Toward a New Theory of Moderate Contingentism: Individuals just are Realized Essences

Naujos nuosaikiojo kontingentizmo teorijos link: individai ir yra realizuotos esmės

Pranciškus Gricius pranciskus.gricius@fsf.stud.vu.lt

Vilnius University, Lituania

Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.

Actualism is the thesis that (unrestrictedly) everything that is, in any sense of is, actually exists. Contingentism is the thesis that what individuals exist is a matter of contingency. There are two brands of actualistic contingentism – full-blooded contingentism and moderate contingentism. According to the former, it is contingent what individuals exist and the same holds for higher-order entities¹. According to the latter, although it is contingent what individuals exist, it is necessary what higher-order entities exist².

Both full-blooded necessitists³ and full-blooded contingentists⁴ have argued that moderate contingentism cannot be upheld because of the problem of unexemplified essences. In this paper, we provide new moderate contingentist modal metaphysics – dub it Fundamental Essentialism – which, we claim, can answer that problem. According to fundamental essentialism, individual things just are realized essences⁵. An essence of Socrates is what it is to be that thing and Socrates himself is realized essence. We take the realization of essence to be a property of it, hence, on the proposed account, Socrates is a property of a property, that is: Socrates just is realized Socrateity.

We motivate the theory of fundamental essentialism via the theoretical virtues it has. First, besides solving the problem of unexemplified essences, our proposed theory enables us to answer other core problems that contingentists face: we can solve the classical objection to orthodox possible worlds semantics with variable domain models and actualistic quantifiers (Kripke 1963), the objection being that if the semantic framework is interpreted realistically, then it cannot accommodate both contingentism and actualism; also, we can rebut Williamson’s (2013: 295–296) deductive argument for necessitism. Secondly, unlike other contingentist theories, our theory depends neither on free logic, nor on the restriction of the rule of necessitation, nor on treating some of the features of the models for modal logics as representationally insignificant. Hence fundamental essentialism challenges Williamson’s claim (2013: 42) that contingentist must either adopt free logic or restrict the rule of necessitation.

Fundamental essentialism is a descendant of Plantinga’s (1974, 1976) and Jager’s (1982) moderate contingentist theory (PJ, for short), so most of our discussion proceeds by way of showing how our proposed theory betters PJ. First, we rehearse the problem that led to PJ, viz. the aforementioned classical objection to orthodox possible worlds semantics. Then, we show how PJ answers this objection, and we spell out the problem of unexemplified essences that is said to haunt moderate contingentists. Afterward, we formulate the theory of fundamental essentialism and we show how it enables us to answer both the classical objection and the problem of unexemplified essences. Then, we refute Williamson’s deductive arguments for necessitism, and we ask whether fundamental essentialism is a contingentist metaphysics.

The problem of creating semantics for modal logics that would accommodate contingentist and actualistic metaphysics – the problem that has been with us ever since the inception of modal logics – persists to this day. Already Prior (1957: 48) worried that “ordinary modal logic is haunted by the myth that whatever exists exists necessarily”, and more recently what Prior called a myth has been declared a fact by necessitists. Necessity of what individuals exist is something that we as contingentist cannot swallow and hence we need to look for a model theory without such a consequence.

Originally Kripke (1963) promised a remedy for the predicament that Prior found himself in – orthodox possible worlds semantics with variable domain models and actualistic quantifiers was born. But now within orthodox semantics, the problem of possibilia looms large. As Fine (2002: 161) puts it, in this semantics

we presuppose an ontology of possibilia twice over. For first, we countenance various possible worlds, in addition to the actual world; and second, each of these worlds is taken to be endowed with its own domain of objects. These will be the actual objects of the world in question, but they need not be actual simpliciter, i.e. actual objects of our world.

And possiblia are something that we as actualists cannot swallow and hence we need to look for model theory without such a consequence.

The first case of possibilia that Fine mentions, namely merely possible worlds, is quite unproblematic. We can remain actualists while committing ourselves to their existence because we can draw a distinction between worlds that exist (are actual) and a world that obtains (is actualized)⁶. So in the case of possible worlds, we actualists rebut the charge of committing ourselves to possibilia by claiming that possible worlds are not possibilia.

So far, so good. However, the second case of possibilia mentioned, namely merely possible individuals, is more troublesome. How can we take the proposition

(1) there could have been an individual distinct from all actual individuals,

to be true, without committing ourselves to merely possible individuals? One might call an argument that this cannot be done within orthodox possible worlds semantics – the classical objection to it. The story goes as follows⁷.

According to orthodox semantics, proposition (1) is true in ⁸there is a possible world such that in there exists an individual that is distinct from every individual in . Hence the set of actually existing individuals is a proper subset of the global domain , the latter being the union of all local domains in the model. Therefore, there is a set that has a member such that is not a member of . Since is a member of , is something; hence, by actualism, actually exists. However, is not a member of contains everything that actually exists, hence does not actually exist. Therefore, we conclude that both actually exist and it does not actually exist. Since we are actualists and contingentists, we take actualism and (1) to be true. Thus the derived contradiction points to the orthodox semantics itself as a culprit and, therefore, it is to be rejected.

The essence of this objection is that for someone who is an actualist, models of modal logic have to consist of the materials available in the actual world. Hence, as Linsky & Zalta (1994: 440) puts it, even if formally we restrict our quantifiers to range over only worldbound entities, as actualistic quantifiers do, we still quantify over merely possible individuals in the metalanguage of the orthodox semantics, and thus we are ontologically committed to their existence.

Because of the classical objection, some have suggested that we should take Kripke models to be, in some respects, representationally insignificant (Stalnaker 2012), while others think it supports, at least to some degree, the claim that necessarily everything exists of necessity (Williamson 2013). However, Plantinga and Jager claim that it is possible to develop realistically interpreted Kripke-style possible worlds semantics that accommodates both contingentism and actualism. We proceed to look at what they have to offer.

The basic philosophical idea of PJ is the following: we provide possible worlds semantics via necessary existent essences of individuals and not individuals themselves. Essence, on their account, is an essential and necessarily unique property of an individual, i.e. a property is an essence

1. a) is exemplified in some possible world, and in any possible world for all

2. b) if has , then has essentially (viz. in all possible worlds where exists, has), and

3. c) in no world anything distinct from has (Jager 1982: 337).

The essence of an individual, by definition, uniquely tracks it: an essence is exemplified in the individual, whose essence it is, exists in ; and this essence cannot be an essence of anything else. This allows PJ to take the domain of a possible world as a domain of exemplified essences therein. Thus, in the official formal semantics of PJ developed by Jager (1982), quantifiers range over essences and not over individuals themselves. Furthermore, since essences exist necessarily, in a model we have a constant domain D and then we simulate variable domains within the constant domain, viz. let there be a function that assigns to each world . a domain of essences that are exemplified in .

Within PJ account we say that

(1) there could have been an individual distinct from all actual individuals,

is true in there is such that in some essence is exemplified, but is not exemplified in . For if there is an essence that is exemplified in, but not in , then had obtained, some individual not identical to anything in the actual world would have existed. Essences exist necessarily, therefore all of them exist actually, and thus the global domain of the model causes no problems. The upshot of PJ account is that if we have essences, we can accept our contingentist assumptions and that only leads us to unexemplified essences, but not to merely possible individuals. However, there are reasons to doubt whether unexemplified essences are metaphysically respectable.

Say that “X is an essence of . By accepting higher-order necessitism, moderate contingentists accept that necessarily, for any necessarily there is an essence of . Henceforth, let stand for an essence of Socrates, let denote Socrates, and let denote a world where does not exist. But now, in the vocabulary of Williamson (2013: 269), how is it that locks onto in ? This is a challenging question for moderate contingentists, and there are few precisifications of what this challenge amounts to⁹.

On the first one, one is challenged to provide metaphysical grounds for holding in . That is, one must provide a sentence Q such that: holds in because (where “because” is understood metaphysically). The sceptic will point out to us that holding in cannot be because is suitably related to there is no Socrates to be related to anything. He will go on to tell us that we have nothing much left to fill the role of Q.

The second one begins with the thought that necessarily if a property exists, it has well-defined conditions of satisfaction¹⁰. has conditions of satisfaction in only if holds in because the latter formula specifies what it takes to satisfy . According to that formula, has conditions of satisfaction such that necessarily for any satisfies those conditions of satisfaction the denotation function assigns the same value to and . However, in there is no Socrates, and hence denotation function has nothing to assign to . But if so, then has no conditions of satisfaction in. Therefore, does not exist in .

Recently few answers to the problem of unexemplified essences were proposed by Pérez Otero (2013) and by Skiba (2022). We will not engage with them here in-depth, but we note a few drawbacks of their positions.

Otero (2013: 404) accepts that there are necessary existent microphysical individuals such that, roughly speaking, each possible individual is essentially uniquely related to some such microphysical individuals. He calls this thesis modal metaphysical atomism. The idea behind it is this: if one has some necessary existent individuals to which, for example, this knife is essentially uniquely related, then one will be able to specify an essence of in worlds where is not. These individuals better not be the handle and the blade of , since all of these could have been nothing by contingentists light. So better go and look what this handle and blade are made of, and go even further till you hit microphysical constituents. When you do so, claim that they exist of necessity. Claim the same for the constituents of each actual individual and of each individual that could have existed but does not.

There are a few problems with this account: first, Otero holds that what microphysical individuals exist is necessary but it is contingent what ordinary individuals exist. However, he does not explain what is the metaphysical basis for such difference. So even if we grant Otero (2013: 405) the claim that “there is no rationale for the contingentist about individuals to think that all basic microphysical entities must be contingent”, still we might wonder: is it the size of microphysical individuals that accounts for their existential modal profile? Or is it the fact that everything else is made of them? If either, then how do these features imply something about their existential modal profile? After all, the distinction between microphysical and ordinary individuals is not as deep as, say, that between pure sets and social objects. The existential modal profiles of the latter might be thought to uncontroversially follow from their respective natures. Secondly, there is no good independent evidence for modal metaphysical atomism, except that it allows us to solve the problem of unexemplified essences (this Otero himself accepts, see 2013: 404–405).

Another answer to the problem of unexemplified essences was recently developed by Skiba (2022). His position is very promising, and I do not find any drawbacks to the way he solves the problem under the first precisification. Hence I will not discuss how he does it. However, I do find some problems with the way he solves the problem under the second precisification (or something very akin to it). Hence let us focus on that one. First, he says that “the position in which term . occurs in sentence is existence-demanding just in case logically entails (Skiba 2022: 26). Secondly, he provides good independent reasons to think that only predications are existence-demanding. Thirdly, he notes that is not a predication. Thus can hold in without Socrates existing in.

The worry I have with this answer is that it depends on free logics and on instrumental treatment of models of modal logic. In holds, however, we cannot infer that holds in (the free logic part). Regarding instrumental interpretation: suppose holds in (remember in Socrates is not). Since is accessible to, thus holds in . Thus on any x-variant variable assignment function, , the following holds:. Denotation function assigns Socrates to . Denotation function is a function. Functions are certain relations. Relations are certain sets of ordered n-tuples. Ordered n-tuples are certain unordered sets. So one can cut the pie anyway one likes, Socrates is a member of some set in a possible world . So if holds in and if one interprets the semantics realistically, one will have to say that Socrates is a member of some set in . However, Skiba (2022: 26) accepts that “Socrates ∊ .” is a predication and thus existence-demanding. Therefore, he has to interpret his semantics instrumentally. If Skiba is willing to go for free logics plus instrumental interpretation of possible worlds semantics, as it seems he must, I have no other objection except that he is willing to go for free logics plus instrumental interpretation of possible worlds semantics¹¹. I will offer another way that involves neither.

It does seem odd that in worlds where Socrates is not, necessary and sufficient conditions for Socrates’ existence (existence-conditions, for short) do not exist. For it seems that these worlds that are devoid of Socrates are precisely such that the conditions under which Socrates would exist are not fulfilled or realized. That is, it seems that there are existence-conditions for Socrates (i.e. Socrateity exists), but the world is not that way as to realize them. Moreover, if in some possible world there are not any existence-conditions for Socrates, then it seems it is impossible for Socrates to exist since there are no circumstances, no way for a world to be such that the existence-conditions for Socrates would be realized because these putative existence-conditions do not exist.

What has gone wrong here, I claim, is due to the fact that individuals are detached from their essences. Socrateity, to put it metaphorically, only follows Socrates wherever he goes in the modal dimension and repels everyone else. But even if it is necessary and sufficient conditions for the existence of Socrates in any possible world that Socrateity be exemplified, nonetheless we are told Socrates is something and Socrateity is something else. I believe Plantinga, Jager, and others assume that individuals are bearers of properties that themselves are not properties (call such bearers of properties basic). Such basic bearers of properties, I believe they assume, are both conceptually irreducible and also metaphysically speaking they are not to be reduced to something else. So, for example, Stalnaker (2012: 36/n10) tells us that “by “individual” here, I mean things that are not themselves properties, propositions, or relations”, and he certainly accepts that individuals are bearers of properties. Hale (2013: 220) says that the essence or “[t]he nature of a thing, ., is a special kind of property <…> – property which anything must have if it is to be ., and possession of which constitutes being .”. Socrates is that which possesses Socrateity and he is constituted by this possession. Once again, Socrates is one thing and Socrateity another. But what is Socrates himself? It seems he is a bearer of properties that is not a property, a relation, or a proposition; that is, Socrates is a basic bearer of properties.

Well, maybe as moderate contingentists we should get rid of this way of thinking. Perhaps we should reject the assumptions they make about individuals. The proposal we offer is this: follow PJ in claiming that there are essences, but do not follow them in postulating basic bearers of those essences. When one says the essence of Socrates is so and so, then, on the proposed account, one should take Socrates himself just to be so and so being the case. When one says that the essence of Socrates is to be a human being that has originated from a particular sperm cell . and a particular ovum ., then one should accept that Socrates just is the part of reality that is that way¹². The important point is that, on the proposed account, the realization of essences results in concrete individuals¹³, but I claim these concrete individuals are not additional entities – they just are realized essences¹⁴. Since essences are understood as fundamentum out of which or from which individuals are built, we call the issuing theory Fundamental Essentialism¹⁵.

Most of Williamson’s arguments for necessitism are abductive in nature, yet to engage with them appropriately would require another entry. Thus, it will be illustrative to engage with his deductive arguments for necessitism. One of them is the following (Williamson 2013: 295–296):

1. (2) necessarily, if Socrates is nothing, then the proposition that Socrates is nothing is true;

2. (3) necessarily, if the proposition that Socrates is nothing is true, then the proposition that Socrates is nothing is something;

3. (4) necessarily, if the proposition that Socrates is nothing is something, then Socrates is something;

4. (5) ∴ necessarily, Socrates is something.

Given the metaphysical picture we are defending, we must translate Williamson’s argument into ours. For us, the proposition that Socrates is nothing states that the essence whose realization is Socrates is not realized. Let . denote this essence, let π(.) mean “the proposition that ”, and let stand for “the proposition that is true”. Our translation proceeds thus:

1. (2FE) necessarily, if

2. 3FE) necessarily, if

3. (4FE) necessarily, if

4. (5FE) ∴ necessarily,

(2FE) and (3FE) seem to be hardly contestable, hence, we must say that (4FE) is false. But it is false, for if there is a possible world where the proposition isn’t realized exists, it does not follow that is realized in . At the end of the day, the proposition that Socrates does not exist, is, on our account, a proposition about the essence whose realization is Socrates.

We, unlike others¹⁷, refute Williamson’s argument in a way that depends neither on free logic nor on the distinction between true in a world / true at a world.

We consider three critical questions regarding our proposed theory and its relationship with the necessitism-contingentism debate.

Is Fundamental Essentialism a Contingentist Metaphysics?

Objector: you develop constant domain models as adequate for your theory, thus according to you the formula

is valid. Williamson (2010: 662–666) defined necessitists to be those who accept NNE. You accept NNE and thus you are necessitists.

Answer: I agree with you in one sense; I disagree in another. I claim that there are two different ways to understand necessitism and contingentism. Let me explain.

First of all, whether one is called a necessitist or a contingentist depends on whether one thinks that necessarily all individuals exist necessarily. One is necessitist if one thinks so; one is contingentist if one does not. Let us call these theses the spirit of necessitism and the spirit of contingentism respectively.

Secondly, we formalize these opinions using possible worlds semantics. Then, we say that, since quantifiers range over individuals, necessitism is a position whose proponents think that NNE and one qualifies as a contingentist if one thinks that ~NNE. We may drop our assumption that quantifiers must range over individuals. Then, we would claim that any position which accepts NNE is necessitism and any position which accepts ~NNE is contingentism, whatever entities over which quantifiers range over are. I think it is appropriate to name necessitism and contingentism thus understood the letter of necessitism and the letter of contingentism.

According to our favored theory, individuals are realized essences. The spirit of necessitism concerns individuals. Hence within fundamental essentialism, it is appropriate to formulate the spirit of necessitism as

We reject that NNE. should be taken as a valid formula in a metaphysically universal modal logic, and hence our proposed theory is contingentist in spirit. We agree that necessarily every essence necessarily exists, thus we accept NNE as a valid formula in a metaphysically universal modal logic, and hence our proposed theory is necessitist in letter. Conclusion: fundamental essentialism is contingentist in spirit, but necessitist in letter. I believe that the spirit, and not the letter, expresses the proper nature of these positions. Therefore, I conclude that fundamental essentialism is contingentist metaphysics.

If you insist that what is genuinely relevant to the necessitism-contingentism debate is only what I called the letter of these positions, then I agree that I am a full-blooded necessitist. But note, a full-blooded necessitist who truthfully claims that it is contingent what individuals exist.

Some material of this paper was presented at the conference Logic and Philosophy: Historical and Contemporary Issues (Vilnius University). I am grateful to the participants of this event, in particular to Daniel Nolan, Elia Zardini, Gabriel Sandu, and Valentin Goranko, for helpful discussion. I am especially thankful to Živilė Pabijutaitė and Jonas Dagys for their fruitful comments on the early draft of this paper and to two anonymous reviewers for their illuminating and challenging comments.