Curva S-N

Serious actualism, as I use the term, is the view that (necessarily) no object has a property in a world in which it does not

exist. That is, every object x is such that forany possible world W and property P, if necessarily, if W had been actual, then x would have had P, then necessarily, if W had been actual, x would have existed. More exactly, serious actualism is the necessity of this proposition. More simply, it is the claim that no object could have had a property without existing. (Frivolous actualism is the conjunction of actualism with the denial of serious actualism.) Pollock accepts actualism, but proposes not-existing as a counterexample to serious actualism; Socrates, he says, has the property of not-existing in worlds in which he does not exist. He then reports me as holding that “there is no such property as that of not existing” and as adding that “There is a property of non-existence, but that is a property nothing can have because in order to have it, an object would have to exist without existing.” Bewildered by this unexpected turn of events, he asks, “Why would anyone say this?” and replies as follows:

There is a very seductive modal fallacy to which I have found myself succumbing on occasion and I suspect that Plantinga is succumbing to it here. The fallacy consists in endorsing instances of the following modal principle: (13) □ (x)(F x ⊃ G x) ⊃ □ (x) □ (F x ⊃ G x).

To see that this principle is invalid, let F be ‘does not exist’ and G be ‘exists’. Assuming that ourquantifiers range only overexisting objects. . . , the antecedent of (13) is true,. . . , but the consequent is false because it says that everything has necessary existence (p. 126).

Now our first problem is to understand (13). Suppose we treat occurrences of ‘□ Fx’ as expressing modality de re, so that ‘□ Fx’, to put it very informally, says that x has essentially the property expressed by F and ‘(x) □ Fx’ says that everything has essentially the property expressed by F3_{; suppose furthermore that an object has a property essentially if}

and only if it has it in every world in which it exists; and suppose finally that actualism is true, so that there neither are norcould have been any nonexistent objects. Then (13) is a special case of

(14) □ (x)F x ⊃ □ (x) □ F x

which (understood as above) is a correct modal principle. What (13) so construed says is

(13*) If necessarily everything is such that if it is F, then it is G, then necessarily everything has essentially the property of being such that if it is F, then it is G

which has no false instances. Specified, as Pollock suggests, to ‘does not exist’ and ‘exists’ the result is

If necessarily, everything is such that if it does not exist, then it exists, then necessarily, everything has essentially the property of being such that if it does not exist, then it exists.

It is easy enough to see that this is true: everything has essentially the property of existing (nothing has existence in any world in which it does not exist); hence everything has essentially the property of being such that if it does not exist, then it exists. This last, furthermore, is necessarily true; so the proposition in question has a true consequent and is therefore true.

Pollock, however, does not understand (13) in this way. How does he understand it? As follows. Let us suppose that forany proposition P, there is such a thing as its denial, and for any object x and property P, there is such a thing as the proposition that x has P. (The proposition that x has P will be true in a world W if and only if some individual essence of x is coexemplified with P in W; its denial (the proposition that it is not the case that x has P) will be true in W if and only if no essence of x is coexemplified with P in W.) What ‘□F x’ says (again, very informally) is that the proposition that x is F is necessarily true. Then both (14) and the weaker

(14*)□ (x)F x ⊃ (x) □ F x

have false substitution instances; forwhile it is necessarily true that everything exists, it is false that everything is such that the proposition that it exists is necessary (and a fortiori false that necessarily, everything that exists is such that the proposition that it exists is necessary). And taken this way, (13) will indeed have false instances: what it says, so taken, is (13**) If necessarily everything is such that if it is F, then it is G, then necessarily everything is such that necessarily,

if the proposition that it is F is true, then the proposition that it is G is true. The specification of this to ‘does not exist’ and ‘exists,’ as Pollock rightly says, is clearly false.

So far, so good; there is so far no disagreement between us. But Pollock goes on to suspect that I endorse serious actualism just because I mistakenly endorse false instances of (13) taken his way; to this I plead innocent. Why then do I endorse serious actualism? Because it follows from actualism, a view that both Pollock and I endorse with unrestrained enthusiasm. The argument is simple enough. I shall begin by explaining why I believe Pollock is mistaken in proposing

nonexistence (which, I take it, is the complement of existence) as a counterexample to serious actualism. Now first, there

is a perfectly

straightforward argument from actualism to the conclusion that nonexistence (call it ‘E’) is not exemplified. Consider (1) Forany property P, if P is exemplified, then there is something that exemplifies P

and

(2) Forany property P, whateverexemplifies P exists.

Here the quantifiers are to be taken as widely as possible; if you think there are things that do not exist, then read the quantifiers as ranging over those things as well as the more conventional existent sort. (1), I take it, is obviously true. (2) is a consequence of actualism, according to which it is necessary that whatever there is, exists. (1) and (2) together entail

(3) If nonexistence is exemplified, then nonexistence is exemplified by something that exists.

Since the consequent of (3) is clearly (necessarily) false, it is false that nonexistence is exemplified. And since (given the truth of actualism) each of the premises of this argument is necessarily true, it follows that nonexistence is necessarily unexemplified; that nonexistence is not exemplified is a necessary truth.

But then nonexistence is not a counterexample to serious actualism. According to the latter, nothing exemplifies a property in a world in which it does not exist. But nothing exemplifies nonexistence in a world in which it does not exist, because nothing exemplifies nonexistence in any world. Alternatively: it's necessary that if any object had exemplified nonexistence, then nonexistence would have been exemplified. Therefore it is necessary that nothing could have exemplified nonexistence.

It is easy to see, I think, that we can go on to deduce serious actualism from actualism. For suppose an object—Socrates, let's say—exemplifies a property P in a world W. Then (necessarily) if W had been actual, Socrates would have exemplified P. Now (necessarily) if Socrates had exemplified P, then eitherSocrates would have exemplified

P & E, the conjunction of P with existence, orSocrates would have exemplified P & E (where E is the complement

of existence). As we have just seen, it is impossible that Socrates exemplify E, and hence impossible that Socrates exemplify P & E. It is therefore necessary that if Socrates had exemplified P, then Socrates would have exemplified existence. In terms of possible worlds; suppose Socrates exemplifies P in W. Then eitherSocrates exemplifies P and

existence in W orSocrates exemplifies P & E in W. There is no world in which Socrates exemplifies P & E. So

Socrates exemplifies existence (that is, exists) in W.4

The above arguments both seem to me to be entirely solid. I am

at a loss to explain why Pollock does not accept them—unless perhaps, it is that his intellect has been clouded by excessive euphoria induced by an unduly sybaritic, southwestern style of life. But there is another, less censorious explanation. Pollock suspects I'm just defining ‘property’ in such a way that serious actualism is (trivially) true; he proposes, therefore, that we speak of conditions:

Suppose we give Plantinga his use of the term ‘property’, agreeing that (19b) and serious actualism are true by stipulation for properties. Then it is natural to want a more general term which includes both properties and things like not existing. I want to say that although objects cannot have properties at worlds in which they do not exist (by the definition of ‘property’), they can satisfy conditions at worlds in which they do not exist, and one such condition is that of not existing. Anothersuch condition is that of being such that if one existed then one would be sentient. Socrates satisfies the latterat worlds in which he does not exist (p. 128).

Pollock goes on to explain that conditions are or determine functions from individuals to states of affairs (and, we might add, propositions):

Conditions and properties alike can be regarded as determining functions from individuals to states of affairs. For example, the property of being snubnosed determines the function which to each individual x assigns the state of affairs x's being snubnosed. Similarly, the condition of not existing determines the function which to each individual x assigns the state of affairs x's not existing. These functions are functions in intension rather than functions in extension. . . . If it is denied that conditions make sense in any otherway, then they can simply be identified with the corresponding functions. That is, a condition becomes any function from objects to states of affairs (p. 128). Then we can say that

C An object x satisfies a condition C at a world W if and only if C(x) (the value of C for x) is tr ue at W. “In this way,” Pollock adds, “we make perfectly good sense of conditions and of objects satisfying conditions at worlds in which they do not exist” (p. 129).

Now all of this seems quite correct. Indeed there are conditions; conditions are just propositional functions (functions in intension) from individuals to propositions. Since there is such a thing as the denial of the proposition Socrates exists (the proposition Socrates does not exist or it's false that Socrates exists) there is a propositional function—call it ‘∼(x

exists)’—whose value for Socrates is that proposition; and since that proposition is true in worlds in which he does not

exist, Socrates satisfies ∼ (x exists) at worlds in which he does not exist. In the same way he satisfies the condition x is

wise or ∼ (x is wise)

at worlds where he does not exist. So an individual x can perfectly well satisfy a condition at a world in which x does not exist.

Then Pollock points out that some conditions are such that an object x cannot satisfy them at a world without existing in that world; other conditions, however—∼(x exists), forexample—can perfectly well be satisfied by x at worlds in which x does not exist. And Pollock suspects that I'm just defining ‘property’ as ‘condition that can't be satisfied at a world by an object that doesn't exist in that world’, thereby making serious actualism trivially true. But here, I believe, Pollock is falling into a confusion (a confusion I was guilty of on p. 14 of “On Existentialism”): he is confusing satisfaction of a condition at a world with satisfaction of a condition in a world. The truth of the matter is that while an object can perfectly well satisfy a condition at a world in which it does not exist, it cannot satisfy a condition in a world in which it does not exist. We may see this as follows.

First (as I've already said), the proposition Socrates does not exist is true in worlds in which Socrates does not exist: hence the value of the condition ∼ (x exists) for Socrates taken as argument is true in worlds in which Socrates does not exist; hence Socrates satisfies this condition at such worlds.

But second, Socrates does not satisfy this condition in a world in which he does not exist, where

C* an object x satisfies a condition C in a world W if and only if necessarily, if W had been actual, then x would have satisfied C.

ForSocrates does not satisfy ∼ (x exists) in any worlds at all. Here we can give an argument exactly paralleling the earlier argument for the conclusion that Socrates does not exemplify E in any possible world. For first, it is impossible that ∼ (x exists) is satisfied. An object x satisfies a condition orpropositional function C if and only if the value of C for x as argument is true. A condition is therefore satisfied only if some object satisfies it—only if, that is, there is an object that satisfies it. Considertherefore

(4) Forany condition C, if C is satisfied, there is something that satisfies C and

(5) Forany condition C, whateversatisfies C exists.

(4), once more, is obviously true; and (5), like (2), is an immediate consequence of actualism.5 _{(And again, take the}

range of the quantifiers as wide as possible.) From (4) and (5) it follows that

(6) If ∼ (x exists) is satisfied, then ∼ (x exists) is satisfied by something that exists.

The consequent of (6), however, is impossible; so the condition ∼ (x exists) is not satisfied. Each of the premises, furthermore, is necessary; so it is necessary that ∼ (x exists) is unsatisfied. You may think it a bit peculiarthat some conditions—∼(x exists) forexample—could not have been satisfied even though there are worlds at which they are satisfied. But this peculiarity is only verbal, and is due to a quirk in our definition of ‘satisfies at’. C is indeed satisfied in some possible world only if C is possibly satisfied; the same cannot be said forsatisfaction at.

But now it follows that there is no possible world in which Socrates satisfies ∼ (x exists). Forsuppose he satisfies it in some world W: then if W had been actual Socrates would have satisfied ∼ (x exists); but if Socrates had satisfied ∼ (x

exists), that condition would have satisfied—which, as we have just seen, is impossible. So if Socrates satisfies ∼ (x exists) in W, then W is not possible after all, contrary to hypothesis. Neither Socrates nor anything else, therefore,

satisfies ∼ (x exists) in any possible world (although Socrates and many other things satisfy ∼ (x exists) at many possible worlds). And as before, we can easily go on to show that Socrates doesn't satisfy any condition in a world in which he doesn't exist. Forsuppose Socrates satisfies C (= x is C) in W. Then eitherSocrates satisfies x is C & x exists in W or Socrates satisfies x is C and ∼ (x exists) in W. As we have seen the latteris impossible; so if Socrates satisfies C in W, then he also satisfies x exists in W, in which case he exists in W.

Now for the less censorious explanation of our differences. Pollock has, I think, overlooked the difference between ‘satisfies at’ and ‘satisfies in.’ It is indeed true that objects can satisfy conditions at worlds in which they do not exist; it doesn't follow (and isn't true) that they can satisfy conditions in worlds in which they do not exist. A fortiori, it doesn't follow that objects can have properties in worlds in which they do not exist. Pollock is entirely correct, therefore, in pointing out that there are conditions, and that objects can satisfy conditions at worlds in which they do not exist. What he says, however, does nothing to show that an object can satisfy a condition or have a property in a world in which it does not exist; and that question, afterall, is the one to which serious actualism is addressed. Serious actualism has nothing to do with the question whetherobjects have properties orsatisfy conditions at worlds in which they do not exist; it has everything to do with the claim that no object has a property or satisfies a condition in such worlds. The distinction between satisfaction in and satisfaction at deserves a little more by way of exploration. As we have seen, it is not in general true that if a condition is satisfied at a world W, then it is satisfied in that world. Some conditions, however—wisdom, being snub-nosed, forexample—do display this feature. If an object x satisfies wisdom at a given world W, then x satisfies wisdom in W. A

property, we may say, is just a condition that is satisfied by an object x at a world W only if it is satisfied in W by x.

Alternatively, suppose we say that a condition C is existence-entailing if (necessarily) whatever satisfies it at a given world

W exists in W. To say that a condition C is existence-entailing is not merely to remark that necessarily, whatever satisfies C exists; that much is a trivial consequence of serious actualism. It is instead to say something much stronger: for any x, if C(x) had been true, then x would have existed. x is wise is thus existence-entailing; any world in which Socrates is wise

is true is one in which Socrates exists. ∼ (x is wise) on the otherhand, is not; forthe proposition it is false that Socrates is

wise is true in worlds in which Socrates does not exist. x exists, obviously, is existence-entailing; ∼ (x exists), just as

obviously, is not. And then we may say that properties are just the existence-entailing conditions. So properties are those conditions forwhich satisfaction at coincides on any possible world with satisfaction in; equivalently, a property is any existence-entailing condition.

We must note further that for any property P and its complement P there are four conditions: x has P, x has P, ∼ (x has

P), and ∼ (x has P). (The distinction between x has P and ∼ (x has P) corresponds to and underlies what is sometimes

called the distinction between external and internal negation.) Thus wisdom and its complement W are properties; ∼ (x

has wisdom) and ∼ (x has W)—conditions that respectively map Socrates onto it is false that Socrates has wisdom and it is false that Socrates has W —are not. The value of an existence-entailing condition for an object x as argument is predicative, with

respect to x;it predicates a property of x, and is true only in those worlds in which x exists. On the otherhand, C (x) is

impredicative with respect to x if C is a condition that does not entail existence;6_{a proposition that is impredicative with}

respect to an object x does not predicate a property of x and can be true in worlds in which x does not exist. Whether we propose to use the word ‘property’ in the way I have suggested (thus distinguishing between properties and conditions) is, of course, a merely verbal matter. What is substantive here are two points: (1) some conditions are existence-entailing and some are not, and (2) necessarily every object O and condition C are such that if O had satisfied

C, then O would have existed (serious actualism).

C. Existentialism

As I use the term, existentialism is the view that singular propositions, singular states of affairs, and haecceities are all ontologically dependent upon the individual they ‘involve’, as are other propositions, properties and states of affairs appropriately related to those of the first sort. Thus, for example, if William F. Buckley had not existed, then such singularpropositions as William F. Buckley is wise would also have failed to exist; and the same holds forhis haecceity, forthe proposition

either William F. Buckley is wise or someone is wise, for possible worlds in which he exists, and the like. In chapters in this

volume, I argued that existentialism is false. Pollock rejects this argument. He then claims that the question of existentialism “makes no difference” to ourmodal intuitions and he proposes, finally, two analyses of states of affairs: one vindicating existentialism and one vindicating its denial (which, to continue my terminological metaphor, I shall call ‘essentialism’). He concludes that “ourconceptual scheme is simply indeterminate in this respect.” I shall comment