Divine Simplicity: Possibilism

In article 4 of Summa Theologiae I, Question 3, Thomas reaches the crux of the matter: his claim that God’s essence is identical to His act of existence. This article provides Thomas with the crucial bridge from the Five Ways to the standard list of divine attributes (infinity, perfection, and so on), as well as to the uniqueness of God. Without this article, Thomas’s natural theology would not be worthy of the name, for there would be no reason to think that the being shown to exist by each of the Five Ways is God.

This is also the most controversial part of Thomas’s natural theological program. It was rejected by nearly all of Thomas’s successors in medieval scholasticism (Scotus, Ockham, Suarez), and it has continued to elicit incredulous stares from modern philosophers, including many theists (Plantinga, Swinburne, Craig, and many others). Nonetheless, we will argue that Thomas’s position is quite a defensible one.

To make good on this claim, we must step back and consider a fundamental metaphysical and meta-ontological question: the nature of existence itself. Or, to be more precise, the nature of actual existence.

Gottlob Frege (1879) and C. S. Peirce (1885) independently discovered the predicate calculus, extending Aristotelian and scholastic logic for the first time to a system adequate for the rigorous formulation of statements about relations, including mathematical relations. Early applications of the predicate calculus focused on the foundations of mathematics (Frege 1884, Russell and Whitehead 1910, 1912, 1913). For these applications, it was possible to ignore modality and time, since mathematical entities and facts are eternal and metaphysically necessary. In such a context, there was no meaningful difference between existence (simpliciter), present existence, and actual existence. When Russell and later physicalists (like W. V. O. Quine) turned to questions of the philosophy of science (especially, the philosophy of theoretical physics), they assumed a block universe picture of time (in which past and future entities and facts are on a bar with present ones) and took a dismissive attitude toward modality. They assumed that no talk of ‘possible worlds’ could be taken seriously in metaphysics.

Consequently, it made perfect sense for Quine to propose that to be is to be the value of a variable. The meaning of existence is fully captured by the existential quantifier of the predicate calculus, together with a set or class the constitutes the domain over which the variable associated with such quantifiers are taken to range. To say that a unicorn exists is just to say that, for some x in the domain, x is a unicorn. Existence is not a property that some things in the domain might have and others lack. To try to say of some particular thing A, that A does not exist, is to express a logical falsehood. If we can refer to thing A at all, then A belongs to the domain of quantification, in which case it is a logical theorem of the standard predicate logic that there is some x in the domain such that x is identical to A.

However, it soon became clear that modality (possibility, necessity, actuality) could not be banished forever from serious philosophy. With Kripke’s work on modal logic (Kripke 1959, 1963, 1970) and Lewis’s Counterfactuals (Lewis 1973), modality secured a position in analytic metaphysics. This immediately raised questions about what it means for something to exist in actuality. There were two options. We could either suppose that some members of the domain were actual and others were merely possible (possibilism), or we could insist that only actual things belong to the domain (actualism). Actualist metaphysicians could simply extend Quine’s motto into modal space: to exist actually is to be a value of a variable. Possibilists, in contrast, need some sort of predicate to distinguish actual members of the domain from non-actual ones. Most possibilists suppose that even non-actual things are self-identical, so the formula ‘x = x’ will not express the claim that x actually exists.

Some Prima Facie Difficulties with Possibilism

Possibilism soon came under heavy fire from a number of sources. Quine argued that it posed innumerable unanswerable questions. It seems possible that there be a fat man in the nearest doorway, but (Quine asks) just how many possible fat men are there? And how do we know which possible fat men are identical to some actual people, and which ones are identical to each other?

As it turns out, there are plausible answers to some of these questions, and few philosophers today would endorse Quine’s assumption that a theory is untenable if it poses questions that it can’t answer. So, both possibilism and actualism are viable options.

There are two ways of building a possibilist metaphysics: an egalitarian and an inegalitarian way. On the egalitarian path, we assume that both actual and non-actual individuals are equally real— ontologically speaking, on a par. On this view, to say that something is actual is simply to say that it exists in this world, the one containing the episode of speech or thought in which the particular token expression of ‘actual’ occurs. The egalitarian view offers an indexical account of ‘actual’: the word ‘actual’ functions in much the same way as ‘I’, ‘here’, or (in a Block Universe) ‘now’ do. This is the form of “modal realism” defended by David Lewis (1984). The various possible worlds are parallel universes. What takes place actually is what takes place here, in our local universe. What is merely possible is what takes place (with equal reality) in some other universe.

In an inegalitarian version of possibilism, the actual things and actual facts are metaphysically privileged. Only actual things are fully real. Merely possible things are lacking some crucial factor, a lack which deprives them of first-class status in our ontology. Typically, this means that the facts about what is merely possible are metaphysically derivative, dependent on some more fundamental facts about what is actual.

Faced with this choice, many possibilists have opted for the inegalitarian version. We think that both Aristotle and Thomas would be compelled, by the logic of their positions, to opt for this view as well. Lewis’s egalitarian possibilism has typically been met by what Lewis himself described as “an incredulous stare.” We think that this incredulity is a manifestation of the fact that we know, as competent users of English, that Lewis’s indexical account of the semantics of ‘actual’ cannot be correct. In addition, there are several extremely powerful metaphysical, epistemological, and ethical objections to Lewis’s theory (see Koons and Pickavance 2017, 317–331).

Inegalitarian possibilism, however, also suffers from an apparently fatal flaw, given a broadly Aristotelian framework.

Possible worlds can be represented by sets of compatible substances and accidents. For simplicity’s sake, we’ll ignore both form/matter and time. Suppose that each possible world consists entirely of timeless, immaterial substances and their accidents. Every fundamental contingent fact can be identified either with a substance or an accident of a substance, assuming that each accident is essentially the accident of a particular substance. So, for example, we can assume that Socrates’ musicality is essentially the musicality of Socrates. It couldn’t be the accident of anything else. With that assumption in mind, we can fully characterize a complete possible world with just two lists: a list of substances (the substances that would exist if that world were actual), and a list of individual accidents (the accidents that would belong to each of those substances if that world were actual).

In addition, there are a set of necessary framework facts: facts about the numerical identity and distinctness of individual substances and accidents, facts about the essences of substances, the species of accidents, the proper accidents of substances, and the compatibility or incompatibility of accidents.

On a possibilist account, every substance or accident, whether actual or potential, “exists” (in the Quinean sense of belonging to the domain of quantification). The substances and accidents that belong to a world would exist (in the non-Quinean sense) only if that world were the unique actual world.

If we suppose that what makes a thing or a fact actual is some accident of actualness, we have to ask whether or not we could find that same “actualish” accident is to be included among the ordinary substances and accidents that make up a possible world. If the answer is Yes, then the accident of actuality has not succeeded in distinguishing the actual from the merely possible, since it is found equally in both. But if the answer is No, if the accident of actuality is missing from all merely possible worlds, then it seems that it was always impossible for those supposedly possible worlds to be actual. If they had been actual, they would have had to have possessed this special accident of actualness, but we’re supposing now that this accident is missing from their constitutive set. Any world that could really have been actual would have had (when it was actual) a different set of accidents from the world that is supposedly possible. But impossible possibilities are obviously absurd.

Think of it this way. Suppose that what makes the difference between an actual mountain (like Mt. Everest) that has a peak with elevation over 29,000 feet and a merely possible mountain with an elevation over 30,000 feet (call it Mountain X) is that Mt. Everest has the accidental quality of actuality and Mountain X lacks it. But if we imagine a situation in which Mountain X would be actual, we must imagine Mountain X possessing that special accident. But that means that possessing that Mountain X’s possessing that special accident is an integral part of the alternative possible world that we are imagining. So, Mountain X must already (in the relevant sense) possess the accident of actuality. What really makes a difference between Everest and X is that Everest actually has that accident and X merely possibly has that accident, that is, Everest has it in the actual world, while X has it only in merely possible worlds. But, then, it is clear that positing the accident has not helped us at all in elucidating the difference between actual mountains and merely possible ones.

A similar problem destroys Gottfried Leibniz’s suggestion that we could define the actual world as the best world (overall). Consider a world W that is less than the best. Could W have been actual? Obviously not, since W could never have been the best possible world, given that the actual world is better than W, and it is essential to both the actual world and W that both are possible and that the actual world is better than W. So, Leibniz’s theory is really incompatible with the existence of merely possible worlds.

Similarly, we can’t solve the problem by introducing a relational accident or other intraworld accident. Suppose we tried to define the actual world as the world with the relational accident of having been created by God. Now consider another possible world W. If W were actual, the substances and accidents W contains would have been created by God. So, it can’t be part of the very definition of W that its substances and accidents were not created by God. The difference between the actual world and W is that God actually created the things that make up the actual world and not the things making up W. So, again we’ve failed to find a non-circular account of actuality.

There’s another intraworld relational account that falls to the same objection, one proposed by Koons and Pickavance (2017, 338-9). On this proposal, to be actual is to belong to the central portion of reality, upon which all merely potential realities depend (by being related to the powers or dispositions of actual things). All mere potentialities are ultimately grounded by the actual facts. Necessary beings (like God) are essentially “central” in this way, so the Koons-Pickavance account would provide some basis for identifying God as actual. However, many actual things are contingent. This means that although they are in fact central, they could have been peripheral. We still need an explanation of what makes one contingent thing actually metaphysically central and another actually peripheral.