An Argument for Existentialism

Abstract

Existentialism about propositions is the view that a proposition expressed in a sentence containing a nonempty name or indexical depends ontologically on the referent of the name or indexical: the proposition could not exist if the referent did not. The paper focuses on names. It discusses some arguments for existentialism and then presents a novel one. That argument does not presuppose that propositions have constituents, and it could be accepted by those who hold broadly Fregean views about names. It shows that, for example, if Aristotle had not existed, no sentence could have meant that Aristotle is a philosopher. The paper also touches on the consequences of existentialism.

1 Introduction

Following A. Plantinga’s terminology, we can say that existentialism about propositions is the view that a proposition expressed in a sentence containing a nonempty name or indexical depends ontologically on the referent of the name or indexical: the proposition could not exist if the referent did not. Let us focus on names. The idea is that if, for example, Aristotle had not existed, then inevitably the proposition that Aristotle is a philosopher would not exist either.

Actually, Plantinga (1983, pp. 2–3) characterizes existentialism about propositions as the thesis that a singular proposition about an object depends ontologically on it, and he defines a singular proposition as one that makes a direct reference to an object. He counts various sentences containing a nonempty name as expressing singular propositions. However, as we can see in (Plantinga 1974, pp. 136–148), he considers that sentences like “Aristotle existed” and “Aristotle did not exist” sometimes express propositions that are not singular. It is better to characterize existentialism without using theoretical terms, such as “direct reference”. Otherwise, it remains unclear which propositions it concerns, since it is controversial which propositions satisfy the theoretical terms.

On the other hand, if we characterize existentialism in terms of sentences containing a nonempty name or indexical, we ought to allow for certain exceptions. One is sentences in which a name occurs within quotation marks. The proposition that “Aristotle” consists of nine letters does not require the existence of Aristotle. Another exception is names within complex demonstratives. The sentence “That female friend of Aristotle’s is a philosopher”, combined with a context in which the person demonstrated is indeed a female friend of Aristotle’s, expresses a proposition that does not seem to require the existence of Aristotle. For it seems to be the proposition that she is a philosopher, since to know that that female friend of Aristotle’s is a philosopher is just to know that she is a philosopher. That proposition could exist even if Aristotle had not.¹ So, throughout this paper, when I talk about sentences or predicates containing a name or indexical, I mean those containing a name or indexical outside devices of quotation or complex demonstratives. The exceptions should not obscure the overall picture.

One sometimes derives existentialism from the premise that propositions have constituents and, in particular, if a proposition is expressed in a sentence that contains a nonempty name, then the referent of the name is a constituent of the proposition. If the referent did not exist, one of the components that give the proposition its identity would be missing, so the proposition would not exist either; for example, see (Menzel 1993, pp. 113–114). This argument relies on a Russellian conception of propositions. It presupposes that concrete things, like Aristotle or the Taj Mahal, are constituents of propositions. Aristotle himself is a component of the proposition that Aristotle is a philosopher, and both the Taj Mahal and India enter into the proposition that the Taj Mahal is in India. So one invites the objection, voiced in a letter from G. Frege (1988a) to B. Russell, that Mont Blanc, with its snowfields, cannot be a component of an abstract object, such as the proposition that Mont Blanc is more than 4000 metres high.² It would be better for existentialism if we could support it without presupposing that concrete things are constituents of propositions and, indeed, without even presupposing that propositions have constituents. The aim of this paper is to improve on arguments for existentialism which lack such presuppositions. One improvement will be that the reasoning is acceptable to those who hold broadly Fregean views about names.³

2 Adams, Williamson and Stalnaker

In the literature we can find arguments which do not presuppose that propositions have constituents. Let P be the proposition that Aristotle is a philosopher.⁴ Here is an argument suggested in (Adams 1981, p. 12). P is a singular proposition about Aristotle; that is, it is a proposition that involves or refers to Aristotle directly, and not by way of his qualitative properties or his relations to another thing. If q is a singular proposition about x, its relation to x (involving or referring to it directly) is part of what makes q what it is, so it is essential to the proposition. In other words, it is necessarily the case that if q exists, it has that relation to x. But it is also necessarily the case that if x bears that relation, then x exists. This follows from a variant of the metaphysical principle known as serious actualism. Serious actualism says that, for any entity x and any property φ, it could not have been that x exemplified φ but did not exist. Its variant about relations is the principle that, for any entity x and any relation R, it could not have been that x bore R but did not exist. Hence, it is necessarily the case that if P exists, Aristotle exists, too.

That argument would not be acceptable to those who hold Fregean views about names. They would say that P does not involve Aristotle directly. By Fregean lights, if a name refers to an object x, it does so because it has a sense and x is the referent determined by that sense. Similarly, if a proposition q is expressed in a sentence containing a name, the proposition is related in the first place to the name’s sense. That sense is a constituent of q or, at any rate, it characterizes q in that q is one of the propositions which, if they are to be conveyed by means of a sentence, require that the sentence should give expression to that sense. Then if q involves x, it does so because x is the referent determined by a sense to which q bears that relation. Reference is mediated by sense.

Even if we do not espouse a Fregean semantics of names, we can see that Adams’s concept of direct reference does not apply to names whose reference is fixed by means of a description, such as the name “Julius” introduced in (Evans 1985a). We stipulate that “Julius” will be a name of the person who invented the zip, whoever that person may have been, and we use the name accordingly. I take it that there was indeed a unique person who invented the zip. Then, the name does not refer to Julius directly but by way of his relation to the zip, and so do e.g. the sentence “Julius is an American” and the proposition that Julius is an American. Thus the argument suggested by Adams does not extend to propositions that are expressed in sentences containing such descriptive names.⁵

Here is another argument for existentialism which does not presuppose that propositions have constituents. It is suggested in (Williamson 2002, pp. 240–242). Necessarily, if P exists then P is the proposition that Aristotle is a philosopher. But to be the proposition that Aristotle is a philosopher is to have a certain relation to Aristotle. So there is a relation R such that, necessarily, if P is the proposition that Aristotle is a philosopher then P has R to Aristotle. By the variant of serious actualism, it is the case for every relation R that, necessarily, if Aristotle bears R then Aristotle exists. Hence, it is necessarily the case that if P exists, Aristotle exists, too.

What is the relation between P and Aristotle which makes the former be the proposition that Aristotle is a philosopher? The reply that suggests itself is that it is the relation we express when we say “P is the proposition that Aristotle is a philosopher”, “Q is the proposition that Plato is a philosopher”, “N is the proposition that Williamson is a philosopher”, and the like. The possibility of this reply is what makes it intuitively appealing to claim that to be the proposition that Aristotle is a philosopher is to have a certain relation to Aristotle. But the reply will not be acceptable to those who hold Fregean views about names. For it presupposes that “… is the proposition that—is a philosopher” expresses a relation.

If the phrase in question expresses a relation, then in either of its argument-places we can interchange names that refer to the same thing. Any two sentences that result from the phrase by filling in the argument-places with pairwise coreferential names are both true or both false, depending on whether the proposition and the person referred to stand or do not stand in the relation expressed by “… is the proposition that—is a philosopher”. But Fregeans will find counterexamples. According to those who consider that the names “Cicero” and “Tully” differ in sense, like “Hesperus” and “Phosphorus”, the proposition that Cicero is a philosopher is other than the proposition that Tully is a philosopher. So, for an appropriate choice of M, the sentence “M is the proposition that Cicero is a philosopher” is true, but “M is the proposition that Tully is a philosopher” is false.

Again, if “… is the proposition that—is a philosopher” expresses a relation, its argument-places are open to existential generalization. For if a sentence of the form “aRb” is true, where “a” and “b” are names, then those names are not empty. As we shall see, that principle has been contested, but at least prima facie it is very plausible. Fregeans will find examples showing that if existential generalization is accepted as a criterion, the phrase “… is the proposition that—is a philosopher” expresses no relation. Those who consider that the name “Rumpelstiltskin” is empty, instead of referring to a character from a fairy tale, will say that, for an appropriate choice of L, the sentence “L is the proposition that Rumpelstiltskin is a philosopher” is true, but “∃x (L is the proposition that x is a philosopher)” is false.⁶

Yet another argument for existentialism which does not presuppose that propositions have constituents is offered in (Stalnaker 2010, pp. 22–23). If Saul Kripke had seven sons, someone x would be his seventh son, and a proposition would be the proposition that x is Kripke’s seventh son. But, given that nothing actually exists that, in the possibility envisaged, would be Kripke’s seventh son, there is no such proposition in fact. For there is no truth-condition that might individuate it, and (according to Stalnaker) propositions are individuated by their truth-conditions. In the absence of the relevant object, we cannot distinguish such a proposition from others of the form “… is Kripke’s seventh son”. Similarly, if Aristotle had not existed, there would be no proposition to the effect that he is a philosopher, so P would not exist.⁷

In reality, we can up to a point distinguish the proposition about the seventh son. Let w be a possible world in which Kripke has seven sons. Stalnaker accepts that there are possible worlds in a sense in which they are properties or propositions. We need to use a modal operator “in w”, which allows us to state how things would be if a certain world obtained (that is, if it were an instantiated property or a true proposition). Using the operator, we can say that in w there is something that is Kripke’s seventh son, but (in fact) there is nothing that, in w, is Kripke’s seventh son. We also need an actuality operator, “@” (“in fact”), which allows us to talk about the actual world even when we are talking within the scope of another modal operator. Then, we may say about a proposition p that

• (1) in w ∃x (x is Kripke’s seventh son ∧ @ (p is the proposition that x is Kripke’s seventh son)).

I believe that there is no such proposition as we describe in (1), but if there is, we have individuated it, relatively to a choice of the possible world w. For there cannot be two propositions satisfying (1). In no possible world are there two people each of whom is Kripke’s seventh son. Thus if a proposition q and a proposition r satisfy (1), then q and r have the same content and so are identical. We have also identified the truth-condition of any such proposition, although we did that relatively to a choice of w. (The identification is relative, since there are many possible worlds in which Kripke has seven sons, and I did not specify which one is w.)

Things may get more difficult if we change the example. Let k be a kind of subatomic particles, and suppose that, in w, there are many particles of that kind and they are qualitatively identical. Also assume that nothing actually exists that, in w, is a particle of kind k. Then, we may say about a proposition p that

• (2) in w ∃x (x is a particle of kind k ∧ @ (p is the proposition that x has electric charge)).

Ιf there is at least one proposition satisfying (2), there are more than one. But then, we have not individuated any one of them. Nor have we identified its truth-condition, since we have not specified what exactly it describes as having electric charge.

Thus, in an argument not too dissimilar from Stalnaker’s, Williamson (2013, pp. 291–293) challenges his opponents to explain how a proposition could be necessary and sufficient for him to exist (or for him not to exist) if he did not exist. And he presses the challenge particularly when there are qualitatively identical particulars z and u and one needs to explain how the proposition that z exists could differ from the proposition that u exists if neither z nor u existed.

However, it is not clear that a proposition satisfying (2) lacks a truth-condition individuating it. If there are many such propositions, we can say that each one of them has a different truth-condition. If one thinks of a truth-condition as a state of affairs, involving one or more objects and a property or relation, then the absence of the relevant objects is a problem. But otherwise, there is no difficulty with considering that the difference between the truth-conditions is modal: in w, they concern distinct particles. I prefer to say that what individuates propositions is their content. But again it may be that we cannot state the difference in content between two propositions q and r except in modal terms: in w (there are distinct things x and y, which do not exist in fact, such that @ (q is the proposition that x has electric charge, while r is the proposition that y has electric charge)). This difference is modal, since it is to do with what objects there would be if w obtained. Nonetheless, it is an actual difference, for it is actually the case that q and r are as we described them. And perhaps nothing makes it the case that the two propositions are that way; this may just be their identity. Likewise, if z and u are two actual identical twins and w′ is a possible world in which they do not exist, it is not clear why we should not consider that in w′ (there are distinct propositions q and r, where q is the proposition that z is a philosopher, while r is the proposition that u is a philosopher).⁸

3 A New Argument

We can argue for existentialism differently. Suppose it is possible that Aristotle should not exist but P should exist. The possibility here is metaphysical, or broadly logical, and it does not matter that our example is a simple predication, P; it could be any proposition expressed in a sentence containing a nonempty name. Propositions have their content essentially. So P could not have existed without being the proposition that Aristotle is a philosopher (it could not have been, say, the proposition that Plato is a comic poet). Then, it is possible that Aristotle should not exist, but a proposition should be the proposition that Aristotle is a philosopher.

To proceed, we need the following premise:

• (3) If the existence of Aristotle is a necessary condition in order for a sentence to mean that Aristotle is a philosopher, it is also a necessary condition in order for a proposition to be the proposition that Aristotle is a philosopher.

More generally, if a condition that does not concern linguistic or mental entities is necessary in order for a sentence to mean that p, it is also necessary in order for a proposition to be the proposition that p. The proposition that p and the sentences meaning that p have the same content; in other words, the way that the proposition represents things as being is the same as the way that the sentences represent them as being. There could have been a great variety of sentences. Actual sentences consist of sounds, letters or gestures (in sign language). It is possible that sentences should consist of material objects, used like words, or of any kind of symbol. So if a sentence is to have some content, there need not be any particular medium. Of course, there must be language and any mental states that are necessary for the existence of language. But if a condition that does not concern linguistic or mental entities is necessary in order for a sentence to have a certain content, then its necessity will be due to the content. Thus the condition will be necessary in order for any representation to have that content, so it will be necessary for a proposition, too.⁹

Further, if Aristotle’s existence is necessary in order for there to be a sentence meaning that p, but not in order for there to be a proposition to the effect that p, this difference will be due to the fact that, unlike propositions, sentences are linguistic items and do not have their content essentially. But then, presumably, Aristotle’s existence is not necessary in order for there to be a thought or a belief to the effect that p. For the thoughts and beliefs that I am talking about here are mental state-tokens, and mental states, whether types or tokens, have their content essentially. (Take the fear I now have of missing a certain deadline. It could not be e.g. a fear of being bitten by a snake. It is another issue that I might now have a different fear instead.) If, however, it is possible that Aristotle should not exist, but some intelligent beings should be thinking that p, then it is possible that Aristotle should not exist and such beings should put their thoughts into words and thus produce a sentence meaning that p. (They could introduce new words if need be.)¹⁰

One can also see (3) as follows. Assume that the existence of Aristotle is not necessary in order for a proposition to be the proposition that p. Then, there could be such a proposition while Aristotle never existed. The presence of a proposition makes it available to be grasped, irrespective of whether anyone really does so. So if there could be a proposition to the effect that p while Aristotle never existed, then there could be, even without Aristotle, both a proposition to the effect that p and intelligent beings who somehow had mental access to it and so grasped it and expressed it in a sentence. That sentence would mean that p. Thus, if our assumption is correct, the existence of Aristotle is not necessary in order for a sentence to have that meaning.

By saying that a proposition is available to be grasped, I mean that if it is not grasped, that is so just because there are no subjects who turn their attention to it and are mentally competent and willing to grasp it. I will similarly talk about something available to be believed. If a proposition could exist without Aristotle, but could not be grasped without him, then the absence of Aristotle would be a metaphysical obstacle hindering access to it. So the reason it was not grasped would not lie solely in the nonexistence of intelligent beings or in the mental features of those that existed.

The idea that, necessarily, a proposition is something available to be grasped is buttressed by certain considerations about propositions. Although there are many views about them, it is reasonable to accept that, of necessity, a proposition, whatever else it may be, is a piece of information about how things are. A piece of information is something available to be believed. Of course, there may be no one who has the kind and degree of intelligence required for forming that belief. Or the information may be absurd, so that no one is willing to believe it. In such cases, the information is not believed, but that is due to the lack of appropriate subjects, not to the unavailability of the object. The notion of information is an epistemic concept. The idea that some information is precluded from being known or at least believed seems contradictory. It is like the idea that some merchandise is permanently unavailable for purchase. And of course if a proposition were available to believe, it would have to be available to grasp.¹¹

Now, by contraposing (3), we infer that if it is possible that Aristotle should not exist but a proposition should be the proposition that Aristotle is a philosopher, it is also possible that Aristotle should not exist but a sentence should mean that Aristotle is a philosopher. Hence, given our earlier supposition,

• (4) it is possible that Aristotle should not exist, but a sentence should mean that Aristotle is a philosopher.

The rest of the argument will be a reductio of (4). Even if in the end it is possible for P to exist without Aristotle, at least (4) is false. Τhe nonexistence of Aristotle would preclude a certain range of meanings. If he had not existed, no sentence could have had the same meaning as a sentence containing the name “Aristotle” has in fact. If some actually existing objects were missing, the representational capability of any language would be correspondingly constrained. It is significant that that can be shown in a way that Fregeans can accept.

It seems that if a sentence meant that Aristotle is a philosopher, it would inevitably contain a singular term having the same meaning as the name “Aristotle” has in fact. I think that that statement is roughly right, but if we are to take into account the variety of languages that could have existed, we must modify it. The meaning of a word is its contribution to determining what the sentences mean in which it occurs. (And it has more than one meaning if it sometimes makes one contribution and sometimes another.) If that is our concept of meaning for words, or generally for subsentential expressions, it can hardly be doubted that words, including names, have meanings, but there is ample room for disagreement about what those meanings are. Fregeans may take the meanings of nonindexical expressions to be Fregean senses. Direct-reference theorists may consider that the meaning of a nonempty name consists simply in referring to a particular object.

If a sentence meant that Aristotle is a philosopher, it would inevitably have a component which contributed the meaning that “Aristotle” has in fact. With no such component, it would not be possible for a sentence to mean what we are supposing. The component might very well be a name. Perhaps it could be a rigid definite description. It might also be an expression that combined the meanings that two words have in fact in the sentence “Aristotle is a philosopher”; for instance, it might be a word that corresponded to our phrase “Aristotle is” and was complemented by a word corresponding to our “a philosopher”. We can imagine more exotic possibilities, but at least the following is right:

• (5) It is necessarily the case that if a sentence means that Aristotle is a philosopher, then it contains an expression that has a meaning which either is the same as the meaning that “Aristotle” has in fact or includes, as one of its aspects, the meaning that “Aristotle” has in fact.¹²

Now,

• (6) it is necessarily the case that if an expression has the meaning that “Aristotle” has in fact, it refers to Aristotle.

We need not here presuppose that the meaning of a nonempty name consists in referring to a particular object. We need not even assume that the reference of a nonempty name is an aspect of its meaning. The point is just that, in the case of nonempty names, there is a close connection between meaning and reference, so that we could not have the former without the latter.

In order to see that there is such a connection, suppose it is possible that a term should have the same meaning as “Aristotle” has in fact but should not refer to Aristotle. Then, it is also possible that someone should use such a term in the argument-place of a monadic predicate, say a predicate having the same meaning as “is wise” has in fact. It is necessarily the case that if someone uses a term having the meaning that “Aristotle” has in fact in the argument-place of a predicate having the meaning that “is wise” has in fact, then she says that Aristotle is wise. For if someone combined such a term with such a predicate, the result could not but mean that Aristotle is wise, so the speaker would have said exactly that. It is also necessarily the case that if someone uses a term that does not refer to Aristotle in the argument-place of a predicate having the meaning that “is wise” has in fact, then she does not attribute wisdom, or anything else, to Aristotle. There is no object to which one could attribute a property without reference to the object. Hence, it is possible that someone should say that Aristotle is wise, but should not attribute wisdom, or anything else, to Aristotle. But, in reality, this is not possible. To say that Aristotle is wise is to ascribe wisdom to him; it involves connecting the property with him. So it is not possible that a term should have the same meaning as “Aristotle” has in fact but should not refer to Aristotle.

We can reason similarly about “Julius”. If it is possible that a term should have the same meaning as “Julius” has in fact but should not refer to Julius, then it is possible that someone should say that Julius is clever without ascribing cleverness, or anything else, to Julius. That is impossible, so having the actual meaning of “Julius” requires referring to Julius. Indeed, we can extend the reasoning. “Julius”, like all nonempty names, is a rigid designator; whoever Julius was in fact, it could not have been that someone else was Julius. Hence, having the actual meaning of “Julius” requires referring to him. And this is independent of what exactly is the actual meaning of the name. (Consequently, if one introduced the name through the same stipulation as we did, but someone else had invented the zip, the meaning of the name would be different, since the reference would be different.)

This close connection between the meaning of “Aristotle” and its reference would inevitably persist if we did not have an expression with that meaning but one with a richer meaning, such as a word that corresponded to our phrase “Aristotle is”. Thus

• (7) it is necessarily the case that if an expression e has a meaning one of whose aspects is the meaning that “Aristotle” has in fact, then e refers to Aristotle.

Further,

• (8) it is necessarily the case that if an expression refers to Aristotle, then Aristotle exists.

Referring to something requires that it exist, though possibly not at the same time that the reference takes place. Referring is a relation, so if Aristotle could be referred to without existing, he could enter into that relation without existing. But it follows from the variant of serious actualism about relations that he could not. Serious actualism is controversial, but (as we have seen) it, or rather its variant about relations, is also presupposed in previous arguments for existentialism.¹³ Even if one has doubts about serious actualism, I think that the case of referring is clear. Referring is like pointing. If something did not exist, no one would be able to point at it.

Admittedly, there is also a different reading of “refer”, on which the verb creates a kind of intensional context just like “talk about”. On that reading, we can refer to golden mountains, although no such mountain exists, just as we can talk about golden mountains. The intensionality of “talk about” becomes apparent from the fact that one can talk about dragons without talking about imps, although the predicates “dragon” and “imp” have the same extension (the null set). We can also talk about great philosophers without talking about any particular great philosopher. Verbs creating that kind of context do not express relations. If “talk about” expressed a relation, then talking about a dragon would amount to being related to such a thing and so would require the existence of one. For we cannot be related to a dragon unless there is one. That reading of “refer” is not frequent in philosophy and anyway is not what is intended in this paper.¹⁴

On the other hand, some philosophers who use “refer” to express a relation would reject (8). So N. Salmon (2005) introduced “Noman” as a name of the possible individual who would have developed from the union of a particular male sperm cell S and a particular ovum E if S had fertilized E in the normal manner. According to Salmon (2005, p. 46), “Noman” refers to Noman although Noman does not exist. If so, then presumably it is possible that a name should refer to Aristotle but he should not exist. A. Bacon (2013) makes similar claims about mythological and fictional names, such as “Pegasus” and “Sherlock Holmes”. In his view, “Pegasus” refers only to Pegasus although Pegasus does not exist. The problem here is that, since Noman does not exist, there is nothing that “Noman” refers to, so the name is empty. On the other hand, if “Noman” refers to Noman, then it refers. Likewise, according to Bacon, “Pegasus” is an empty name, but it refers. I find the idea of an empty but referring name hard to accept.

Bacon’s view stems from an effort to explain how intersubstituting empty names can change truth-value. He believes that this can happen in simple predications, formed by filling in the argument-places of a predicate with names. Indeed, if “a is F” and “b is F” differ in truth-value, the names “a” and “b” must differ in reference. So if they are both empty, there must be something more to their reference than the fact that they refer to nothing. However, many of Bacon’s examples are not simple predications, for they involve verbs like “talk about” or other intensional contexts. Let us assume that the names “Pegasus” and “Zeus” are empty (and so do not refer to entities of a special kind, mythological characters). Still, they differ in meaning, since they are evidently not synonymous. Say that the sentences “John is talking about Pegasus” and “John is talking about Zeus” are true and false respectively. Then, instead of postulating a difference in reference between the names, we can explain the divergent truth-values by invoking the difference in meaning and considering that, in the case of empty names, meaning is not identical with reference. We are accustomed to the idea that, in an intensional context, intersubstituting expressions that have the same reference but are not synonymous may change truth-value.

The point is that the theoretical pressure towards a view such as Bacon’s—and so away from accepting (8)—is not as great as it may seem. (8), on the other hand, both carries considerable intuitive force on its own and follows from a principle, the variant of serious actualism about relations, to which many of us subscribe.

(6) and (8) show it to be necessarily the case that if an expression has the same meaning as “Aristotle” has in fact, then Aristotle exists. Having the actual meaning of “Aristotle” requires the existence of the referent.¹⁵ Those who hold broadly Fregean views about names may accept that any nonempty name has such a meaning or sense. It will be what Evans (1985b, p. 302) describes as an existence-dependent Fregean sense.¹⁶

(4)–(8) imply that it is possible that Aristotle should both exist and not exist. But of course that is impossible. So (4) is wrong, as is the supposition on which (4) was based. It is not possible that Aristotle should not exist but P should. It is necessarily the case that if P exists, so does Aristotle. And this generalizes to any proposition expressed in a sentence containing a nonempty name.

Indeed, the argument can be extended to existentialism about concepts. This is the view that a concept expressed in a predicate containing a nonempty name or indexical depends ontologically on the referent of the name or indexical. Focusing once more on names, we may consider the concept, Q, of reading Aristotle’s works, and suppose it possible that Aristotle should not exist but Q should. The analogue of (3) here is the claim that if Aristotle’s existence is a necessary condition in order for a predicate F to have such a meaning that to call someone F is to describe them as reading Aristotle’s works, it is also a necessary condition in order for a concept to be the concept of reading Aristotle’s works. That claim can be supported in the same way as (3), since concepts are (mental) representations. The rest of the reasoning proceeds as before, and we conclude that, necessarily, if Q exists then so does Aristotle.

I have talked about the meaning that “Aristotle” has in fact. However, those who hold Fregean views about names may follow (Frege 1988b, p. 41) and consider that, as regards names, we do not all speak the same language, so “Aristotle” may differ in meaning from speaker to speaker. Adopting that position requires a small modification of the argument at some points where the name is mentioned. The phrase “the meaning that ‘Aristotle’ has in fact” in (5), (6) and (7) should become “the meaning that ‘Aristotle’ has in fact in my idiolect”. There is no reason to modify the points where the name is used. If we do not speak the same language, then whenever I used “Aristotle”, it had the meaning it has in my idiolect, and whenever I said “the proposition that Aristotle is a philosopher”, the reference was to the proposition that the sentence “Aristotle is a philosopher” expresses in my idiolect. Thus modified, the argument shows that proposition to be ontologically dependent on Aristotle, but of course anyone can repeat the argument referring to the proposition that “Aristotle is a philosopher” expresses in their idiolect. So all those propositions depend on Aristotle.¹⁷

4 The Consequences of Existentialism

It is well known that existentialism about propositions has some significant consequences when combined with the contingentist view that ordinary objects and persons could have failed to exist. One consequence is that many propositions, such as the proposition that Rome is a capital city, are also contingent entities. The proposition in question would not exist if Rome did not. Another consequence is that the schema.

Necessarily, p iff the proposition that p is true

has many false instances (Fine 2005, p. 149). We get one by replacing “p” with the sentence “Aristotle is not a philosopher”. If Aristotle had not existed, Aristotle would not be a philosopher; philosophers would not include him. But also, as is shown by an argument similar to the one we have seen about P, there would be no such thing as the proposition that Aristotle is not a philosopher. So it would not be the case that the proposition that Aristotle is not a philosopher was true. Thus it could have been that Aristotle was not a philosopher, yet it was not the case that the proposition that Aristotle is not a philosopher was true.

It is perhaps less well known that existentialism, when combined with contingentism and serious actualism, requires a modification of the usual definition of “valid argument”. Let us think of arguments as made up of propositions rather than sentences. According to the usual definition, an argument is valid iff it is impossible for the premises to be true but the conclusion false. Let N be the proposition that Aristotle does not exist. By existentialism and serious actualism, it is impossible for N to be true. For if it were true, it would exist (by serious actualism), so Aristotle would both exist and not exist. Thus, according to the usual definition of validity, every argument in which N is a premise is valid. But if we are contingentists, we certainly do not want to say that. It is easy to modify the definition so as to avoid the problem. The premises of an argument jointly say that things are a certain way, and the conclusion also says that things are a certain way. We can define the argument as valid iff it is impossible that things should be the former way without being the latter (cf. Williamson 2013, p. 298, fn. 28). Then contingentists can declare that e.g. the argument expressed in “Aristotle does not exist, hence Aristotle exists” is invalid.¹⁸