Existence – Page 11 – Maverick Philosopher

Can a Thing Exist Without Existing Now?

Clearly, a thing can exist without existing here. The Washington Monument exists but not in my backyard. Accordingly, 'x exists here' can be split up as follows:

1. x exists here iff (i) x exists & (ii) x is in the vicinity of the speaker.

It seems pretty obvious that existence and the indexical property of hereness are different properties if you want to call them properties.

A much more difficult question is whether a thing can exist without existing now. Is it true that:

2. x exists now iff (i) x exists & (ii) x is temporally present?

Clearly, we can prise apart the existence of a (spatially located) thing and its hereness. Anyone who maintained that to exist = to be here we would deem either crazy or not conversant with the English language, a sort of 'local yokel' in excelsis. But can we prise apart the existence of a thing and its temporal presentness? Is there a real distinction between the existence of a thing and its temporal presentness?

A. A negative answer will be returned by the presentist who maintains that only the temporally present exists. He will maintain that what no longer exists and what does not yet exist does not now exist, and therefore does not exist at all.

Note that it ought to be is perfectly obvious to anyone who understands English that what no longer exists and what does not yet exist does not now exist. What is not at all obvious is the part after 'therefore' in the sentence before last. It is not at all obvious that an individual or event or time that is wholly past or wholly future does not exist at all.

B. An affirmative answer will be returned by all those who reject presentism. Some will reject presentism on the ground that abstracta exist, but are not in time at all, and so cannot be said to exist now. A presentist can accommodate this point by restricting his thesis:

Restricted Presentism: Necessarily, only temporally present concreta exist.

Nevertheless, the anti-presentist will insist that there are past and perhaps also future concreta that exist but do not exist now. Scollay Square, for example, no longer exists. But that it not to say that it is now nothing. After all, we still refer to it and say true things about it. It is true, for example, that my father visited Scollay Square while on shore leave during WW II on a break from service on destroyer escorts in the North Atlantic. So it is true that a a sailor who no longer exists visited a place that no longer exists and was involved in events that no longer exist. It also true that Scollay Square had been demolished by the time I arrived in Boston in 1973. I can now argue as follows:

1. Various predicates (e.g., is remembered by some Bostonians) are true of Scollay Square.
2. Scollay Square does not exist now.
3. If x does not exist, then no predicate is true of x.
Therefore
4. Scollay Square exists. (From 1 and 3)
Therefore
5. Scollay Square exists but is not temporally present. (From 2 and 4)
Therefore
6. Restricted Presentism is false.

I think there are three ways to attack this argument: (a) reject one or more of the premises; (b) find fault with the reasoning; (c) complain that it is not clear what Restricted Presentism amounts to.

Have at it, boys.

Scollay Square No Longer Exists

London Ed sends me a puzzle that I will formulate in my own way.

1. Boston's Scollay Square no longer exists. Hence 'Scollay Square no longer exists' is true.

2. Removing 'Scollay Square' from the closed sentence yields the open sentence, or predicate, or sentential function, '____ no longer exists.'

3. If a subject-predicate sentence is true, then its predicate is true of, or is satisfied by, the referent of the sentence's subject term.

4. If x is satisfied by y, then both x and y exist. (Special case of the principle that if x stands in a relation to y, then both relata exist.)

5. What no longer exists, does not exist. (An entailment of presentism.)

6. The referent of 'Scollay Square' does not exist. (from 1 and 5)

7. The referent of 'Scollay Square' exists. (from 1, 3, and 4)

How do we avoid the contradiction? As far as I can see we have exactly three options. The first is to posit an haecceity property that individuates Scollay Square across all possible worlds, and then construe the original sentence as saying, of that haecceity property, that it is no longer instantiated. Thus the original sentence is not about Scollay Square, which does not exist, but about an ersatz item, an abstract deputy that does exist., and indeed necessarily exists. About this ersatz item we say that it now fails of instantiation. The second option is to reject the principle that if a relation obtains between x and y, then both x and y exist. One might say that past objects are Meinongian nonexistent objects. The third option is to reject presentism and say that what no longer exists exists alright, it just doesn't exist now. (Analogy: the cat that is no longer in my lap exists alright, it just doesn't exist here.)

None of these options is palatable. I should like London Ed to tell me which he favors. Or does he see another way out?

Being is Said in Many Ways: On the Uses of ‘Is’

Chad reports:

In the opening pages of More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms (Blackwell, 2009), E. J. Lowe distinguishes five uses of ‘is’ as a copula: 1. The ‘is’ of attribution, as in ‘Socrates is wise’ and ‘Grass is green’.2. The ‘is’ of identity, as in ‘Napoleon is Bonaparte’ and ‘Water is H2O’.3. The ‘is’ of instantiation, as in ‘Mars is a planet’ and ‘A horse is a mammal’.4. The ‘is’ of constitution, as in ‘This ring is gold’ and ‘A human body is a collection of cells’.5. The ‘is’ of existence, as in ‘The Dodo is no more’.He says some may be reducible to others, and that one or two must be primitive. I thought this was a helpful spread.

That is indeed helpful, but here are some comments and questions.

1. First of all, I would be surprised if Lowe referred to the five uses as five uses of 'is' as a copula. The 'is' of existence is not a copula because it doesn't couple. There is no copulation, grammatical or logical, in 'God is.' The 'is' of existence does not pick out any sort of two-termed relation such as identity, instantiation, or constitution. Calling the 'is' of identity a copula is a bit of a stretch, and I don't think most philosophers would.

2. Is there a veritative use of 'is'? 'It is so.' 'It is the case that Frege died in 1925.' One could say, though it is not idiomatic: 'Obama's being president is.' One would be expressing that the state of affairs obtains or that the corresponding proposition is true. So it looks as if there is a veritative use of 'is.'

3. Reducibility of one use to another does not show that they are not distinct uses. Perhaps the veritative use can be reduced to what Lowe calls the attributive use. Attributions of truth, however, imply that truth is a property. Frege famously argued that truth cannot be a property. That is a messy separate can of worms.

4. There are also tensed and tenseless uses of 'is.' 'Obama is president' versus '7 + 5 is 12.' With respect to the latter, it would be a bad joke, one reminiscent of Yogi Berra, were I to ask,"You mean now?" Yogi Berra was once asked the time. He said,"You mean now?"

'Hume is an empiricist' can be used both in a tensed way and an untensed way. If I say that Hume is an empiricist what I say is true despite the present nonexistence of Hume. 'Grass is green,' however, is never used in a tensed way, though one can imagine circumstances in which it could.

5. One and the same tokening of 'is' can do more than one job. Is the 'is' in 'Max is black' as used by me in the presence of my cat Max the 'is' of predication merely? I don't think so. It also expresses existence. But this requires argument:

1. 'Max is black' and 'Black Max exists' are intertranslatable.
2. Intertranslatable sentences have the same sense.
Therefore
3. 'Max is black' and 'Black Max exists' express the very same (Fregean) sense.
Therefore
4. Both sentences express both predication and existence: a property is predicated of something that cannot have properties unless it exists.
Therefore
5. The 'is' in 'Max is black' has a double function: it expresses both predication and existence.

Note that both sentences include a sign for the predicative tie. The sign is 'is' in the first sentence and in the second sentence the sign is the immediate concatenation of 'black' and 'Max' in that order. This shows that to refer to logical (as opposed to grammatical) copulation does not require a separate stand-alone sign. 'Black Max exists' expresses both existence via the sign 'exsts' and predication via the immeditae concatenation of 'black' and 'Max' in that order in the context of the sentence in question.

Phenomenon and Existence

E. C. writes:

In the recent post Mary Neal’s Out of Body Experiences you state: "No experience, no matter how intense or unusual or protracted, conclusively proves the veridicality of its intentional object. Phenomenology alone won't get you to metaphysics."

I have been attempting to reconstruct your reasoning here, and the following is the best I could come up with.

1) No experience, no matter how intense or unusual or protracted, conclusively proves the veridicality of its intentional object.

2) The subject matter of phenomenology is experience.

3) The subject matter of metaphysics is existence, which includes the quest of proving the veridicality of intentional objects. Therefore:

C) Phenomenology alone won't get you to metaphysics.

I have an issue with (1). Surely, the very meaning of ‘veridical experience’ designates a harmonious pattern of interconnected experiences, the paradigm case being perceptual experiences. Correlatively, when one speaks about the intentional object existing, one means nothing other than the reappearance of the self-same object across this harmonious flow.

Non-veridical experiences, e.g. hallucinations, are then just those experiences that promise, but fail, to endure harmoniously. Whenever non-veridical experiences obtain so do veridical experiences. For example, I was mistaken that there was a cat walking outside on the pavement, and hence had a non-veridical experience of the cat, but I had a veridical experience of the pavement itself. Ultimately, the experience of the world is given as the veridical background that serves as a foundation for all non-veridical experiences. To speak ontologically, the existence of non-veridical experiences depends on veridical experiences and likewise non-existence objects demand existent objects. Therefore, non-veridical experience could never exist on their own, which does not prevent us as talking about them as self-sufficient.

In relation to (2), I would argue that the subject matter of phenomenology is not just experience but also the object experienced just as it is experienced. But if existence is just the reappearance of an object through a harmonious flow of experience, then phenomenology does have metaphysical implication.

I do not think that perceptual experience is the only mode of experience through which existence is experienced; the room is left often for experiences that reveal the divine.

As always, I am very grateful for the existence of your blog.

Thanks for reading, E. C., for the kind words, and for the above response.

First of all, you did a good job of setting forth my reasoning in support of (C). But I take issue with your taking issue with (1). You are in effect begging the question by just assuming that what makes veridical experience veridical is its internal coherence. That is precisely the question. It may well be that coherence is a criterion of truth without being the nature of truth. By a criterion I mean a way of testing for truth. It could be that coherence is a criterion, or even the criterion, of truth, but that correspondence is the nature of truth. One cannot just assume that truth is constituted by coherence. I am not saying the view is wrong; I am saying that it cannot be assumed to be true without argument or consideration of alternatives. Such arguments and considerations, however, move us beyond phenomenology into dialectics.

To say of an experience that it is veridical is to say that it is of or about an object that exists whether or not the experience exists. If so, then the existence of the object in reality cannot be explicated in terms of its manners and modes of appearing. If you say that it can, then you are opting for a form of idealism which, in Husserlian jargon, reduces Sein to Seinsinn. I would insist, however, that it part of the plain sense of outer perception that it is of or about objects whose existence is independent of the existence of perceivers and their experiences. To borrow a turn of phrase from the neglected German philosopher Wolfgang Cramer, it is built into the very structure of outer perception that it is of or about objects as non-objects. That may sound paradoxical, but it is not contradictory. The idea is that the object is intended in the act or noesis as having an ontological status that surpasses the status of a merely intentional object. Whether it does have that additional really existent status is of course a further question.

For example, my seeing of a tree is an intentional experience: it is of or about something that may or may not exist. (Note that, phenomenologically, 'see' is not a verb of success. If I see x in the phenomenological sense of 'see,' it does not follow that there exists an x such that I see it.) Now if you say that the existence of the tree intended in the act reduces to its ongoing 'verification' in the coherent series of Abschattungen that manifest it, then you are opting for a form of idealism. And this seems incompatible with the point I made, namely, that it is part and parcel of the very nature of outer perception that it be directed to an object as non-object. The tree is intended as being such that its existence is not exhausted by its phenomenological manifestation.

But the point is not to get you to agree with this; the point is to get you to see that there is an issue here, one subject to ongoing controversy, and that one cannot uncritically plump for one side. If you haven't read Roman Ingarden on Husserl, I suggest that you do.

As for premse (2), we will agree that there are acts, intentional experiences (Erlebnisse), and that they are of an object. Throughout the sphere of intentionality there is the act-object, noesis-noema correlation. But this leaves wide open the question whether the being of the thing in reality is exhausted by its noematic being, whether its Sein reduces to its Seinsinn. On that very point Ingarden disagreed strenuously with his master, Husserl.

"But if existence is just the reappearance of an object through a harmonious flow of experience, then phenomenology does have metaphysical implications." That is true. But I deny the consequent of your conditional and so I deny the antecedent as well.

My point, in sum, is that you cannot just assume the truth of the antecedent. For that begs the question against realism. From the fact that an object manifests its existence in the manner you describe, it does not follow that the very existence of the object is its manifestation.

It may be methodologically useful to bracket the existence of the object the better to study its manners and modes of appearing, but this very bracketing presupposes that there is more to the existence of the object than its appearing. One could say that Husserl was right to bracket the existence of the object for purposes of phenomenology, but then, in his later idealistic phase, he forgot to remove the brackets.

Stanislav Sousedik’s “Towards a Thomistic Theory of Predication”

Enough of politics, back to some hard-core technical philosophy. If nothing else, the latter offers exquisite escapist pleasures not unlike those of chess. Of course I don't believe that technical philosophy is escapist; my point is a conditional one: if it is, its pleasures suffice to justify it as a form of recuperation from this all-too-oppressive world of 'reality.' It's what I call a 'fall-back position.'

I have been commissioned to review the collection of which the above-captioned article is a part. The collection is entitled Metaphysics: Aristotelian, Scholastic, Analytic (Ontos Verlag 2012) and includes contributions by Peter van Inwagen, Michael Loux, E. J. Lowe, and several others. My review article will address such topics as predication, truth-makers, bare particulars, and the advantages and liabilities of constituent ontology. I plan a series of posts in which I dig deep into some of the articles in this impressive collection.

Stanislav Sousedik argues for an "identity theory of predication" according to which a predicative sentence such as 'Peter is a man' expresses an identity of some sort between the referent of the subject 'Peter' and the referent of the predicate 'man.' Now to someone schooled in modern predicate logic (MPL) such an identity theory will appear wrongheaded from the outset. For we learned at Uncle Gottlob's knee to distinguish between the 'is' of identity ('Peter is Peter') and the 'is' of predication ('Peter is a man').

But let's give the Thomist theory a chance. Sousedik, who is well aware of Frege's distinction, presents an argument for the identity in some sense of subject and predicate. He begins by making the point that in the declarative 'Peter is a man' and the vocative 'Peter, come here!' the individual spoken about is (or can be) the same as the individual addressed. But common terms such as 'man' can also be used to address a person. Instead of saying, 'Peter, come here!' one can say 'Man, come here!' And so we get an argument that I will put as follows:

1. Both 'Peter' and 'man' can be used to refer to the same individual. Therefore

2. A common term can be used to refer to an individual. But

3. Common terms also refer to traits of individuals. Therefore

4. The traits must be identical in some sense to the individuals. E.g., the referent of 'Peter' must be in some sense identical to the referent of 'man.'

But in what sense are they identical? Where Frege distinguishes between predication and identity, Sousedik distinguishes between weak and strong identity. 'Peter is Peter' expresses strong identity while 'Peter is a man' expresses weak identity. "Strong identity is reflexive, symmetric, and transitive, weak identity has none of these formal properties." (254) It thus appears that strong identity is the same as what modern analytic philosophers call (numerical) identity. It is clear that 'Peter is a man' cannot be taken to express strong identity. But what is weak identity?

S. is a constituent ontologist. He holds that ordinary substances such as Peter have what he calls "metaphysical parts." Whereas Peter's left leg is a physical part of him, his traits are metaphysical parts of him. Thus the referents of the common terms 'man,' 'animal,' living thing,' etc. are all metaphysical parts of Peter. Clearly, these are different traits of Peter. But are they really distinct in Peter? S. says that they are not: they are really identical in Peter and only "virtually distinct" in him. The phrase is defined as follows.

(Def. 1) Between x, y there is a virtual distinction iff (i) x, y are really identical; (ii) x can become an object of some cognitive act Φ without y being the object of the same act Φ . . . . (251)

For example, humanity and animality in Peter are really identical but virtually distinct in that humanity can be the intentional object of a cognitive act without animality being the object of the same act. I can focus my mental glance so to speak on Peter's humanity while leaving out of consideration his animality even though he is essentially both a man and an animal and even though animality is included within humanity.

The idea, then, is that Peter has metaphysical parts (MPs) and that these items are really identical in Peter but virtually distinct, where the virtual distinctness of any two MPs is tied to the possibility of one of them being the object of a cognitive act without the other being the object of the same act.

Is S. suggesting that virtual distinctness is wholly mind generated? I don't think so. For he speaks of a potential distinction of MPs in concrete reality, a distinction that becomes actual when the understanding grasps them as distinct. (253) And so I take the possibility mentioned in clause (ii) of the above definition to be grounded not only in the mind's power to objectify and abstract but also in a real potentiality in the MPs in substances like Peter.

One might be tempted to think of weak identity as a part-whole relation. Thus one might be tempted to say that 'Peter' refers to Peter and 'man' to a property taken in the abstract that is predicable not only of Peter but of other human beings as well. 'Peter is a man' would then say that this abstract property is a metaphysical part of Peter. But this is not Sousedik's or any Thomist's view. For S. is committed to the idea that "Every empirical individual and every part or trait of it is particular." (251) It follows that no metaphysical part of any concrete individual is a universal. Hence no MP is an abstract property. So weak identity is not a part-whole relation.

What is it then?

First of all, weak identity is a relation that connects a concrete individual such as Peter to a property taken abstractly. But in what sense is Peter identical to humanity taken abstractly? In this sense: the humanity-in-Peter and the humanity-in-the-mind have a common constituent, namely, humanity taken absolutely as common nature or natura absoluta or natura secundum se. (254) What makes weak identity identity is the common constituent shared by the really existing humanity in Peter and the intentionally existing humanity in the mind of a person who judges that Peter is human.

So if we ask in what sense the referent of 'Peter' is identical to the referent of 'man,' the answer is that they are identical in virtue of the fact that Peter has a proper metaphysical part that shares a constituent with the objective concept referred to by 'man.' Sousedik calls this common constituent the "absolute subject." In our example, it is human nature taken absolutely in abstraction from its real existence in Peter and from its merely intentional existence in the mind.

Critical Observations

I am deeply sympathetic to Sousedik's constituent-ontological approach, his view that existence is a first-level 'property,' and the related view that there are modes of existence. (253) But one of the difficulties I have with S.'s identity theory of predication is that it relies on common natures, and I find it difficult to make sense of them as I already spelled out in a previous post. Common natures are neither one nor many, neither universal nor particular. Humanity is many in things but one in the mind. Hence taken absolutely it is neither one nor many. It is this absolute feature that allows it be the common constituent in humanity-in-Peter and humanity-in-the-mind. And as we just saw, without this common constituent there can be no talk of an identity between Peter and humanity. The (weak) identity 'rides on' the common constituent, the natura absoluta. Likewise, humanity is particular in particular human beings but universal in the mind (and only in the mind). Hence taken absolutely it is neither particular nor universal.

But it also follows that the common nature is, in itself and taken absolutely, neither really existent nor intentionally existent. It enjoys neither esse naturale (esse reale) nor esse intentionale. Consequently it has no being (existence) at all. This is not to say that it is nonexistent. It is to say that it is jenseits von Sein und Nichtsein to borrow a phrase from Alexius von Meinong, "beyond being and nonbeing."

The difficulty is to understand how there could be a plurality of distinct items that are neither universal nor particular, neither one nor many, neither existent nor nonexistent. Note that there has to be a plurality of them: humanity taken absolutely is distinct from animality taken absolutely, etc. And what is the nature of this distinctness? It cannot be mind-generated. This is because common natures are logically and ontologically prior to mind and matter as that which mediates between them. They are not virtually distinct. Are they then really distinct? That can't be right either since they lack esse reale.

And how can these common or absolute natures fail to be, each of them, one, as opposed to neither one nor many? The theory posits a plurality of items distinct among themselves. But if each is an item, then each is one. An item that is neither one nor many is no item at all.

There is also this consideration. Why are common natures more acceptable than really existent universals as constituents of ordinary particulars such as Peter? The Thomists allow universals only if they have merely intentional existence, existence 'in' or rather for a mind. "Intentional existence belongs to entities which exist only in dependence upon the fact that they are objects of our understanding." (253) They insist that, as S. puts it, "Every empirical individual and every part or trait of it is particular." (251) S. calls the latter an observation, but it is not really a datum, but a bit of theory. It is a datum that 'man' is predicable of many different individuals. And it is a datum that Peter is the subject of plenty of essential predicates other than 'man.' But it is not a clear datum that Peter is particular 'all the way through.' That smacks of a theory or a proto-theory, not that it is not eminently reasonable.

One might 'assay' (to use G. Bergmann's term) an ordinary particular as a complex consisting of a thin or 'bare' particular instantiating universals. This has its own difficulties, of course, but why should a theory that posits common natures be preferrable to one that doesn't but posits really existent universals instead? Either way problems will arise.

The main problem in a nutshell is that it is incoherent to maintain that some items are such that they have no being whatsoever. 'Some items are such that they have no being whatsoever' is not a formal-logical contradiction, pace van Inwagen, but it is incoherent nonetheless. Or so it seems to me.

Still Trying to Understand Van Inwagen’s Half-Way Fregeanism about Existence

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.

My concern in this entry is the logical relation between the 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.

(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.

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. What I don't understand is why van Inwagen says that 'the number of . . . is not zero' is a variably polyadic predicate. As far as I can see, it is not even polyadic, let alone variably polyadic. What is the relation that the predicate expresses, and why is that relation multigrade? I grant that there are indefinitely many ways the number of horses could be not zero: there could be one horse, two, three, and so on. But what is the relation between or among horses that this supposedly polyadic predicate expresses?

'. . .exist(s)' is monadic. It expresses no relation. Why not say the same about 'such that their number is not zero'?

Now 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 not about the concept horse or 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 evlutionary 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 non-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) doe 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 evilutionary 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.

The ComBox is open if there is anyone who knows this subject and has read PvI's paper and can set me straight.

More Fun With Existential Generalization

Intuitively, if something is identical to Venus, it follows that something is identical to something. In the notation of MPL, the following is a correct application of the inference rule, Existential Generalization (EG):

1. (∃x)(x = Venus)
2. (∃y)(∃x)(x = y) 1, EG

(1) is contingently true: true, but possibly false. (2), however, is necessarily true. Ought we find this puzzling? That is one question. Now consider the negative existential, 'Vulcan does not exist.'

3. ~(∃x)( x = Vulcan)
4. (∃y)~(∃x)(x = y) 3, EG

(3) is contingently true while (4) is a logical contradiction, hence necessarily false. The inference is obviously invalid, having taken us from truth to falsehood. What went wrong?

Diagnosis A: "You can't existentially generalize on a vacuous term, and 'Vulcan' is a vacuous term."

The problem with this diagnosis is that whether a term is vacuous or not is an extralogical (extrasyntactic) question. Let 'a' be an arbitrary constant, and thus neither a place-holder nor a variable. Now if we substitute 'a' for 'Vulcan' we get:

3* ~(∃x)( x = a)
4. (∃y)~(∃x)(x = y) 3*, EG

The problem with this inference is with the conclusion: we don't know whether 'a' is vacuous or not. So I suggest

Diagnosis B: Singular existentials cannot be translated using the identity sign as in (1) and (3). This fact, pace van Inwagen, forces us to beat a retreat to the second-level analysis. We have to analyze 'Venus exists' in terms of

5. (∃x)(Vx)

where 'V' is a predicate constant standing for the haecceity property, Venusity. Accordingly, what (5) says is that Venusity is instantiated. Similarly, 'Vulcan does not exist' has to be interpreted as saying that Vulcanity is not instantiated. Thus

6. ~(∃x)(Wx)

where 'W' is a predicate constant denoting Vulcanity.

It is worth noting that we can existentially generalize (6) without reaching the absurdity of (4) by shifting to second-order logic and quantifying over properties:

7. (∃P)~(∃x)Px.

That says that some property is such that it is not instantiated. There is nothing self-contradictory about (7).

But of course beating a retreat to the second-level analysis brings back the old problem of haecceities. Not to mention the circularity problem.

The thin theory is 'cooked' no matter how you twist and turn.

The Aporetics of Existence and Self-Identity

Andrew B. made some powerful objections to a recent existence post. His remarks suggest the following argument:

Argument A

1. Existence is self-identity
2. My existence is contingent: (∃x)(x = I) & Poss ~(∃x) (x = I)
Therefore
3. My self-identity is contingent: I = I & Poss ~ (I = I)

Argument A may be supplemented by the following consideration. Since I am contingent, there are possible worlds in which I do not exist. Not being in those worlds, I cannot have properties in them, including the property of self-identity. So it is not the case that I am necessarily self-identical; I am self-identical only in those worlds in which I exist, which is to say: I am contingently self-identical. I am self-identical in some but not all worlds.

The argument can be rationally resisted.

Consider a possible world w in which I do not exist. In w, the proposition expressed by an utterance by me of 'I am not self-identical' is true. But if it is true in w, then the proposition exists in w. Now if the proposition exists in w, then so do its constituents. On a Russellian view of propositions, I am one of the proposition's constituents. So for the proposition *I am not self-identical* to be true in w, I must exist in w. But if I exist in w, then of course I am self-identical in w, and the proposition is false in w. But the same goes for every world in which I do not exist. It follows that I am self-identical in every world and I exist in every world.

Of course, one needn't take a Russellian line on propositions. One could take a Fregean view according to which propositions about me do not have me as a constituent but an abstract representative of me, a sense or mode of presentation. But the first-person singular pronoun 'I' has the peculiarity that it cannot be replaced salva significatione by any description; so even if there is an abstract representative of me in the Fregean proposition expressed by my utterance of 'I am not self-identical,' there still has to be a referent of the representative external to the proposition. So I have to exist in w for the proposition *I am not self-identical* to be true in w. But if I exist in w then I am self-identical in w. This in turn implies that the proposition is not true.

The cognoscenti will appreciate that what I have been doing in a rough and dirty way is reproducing some of the thoughts in Timothy Williamson's paper Necessary Existents. I am doing so to show that Argument A is not convincing. Making use of materials from Williamson's paper, we can 'throw Argument A into reverse':

Argument B

1. Existence is self-identity
~3. My self-identity is necessary: Nec (I = I)
Therefore
~2. My existence is necessary.

In point of validity, there is nothing to choose between A and B: both are valid. And both, I submit, have counterintuitive conclusions. It seems to me that the arguments cancel each other out. So I propose that we think very skeptically about the common premise that existence is self-identity, and the Quinean thin theory that commits us to it.

Beating the Dead Horse of the Thin Theory Some More

It is obviously true that something exists. This is not only true, but known with certainty to be true: I think, therefore I exist, therefore something exists. That is my Grand Datum, my datanic starting point. Things exist!

Now it seems perfectly clear to me that 'Something exists' cannot be translated adequately as 'Something is self-identical' employing just the resources of modern predicate logic (MPL), i.e., first-order predicate logic with identity. But it seems perfectly clear to van Inwagen that it can. See my preceding post on this topic. So one of us is wrong, and if it is me, I'd like to know exactly why. Let me add that 'Something is self-identical' is the prime candidate for such a thin translation. If there is a thin translation, this is it. Van Inwagen comes into the discussion only as a representative of the thin theory, albeit as the 'dean' of the thin theorists.

Consider the following formula in first-order predicate logic with identity that van Inwagen thinks adequately translates 'There are objects' and 'Something exists':

1. (∃x) (x = x).

It seems to me that there is nothing in this formula but syntax: there are no nonlogical expressions, no content expressions, no expressions like 'Socrates' or 'cat' or placeholders for such expressions such as 'a' and 'C.' The parentheses can be dropped, and van Inwagen writes the formula without them. This leaves us with '∃,' three bound occurrences of the variable 'x,' and the identity sign '=.'

Now here is my main question: How can the extralogical and extrasyntactical fact that something exists be a matter of pure logical syntax? How can this fact be expressed by a string of merely syntactical symbols: '∃,' 'x,' '='?

It is not a logical truth that something exists; it is a matter of extralogical fact. There's this bloody world out there and it certainly wasn't sired by the laws of logic. Logically, there might not have been anything at all. It is true, but logically contingent, that something exists. Compare (1) with the universal quantification

2. (x)(x =x).

If (1) translates 'Something exists,' then (2) translates 'Everything exists.' But (2) is a logical truth, and its negation a contradiction. Since (1) follows from (2), (1) is a logical truth as well. But (1) is not a logical truth as we have just seen. We face an aporetic triad:

a. '(x)(x =x)' is logically true.
b. '(∃x) (x = x)' follows from '(x)(x = x).'
c. '(∃x) (x = x)' adequately translates 'Something exists.'

Each limb is plausible, but they cannot all be true. The truth of any two linbs entails the falsehood of the remaining one. For example, the first two entail that '(∃x) (x = x)' is logically true. But then (c) is false: One sentence cannot be an adequate translation of a second if the first fails to preserve the modal status of the second. To repeat myself: 'Something exists' is logically contingent whereas the canonical translation is logically necessary.

Now which of the limbs shall we reject? It is obvious to me that the third limb must be rejected, pace van Inwagen.

Now consider 'Everything exists.' Can it be translated adequately as '(x)(x = x)'? Obviously not. The latter is a formal-logical truth. and its negation is a formal-logical contradiction. But the negation of 'Everything exists' — 'Something does not exist' — is not a formal logical contradiction. Therefore, 'Everything exists' is not a formal-logical truth. And because it is not, it cannot be given the canonical translation.

Finally, consider 'Nothing exists.' This is false, but logically contingent: there is no formal-logical necessity that something exist. One cannot infer the existence of anything (or at least anything concrete) from the principles of formal logic alone. The canonical translation of 'Nothing exists,' however — (x)~(x = x)' - is not contingently false, but logically false. Therefore, 'Nothing exists' cannot be translated adequately as 'Everything is not self-identical.'

Van Inwagen and his master Quine are simply mistaken when they maintain that existence is what 'existential' quantification expresses.

My Argument That ‘Exist(s)’ is not Univocal Revisited: No ‘Is’ of Predication?

On August 11th I wrote:

Suppose we acquiesce for the space of this post in QuineSpeak.

Then 'Horses exist' says no more and no less than that 'Something is a horse.' And 'Harry exists' says no more and no less than that 'Something is Harry.' But the 'is' does not have the same sense in both translations. The first is the 'is' of predication while the second is the 'is' of identity. The difference is reflected in the standard notation. The propositional function in the first case is Hx. The propositional function in the second case is x = h. Immediate juxtaposition of predicate constant and free variable [with the predicate constant coming first] is the sign for predication. '=' is the sign for identity. Different signs for different concepts. Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.

Those heir to the 'Fressellian' position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.

So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot [pace van Inwagen] be upheld. It cannot be upheld across the divide that separates general from singular existentials.

But the next morning I had a doubt about what I had written. Is there an 'is' of predication in MPL (modern predicate logic)? I argued (above) that 'exist(s)' is not univocal: it does not in MPL have the same sense in 'Fs exist' and 'a exists.' The former translates as 'Something is (predicatively) an F' while the latter translates as 'Something is (identically) a.' Kicked out the front door, the equivocity returns through the back door disguised as an equivocation on 'is' as between predication and identity.

But if the 'is' in 'Grass is green' or 'Something is green' is bundled into the predicate in the Fregean manner, then it could be argued that there is no 'is' of predication in MPL distinct from the 'is' of identity and the 'is' of existence. If so, my equivocity argument above collapses, resting as it does on the unexpungeable distinction between the 'is' or identity and the 'is' of predication.

Yesterday a note from Spencer Case shows that he is on to the same (putative) difficulty with my argument:

Hey Bill, I have a professor whose pet peeve is the claim that there is an 'is' of identity and an 'is' of predication. I don't know his arguments for thinking so, but his view is that 'is' is univocal and what differs is the content of the copula. If he's right, that would be a problem for you here. Do you know more about this position than I do?

To sort this out we need to distinguish several different questions:

Q1. Is there a predicative use of 'is' in English? Yes, e.g., 'Al is fat.' This use is distinct from the existential use and the identitative use (and others that I needn't mention). So I hope Spencer's professor is not denying the plain linguistic fact that in English there is an 'is' of predication and an 'is' of identity and that they are distinct.

Q2. Must there be a separate sign for the predicative tie in a logically perspicuous artificial language such as MPL (modern predicate logic, i.e., first-order predicate logic with identity)? No. When we symbolize 'Al is fat' by Fa, there is no separate sign for the predicative tie. But there is a sign for it, namely, the immediate juxtaposition of the predicate constant and the individual constant with the predicate constant to the left of the individual constant. So we shouldn't confuse a separate or stand-alone sign with a sign. Other non-separate signs are conceivable exploiting different fonts and different colors, etc.

Q3. Must there be some sign or other for predication in a logically adequate language such as MPL? How could there fail to be? If our logical language is adequate, then it has to be able to symbolize predications such as 'Al is fat.' And note that existentials such as 'Fat cats exist' cannot be put into MPL without a sign for predication. '(∃x)(Fx & Cx)' employs non-separate signs for predication.

Q4. Is the predicative tie reducible or eliminable? No. For Frege, there is no need for a logical copula or connector to tie object a to concept F when a falls under F. The concept is "unsaturated" (ungesaettigt). Predicates and their referents (Bedeutungen) are inherently gappy or incomplete. So the predicate 'wise' would be depicted as follows: '___ wise.' What is thereby depicted is a sentential function or open sentence. A (closed) sentence results when a name is placed in the gap. The concept to which this predicate or sentential function refers is gappy in an analogous sense. Hence there is no need for for an 'is' of predication in the logical language or for an instantiation relation. Object falls under concept without the need of a tertium quid to connect them.

I would imagine that Spencer Case's professor has some such scheme in mind. One problem is that it is none too clear what could be meant by a gappy or incomplete or unsaturated entity. That a predicate should be gappy is tolerably clear, but how could the referent of a predicate be gappy given that the referent of a predicate is a single item and not the manifold of things to which the predicate applies? The idea is not that concepts exist only when instantiated, but that their instantiation does not require the services of a nexus of predication: the concept has as it were a slot in it that accepts the object without the need of a connector to hold them together. (Think of a plug and a socket: there is no need for a third thing to connect the plug to the socket: the 'female' receptacle just accepts the 'male' plug.)

There are other problems as well.

But here is the main point. Frege cannot avoid speaking of objects falling under concepts, of a's falling under F but not under G. If the notion of the unsaturatedness of concepts is defensible, then Frege can avoid speaking of a separate predicative tie that connects objects and concepts. But he cannot get on without predication and without a sign for predication.

I conclude that my original argument is sound. There is is and must be a sign for predication in any adequate logic, but it needn't be a stand-alone sign. (Nor need its referent be a stand-alone entity.) Compare '(∃x)Hx' to '(∃x)(x = h)' as translations of 'Horses exist' and 'Harry exists,' respectively. The identity sign occurs in only one of the translations, the second. And the sign for predication occurs only in the first. There is no univocity of 'exist(s)' because there is no univocity of 'is' in the translations.

Existentials and Their Equivalents: Aid and Comfort for the Thin Theory?

I grant that logical equivalents not containing 'exist(s)' or cognates can be supplied for all singular and general existentials. Thus, 'Socrates exists' can be translated, salva veritate, as 'Something is identical to Socrates,' or, in canonical notation, '(∃x)(x = Socrates).' Accordingly,

Socrates exists =_df (∃x)(x = Socrates).

But if the definiens preserves the truth of the definiendum, then the definiendum must be true, hence must be meaningful, in which case first-level uses of 'exist(s)' must be meaningful. Pace Russell, 'Socrates exists' is nothing like 'Socrates is numerous.'

What's more, the definiendum is prior in the order of understanding to the definiens. If I didn't already understand 'Socrates exists,' then I would not be able to understand '(∃x)(x = Socrates).' You couldn't teach me the Quinean translation if I didn't already understand the sentence to be translated.

One conclusion we can draw from this is that if 'exist(s)' is univocal across general and singular existentials, then existence cannot be instantiation. For the left-hand side of the definition does not make an instantiation claim. It is simply nonsense to say of an individual that it is instantiated. And if the right-hand side makes an instantiation claim, then we need those creatures of darkness, haecceity-properties.

But we don't have to give the RHS a Fressellian reading; we can give it a Quinean-Inwagenian reading. (We could call this the 'Van' reading.) Accordingly: There exists an x such that x = Socrates. On the Van reading, in stark contrast to the Fressellian reading, 'exist(s)' can be construed as a first-level predicate, as synonymous to the predicate 'is identical to something.' Accordingly:

y exists =_df(∃x)(x = y).

On the reasonable assumptions that (i) 'exist(s)' is an admissible first-level predicate and that (ii) there are no nonexistent objects, this last definition is unobjectionable. If Tom exists, then there exists an object to which he is identical. And if there exists an object to which Tom is identical, then Tom exists. No doubt!

The interesting question, however, is whether any of this affords aid and comfort to the thin theory. Well, what exactly is the thin theory? It is the theory that existence is exhaustively understandable in purely logical, indeed purely syntactical, terms. The thin theory is a deflationary theory that aims to eliminate existence as a metaphysical topic. It aims to supplant the metaphysics of existence (of whatever stripe: Thomist, Heideggerian, etc.) with the sober logic of 'exist(s).' The aim of the thin theory is to show that there is no sense in which existence is a non-logical property of individuals. The aim is to be able to consign all those tomes of metaphysical rubbish to the flames with a good conscience.

Now glance back at the definition. Every mark on the RHS is a bit of logical syntax. Ignoring the parentheses which in this instance can be dropped, we have the backwards-E, two bound occurrences of the variable 'x,' a free occurrence of the variable 'y,' and the sign for identity. There are no non-logical expressions such as 'Socrates' or 'philosopher.' On the LHS, however, we find 'exists' which is not obviously a logical expression. Indeed, I claim that it is not a logical expression like 'some' or 'all' or 'not.' It is a 'content' expression. What could be more important and contentful than a thing's existing? If it didn't exist it would be nothing and couldn't have properties or stand in relations.

Surely my sheer be-ing is my most impressive 'feature.' "To be or not to be, that is the question."

Since there is content on the LHS there has to be content on the RHS. But how did it get there, given that every expression on the RHS is just a bit of syntax? In only one way: the domain of the bound variables is a domain of existents. But now it should be clear that the definition gives us no deflationary account of existence. What it does is presuppose existence by presupposing that the domain of quantification is a domain of existents. Existence is that which existents have in common and in virtue of which they exist.

In short, I have no objection to the definition read in the 'Van' as opposed to the 'Fressellian' way. It is perfectly trivial! My point, however, is that it gives no aid and comfort to the thin theory. A decent thin theory would have to show how we can dispence with existence entirely by eliminating it in favor of purely logical concepts. But that is precisely what we cannot do given that the domain of quantification is a domain of existents. (Of course, if the domain were populated by Meinongian nonexistent objects, then the definition would be false).

Van Inwagen on Quine on Existence

From Peter van Inwagen, "McGinn on Existence" in Modes of Existence: Papers in Ontology and Philosophical Logic, eds. Bottani et al., Ontos Verlag, 2006, p. 106:

There is the theory of Quine, according to which the two oppositions [that between being and non-being and that between existence and non-existence] are not two but one. Existence and being are the same. Existence or being is what is expressed by phrases like 'there is,' 'there are,' and 'something is.' And, similarly, non-existence is what is expressed by phrases like 'there is no, 'there are,' and 'nothing is.' Thus, 'Universals exist' means neither more nor less than 'There are universals,' and the same goes for the pairs 'Carnivorous cows do not exist'/'Nothing is both carnivorous and a cow' and 'The planet Venus exists'/'Something is the planet Venus.' This outline constitutes the essence of Quine's philosophy of being and existence.

And an accurate and succinct outline it is. But it just reinforces me in my conviction of the wrongheadedness of Quine's version of the thin theory of existence.

I grant that existence and being are the same. My objections begin with the assimilation of 'exists' to 'something.' The following are logically equivalent:

Cats exist
There are cats
Something is a cat.

and the same goes for:

Mermaids do not exist
There are no mermaids
Nothing is a mermaid.

But the thin theorist goes beyond the relatively uncontroversial claim of logical equivalence to the eminently dubious claim that the meaning (van Inwagen uses this word above) of 'exist(s)' is exhausted by the meaning of 'something' and the meaning of 'not exist' is exhausted by the meaning of 'nothing.'

To sort this out, we first note that 'something' splits into 'some' and 'thing.' To appreciate this, observe that the following are nonsensical

Some is a cat
Thing is a cat.

Equally nonsensical are their canonical counterparts:

(∃ )(x is a cat)
( x) (x is cat).

So both 'some' and 'thing' are needed for 'Something is a cat' — '(∃x)(x is a cat)' — to make sense.

Now it is obvious that existence is not expressed by 'some' or '∃' since these are merely signs for particular (as opposed to universal) logical quantity. Existence is not someness. Existence is not expressed by '∃.' And it is obvious that existence is not expressed by the variable 'x,' which is merely the canonical stand-in for the third-person singular pronoun, 'it.' It is obvious, I hope, that one cannot express the thought that cats exist by saying 'It is a cat.' Existence is not 'itness.' Existence is not expressed by 'x' any more than it is expressed by '∃.'

So existence cannot be expressed by the quantifier part of 'something' or the variable part. Is existence expressed by both together? No. Putting together two pieces of mere logical syntax just gves you more logical syntax. If existence is to come into the picture, we have to get off the plane of mere logical syntax: there has to be some reference to the real world. Suppose we write 'Something is a cat' as

Some thing is a cat.

But now the cat is out of the bag. For surely these things one is quantifying over are existing things: 'thing' is a variable having existing values. So to be perfectly clear, one must write:

Some existing thing is a cat.

And now the explanatory circularity of the Quinean account is obvious. We were promised an account of existence in terms of the so-called existential quantifier. But the account on offer presupposes the very 'thing' we want an account of, namely, existence. Clearly, one must presuppose that the objects in the domain of quantification are existing objects if the logical equivalences above mentioned are to hold.

My Existence and My Possible Nonexistence

Leo Mollica made a good objection to my earlier argument, an objection I need to sort out. I exist, but I might not have existed. How might a thin theorist translate this truth?

On the thin theory, my existence is my identity-with-something. It follows that my nonexistence is my diversity-from-everything, and my merely possible nonexistence is my diversity from everything in one or more merely possible worlds. But — and this I take it is Leo's point — I needn't exist in merely possible world w for it to be true in w that I am diverse from everything in w. So w is not a world in which I am self-diverse, but simply a world in which I am diverse from everything in w. Had w been actual, I would not have been self-diverse; I would not have existed at all, i.e., I would not have been identical to any of the things that would have existed had w been actual.

To put it another way, on the thin theory, my actual existence is my self-identity, my identity with me. Opposing this reduction of singular existence to self-identity, I argued that if my existence is my self-identity, then the possibility of my nonexistence is the possibility of my being self-diverse — which is absurd. Mollica's rejoinder in effect was that my possible nonexistence is not my possible self-diversity, but my possible diversity from everything distinct from me.

I could respond by saying that this objection begs the question by assuming the thin theory. But then Mollica could say that I am begging the question against him. Let me try a different tack.

If I am diverse from everything in w, but I don't exist in w, then something must represent me there. For part of what makes w w is that it lacks me. It is essential to w that it not contain me. But how express this fact if there is no representative of me in w? Now the only possible candifdate for a representative of me in possible worlds in which I do notr exist is my haecceity-property: identity-with-BV. If there is such a property, then it can go proxy for me in every possible world in which I do not exist, worlds which in part are defined by my nonexistence.

So it seems that Mollica's objection requires that there be haecceities such as identity-with-BV, and that these be properties that can exist unexemplified. But now two points.

First, there are no such haecceity properties for reasons given elsewhere, for example, here.

Second, if haecceities are brought into the picture, then we are back to the Fregean version of the thin theory according to which 'exists(s)' is a second-level property. But what I have been pounding on is the latest and most sophisticated version of the thin theory, that of van Inwagen. And we have seen that he rejects the view that 'exist(s)' is second-level.