For Francesco Orilia

1) 'Cats exist' is an example of an affirmative general existential sentence. 'Max exists' is an example of an affirmative singular existential sentence. 'Max' names a cat of my acquaintance.  The problem that concerns me is whether there is an adequate analysis that does justice to both types of existential sentence, one that preserves the contingency of both and their semantic connection. 

2) 'Cats exist' is contingently true. Its negation is possible. 'Cats do not exist' could have been true.  There is no metaphysical (broadly logical) necessity that there be cats. The same holds for negative general existentials. 'Gryphons do not exist' is contingently true, which implies that its negation, 'Gryphons exist,' could have been true. 

3) The surface grammar of 'Cats exist' suggests that it is about cats and predicates existence of them. This surface construal has long been recognized as problematic. For example, is the sentence about all cats or some cats?  Presumably all. But 'All cats exist' cannot accommodate the contingency of 'Cats exist.' The latter is contingent if and only if its negation is possible. Now the negation of 'All cats exist' is 'Some cats do not exist' which is not possible, but self-contradictory.  To be explicit, it is self-contradictory on the extremely plausible anti-Meinongian  assumption that there are no nonexistent objects.  Plausible or not, I assume it here.  Everything exists.

4) How must we construe 'Cats exist' so that it and its negation both come out contingent? The contingency is easily captured if we take 'Cats exist' to predicate instantiation or exemplification of the concept cat or the property of being a cat. Accordingly, 'Cats exist' is not about cats at all, but about the property of being a cat and predicates of this first-level property the second-level property of being exemplified or having one or more instances.  'Cats exist' expresses the (true, but possibly false) proposition that felinity is exemplified and 'Cats do not exist' expresses the (false, but possibly true) proposition that felinity is not exemplified.  If existence is exemplification, we seem to get what we want: a meaningful contrast between existence and nonexistence that accommodates the contingency of contingent general existentials, whether affirmative or negative.

The exemplification account of existence also provides a neat solution to the ancient problem of negative existentials. Given that 'Unicorns do not exist' is true, the sentence cannot be about unicorns. What then is it about? It is about the concept unicorn and predicates of this concept the property of having no instances.  The theory is easily extended to cover singular negative existentials if we think of proper names in a Russellian way as definite descriptions in disguise as opposed to thinking of them in a Kripkean way as rigid designators. Charitably understood, when an atheist denies the existence of God, he is not presupposing God's existence; he is denying that the divine attributes are jointly instantiated.  He is denying that the concept God is exemplified.

This approach to existence could be called 'Fressellian.'  It is essentially the tack that Frege and Russell take if we lump them together and ignore certain differences between the two logicians.  For both of these luminaries, existence is a property of concepts/properties only, and cannot be predicated meaningfully of objects or individuals. As Saul Kripke explains, 

To deny that it [existence] is a first-level concept is to deny that there is a meaningful existence predicate that can apply to objects or particulars.  One cannot, according to Frege and Russell, say of an object that it exists or not because, so they argued, everything exists: how can one then divide up the objects in the world into those which exist and those which don't? (Reference and Existence: The John Locke Lectures, Oxford UP, 2013, p. 6)

At the level of individuals there is no meaningful contrast between existence and non-existence because, pace Meinong, everything exists.  At the level of individuals, existence is not classificatory: it does not divide items into the existents and the nonexistents, the entities and the nonentities.  But when existence is 'kicked upstairs' and construed as exemplification, it becomes classificatory: it divides first-level properties into those that have instances and those that do not.

Russell goes so far as to liken existence to numerousness. Men are numerous, and Socrates is a man;  it does not follow, however, that Socrates is numerous. To think otherwise would be to embrace the fallacy of division. In this case, what can be predicated of the class cannot be predicated of its members. Similarly, men exist, and Socrates is a man; it does not follow, however, that Socrates exists. Not only does it not follow, it is meaningless to say of Socrates that he exists or that he does not exist. Or so maintains Russell. For if existence is exemplification, then of course individuals or objects such as Socrates can neither  exist nor not exist because they can neither be exemplified nor the opposite. If existence is exemplification, then it would be something like a Rylean category mistake to think of objects or individuals as either existing or not existing.

Characteristic of the Fressellian approach is the radical separation of existence from  individuals.  Well-motivated as it is, it leads to trouble.

If existence = exemplification, and thus a property of properties only, then there is no such 'property' as singular existence. A highly counter-intuitive result!  For if a first-level concept/property is exemplified, then it is exemplified by at least one individual.  How could that individual not exist?  If it didn't exist it would either be nothing at all, or it would be a Meinongian nonexistent item, an option we have already excluded. (If there are no nonexistent items, then everything exists, including all individuals.) Suppose the concept cat is exemplified by Max. How could Max fail to exist?  If exemplification is a relation, then, for the relation to hold, both relata must exist, the property and the individual.The attempt to reduce existence to exemplification fails.  For we are left with the singular existence of  the individuals that exemplify first-level properties.

At this point one might object that the existence of Max just is the being-exemplified of the concept cat.  But this can't be right.  For one thing, the concept could be exemplified even if Max does not exemplify it.  'Cats exist' does not entail 'Max exists.' Therefore, the existence of Max cannot be identified with the being-exemplified of  the concept cat. Even if it makes sense to say that the existence of a property is its being exemplified, which I rather doubt, it makes no sense to say that the existence  of Max, that very cat, is the being-exemplified of the concept cat.  This is also clear from the fact that  Manny, Mungo, and Maya are also cats, and their singular existence is different from that of Max. Each individual has its own existence, and each differs from every other one in its existence.  The concept cat, however, cannot serve to individuate/differentiate  the various individuals falling under the concept.  If the existence of Max = the being-exemplified  of  the concept cat, then there could only be one cat and Manny, Mungo,and Maya would be out in the cold.

In sum, if cat is exemplified, then cats exist, and if cats exist, then cat is exemplified.  This is necessarily true but it remains on the plane of general existence. Cats cannot exist, however,  unless one or more individual cats exist, and the singular existence of these individuals cannot be the exemplification of the property of being a cat.  One cannot therefore identify existence with exemplification; the most one can do is identify general existence with exemplification.

5) At this point one might try an eliminativist move and deny that there is singular existence.  This is what the Fressellian approach implies. For Frege and Russell, first-level predications of existence are meaningless: '___exist(s)' is not an admissible first-level predicate. But this flies in  the face of what seems obvious, namely, that sentences like 'Max exists' are true, and are true as predicating existence of the referents of their subject terms.  But if true, then meaningful.  Something similar holds for 'Max does not exist' when embedded in such sentences as 'Possibly, Max does not exist' and 'It will be the case that Max does not exist.'  The embedded sentences are meaningful.  Existence can be meaningfully affirmed and denied of individuals. 

Whether or not we say that existence is a property of individuals in any usual sense of 'property,' it is a datum that existence belongs to individuals in a way that would be impossible if existence is exemplification. (How existence belongs to individuals is a difficult question. I propose an answer in my book, A Paradigm Theory of Existence, Kluwer 2002.)  For again, it makes no sense to say of an individual that it is exemplified. Only concepts, properties, and cognate items can be exemplified.  If existence reduces to exemplification, then no individual exists.

6) So we have a problem. We seem driven by cogent argumentation to identify existence with the second-level property of exemplification.  We seem driven in this direction by the need to maintain the contingency of such sentences as 'Cats exist' (true but possibly false) and 'Cats do not exist' (false, but possibly true), and the related need to explain how true negative existentials are possible. But the exemplification approach breaks the connection between general and singular existentials.  Both affirm existence. We cannot rest content with a theory that consigns singular existentials such as 'Max exists' to meaninglessness.  'Max exists' is nothing like 'Max is numerous,' pace Russell.

Max exists, but he might not have. He is a contingent being.  We need to find a way to accommodate the contingency of contingent existents, and with it, the contrast between existence and (possible) nonexistence at the level of individuals.  And somehow we have to do this without reaching for Meinongian nonexistent individuals. 

7) At this juncture I will be told that  'x exists' may be defined in terms of '(Ǝy)(x = y).'  But this move only generates further problems. One of them is that this definition cannot be meaningfully formulated  if 'exists' is an inadmissible first-level predicate.   Kripke spots the problem.  He  points out (Reference and Existence, p. 37) that the Frege-Russell logical apparatus seems to allow for a definition of 'x exists' in terms of

 (Ǝy)(x = y).

Kripke then remarks that "it is hard for me to see that they [Frege and Russell] can consistently maintain that existence is only a second-level concept (in the Fregean terminology) and does not apply to individuals." (37)  Kripke's point is that on the above definition 'exists' is an admissible first-level predicate contra the official 'Fressellian' doctrine according to which 'exists' is never an admissible first-level predicate.

This is a serious problem. If existence is exemplification, then individuals do not exist. But if everything exists, then individuals do exist. To avoid the contradiction we must distinguish two senses of 'exist(s),' the general and the singular.  Accordingly, general existence is exemplification and is not predicable of individuals while singular existence is. 

But even if we relax the Fressellian stricture and admit 'exists' as a first-level predicate we still face serious problems. One of them is that 'exist(s)' becomes equivocal across general and singular existentials. Another is that singular existence cannot be identity with something (or other).   The idea is that Max exists just in case he is identical to something.  Since the only thing to which Max could be identical is himself, that is equivalent to saying that Max exists if and only if he is self-identical.  No doubt this is true, but it doesn't sanction the reduction of (singular) existence to self-identity.  It cannot be that Max exists in virtue of being identical to something, for that would imply that his possible nonexistence = his possible diversity from everything. But if he is possibly diverse from everything, then he possible diverse from himself, i.e., possibly self-diverse.  But it is impossible that he, or anything, be self-diverse. Therefore, it cannot be the case that the existence of Max reduces to his self-identity.

Furthermore, if for Max to exist is for Max to be self-identical, then, given that everything is essentially self-identical, it follows that Max essentially exists and so cannot cease to exist once he exists, which is absurd. If you tell me that Max is self-identical only as long as he exists, then, on the theory under discussion, that amounts to saying that Max is self-identical only as long as he is self-identical, which is a tautology.  You  are in effect admitting that the existence of  a thing is not its identity with something. We ought to conclude that singular existence cannot be reduced to self-identity.

8) The only solution I can see to the problem of accounting for singular existence within the exemplification account is by way of haecceity properties. 'Haecceity' is from the Latin haecceitas, thisness. An haecceity property, then, is a property that captures the very thisness of an individual. These properties, though supposedly distinct from the things that exemplify them, are as singular as they are.  If there are such properties, then we can give a unitary exemplification account of both general and singular existentials that preserves their contingency and also explains the semantic connection between the two types of existential. It would then be possible to say that 'exist(s)' is univocal across general and singular existentials.  We could then say that general existentials express the exemplification of multiply exemplifiable properties while singular existential express the exemplification of haecceity properties. Now to the details.

We assume  that (i) properties are abstract objects, that (ii) they can exist unexemplified, and that (iii) they are necessary beings. We may then define the subclass of haecceity properties as follows.

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

So if there is a property of Socrates that is his haecceity, then there is a property that individuates him, and indeed individuates him across all times and worlds at which he exists: it is a property that he must have, that nothing distinct from him has, and that nothing distinct from him could have. Call this property Socrateity. Being abstract and necessary, Socrateity is obviously distinct from Socrates, who is concrete and contingent. Socrateity exists in every world, but is exemplified (instantiated) in only some worlds. What's more, Socrateity exists at every time in every world that is temporally qualified, whereas Socrates exists in only some worlds and only at some times in the worlds in which he exists. Haecceity properties have various uses. I'll mention just the one of present interest.

Suppose I need to analyze 'Socrates might not have existed.' I start with the rewrite, 'Possibly, Socrates does not exist' which features a modal operator operating upon an unmodalized proposition. But 'Socrates does not exist,' being a negative existential proposition, gives rise to an ancient puzzle dating back to Plato. How is reference to the nonexistent possible? The sentence 'Socrates does not exist' is apparently about Socrates, but how so given that he does not exist? If the meaning of 'Socrates' is the name's referent, and nothing can be a referent of a term unless it exists, then Socrates must exist if he is to have nonexistence predicated of him. But the whole point of the sentence is to say that our man does not exist. How can one say of a thing that it does not exist without presupposing that it exists? Haecceities provide a solution. We can understand 'Socrates does not exist' to be about Socrateity rather than about Socrates, and to predicate of Socrateity the property of being exemplified. Recall that Socrateity, unlike Socrates, exists at every time and in every world. So this property, unlike Socrates, is always and necessarily available. Accordingly, we analyze 'Possibly, Socrates does not exist' as 'Possibly, Socrateity is not exemplified.' Socrates' possible nonexistence boils down to Socrateity's possible non-exemplification. It is a nice, elegant solution to the puzzle –assuming that there are haecceity properties.  There are reasons to be skeptical.

9) One of the stumbling blocks for me is the strange notion that the thisness of an individual could exist even if the individual whose thisness it is does not exist. Consider the time before Socrates existed. During that time, Socrateity existed. But what content could that property have during that time (or in those possible worlds) in which Socrates does not exist? Socrateity is identity-with-Socrates. Presumably, then, the property has two constituents: identity, a property had by everything, and Socrates. Now if Socrates is a constituent of identity-with-Socrates, then it seems quite obvious that Socrateity can exist only at those times and in those worlds at which Socrates exists. Socrateity would then be like Socrates' singleton, the set consisting of Socrates and Socrates alone: {Socrates}. Clearly, this set cannot exist unless Socrates exists. It is ontologically dependent on him. The same would be true of identity-with-Socrates if Socrates were a constituent of this property.

If, on the other hand, Socrates is not a constituent of Socrateity, then what gives identity-with-Socrates the individuating content that distinguishes it from identity-with-Plato and identity-with-Pegasus? Consider a possible world W in which Socrates, Plato, and Vulcan (the planet) do not exist. In W, their haecceities exist since haecceities ex hypothesi exist in every world. What distinguishes these haecceities in W? Nothing that I can see. The only things that could distinguish them would be Socrates, Plato, and Vulcan; but these individuals do not exist in W. It might be said that haecceity properties are simple: identity-with-Socrates is not compounded of identity and Socrates, or of anything else. Different haecceities just differ and they have the content they do in an unanalyzable way. But on this suggestion haecceities seem wholly ungraspable or inconceivable or ineffable, and this militates against thinking of them as properties. I have no problem with the notion of a property that only one thing has, nor do I have a problem with a property that only one thing can have; but a property that I cannot grasp or understand or conceive or bring before my mind — such an item does not count as a property in my book. It would be more like a bare particular and inherit mutatis mutandis the unintelligibility of bare particulars.

Haecceities must be nonqualitative.  Consider a conjunctive property the conjuncts of which are all the mutiply exemplifiable properties a thing has in the actual world. Such a property would individuate its possessor in the actual world: it would be a property that its possessor and only its possessor would have in the actual world. Such a property is graspable in that I can grasp its components (say, being barefooted, being snubnosed, being married, etc.) and I can grasp its construction inasmuch as I understand property conjunction. But the only way I can grasp Socrateity is by grasping is as a compound of identity and Socrates — which it cannot be for reasons given above.

Note that Socrateity is not equivalent to the big conjunctive property just mentioned. Take the conjunction of all of Socrates' properties in the actual world and call it K. In the actual world, Socrates has K. But there are possible worlds in which he exists but does not exemplify K. And there are possible worlds in which K is exemplified by someone distinct from him. So Socrateity and K are logically nonequivalent. What we need, then, if we are to construct a qualitative thisness or haecceity of Socrates is a monstrous disjunctive property D[soc] the disjuncts of which are all the K's Socrates has in all the possible worlds in which he exists. This monstrous disjunction of conjunctions is graspable, not in person so to speak, but via our grasp of the operations of conjunction and disjunction and in virtue of the fact that each component property is graspable. But D[soc] is not identical to Socrateity. The former is a qualitative thisness whereas the latter is a nonqualitative thisness. Unless the Identity of Indiscernibles is true, these two thisnesses are nonequivalent. And there are good reasons to think that the Identity of Indiscernibles is not true.  (Max Black's iron spheres, etc.) So D[Soc] is not identical to Socrateity. 

To compress my main point about haecceities  into one sentence: identity-with-Socrates is graspable only as a compound of identity and Socrates; but then this property cannot exist unexemplified. Hence haecceity properties as defined above do not exist.

10) Suppose now that, despite the above argumentation, there are haecceity properties.  It will then be necessarily true both that Socrates exists iff Socrateity is exemplified, and that Socrates is contingent iff Socrateity is contingently exemplified.  But a Euthyphro-type question arises. Does Socrates exist because Socrateity is exemplified, or the other way around?  The latter: Socrateity is exemplified because Socrates exists.  We therefore move in an explanatory circle if we try to account for the existence of an individual in terms of the exemplification of the individual's haecceity.

As for contingency, Socrateity is contingently exemplified because Socrates contingently exists, and not the other way around.

11) I conclude that the exemplification account of existence is untenable. This does not imply that some other view is tenable. For it may be that every view that it is possible for us to formulate is untenable.