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DOI: 10.24234/wisdom.v21i1.605 Oleh BONDAR
BETWEEN EXISTENTIALISM AND ANTI-EXISTENTIALISM
Abstract
The article is an evaluation of Pollock's anti-existentialist argument and its place in the contemporary debates about Existentialism. We demonstrate that the main contemporary objections to Pollock's Anti-Existentialism can be grouped into two argumentative directions: (1) Pollock's supposed confusion of inner and outer truth (Fine, Speaks); (2) Pollock's assumption that there is such state of affairs as Socrates's not existing (Kroon). We also introduce an argument against Pollock's crucial argumentative step against existentialism.
Keywords: existentialism, anti-existentialism, truth, propositions, possible worlds, closure under containment.
Introduction: What is Existentialism?
Existentialism, according to Plantinga (1983), is a view that singular propositions depend onto-logically on their constituents - that is, on what these propositions are about. Take, for example, the proposition [Socrates is a philosopher]. Existentialists believe that [Socrates is a philosopher] involves Socrates as its constituent (because [Socrates is a philosopher] refers directly to Socrates); thus, by Existentialism, if Socrates does not exist, [Socrates is a philosopher] does not exist too. Existentialism is a very influential and widespread view in philosophy, and there are many ways to argue for it. One might argue that Existentialism follows from Millianism, according to which the meaning of a name is its referent (Ryckman, 1988). The defender of Kripkean point of view (Kripke, 1980) might argue that proper names are rigid designators, and thus the sentence [Socrates was a teacher of Plato] is meaningless if there is no such a person as Socrates - the proper name Socrates would designate nothing if Socrates did not exist. Williamson (2002) argues for Existentialism as follows (pp. 200-242). Consider the proposition [Socrates is a philosopher]. It is necessarily the case that if
[Socrates is a philosopher] exists, then Socrates is a philosopher. So, if [Socrates is a philosopher] is about Socrates, [Socrates is a philosopher] must bear a relation to Socrates. But if Socrates bears a relation to [Socrates is a philosopher], Socrates must be existent in order to be a bearer of this relation. How could Socrates stand in relation to [Socrates is a philosopher], being nonexistent? Thus, if [Socrates is a philosopher] exists, and if [Socrates is a philosopher] is about Socrates, Socrates exists too. Similarly, (Stephanou, 2020) argues that the existence of Socrates is a necessary condition for [Socrates is a philosopher] to be a proposition that Socrates is a philosopher - it is not the case that [Socrates is a philosopher] could be a proposition about Socrates if Socrates is nothing or the meaning of the proper name Socrates is empty.
Another strong argument for Existentialism was suggested by (Stalnaker, 2010, pp. 22-23). Suppose Kant could have had a son. If so, there is someone, X, such that X is Kant's son. But given that nothing in the actual world is the son of Kant (X), there couldn't be such a sentence as [X is the son of Kant]. For suppose otherwise. Let us accept that [X is the son of Kant] exists, such that [X is the son of Kant] is about possible
Kant's son. Now consider:
a) [X is the son of Kant].
b) [Y is the son of Kant].
How could we distinguish between (a) and (b) if X and Y are both nonexistent? It is obvious that (a) and (b) express different propositions -(a) is about X, and (b) is about Y. But if X is nonexistent, and the proposition expressed in (a) refers to nothing, we have no truth-conditions for (a) to individuate its meaning. If X is nonexistent, and [X is the son of Kant] refers to nothing, then it is impossible for us to distinguish between (a) and (b).
Existentialism also meets some objections. One of them can be inferred from the following example of Bennett (2005, pp. 317):
(1) Kant could have had a son who was a philosopher who could have been a football player.
It is obviously true that a philosopher could have been a football player. But if (1) is true, the existentialist seems to be forced to accept that the philosopher, who is the (possible) son of Kant, has a de re modal property of being a possible football player. However, if Existentialism is true, then the proposition that Kant's son could have been a football player is a singular proposition about the possible son of Kant. Thus, following Existentialism, such a singular proposition is nonexistent, since its constituent does not exist. Nevertheless, we can guarantee that, necessarily, every philosopher could have been a football player:
(2) mVx (Px ^ OFx).
Again, by (2), Kant's son could have been a football player. Kant's son, a possible philosopher, could have been existent, and thus could have been a football player, so [Kant's possible son could have been a football player] is existent in the actual world (since this proposition attributes a de re property to Kant's son), contradicting Existentialism.
Existentialists could reject this objection by claiming that "there are no de re modal claims about things that do not actually exist" (Bennett,
2005, pp. 317). But this solution seems to be half-hearted (at least for the problem with Existentialism). For suppose we agree that propositions do not exist if their constituent is nonexistent. We can agree that everything is such that it could be nonexistent
(3) mVx 0~3y y = x.
Say that, by (3), every contingent proposition could fail to exist. Also, by Existentialism, any proposition could be nonexistent if its constituent is a contingent object. Let P be a proposition "Fichte could have failed to exist". This proposition, P, is about Fichte. Thus, by Existentialism, "Fichte could have failed to exist" do not exist if Fichte does not exist. P expresses a contingent truth, and so there is a possible world W such that Fichte does not exist in W. Then in @ (in the actual world), it is possible that Fichte is nonexistent, and the proposition that Fichte is nonexistent is true. If the proposition that Fichte is nonexistent, P, is true, then according to Existentialism, the constituent of P must be existent. Thus, it is possible for the proposition that Fichte could have failed to exist not to exist and, by Existentialism, Fichte must be existent to be a referent of P. Within this counterexample, we do not need to refer to a certain possible object (Kant's son) to provide an argument against Existentialism. Even if we are not allowed to attribute a de re modal truth to nonexistent objects (like Kant's possible son), this restriction still leaves the door open for a most pressing challenge for Existentialism - Plantinga's anti-existentialist argument.
Plantinga's Anti-Existentialism and Pollock's Existentialism
Plantinga's reductio of Existentialism (Plant-inga, 1983) runs as follows. Let "a" abbreviate Socrates, "T" - "truth", %.." - "the sentence that...", "E" - "exists", O and □ - "possible" and "necessary", respectively. The argument is this:
(4) O-Ea
(5) O-Ea ^O^-Ea
(6) 0^~Ea
(7)n(T^~Ea ^E^~Ea)
(8)n(T^~Ea ^~Ea)
(9) OT^~Ea
(10) □ (T^~Ea ^ (E^~Ea & ~Ea))
(11) 0(~Ea & E^~Ea).
In words, Plantinga's argument against Existentialism has the following form. Consider a possibility of Socrates's nonexistence (4). If it is possible that Socrates does not exist, the proposition Socrates does not exist is possible (5), and thus possibly true (6). Now we have that, necessarily, if the proposition Socrates does not exist had been true, then the proposition Socrates does not exist would be existent (7). However, it is necessarily the case that if the proposition that Socrates does not exist is true, then Socrates does not exist (8). From (4-6) we have that the proposition Socrates does not exist is possibly true (9). From (7-8) we have that, necessarily, if the proposition Socrates does not exist is true, then Socrates does not exist exists, and Socrates does not exist (10). Finally, from (9-10) we have the following: it is possible that Socrates does not exist, and the proposition Socrates does not exist exists (11). But (11) contradicts Existentialism. According to Existentialism, a singular proposition Socrates does not exist requires the existence of Socrates, because Socrates is a constituent of this proposition. Thus, if Socrates does not exist, existentialists should claim that the proposition Socrates does not exist must be nonexistent too. It is not possible for a singular proposition about Socrates's nonexistence to be existent while Socrates is not.
In his "Plantinga on Possible Worlds" (Pollock, 1984a), Pollock was enthusiastic about Existentialism. He offers an argument against Plant-inga's Anti-Existentialism, according to which Plantinga's argument relies on the modal fallacy, that is, on the confusion between
(12) mVS (S obtains ^ S exists)
and
(13) mVS □ (S obtains ^ S exists),
where "S" is such a state of affairs as "Socra-tes's nonexistence". This argument is a particular instance of Pollock's argument against Plantinga's Serious Actualism, according to which Plantinga illegitimately concludes that
(14) mVx (Fx ^ Gx) ^ mVx □ (Fx ^ Gx).
Pollock argues as follows. Let F be "does not exist", and G is "exists". Now, "assuming that our quantifiers range only over existing objects ... the antecedent of (14) is true because it is necessary that everything which exists exists; but the consequent is false because it says that everything has necessary existence" (Pollock, 1984a, p. 126). From this perspective, Pollock asserts that Plantinga fails to prove that propositions are bound to be existent to be true - it is not the case that the truth of Socrates does not exist necessarily implies the existence of Socrates does not exist. Thus, according to Pollock, Plantinga is not able to provide a successful argument for (13), which is a necessary premise of his Anti-Existentialism.
In response to Pollock, Plantinga defends the essentialist reading of (14); he argues that the right side of our conditional should be read as a de re modal claim. Say that mFx attributes an essential property F to X, such that for every possible world W, if X has F in W, X exists in W - that is, X has F in every possible world. So, following this reading of (14), it expresses the claim that if everything is such that if it is F, it is G, then necessarily everything has essentially a property of being such that if it is F, it is G (Plantinga, 1985, p. 179). Now, we do not have a problem with the counterexample of Pollock. Assume the truth of Actualism, according to which there are no (and couldn't be) any nonexistent objects. We have thus a sentence that "if necessarily everything is such that if it is nonexistent, then it is existent, then necessarily, everything necessarily has a property of being existent, if nonexistent", which expresses a necessary truth, given that necessarily, everything necessarily exists, and nonexistence is non-exemplified. However, Pollock, as Plantinga convincing-
ly argues, understands the nature of (14) in a somewhat different way. His reading is rather (15) If necessarily everything is such that if it is F, then it is G, then necessarily, everything necessarily has a property of being such that if the proposition that it is F is true, then the proposition that it is G is true (Plantinga, 1985, p. 180). And this claim obviously has false instances. Consider, for example, God. In theology, God is usually seen as a necessary being. Thus, it is true that God necessarily exists, but it is not true that God is such that the proposition that God necessarily exists couldn't fail to be existent. The proposition that God is a necessary being is not a necessary being; thus, God is a necessary being could have been nonexistent. However, God is a necessary being could lack existence, but it couldn't lack the property of being (necessarily) true. So the question is: how could a certain proposition be true without having existence in the world?
Pollock (1984a) gives the following example (pp. 135-136):
"Consider pictures. Pictures can correctly depict a state of affairs. We can even have a picture that correctly depicts a state of affairs in which there are no pictures (e.g., a picture of a big empty Louvre) and hence in which it does not itself exist. There is an analogy between pictures and states of affairs. A currently existing state of affairs can be said to represent part of the structure of a possible world at which it obtains, and just as in the case of pictures, there is no obvious reason why it must exist in that world in order to achieve the representation. To say that the state of affairs represents the world is to say something about the relationship between two currently existing objects - the state of affairs and the world. Whether the state of affairs would exist if the world were actual seems irrelevant to the relationship in question".
This objection is very close to Fine's argument about the need to distinguish between inner
(truth-in-W) and outer (truth-at-W) truth1 (Fine, 1985, p. 194). If P is a proposition, and W is a possible world, say that P is true in W if P exists in W, and let's say that P is true at W if the following holds - P would be true in W if W existed. Consider now the truth of Socrates does not exist. This proposition is usually equivalent to the following sentence - "There is a possible world W such that Socrates does not exist in W". Now, the proposition "X does not exist" can be expressed in two following ways2: either predica-tively, by attributing the property of nonexistence to X of W (truth-in-W), or impredicatively, that is, by a formula that indicates the nonexistence of X with respect to a certain possible world W(truth-at-W), but not being true in the world being evaluated by this formula. Say that "X does not exist" (P) is true in W. If P expresses the inner truth about X, then X is among the constituents of P, and the constituent of P, X, is existent in W. But if P is true at W (that is, P expresses the truth about W in the outer sense), P is not among the constituents of W and cannot be deduced from W. Regarding this issue, Morato (2006) distinguishes between the truth's "being generated" and "being evaluated" (p. 224). It is not the case that the constituents of outer truth are bound to be existent in the world of what P is about.
Given this distinction, let us now return to Pollock's example with pictures which, as Pollock believes, works successfully against Plantinga's Anti-Existentialism. Say that picture is a certain state of affairs representing another state of affairs. So, the picture says something true about these states of affairs. But according to Plantinga's anti-existentialist argument, being true entails being existent. If the picture is bound
1 Fine credits this distinction to Arthur Prior (see Prior, 1969).
2 In World Stories andMaximality Morato (2017, p. 268) distinguishes two possible ways of the representation of possible object's nonexistence in w: nonexistence in virtue of direct information about object's nonexistence and nonexistence in virtue of lack of the information about an object. This distinction can be easily compared with two concepts of truth, mentioned above.
to be existent, the picture must be among the objects (more accurately, states of affairs) in the picture. This, of course, is not true. The picture is not a part of itself. Thus, the picture says something true about W, and is not among the constituents of W - the picture does not exist in W, because the picture is not in the picture. For example, let's say that propositions do not exist. One can argue that this proposition says something false because [Propositions do not exist] is itself a proposition, and thus the proposition [Propositions do not exist] is never true. But suppose a possible propositionless world W (for instance, the defenders of God's omnipotence might argue that it is within God's power to create a world without propositions, to destroy all propositions in the actual world, etc.). Now, the proposition [Propositions do not exist] says something true about W. But is the proposition [Propositions do not exist] true being expressed in W? Surely not. Otherwise, this proposition would be self-defeating. So, "Propositions do not exist" is true in W only if W contains no propositions as its constituents, and thus the proposition [Propositions do not exist] is not among the constituents of W. We have that [Propositions do not exist] expresses a truth about W. Pollock now asks: why should we believe that [Propositions do not exist], in order to be able to say something true about W, must be existent in W, - that is, to be a part of W? Similarly, Fine asks: why should we believe that the premise (6) of Plantinga's anti-existentialist argument is true?
As we see, the crucial premise of Pollock's defence of Existentialism is his distinction between S's obtaining and S's existing. In his "Plantinga on Possible Worlds" (Pollock, 1984a), Pollock accepts this distinction and thus rejects Plantinga's Anti-Existentialism. But later, in "The Foundation of Philosophical Semantics", Pollock has become convinced that this distinction is false (more accurately, in this work, Pollock shows the falsity of distinction between the possible world's being actual (actually existent) and being obtained. But possible worlds are
states of affairs. Thus, what goes for S, also goes for W), and Existentialism is false too (because Existentialism relies on this distinction).
Pollock's Anti-Existentialist Argument
Pollock addresses Existentialism with the following challenge. Existentialist believes that states of affairs rigidly depend on their constituent, in the same way as sets depend on their members. Thus, such a state of affairs as Socrates s not existing (S) would not exist if Socrates is not. Consider now the possible world W such that S is a member of W - that is, W is a world that does not include Socrates. W, by definition, is a maximal and consistent state of affairs (that is, for every possible world W and a state of affairs S, either S or the complement of S is included in W, and it is not the case that W could include both S and its complement). So, existentialists suppose that S does not exist if Socrates does not exist. W is a possible world in which S obtains, and Socrates is a constituent of S. Thus, given that W is a state of affairs, Socrates is a constituent of W. Now, existentialists must conclude that if S does not exist if Socrates does not exist, W does not exist too. So, if W (such that W includes S) obtains, W does not exist, and thus "if W obtained then W would not be the actual world" (Pollock, 1984b, p. 99). Thus, Existentialism implies the distinction between W's obtaining and W's being actual. But Pollock argues that this is wrong, and thus Existentialism is inconsistent.
Pollock's argument runs as follows. Suppose that W is a possible world that includes S. Hence, it is necessarily the case that W's obtaining implies S's obtaining. Given that S, by definition, obtains only if Socrates does not exist ("Socrates does not exist" is true only if Socrates does not exist), we have that, necessarily, W's obtaining implies the nonexistence of Socrates (~Ea). But if Socrates is a constituent of S, and W includes S, then Socrates is a constituent of W. Thus, if ~Ea implies ~ES (by Existentialism),
then ~Ea implies ~EW. Hence, necessarily, if W obtains (that is, if S is a member of W), then ~EW - W does not exist. Given that, necessarily, there is the actual world W* among the collection of possible worlds, W* would exist if W obtained [Pollock 1984b: 100]. So, necessarily, if W obtains, then W* obtains, such that W 4 W*. Given that W*, by definition, is necessarily existent, we reach the distinction between W's obtaining and W's existing, and this distinction follows naturally from the metaphysical premises of Existentialism. In order to show that this distinction is incoherent, Pollock introduces the following proof. We have that, necessarily, W's obtaining implies W*'s obtaining, and W* is the existing world. But EW* entails that W* does not include S:
(15) S g W*.
For suppose otherwise - S £ W*. By definition of S, S implies ~Ea. Given that Socrates is a constituent of W*, ~Ea would imply ~EW*. Thus, W's obtaining would imply ~EW*. We have that W's obtaining implies ~Ea (because W is a world in which S obtains), and W implies EW*. So, necessarily, W's obtaining implies (~Ea & EW*). But suppose that S e W*. S implies ~Ea, and thus ~Ea implies ~EW*. So, if W* includes S, then there is a possible world W such that W implies (~Ea & EW* & ~EW*). No contradiction is possible, thus (15) is true - W* does not include S.
But now we have that (15) implies that W*s obtaining implies ~Ea: "However, because it3 would be maximal, W* would have to contain an "enumerative" state of affairs E listing all of the contingent objects existing at W*. E would be a state of affairs of the form being the set of all contingent objects. As Socrates is not among the contingent objects existing at W*, E, and hence also W*, is necessarily such that if it obtains then Socrates does not exist" (Pollock, 1984b, p. 100). Now, ~Ea implies S - if Socrates does not exist, then Socrates's not existing obtains. So, if W* implies ~Ea, then W* implies S (that is, S £
3 That is, W*.
W*), contradicting (15). Thus, by Existentialism, W* includes and precludes S, and so Existentialism is inconsistent.
Objections to Pollock's Anti-Existentialism
As we see, Pollock's Anti-Existentialism differs slightly from Plantinga's Anti-Existentialism: Pollock prefers to talk about states of affairs, while Plantinga talks about propositions. It is intuitively plausible to think that if [Socrates does not exist] is true, then Socrates does not exist and so Socrates^s not existing obtains. However, it is not clear whether such entity as Socrates 's not existing is acceptable for existentialists, and why the existentialist must allow for [Socrates do not exist] to be S (that is, why existentialists should endorse the equivalence of [Socrates does not exist] and S). So, one possible problem with Pollock's Anti-Existentialism is that Pollock uses a much stronger formulation of Existentialism than Plantinga. Pollock's (1984b) formulation of Existentialism is as follows (p. 98):
(E) For any state of affairs S, if [x1,.. ,,xn I a] £ S then, necessarily, S does not exist if any of x1,.,xn fail to exist.
By (E), if we have a set (call it SET) of states of affairs of the form x1, ...,xn having a, then S does not exist without the existence of x1,.,xn, because x1,.,xn are constituents of S. Now, for any xi £ SET, if SET £ S, then □ (xi s implying S £ SET). This formulation crucially depends on Pollock's Closure Under Containment Principle (hereafter CUC) - for any state of affairs S, S £ S* iff S and S* are necessarily such that if S* obtains then S obtains (Pollock, 1984b, p. 105). It follows from CUC that if X is a constituent of S, and S is included in S*, then X is a constituent of S*. Following CUC, Pollock concludes that if Socrates is a constituent of S (Socrates s not existing), and S £ W, then Socrates must be a constituent of W.
Kroon offers the following objection (Kroon, 1989, p. 219). Let SET be a list of Roman philosophers. Then, given that Socrates is not a Roman philosopher, Socrates is not a member of SET and thus does not exist in SET. Pollock believes that states of affairs are necessary existents [98], and thus the fact that Socrates does not exist entails S. By CUC, we have then □ (SET's obtaining implies S's obtaining). But Socrates is a constituent of S, hence, by CUC, Socrates must be a constituent of SET. However, this is obviously false - the only constituents of SET are Roman philosophers, so Socrates is not a constituent of SET. Socrates is a constituent of S. S is included, by CUC, in SET (because SET implies S), so the constituents of SET must be the constituents of S. But it is not the case that Roman philosophers could be the constituents of S because the only constituent of S is Socrates. Thus, CUC fails. Also, Pollock's inference that, necessarily, ~Ea implies ~EW, and thus if W obtains, Socrates does not exist, by Kroon, also fails. Let W be SET. W exists only if every Roman philosopher in SET exists. Thus, the existence of Roman philosophers guarantees the existence of W. Socrates is not a member of SET, and thus Socrates is not included in W. So, Socrates does not exist in W. Given that W possibly obtains, it is possible for W to exist without Soc-rates's existence, contrary to Pollock's inference that necessarily, ~Ea implies ~EW.
Kroon's argument, as opposed to Pollock's argument, tries to block the possibility of anti-existentialist argumentation in terms of states of affairs, that is, by Kroon, the existentialist asserts that the talk about Socrates's nonexistence must be formulated reductively, in terms of propositions. Let us take some xi G SET (say, Cicero). Cicero is a Roman philosopher and thus a constituent of SET. Cicero, of course, is necessarily self-identical (that is, Cicero has a property of being Cicero essentially), and thus Cicero is necessarily non-self-diverse. Say now that Cicero is not Harry Potter. It is necessarily the case that Cicero exemplifies a property of not being Harry
Potter, and thus, as it follows from Pollock's argument, such a state of affairs as Cicero's not being Harry Potter (hereafter HP) must be a member of SET. But if Pollock's argumentation is formulated properly and is adequate to Existentialism, HP could be adequately expressed by a proposition of the form [Cicero is not Harry Potter]. However, if Harry Potter is nothing in W (that is, in SET), the existentialist must conclude that [Cicero is not Harry Potter] is nothing in W, as long as Harry Potter is a constituent of [Cicero is not Harry Potter]. Thus, it is not the case that existentialists could agree to accept the equivalence between HP - Cicero's not being Harry Potter - and [Cicero is not Harry Potter]. Assume that Harry Potter is a constituent of HP. Following Pollock's argument, it means that HP is included in SET, and thus Harry Potter is a constituent of SET. Given Pollock's formulation of CUC, if HP is included in SET, then it is necessarily the case that SET entails HP's obtaining. Now, if HP is necessarily a member of SET, then Harry Potter is necessarily a member of SET. So, if [Cicero is not Harry Potter] is nothing in SET, Cicero is nothing in SET, and thus the existence of SET (that is, Roman philosophers) rigidly depends on the existence of Harry Potter. This conclusion is unacceptable for existentialists. Even if the existentialist agrees that Cicero is essentially not Harry Potter, he disagrees that the fact that Cicero is essentially not Harry Potter necessarily implies HP, because it would mean that Cicero, in W, could not be Cicero without Harry Potter's existence in W. Thus, the existentialist tries to show that S - Socrates's not existing - is not a possibility in a proper sense. The existentialist response to Pollock is that the truth of [Socrates do not exist in W] does not necessarily imply that Socrates's not existing obtains in W. Following the distinction between strong (always true) and weak (never false) propositional truth, the existentialist would reply to Pollock that the proposition's being possible in W does not entail proposition's being possibly true in W if a state of affairs like Socrates's not existing could be
properly translated into the language of propositions. Now, Pollock's Anti-Existentialism faces the same objection as Plantinga's Anti-Existentialism. The core of this objection is that some propositions are possible without being possibly true. For instance, consider the proposition [I do not exist]. I am not a necessary being, so I could have failed to exist. Thus, [I do not exist] is possible. Let us accept now the following principles borrowed from (Williamson, 2002):
(A) Necessarily, if P, then the proposition that P is true.
□ (P ^T(p).
(B) Necessarily, if the proposition that P is true, then the proposition that P exists.
□ (T(p)^3q (q = p).
(C) Necessarily, if the proposition that P exists, and X is a constituent of P, then X exists.
Note that (C) is exactly what Existentialism asserts - P does not exist if X is nonexistent. By applying (A), (B), and (C) to the fact that I am possibly nonexistent, we have the following ar-
4
gument
(a) Possibly, I do not exist (Assumption).
(b) Necessarily, if I do not exist, [I do not exist] is true. (a), (A).
(c) Necessarily, if [I do not exist] is true, [I do not exist] exists. (b), (B).
(d) Necessarily, if [I do not exist] exists, I exist. (c), (C).
(e) Necessarily, if I do not exist, I exist. (b),
(c), (d),
Conditional Proof.
Another consequence of (a) - (e) is what the existentialist wants to demonstrate: some propositions are possible but never possibly true. Consider again the proposition [Propositions do not exist]. What is a truth-condition for [Propositions do not exist]? Of course, it is possible for propositions to fail to exist. But the proposition [Propositions do not exist] is never true in the world in which this proposition is uttered. This truth is true regarding the possible world, but it is not the
4 This argument was first formulated by Williamson (2002).
case that it could be true in this world. The proposition [Propositions do not exist] is possible without being possibly true, and that is what the existentialist can oppose to Pollock and Plantinga. Another variation of this argument, but without using indexicals, was suggested by David5 (2009). Let "Socrates" be the name of Socrates. Then, the inference If,possibly, "Socrates" does not exist, then ["Socrates " does not exist] is possibly true seems to be false, at least for the proponents of Serious Actualism (Plantinga is among them). For if "Socrates" does not exist, but the proposition ["Socrates" does not exist] bears a property of being true (in some possible world), then ["Socrates" does not exist], following Serious Actualism, must exist, and thus "Socrates" must be existent too. But if "Socrates" exists, then ["Socrates" does not exist], contrary to our assumption, cannot be true. So, ["Socrates " does not exist] is possible, but never possibly true. "Socrates" is a contingent entity and thus could have failed to exist, but ["Socrates" does not exist is true] does not express the possible truth - only possible non-falsehood. If so, Plantinga's (6) fails, and Pollock's argument fails too.
In response to this objection, Plantinga (1979) asserts that the distinction between the proposition's being possible and being possibly true is false because the only way for the proposition to be possible is to be possibly true (pp. 155-156). Consider SOC - [[Socrates does not exist] exists and Socrates does not exist]]. Given that Socrates is a constituent of SOC, the existentialist will reply that SOC is impossible. But then, as Plantinga remarks, SOC, by Existentialism, is possibly non-false, and SOC could have failed to be false if Socrates did not exist. If "possibly non-false" is a possibility, then SOC is possible, contradicting Existentialism; and if SOC is a proposition, then SOC is possibly true, if possible. If this claim is true, it allows us to eliminate the main objection to Pollock's Anti-Existentialism
5 See also (Speaks, 2012) for the development of this argument.
by validating the possibility of S, which is the main premise of Pollock's argument.
No Equivalence Between Propositions and States of Affairs
A crucial step of Pollock's argument is his move from [Socrates does not exist] to Socra-tes's not existing obtains. This move could be acceptable for existentialists only if there is equivalence between states of affairs and propositions. Suppose there is such equivalence. Thus, there is a possible Socratesless world W such that if S belongs to W, then P (that is, a proposition [Socrates does not exist] belongs to W. By Pollock's CUC, we have that if S is a member of W then, necessarily, W's obtaining entails P's obtaining (obviously, P's obtaining implies that P is true). Now, the existentialist can easily respond to Pollock that it will be improper to accept that Socrates is a constituent of P - for if P is true, Socrates does not exist, and P, therefore, does not exist too. But the most pressing challenge for Pollock is this - why should we believe that if P belongs to W (suppose, for the sake of argument, that P is possible in W, contrary to the existentialist claim), then the constituent of P must be the constituent of W (by CUC)? This objection was offered by Kroon (Kroon, 1989, p. 217). It is not obvious that the fact, according to which Socrates does not exist in W, could be appropriately characterized by P's obtaining in W. The existentialist, of course, will simply reject the idea that P expresses truth in W (that is, an inner truth about Socrates); at best, the existentialist will assume that P is a truth ofW (that is, P is true at W). But the latter does not entail that P must exist in W in order to be able to express the truth about W. Existentialists like (Fine, 1985), (Kroon, 1989), and (Prior, 1969) disagree that P's being true of W necessarily implies P's existence in W (see also Turner, 2005; Adams, 1981; Bealer, 1998). But if, possibly, P is true at W, and does not exist in W, then in W, if we have the truth of P, we do not have S. Thus, Pollock's
crucial move becomes unacceptable for existentialists. Of course, the inference If [Socrates does not exist], then Socrates does not exist, and so the nonexistence of Socrates obtains seems to be plausible, but in fact, it is not. Fine argues convincingly (Fine 2005) that the inferences like Necessarily, P, if the proposition that P is true, and Necessarily, P is true if P are not always true. Also, the arguments of David (2009), Speaks (2012), and Williamson (2002) are other counterexamples to Pollock's Anti-Existentialism, which are very close to Fine's argument. Consider the propositions like [I do not exist] or [Propositions do not exist]. Following Fine, these propositions are never true in W being expressed in W. Thus, it is not the case that my nonexistence or proposition's not existing obtain in W, and so Fine's line of reasoning allows us to reject the essential step of Pollock's argument. Again, consider [I do not exist] from Williamson's point of view. Williamson argues that such a proposition is true if we accept Necessitism - the view that necessarily, everything necessarily exists. However, it is obvious that Williamson's Necessitism is incompatible with Anti-Existentialism (both Plantinga's and Pollock's) because they argue that it is possible for an object X not to exist if the proposition [X does not exist] is true. Thus, both Fine's Contingentism and Williamson's Necessitism pose a serious challenge for Pollock's argument.
From the counterexamples above, we see that the main existentialist objection to Pollock's argument is as follows. If S is equivalent to P, then this equivalence violates the constituent principle (because Socrates, as a constituent of P, is not a constituent of W). But it is not the case that P's being true of W necessarily implies P's existence in W, and so P is not identical to S. Thus, Pollock's argument fails since this identity is a necessary premise of Pollock's Anti-Existentialism. This is the argument of Fine, and the arguments of Kroon, David, and Speaks are, in general, instances of Fine's argument. But this argument is based on the distinction between two types of
truth, and it is not clear whether we should accept this argument, especially if we agree with Plantinga's (1979) argument in De Essentia that this distinction is self-defeating (pp. 155-156). However, we can derive the same result without appealing to the distinction between inner and outer truth.
Our argument is this. Pollock accepts the equivalence between propositions and states of affairs. Now, let us accept the equivalence between states of affairs and properties - say that S, Socrates not existing, is equivalent to Socrates exemplifies F - the property of not existing. It is well-known that some properties exemplify themselves, and some do not. For instance, consider a property of being property. Every property has a property of being a property. Thus, a property of being property is itself a property, and so it exemplifies itself. On the other hand, consider the property of being red. The property of being red is not red and thus does not exemplify itself. Now, what kind of property is a property of not existing? If Socrates exemplifies the property of not existing, Socrates exemplifies something; thus, the property of not existing is something existent. Thus, F does not exemplify itself. We have that Socrates exemplifies F if S obtains, and F is a property that does not exemplify itself. But then we can derive the following conclusion:
(16) Necessarily, if F does not exemplify itself, then F exemplifies the property of non-self-exemplification
If (16) is true, we can conclude that if F exemplifies the property of non-self-exemplification, then there is such a property as F's non-self-exemplification. But if F exemplifies F's non-self-exemplification, then F does not exemplify itself - that is, F does not exemplify F's non-self-exemplification. Thus, we have a contradiction -given (16), necessarily, F does not exemplify F's non-self-exemplification only if F exemplifies F's non-self-exemplification. It is well-known that the property of non-self-exemplification "is at best extremely problematic" (Plantinga &
Grim, 1993, p. 275); and it seems to be that "we can avoid the contradiction by claiming that there is no such property as non-self-exemplification" (Stephanou, 2007, p. 226).
What is a connection between our reductio of F's non-self-exemplification and Pollock's argument? Suppose we have such a proposition as [F does not exemplify itself]. This proposition is true in virtue of the fact that F does not exemplify itself. Now, the crucial move of Pollock's argument is as follows: if [F does not exemplify itself] is true, then there is such property as F's non-self-exemplification, and then, given the presupposed equivalence between properties and states of affairs, there is such state of affairs F's non-self-exemplification. But it follows from the argument above that there is no such property as F's non-self-exemplification, and thus there is no such state of affairs as F's non-self-exemplification. Even if the proposition [F does not exemplify itself] is true, it is not the case that the truth of this proposition implies the obtaining of F's non-self-exemplification. It means that Pollock's proof (if our argument is correct) has a false instance. Within our counterexample, we do not need to appeal to Fine's distinction between inner and outer truth - of course, [F does not exemplify itself] is true in W, but in W, there is no F's non-self-exemplification.
Conclusion. Pollock's Anti-Existentialism and Modern Existentialism
As we see, the premises of Pollock's argument are, in general, not valid. However, this argument, I believe, can be easily reformulated in terms of classical propositional Existentialism, and in this form, Pollock's solution looks acceptable, more or less. For example, let us compare this argument with Williamson's solution. Williamson (2002) proposes the following challenge for classical Existentialism - either [I do not exist] exists if I do not exist, and so I exist if I do not exist, or it is not the case that I could have failed to exist. By Williamson, we do not have
problems with sentences like [I do not exist] if we accept Necessitism - a thesis that, necessarily, everything necessarily exists. However, Ne-cessitism is a too high price to pay for the possibility to save Existentialism. If we have, as Williamson believes, a choice between Necessitism or Anti-Existentialism, we think it would be plausible to reject Existentialism and accept Anti-Existentialism. Most modern philosophers do not build up their Existentialism on the neces-sitist fundament. Also, some existentialists think that Necessitism is, in fact, a false challenge for classical propositional Existentialism because Williamson's argumentation for Necessitist Existentialism can be blocked by appealing to the distinction of truth in W and truth at W (Morato, 2006). Even if we do not agree with this solution (for obvious reasons), we can say that Williamson's Necessitist Existentialism is much closer to Anti-Existentialism than to Classical Proposi-tional Existentialism. However, for the sake of ideological parsimony, philosophers (who are sceptical about Classical Existentialism) do not need to appeal for Williamson's radical position because we already have Pollock's moderate solution. Thus, Williamson's Necessitism is an ally of Pollock's Abstractionist Anti-Existentialism. Some philosophers try to combine Williamson's Necessitism with Plantinga's (and particularly Pollock's one) Contingentism (Jacinto, 2016) but without endorsing Anti-Existentialism (both Plantinga's and Pollock's one). Thus, the necessitist line of argumentation for and against Existentialism is not very popular among contemporary existentialists
Pollock's criticism of Existentialism also had a strict impact on Moderate Existentialism. Moderate existentialists (for instance, (Forbes, 1989)) believe that only positive existential statements have constituents, while negative existential statements lack them. Also, Pollock's argumentation for Anti-Existentialism contributed to the emergence of a revised form of Existentialism that does not presuppose the principle that propositions have constituents (Stalnaker, Stephanou,
Williamson).
In the light of Pollock's argument, several philosophers introduced a revised form of the argument concerning the distinction between truth in W and truth at W. One of the most notable attempts regarding this issue is the argument of Speaks (2012). Speaks accepts Fine's distinction but disagrees with Fine that truth at W expresses an outer truth. Thus, Speaks rejects the idea that if P is true at (or truth of) W, P would be true in W had W be actualized. Rather, Speaks tries to show that the difference between two types of truths must be understood in terms of context and circumstance, without appealing to such "transcendental" notions as "outer truth".
Also, Pollock's argument has sparked discussions concerning the question of what can serve as an identity criterion for different possible worlds. Pollock argues that the possible (Socra-tesless) world W, being obtained, necessarily implies the existence of the actual world W*, and thus W must share with W* its constituents. Following Fine, Kroon, the most prominent contemporary critic of Pollock's argument, argues that existentialists must accept the more strong version of logical equivalence between states of affairs than Pollock's identity-criterion - the existentialist could accept that "X1 and X2 are identical just when X1 and X2 are logically equivalent and share all their individual constituents (and hence necessarily co-exist)" (Kroon, 1989, p. 221). This problem is widely discussed in contemporary debates, in particular about the principle of Existence Requirement and the proposal of Takashi Yagisawa on how to reject this principle (see Yagisawa, 2010, p. 59; Caplan, 2007). Pollock's argument also contributed to the development of discussions regarding the following issue: what is for propositions and states of affairs to be identical? Pollock argues that if S is a member of W, then W and W* have common constituents - that is, the constituents of S. But if S is equivalent to the proposition P - [Socrates does not exist] - how could P be nonexistent in the world in which S obtains? This question is
part of a broader debate about the nature of propositions and states of affairs, and Pollock, without doubt, greatly contributed to these issues.
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