn't be universals. They might be (abstract) particulars (unrepeatables) such as the tropes of D. C. Williams and Keith Campbell. Properties must, however, be extralinguistic and extramental, by definition.
Note 3: Property-possession needn't be understood in terms of instantiation or exemplification or Fregean 'falling-under'; it might be construed quasi-mereologically as constituency: a thing has a property by having it as a proper ontological part.
Against Ostrich Nominalism
On (A) there are neither properties, nor do properties enter into any explanation of predication. Predication is primitive and in need of no explanation. In virtue of what does 'black' correctly apply to Max? In virtue of nothing. It just applies to him and does so correctly. Max is black, but there is no feature of reality that explains why 'black' is true of Max, or why 'Max is black' is true. It is just true! There is nothing in reality that serves as the ontological ground of this contingent truth. Nothing 'makes' it true. There are no truth-makers and no need for any.
I find ostrich nominalism preposterous. 'Black' is true of Max, 'white' is not, but there is no feature of reality, nothing in or at or about Max that explains why the one predicate is true of him and the other is not!? This is not really an argument but more an expression of incomprehension or incredulity, an autobiographical comment, if you will. I may just be petering out, pace Professor van Inwagen.
Can I do better than peter? 'Black' is a predicate of English. Schwarz is a predicate of German. If there are no properties, then Max is black relative to English, schwarz relative to German, noir relative to French, and no one color. But this is absurd. Max is not three different colors, but one color, the color we use 'black' to pick out, and the Germans use schwarz to pick out. When Karl, Pierre, and I look at Max we see the same color. So there is one color we both see — which would not be the case if there were no properties beyond predicates. It is not as if I see the color black while Karl sees the color schwarz. We see the same color. And we see it at the cat. This is not a visio intellectualis whereby we peer into some Platonic topos ouranos. Therefore, there is something in, at, or about the cat, something extralinguistic, that grounds the correctness of the application of the predicate to the cat.
A related argument. I say, 'Max is black.' Karl says, Max ist schwarz. 'Is' and ist are token-distinct and type-distinct words of different languages. If there is nothing in reality (no relation whether of instantiation or of constituency, non-relational tie, Bergmannian nexus, etc.) that the copula picks out, then it is only relative to German that Max ist schwarz, and only relative to English that Max is black. But this is absurd. There are not two different facts here but one. Max is the same color for Karl and me, and his being black is the same fact for Karl and me.
Finally, 'Max is black' is true. Is it true ex vi terminorum? Of course not. It is contingently true. Is it just contingently true? Of course not. It is true because of the way extralinguistic reality is arranged. It is modally contingent, but also contingent upon the way the world is. There's this cat that exists whether or not any language exists, and it is black whether or not any language exists.
Therefore, I say that for a predicate to be contingently true of an individual, (i) there must be individuals independently of language; (ii) there must be properties independently of language; and there must be facts or truth-making states of affairs independently of language. Otherwise, you end up with (i) total linguistic idealism, which is absurd; or (ii) linguistic idealism about properties which is absurd; or (iii) a chaos, a world of disconnected particulars and properties.
The above is a shoot-from-the hip, bloggity-blog exposition of ideas that can be put more rigorously, but it seems to to me to show that ostrich nominalism and ostrich realism for that matter are untenable — and this despite the fact that a positive theory invoking facts has its own very serious problems.
Metaphilosophical Coda: If a theory has insurmountable problems, these problems are not removed by the fact that every other theory has problems. For it might be that no theory is tenable,while the problem itself is genuine.
Predication as Identity: Another Round
The Opponent is a patient man:
Trying again.
(1) Sam is poor at t1 iff Sam is identical with some poor person at t1
(2) Sam is poor at t1 iff Sam is self-identical at t1(1) is self-evidently true. For it cannot be true that Sam is poor, but not identical with some poor person. Nor can it be false that Sam is poor, but true that he is identical with some poor person.
But (2) is false. Sam is necessarily self-identical, but not necessarily poor. Therefore (2) does not follow from (1), for a false statement cannot follow from a true one.
The fallacy is in assuming that being identical with some poor person is the same fact as being identical with oneself.
I plead innocent of the charge of having committed a logical mistake. I accept (1) but I reject (2) and for the very reason the Opponent supplies: "Sam is necessarily self-identical, but not necessarily poor." In fact, this is the very point I use against him. I claim that his theory cannot accommodate it.
The Issue
The issue is whether predication can be assimilated to identity. 'Sam is poor' is an example of a sentence which, on the face of it, features a predicative use of 'is' as opposed to an identitarian use. Connected with this is the fact that 'poor' is a predicate adjective, not a noun proper or common. So surface indications are that predication cannot be assimilated to identity, or vice versa, and that the 'is' of identity and the 'is' of predication are distinct and mutually irreducible.
When we say that Sam is poor we cannot possibly mean that Sam is identical to the property of being poor. Why not? First, if Sam is identical to a property, then he is a property — which is precisely what he isn't. Second, if Sam is poor and his father Dave is poor, and to be poor is to be identical to the property of being poor, then, by the Transitivity of Identity, Sam is identical to Dave, which is absurd.
On the other hand, 'Sam is poor' is equivalent to 'Sam is a poor man.' What we have done is replace the adjective with a (common) name. This lends sanction to the notion that our original sentence can be construed to express an identity between the denotatum of 'Sam' and exactly one of the denotata of 'poor man.' We can give this poor guy a (proper) name: 'Poboy.'
I now ask: what is the truth-maker of 'Sam is a poor man' given that the 'is' expresses numerical identity? What in the world makes-true 'Sam is a poor man'? (If the Opponent declares that there is no need for a truth-maker for this obviously contingent true sentence, then Game Over, and we have nothing more to discuss.) The answer has to be, on the theory under discussion: the numerical identity of Sam with Poboy. Since Sam and Poboy are one and the same, this amounts to saying that the truth-maker of 'Sam is a poor man' is Sam's being Sam.
The Problem
The difficult with this identity theory of predication ought to be obvious. It succumbs to two related objections as I said earlier:
Objection 1. Sam might not have been poor. But it is not the case that Sam might not have been Sam. So the manifestly contingent truth of 'Sam is poor' cannot be explained in terms of identity.
Objection 2. That was a modal objection; now for a temporal one. The poor have been known to become rich. Suppose Sam goes from poor to rich. The identity theory implies that Sam, who was identical to Poboy, ceases to be identical to Poboy and becomes identical to Richboy. But surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.
This is absurd because, if Sam changes in respect of wealth, going from poor to rich, there has to be a self-same substrate of this change. Sam must remain numerically the same through the change. After all, the change is accidental, not substantial. The identity theory of predication, however, cannot accommodate these truisms. For if Sam is poor in virtue of being identical to one of the poor individuals, then he cannot become rich without ceasing to be himself.
An Alternative Which Avoids These Objections
Suppose we construe 'Sam is poor' to express the instantiation by Sam of the property of being poor. Then the objections can't get started. The Opponent, however, cannot avail himself of this way out since he is a nominalist, one who rejects properties. He may appreciate that man does not live by bread, or bed, alone, but he does not appreciate that the philosopher does not live by predicates alone — even if he turns them into names.
But I am not endorsing the alternative since it too has difficulties. Here is one. Sam's going from poor to rich or hot to cold or whatever is an intrinsic accidental change, a real change in Sam. It is not a relational change. But if Sam merely instantiates the property of being poor, and this property is a universal, and indeed a universal that is not a constituent of Sam, then it would seem that what is plainly an intrinsic change has been misconstrued as a relational change.
An Identity Theory of Predication
I will sketch a two-name, quasi-Scholastic, nominalistic/reistic theory of predication that I believe is quite hopeless. But it may serve as a foil against which and in comparison to which a more plausible theory may be developed.
Suppose it is true that Sam is poor. What are the truth-conditions of 'Sam is poor'? Rewrite the sentence as 'Sam is a poor individual.' Think of 'Sam' ('S') and ''poor individual' ('P') as names where the first name is proper and the second common. We assume that there are no universals. Accordingly, 'poor' in our original sentence cannot be construed as an abstract substantive, as a proper name for the universal poorness. It must be construed as a common name for poor individuals.
And because we are assuming that there are no universals, we cannot parse 'Sam is poor' as 'Sam instantiates poorness.' Nor can we take the truth-maker of 'Sam is poor' to be the state of affairs, Sam's being poor.
First idea. 'Sam is a poor individual' is true just in case:
A. For some x, 'S' denotes x and for some x, 'P' denotes x.
This is obviously insufficient since it doesn't guarantee that the item denoted by 'S' is numerically the same as one of the items denoted by 'P.' While the second two occurrences of 'x' are bound variables, they are not bound by the same quantifier. So we try
B. For some x, 'S' denotes x and 'P' denotes x.
This is much better. The second and third occurrences of 'x' are bound by the same quantifier. This ensures that the item denoted by 'S' is identical to one of the items denoted by 'P.' The first item is called 'Sam' and the second we can call 'Poboy.' Obviously these names denote one and the same item given that our sentence is true.
This yields an identity theory of predication. A simple predicative sentence such as 'Sam is poor' is true just in case the denotatum of the subject term is identical to one of the denotata of the predicate term. The truth-maker of the sentence is the identity of Sam with Poboy, i.e., the identity of Sam with himself.
Objection 1. Sam might not have been poor. But it is not the case that Sam might not have been Sam. So the manifestly contingent truth of 'Sam is poor' cannot be explained in terms of identity.
Objection 2. That was a modal objection; now for a temporal one. The poor have been known to become rich. Suppose Sam goes from poor to rich. The identity theory implies that Sam, who was identical to Poboy, ceases to be identical to Poboy and become identical to Richboy. But surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.
This is absurd because, if Sam changes in respect of wealth, going from poor to rich, there has to be a self-same substrate of this change. Sam must remain numerically the same through the change. After all, the change is accidental, not substantial. The identity theory of predication, however, cannot accommodate these truisms. For if Sam is poor in virtue of being identical to one of the poor individuals, then he cannot become rich without ceasing to be himself.
Notice how these problems disappear if properties are admitted. Sam instantiates the property of being poor, but he might not have. Sam instantiates the property of being poor at one time but not at others.
I now invite the Noble Opponent to show how his version of the identity theory circumvents these objections, if it does.
Related articles
Two Good Articles on Predication Theory
Ignacio Angelelli, Predication Theory: Classical versus Modern
Gyula Klima, The Essentialist Nominalism of John Buridan
The ‘Is’ of Identity and the ‘Is’ of Predication: Contra Sommers
Dedication: To Bill Clinton who taught us that much can ride on what the meaning of 'is' is.
………………
The Opponent has a very good post in which he raises the question whether the standard analytic distinction between the 'is' of identity and the 'is' of predication is but fallout from an antecedent decision to adhere to an absolute distinction between names and predicates according to which no name is a predicate and no predicate is a name. If the distinction is absolute, as Gottlob Frege and his epigoni maintain, then names cannot occur in predicate position, and a distinction between the two uses of 'is' is the consequence. But what if no such absolute distinction is made? Could one then dispense with the standard analytic distinction between the two uses of 'is'? Or are there reasons independent of Frege's function-argument analysis of propositions for upholding the distinction between the two uses?
To illustrate the putative distinction, consider
1. George Orwell is Eric Blair
and
2. George Orwell is famous.
Both sentences feature a token of 'is.' Now ask yourself: is 'is' functioning in the same way in both sentences? The standard analytic line is that 'is' functions differently in the two sentences. In (1) it expresses (numerical) identity; in (2) it expresses predication. Identity, among other features, is symmetrical; predication is not. That suffices to distinguish the two uses of 'is.' 'Famous' is predicable of Orwell, but Orwell is not predicable of 'famous.' But if Blair is Orwell, then Orwell is Blair.
Now it is clear, I think, that if one begins with the absolute name-predicate distinction, then the other distinction is also required. For if 'Eric Blair' in (1) cannot be construed as a predicate, then surely the 'is' in (1) does not express predication. The question I am raising, however, is whether the distinction between the two uses of 'is' arises ONLY IF one distinguishes absolutely and categorially between names and predicates.
Fred Sommers seems to think so. The Opponent follows him in this. Referencing the example 'The morning star is Venus,' Sommers writes, "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity." (The Logic of Natural Language, Oxford 1982, p. 121, emphasis added) The contemporary reader will of course wonder how else 'a is b' could be read if it is not read as expressing a dyadic relation between a and b. How the devil could the 'is' in 'a is b' be read as a sign of predication?
The question can be put like this. Can we justify a distinction between the 'is' of identity and the 'is' of predication even if we do not make an absolute distinction between names (object words) and predicates (concept words)? I think we can.
Is it not obvious that if an individual has a property, then it is not identical to that property? Tom is hypertensive. But it would be absurd to say that Tom is identical to this property. This is so whether you think of properties as universals or as particulars (tropes). Suppose the property of being hypertensive (H-ness) is a universal and that Tom's brother Sal is also hypertensive. It follows that they share this property. So if Tom = H-ness, and Sal = H-ness, then, by the transitivity and symmetry of identity, Tom = Sal, which is absurd.
If properties are tropes, we also get an absurdity. On a trope bundle theory, Tom is a bundle of tropes. But surely Tom cannot be identical to one of his tropes, his H-trope. On a trope substratum theory, tropes are like Aristotelian accidents inhering in a substance. But surely no substance is identical to one of its accidents.
So whether properties are universals or tropes, we cannot sensibly think of an individual's having a property in terms of identity with that property. If H-ness is a universal, then we would speak of Tom's instantiating H-ness, where this relation is obviously asymmetrical and for this reason and others distinct from identity.
Now 'H' is a predicate whereas 'H-ness' is a name. But nothing stops us from parsing 'Tom is hypertensive' as 'Tom instantiates hypertensiveness.' This shows that we can uphold the distinction between the 'is' of identity and the 'is' of predication with a two-name theory of predication, and thus without making Frege's absolute distinction between names and predicates. It appears that Sommers is mistaken in his claim that "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity."
I am assuming of course that we cannot eke by on predicates alone: we need properties. By my lights this should not be controversial in the least. My nominalist Opponent will demur. In 'Orwell is famous' he seems to be wanting to say that 'Orwell' and 'famous' refer to the same thing. But what could that mean?
First of all, 'Orwell' and 'famous' do not have the same extension: there are many famous people, but only one Orwell. 'Orwell is famous' is true. What makes it true? Presumably the fact that 'Orwell' and 'famous' denote one and the same individual. And which individual is that? Why, it's Orwell! But Orwell might not have been famous. Since it is contingent that Orwell is famous, but noncontingent that Orwell is Orwell, the truth-maker of 'Orwell is famous' cannot be Orwell alone. It has has to be the fact of Orwell's being famous, which fact involves the property of being famous in addition to Orwell.
Nominalists insist that we ought not multiply entities beyond necessity. They are right! But there is no multiplication beyond necessity here since we need to admit properties as features of extralinguistic reality. To explain why 'Orwell is famous' is contingent, one must distinguish Orwell from his contingently possessed properties. Man does not live or think truly by predicates alone.
Nominalism and an Identity Theory of Predication
The Worthy Opponent comments,
We nominalists hold that 'God is good' is true when what is signified by 'God' and what is signified by 'good' are numerically one and the same thing.
I stumble over this.
Apparently, it is The Opponent's view that a sentence such 'Socrates is good' is true when what is signified by 'Socrates' and what is signified by 'good' are numerically one and the same thing. I don't understand. 'Good,' unlike 'Socrates,' is a common term: it applies to many individuals. So there cannot be numerically one thing that both 'Socrates' and 'good' signify. 'Socrates' signifies one thing; 'good' signifies many things.
If, contrary to fact, there were only one good thing, then it would make some sense to say that 'Socrates is good,' which is by its surface grammar a predication, could be read as asserting the numerical identity of Socrates with the one good thing. But if Socrates is good, or seated, or conversing with Theaetetus, this is only contingently the case. So how analyze the possibly true 'Socrates is not good' on the assumption that there is only one good thing? We would have to say that Socrates is distinct from himself — which is absurd. For if, in actuality, Socrates is good in virtue of being identical to the one good thing, then, in the possible counterfactual situation in which he — the very same individual — is not good, he would have to be numerically diverse from the one good thing, namely, himself!
The same argument goes through even if there are many good things. For the Opponent's claim is that Socrates is good in virtue of being identical to one of the many good things. Call this good thing G. The claim is that 'Socrates is good' is an identity proposition in disguise, and that its deep logical form is: S = G.
The problem is that 'Socrates is good' is contingently true. But 'S = G' is not contingently true. So the predication is not an identity proposition in disguise.
This looks to be a pretty powerful objection.
I am assuming something that is well-nigh self-evident, but which I fear the Illustrious Opponent will deny, namely, that if a = b, then this is non-contingently the case. In other words, I am assuming that if a = b, then there is no possible situation in which a and b both exist but are numerically distinct.
Curiously, the Opponent's theory works in one case and one case only. But he has to admit the divine simplicity. So assume that God exists, that God is essentially good, and that God is identical to his attributes, and that therefore God alone is good in this sense. If God is identical to his attributes, then God = the one and only good thing. (Socrates is good only in an analogical and derivative sense.) In this one case, 'God is good' is an identity proposition in disguise.
Half-Way Fregeanism About Existence
Another subtle existence entry to flummox and fascinate the Londonistas. Hell, this Phoenician is flummoxed by it himself. Ain't philosophy grand?
………………..
In section 53 of The Foundations of Arithmetic, Gottlob Frege famously maintains that
. . . existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. (65)
Frege is here advancing a double-barreled thesis that splits into two subtheses.
ST1. Existence is analogous to number.
ST2. Existence is a property (Eigenschaft) of concepts and not of objects.
In the background is the sharp distinction between property (Eigenschaft) and mark (Merkmal). Three-sided is a mark of the concept triangle, but not a property of this concept; being instantiated is a property of this concept but not a mark of it. The Cartesian-Kantian ontological argument "from mere concepts" (aus lauter Begriffen), according to Frege, runs aground because existence cannot be a mark of any concept, but only a property of some concepts. And so one cannot validly argue from the concept of God to the existence of God.
Existence as a property of concepts is the property of being-instantiated. We can therefore call the Fregean account of existence an instantiation account. A concept is instantiated just in case it has one or more instances. So on a Fregean reading, 'Cats exist' says that the concept cat is instantiated. This implies, of course, that 'Cats exist' is not about cats, but about a non-cat, a concept, and what it says about this concept is not that it (singulatly) exists, but that it is instantiated! A whiff of paradox? Or more than just a whiff?
My concern in this entry is the logical relation between the above two subtheses. Does the first entail the second or are they logically independent? There is a clear sense in which (ST1) is true. Necessarily, if horses exist, then the number of horses is not zero, and vice versa. So 'Horses exist' is logically equivalent to 'The number of horses is not zero.' This is wholly unproblematic for those of us who agree that there are no Meinongian nonexistent objects. But note that, in general, equivalences, even logical equivalences, do not sanction reductions or identifications. So it remains an open question whether one can take the further step of reducing existence to instantiation, or identifying existence with instantiation, or even eliminating existence in favor of instantiation. Equivalence, reduction, elimination: those are all different. But I make this point only to move on.
(ST1), then, is unproblematically true if understood as expressing the following logical equivalence: 'Necessarily Fs exist iff the number of Fs is not zero.' My question is whether (ST1) entails (ST2). Peter van Inwagen in effect denies the entailment by denying that the 'the number of . . . is not zero' is a predicate of concepts:
I would say that, on a given occasion of its use, it predicates of certain things that they number more than zero. Thus, if one says, 'The number of horses is not zero,' one predicates of horses that they number more than zero. 'The number of . . . is not zero' is thus what some philosophers have called a 'variably polyadic' predicate. But so are many predicates that can hardly be regarded as predicates of concepts. The predicates 'are ungulates' and 'have an interesting evolutionary history,' for example, are variably polyadic predicates. When one says, 'Horses are ungulates' or 'Horses have an interesting evolutionary history' one is obviously making a statement about horses and not about the concept horse. ("Being, Existence, and Ontological Commitment," pp. 483-484)
It is this passage that I am having a hard time understanding. It is of course clear what van Inwagen is trying to show, namely, that the Fregean subtheses are logically independent and that one can affirm the first without being committed to the second. One can hold that existence is denial of the number zero without holding that existence is a property of concepts. One can go half-way with Frege without going 'whole hog' or all the way.
But I am having trouble with the claim that the predicate 'the number of . . . is not zero' is 'variably polyadic' and the examples van Inwagen employs. 'Robbed a bank together' is an example of a variably polyadic predicate. It is polyadic because it expresses a relation and it is variably polyadic because it expresses a family of relations having different numbers of arguments. For example, Bonnie and Clyde robbed a bank together, but so did Ma Barker and her two boys, Patti Hearst and three members of the ill-starred Symbionese Liberation Army, and so on. (Example from Chris Swoyer and Francesco Orilia.)
Now when I say that the number of horses is not zero, what am I talking about? It is plausible to say that I am talking about horses, not about the concept horse. (Recall the whiff of paradox, supra.) What I don't understand are van Inwagen's examples of variably polyadic predicates. Consider 'are ungulates.' If an ungulate is just a mammal with hooves, then I fail to see how 'are ungulates' is polyadic, let alone variably polyadic. 'Are hooved mammals' is monadic.
The other example is 'Horses have an interesting evolutionary history.' This sentence is clearly not about the concept horse. But it is not about any individual horse either. Consider Harry the horse. Harry has a history. He was born in a certain place, grew up, was bought and sold, etc. and then died at a certain age. He went through all sorts of changes. But Harry didn't evolve, and so he had no evolutionary history. No individual evolves; populations evolve:
Evolutionary change is based on changes in the genetic makeup of populations over time. Populations, not individual organisms, evolve. Changes in an individual over the course of its lifetime may be developmental (e.g., a male bird growing more colorful plumage as it reaches sexual maturity) or may be caused by how the environment affects an organism (e.g., a bird losing feathers because it is infected with many parasites); however, these shifts are not caused by changes in its genes. While it would be handy if there were a way for environmental changes to cause adaptive changes in our genes — who wouldn't want a gene for malaria resistance to come along with a vacation to Mozambique? — evolution just doesn't work that way. New gene variants (i.e., alleles) are produced by random mutation, and over the course of many generations, natural selection may favor advantageous variants, causing them to become more common in the population.
'Horses have an interesting evolutionary history,' then, is neither about the concept horse nor about any individual horse. The predicate in this sentence appears to be non-distributive or collective. It is like the predicate in 'Horses have been domesticated for millenia.' That is certainly not about the concept horse. No concept can be ridden or made to carry a load. But it is also not about any individual horse. Not even the Methuselah of horses, whoever he might be, has been around for millenia.
A predicate F is distributive just in case it is analytic that whenever some things are F, then each is F. Thus a distributive predicate is one the very meaning of which dictates that if it applies to some things, then it applies to each of them. 'Blue' is an example. If some things are blue, then each of them is blue.
If a predicate is not distributive, then it is non-distributive (collective). If some Occupy-X nimrods have the building surrounded, it does not follow that each such nimrod has the building surrounded. If some students moved a grand piano into my living room, it does not follow that each student did. If bald eagles are becoming extinct, it does not follow that each bald eagle is becoming extinct. Individual animals die, but no individual animal ever becomes extinct. If the students come from many different countries, it does not follow that each comes from many different countries. If horses have an interesting evolutionary history, it does not follow that each horse has an interesting evolutionary history.
My problem is that I don't understand why van Inwagen gives the 'Horses have an interesting evolutionary history' example when he is committed to saying that each horse exists. His view , I take it, is that 'exist(s)' is a first-level distributive predicate. 'Has an interesting evolutionary history,' however, is a first-level non-distributive predicate. Or is it PvI's view that 'exist(s)' is a first-level non-distributive predicate?
Either I don't understand van Inwagen's position due to some defect in me, or it is incoherent. I incline toward the latter. He is trying to show that (ST1) does not entail (ST2). He does this by giving examples of predicates that are first-level, i.e., apply to objects, but are variably polyadic as he claims 'the number of . . . is not zero' is variably polyadic. But the only clear example he gives is a predicate that is non-distributive, namely 'has an interesting evolutionary history.' 'Horses exist,' however, cannot be non-distributive. If some horses exist, then each of them exists. And if each of them exists, then 'exists' is monadic, not polyadic, let alone variably polyadic.
Modality, Possible Worlds, and the Accidental-Essential Distinction
This from a reader:
The Stanford Encyclopedia notes in its article on Essential vs. Accidental Properties, "A modal characterization of the distinction between essential and accidental properties is taken for granted in nearly all work in analytic metaphysics since the 1950s.” Personally, I find modal definitions of this type very hand wavy. Ed Feser states my objection more eloquently than I can:
From an Aristotelian-Thomistic point of view, the possible worlds analysis of essence has things backwards: we need to know what the essence of a thing is, before we can know what it would be like in various possible worlds; talk of possible worlds, if legitimate at all, must get explained in terms of essence, not essence in terms of possible worlds ( Aquinas, iBooks edition, page 90).
I think the modal characterization will be a dead end for us.
Response
Two points. First, I do not understand how one could characterize the essential versus accidental distinction except modally. Second, a modal characterization need not be in terms of so-called 'possible worlds.' One should not suppose that a characterization is modal if and only if it is in terms of possible worlds.
First point first. I am a blogger and a native Californian. I might not have been either. So being a blogger and being a native Californian are accidental properties of me. I could have existed without possessing these properties. But I could not have existed without being human. So being human is an essential property of me. Generalizing, if P is an essential property of x, then x must have P, it cannot not have P. If P is an accidental property of x, then x need not have P, it could lack P. And conversely in both cases.
Note that I had to use modal words to characterize the distinction: 'might,' 'could,' 'must,' 'need not,' 'cannot.' I conclude that the accidental-essential distinction is irreducibly modal: it cannot be made except modally. It is indeed essentially modal!
To appreciate this, consider the first two accidental properties I mentioned. I was not always a blogger: speaking tenselessly, there are times at which I am not a blogger. But I was always and will always be a native Californian. Speaking tenselessly again, there are no times at which I am not a native Californian.* It follows that we cannot define an essential (accidental) property of x as a property x has (does not have) at every time at which it exists. The distinction cannot be made in temporal terms; one needs to employ modal language.
If a thing has a property essentially, then it has the property at every time at which it exists. But not conversely: if a thing has a property at every time at which it exists, it does not follow that it has the property essentially. So again it should be clear that the distinction in question is ineliminably modal.
I should make it clear that the modality in question here is non-epistemic/non-doxastic. Suppose Tom died an hour ago, unbeknownst to me. I ask you, "Is Tom teaching now?" You say, "Could be!" But of course it can't be that he is teaching now if he is dead now. You are not saying that it is (really) possible that he be teaching now; you are saying that his teaching now is logically consistent with what you know or believe, that it is not ruled out by what you know/believe.
Second point second. From what I have written it should be clear that we don't need the jargon of possible worlds to talk modally. But it is a very useful and graphic way of talking. Accordingly,
D1. P is an accidental property of x =df there are possible worlds in which x exists but does not instantiate P.
D2. P is an essential property of x =df there are no possible worlds in which x exists but does not instantiate P.
We can add a third definition:
D3. P is a necessary property of x =df there are no possible worlds in which x exists but does not instantiate P, and x exists in every possible world. Example: Omniscience is a necessary property of God: he has it in every world in which he exists, and, since he is a necessary being, he exists in every world. Non-theological example: Being prime is a necessary property of the number 7: 7 has it in every metaphysically possible world in which it exists, and it exists in every such world.
The above definitions do not sanction the reduction of the modal to the non-modal. For modal terms appear on both sides of the biconditionals. Nor could we say that the right-hand sides explicates or analyzes the left-hand sides. So I agree with Feser as quoted above. What is first in the order of metaphysical explanation is a thing's being essentially thus and so or accidentally thus and so. We can then go on to represent these states of affairs in possible worlds terms, but we need not do so.
Jenner and Dolezal. Is Jenner essentially male? I should think so. Being male is a biological determination. It can be spelled out in terms of sex chromosomes. They are different in males and females. Jenner as he is today is a sort of super-transvestite: he is not just a male in women's clothing, but a male who has had his body surgically altered to have female anatomical features. But he is still male. How could he be a woman? You can't be a woman without first being a girl, and he was never a girl.
If you deny that Jenner is essentially biologically male, will you also deny that he is essentially biologically human? If not, why not? If literal sex change is possible, is species change possible?
Is Rachel Dolezal essentially Caucasian? Well, of course. Race, like sex, is biologically based. It is not something you choose. Nor is it a social construct. Barack Obama thinks that we Americans have racism in our DNA. That's bullshit, of course. There is nothing biological about being a racist. But there is something biological about race. You can be a traitor to your country, but not to your race.
Biology matters! And so does clear thinking and honest talk. Obama take note.
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*Ignoring the fact, if it is a fact, that I existed pre-natally. If this wrinkle troubles you, I can change my example.
Van Inwagen, Properties, and Bare Particulars
In this entry I expand on my claim that Peter van Inwagen's theory of properties commits him to bare particulars, not in some straw-man sense of the phrase, but in a sense of the phrase that comports with what proponents of bare particulars actually have claimed. I begin by distinguishing among four possible senses of 'bare particular.'
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.
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.
(I should think that the first occurrence of 'P' should be replaced by 'P-ness' despite the unfortunate sound of that.) 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. 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. 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.
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 particular are bare particulars in the sensedefined 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 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. PvI-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?
Peter van Inwagen, “A Theory of Properties,” Exposition and Critique
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.