Introduction

While Aquinas’ position on God’s necessary existence is subject to conflicting interpretations, there are strong reasons for assuming that he conceived of it in terms of logical necessity in a broad sense. This, however, seemingly stands in some tension with the fact that he excludes the possibility of a priori arguments for the existence of God. One apparently attractive way of handling this tension in Aquinas is to use a two-dimensional framework inspired by Saul Kripke, according to which God exists by necessity on the premise that he actually exists. This, so the assumption goes, allows for the existence of God to remain inapprehensible for a priori reasoning, while still being logically necessary.

In this paper, I provide reasons for why this Kripke-inspired framework is inapt for reconstructing Aquinas’ position and suggest a different route. After arguing, in Part Two, that Aquinas indeed held God’s existence to be logically necessary, I will contend, in Parts Three and Four, that it is hard to distinguish between God’s existence as a brute fact and as logically necessary if viewed in a Kripkean framework. Ultimately, God as a brute fact, on the one hand, and God as a necessary existent in this framework, on the other hand, represent two labels for one and the same thing. This is because the conceivability of God’s non-existence within the Kripkean framework makes God’s non-existence possible in some important sense. Part Five expands on this by reviewing David Chalmers’ writings on modality in order to track the relationship between conceivability and possibility more thoroughly. It establishes that conceivability is a good guide to possibility, which is why the conceivability of God’s non-existence indeed implies the possibility of God’s non-existence. However, as Parts Six and Seven suggest with reference to Aquinas, the alleged conceivability of God’s non-existence is ultimately due to our ignorance, as human beings in statu viatoris, of the nature of being, whereas creatures who grasp the nature of being are unable to conceive of God’s non-existence. This removes God’s non-existence from the realm of relevant conceivability and, therefore, from the range of possible worlds. Part Eight, finally, reflects briefly on the perspective of those who do grasp God’s nature as subsistent being.

What kind of necessity?

Among people who believe that God exists, it is commonly assumed that his existence is necessary. What this means, however, is highly controversial. For some, it is clear that the kind of necessity in question is factual necessity. If God’s existence is factually necessary, then God exists, has always existed and never ceases to exist, and his existence depends on nothing. A prominent contemporary proponent of this view is Richard Swinburne:

To say that ‘God exists’ is necessary [on the relevant criterion of necessity] is to say that God does not depend for his existence on himself or on anything else. No other agent or natural law or principle of necessity is responsible for the existence of God. His existence is an ultimate brute fact. (1977, 267)


Although God’s existence is necessary in the factual sense, God’s non-existence remains conceivable, and there are possible worlds—ways the world could have been—in which there is no God.

Others demand a stronger kind of necessity. According to Alvin Plantinga (1992), for example, the maximal greatness of God implies that he displays maximal excellence in every possible world. This requires of God that he exists in every possible world. On this account, God cannot possibly fail to exist, since this would deprive him of his maximal greatness.

What did Thomas Aquinas think about the modalities of God’s existence? In this context, some interpreters have pointed out that Aquinas’ notion of necessity (necessitas) differs from the modern modal logician’s understanding of necessity.Footnote 1 A necessary being for Aquinas is a being that is not subject to corruption and cannot suffer any other form of substantial change. Non-material beings are necessary in this sense since they lack the potentiality associated with matter. According to those interpreters, this general understanding of necessity suggests that Aquinas thought of God’s necessary existence merely in terms of incorruptibility, unchangeability, eternity and causal independence.

While this certainly represents a correct interpretation of Aquinas’ notion of necessary being in general, Footnote 2 there are strong indications that Thomas had a more far-reaching kind of necessity in mind when it comes to God’s existence.Footnote 3 Perhaps the strongest indication is that the Third Way and related arguments seem to presuppose a kind of necessity that surpasses factual necessity. At the end of his Third Way (ST I, q. 2, 3), Aquinas distinguishes a notion of per se necessity pertaining to God alone from the necessity predicated of incorruptible beings other than God. This is done in order to avoid an infinite regress. A similar argument can be found in Summa Contra Gentiles:

We find in the world, furthermore, certain beings, those namely that are subject to generation and corruption, which can be and not-be. But what can be has a cause because, since it is equally related to two contraries, namely, being and non-being, it must be owing to some cause that being accrues to it. Now, as we have proved by the reasoning of Aristotle, one cannot proceed to infinity among causes. We must therefore posit something that is a necessary being. Every necessary being, however, either has the cause of its necessity in an outside source or, if it does not, it is necessary through itself. But one cannot proceed to infinity among necessary beings the cause of whose necessity lies in an outside source. We must therefore posit a first necessary being, which is necessary through itself (per seipsum necessarium). This is God, since, as we have shown, He is the first cause. God, therefore, is eternal, since whatever is necessary through itself is eternal. (Aquinas 1975, I, 15)


While this passage is an argument for the eternity of God, it also establishes the fact that God is necessary in a way distinct from the necessity of other necessary beings, like angels. The argument for this conclusion is based on the premise that the chain of causal dependencies must stop at some point, non-arbitrarily. After arriving at a being that cannot not exist—which is necessary through itself—we can rest our case, since a being that cannot not exist does not require a further cause, or explanation, of its existence. On the other hand, it seems that a brute fact would be insufficient for stopping the chain of explanation in a non-arbitrary way. Therefore, the most plausible interpretation of Aquinas suggests that he attributed some kind of necessity stronger than factual necessity to God.

A different but related argument establishes the necessity of God by concluding that God’s essence is identical to his being.Footnote 4 According to Aquinas’ early treatise De Ente et Essentia, the real distinction between essence and being, and the dependence of a thing’s being on something else, triggers the same kind of explanatory chain as seen in the Third Way and in the argument from contingency in Summa Contra Gentiles:

Everything that pertains to a thing, however, either is caused by the principles of its own nature, as risibility in man, or else comes from some extrinsic principle, as light in the air from the influence of the sun. Now, it cannot be that existence itself is caused by the very form or quiddity of the thing (I mean as by an efficient cause), because then the thing would be its own efficient cause, and the thing would produce itself in existence, which is impossible. Therefore, everything the existence of which is other than its own nature has existence from another. And since everything that is through another is reduced to that which is through itself as to a first cause, there is something that is the cause of existing in all things in that this thing is existence only. Otherwise, we would have to go to infinity in causes, for everything that is not existence alone has a cause of its existence, as said above. It is clear, therefore, that the intelligences are form and existence and have existence from the first being, which is existence alone, and this is the first cause, which is God. (Aquinas 1965, cap. 3)


The fact that every entity that is distinct from its own being receives its being from another forces us, on pain of ending up in an infinite regress,Footnote 5 to conclude that there must be a being who is identical to its own existence. This is God. The characterization of God as a being who is its own being and whose essence is identical to its existence appears, once again, to result in a kind of necessity far stronger than mere factual necessity. In Summa Contra Gentiles, the connection between God’s esse and his necessity is made explicit:

Each thing is through its own being. Hence, that which is not its own being is not through itself a necessary being. But God is through Himself a necessary being (per se necesse esse). He is, therefore, His own being. (Aquinas 1975, I, 22)


By combining the reasoning of the argument for God’s existence based on contingency and necessity with the argument from the dependency related to being, we have a rather strong case for the interpretative claim that Aquinas had more than factual necessity in mind. This all suggests that we can ascribe to Aquinas an understanding that comes close to what was formulated by Leibniz more than four hundred years later: from the identity of essence and existence in God, it follows that God exists by a stronger kind of necessity, assumedly by logical necessity.Footnote 6

So, what kind of logical necessity is this? What does it mean to say that something is logically necessary? I will henceforth understand the notion of ‘logical necessity’ as expressing what Plantinga (1992) has coined as ‘broad logical necessity.’ This notion cannot, and should not, be defined exhaustively here, since the meaning of modal predicates is one of the things this article seeks to delineate, and since broad logical necessity (sometimes referred to as ‘metaphysical necessity’) is arguably one of the most controversial notions in modern philosophy. At this point, I will merely mention two characteristics of logical necessity in this broad sense. First, broad logical necessity is stronger than factual necessity. If it is broadly logically necessary for God to exist, it could not have been the case that God did not exist; thus, there is no possible world in which there is no God.Footnote 7 This sets broad logical necessity apart from mere factual necessity. A proposition p is factually necessary iff (i) p is the case, has always been the case and will always be the case, and (ii) there is no other proposition q, so that p being the case depends causally upon q being the case. Broad logical necessity is stronger than that since the factual necessity of p is compatible with the existence of possible worlds in which non-p holds. Second, broad logical necessity is, as the term suggests, broader than logical necessity in the narrow sense. In a narrow sense, modal notions rest on the assumption that impossibility can be explicated in terms of some syntactically conceived notion of contradiction (in contrast to logical validity).Footnote 8 Some proposition p is narrowly logically necessary iff non-p is impossible in the sense that the assertion of non-p engenders a contradiction that is not dependent on the meaning of some non-logical term.Footnote 9 Thus, the fact that 4 is bigger than 2 is not logically necessary in the narrow sense, because this necessity derives from properties of the natural numbers involved, as expressed by the meaning of the numerals ‘4’ and ‘2’. The sentence ‘4 is bigger than 2 or 4 is not bigger than 2’ is necessarily true in the narrow sense, by contrast, because its necessity derives from formal features of the sentence (specifically, the truth-functional character of the logical operators ‘or’ and ‘not’) rendering it true on all interpretations. The narrow notion is not the notion we are primarily interested in since it would render far too much possible, and far too little necessary. It would make DNA-less human beings possible and render the identity of Marilyn Monroe and Norma Jeane Mortenson contingent. To avoid this, we need a notion of necessity (and possibility) that accounts for syntax as well as meaning relations, and possibly also for relations holding in mind-independent reality. It is this broader form of logical necessity that we are interested in and that we should consider in connection to God’s existence, in general and with reference to Aquinas.

Aquinas and the necessary a posteriori

The picture emerging at this point is that Aquinas thought of God’s existence as necessary in the broad logical sense just delineated. However, if God’s existence were logically necessary, we would expect it to be demonstrable a priori. If it cannot be the case that God does not exist, it seems we have no need for any arguments starting in experience. It must be possible to derive God’s existence from our understanding of the concept of God, or from our understanding of what kind of thing God is.Footnote 10

This is explicitly eschewed by Aquinas. Alluding to Anselm’s famous argument for God’s existence, he says:

… granted that everyone understands that by this word ‘God’ is signified something than which nothing greater can be thought, nevertheless, it does not therefore follow that he understands that what the word signifies exists actually, but only that it exists mentally. Nor can it be argued that it actually exists, unless it be admitted that there actually exists something than which nothing greater can be thought; and this precisely is not admitted by those who hold that God does not exist. (Aquinas 1947, I, q. 2, 1, ad 2)


Regardless of how we think of a supreme being, its actual existence can always be consistently denied. Adjusting this to Aquinas’ own understanding of God as a being who is its own existence and therefore exists necessarily, it seems that a person can flatly deny, consistently, that such a being exists. Aquinas’ position on this, as we will discuss in Part Six, is that we cannot really grasp the nature of God, which is why we fail to infer God’s existence from a definition of God encapsulating God’s nature.Footnote 11 For us, the existence of God is something we can only demonstrate by means of God’s effects on Aquinas’ view, that is, a posteriori in the scholastic sense of a posteriori,Footnote 12 and also in the modern sense of a posteriori, relying on experience. That God exists, then, is a necessarily true proposition that can only be shown to be true by arguments starting in experience.Footnote 13

This suggests a certain closeness between Aquinas’ position and the modern notion of a posteriori necessary truths made familiar by Saul Kripke. Up until some fifty years ago, philosophers were prone to assume the co-extensionality of a priority and necessity. This changed rapidly due to the impact of Kripke’s seminal lectures published under the title Naming and Necessity. Kripke rejects our intuitive inclination to identify the necessary with the a priori:

There is a very strong feeling that leads one to think that, if you can’t know something by a priori ratiocination, then it’s got to be contingent: it might have turned out otherwise; but nevertheless I think this feeling is wrong. (1980, 101)

Famously, there are plausible counterexamples undermining this feeling:

We use ‘Hesperus’ as a name of a certain body and ‘Phosphorus’ as the name of a certain body. We use them as names of those bodies in all possible worlds. If, in fact, they are the same body, then in any other possible world we have to use them as a name of that object. And so in any other possible world it will be true that Hesperus is Phosphorus. (1980, 104)


The interesting thing about this, of course, is that we cannot know a priori that they are, in fact, the same body. Rather, this can only be known by empirical examination. We do know a priori that if two names refer to the same body, then the referents of those two names are necessarily identical due to the necessity of self-identity. Whether they, in fact, do refer to the same body, however, cannot be known a priori and is subject to a posteriori assessment. As a result, the proposition ‘Hesperus is Phosphorus’ happens to be necessarily true without being assessable purely a priori.

The reasons for this are, first, that the actual world has a special status among all possible worlds in that our terms gain their reference in the actual world. Those people who introduced the names ‘Hesperus’ and ‘Phosphorus’ did—in the actual course of affairs—apply those names to one and the same celestial body. Second, although terms are being associated with descriptions when introduced, some of them (prominently proper names and natural kind terms) gain a reference/extension that is rigid in the sense that the term picks out the same entity/entities in every possible world independently of associated descriptions. Thus, even though those who introduced the names of that celestial body associated the name with some description (like ‘brightest star visible in the morning sky’ etc.), these names stay fixed on that body across possible worlds – the reference of the term is fixed across possible worlds, while having been fixed in the actual world. As a consequence, conditions of the actual world determine the modal status of the proposition while those conditions are not a priori knowable.

Inspired by Kripke, some philosophers of religion treat ‘God exists’ in the same way, as a necessary a posteriori truth. This is William Forgie’s accommodation of Aquinas to Kripke’s framework:

Suppose we think of proper names [such as ‘God’] not as having ‘senses’ or as ‘expressing’ the essence, or any property, of their bearers, and think about them instead more as Kripkean ‘rigid designators’, or in the way Mill thought of proper names – as terms which simply denote but lack connotation. Then we can regard the subject term ‘God,’ in ‘God exists’, as a proper name, not a disguised description, without requiring a grasp of the essence of God for the proposition to be intelligible. (1995, 98)

We are supposing [Aquinas] has the Leibnizian idea of God’s essence involving (indeed, for Aquinas, being) His existence. Thus it will be necessarily true that God exists. But since that truth is a posteriori, we should not be surprised that Aquinas rejects a priori attempts to demonstrate it, such as the ontological argument, and that he endorses the sort of a posteriori demonstration found in the Third Way. (1995, 99)

The Kripkean rendering can be articulated without ‘God’ being treated as a proper name and without existence being treated as a property. ‘God exists’ as a general proposition stating that the definite description ‘the subsistent being’ has a referent, a position taken by Petr Dvořák:

First, the truth of ‘there is a subsistent being’ can be ascertained only a posteriori. Secondly, it is a priori (and [broadly logically] necessary) that ‘if there is a subsistent being, then it is [broadly logically] necessary that there is a subsistent being.’ As we already know, this follows from the fact that such a being enjoys temporally and modally stable existence. Thus, thirdly, the [broadly logically] necessary status of ‘there is a subsistent being’ is derived based on the a posteriori knowledge of its truth and hence cannot be known purely a priori. (2015, 64)

Dvořák defines broad logical possibility as ‘that which is allowed by formal logical laws (narrow logical possibility), such as the principle of non-contradiction, and also that made possible by meaning relationships’ (2015, 58). If God exists, then, his existence ought to be necessary in virtue of logical laws or meaning relationships. If the expression ‘God’ has a referent, this referent should exist by necessity in some strong sense, on Forgie’s account. Can the Kripke-inspired thinking ensure that this will be the case?

A posteriori necessity and logical necessity

A first observation would be this: to say, like Dvořák, that a subsistent being’s existence is broadly logically necessary due to the fact that such a being has a ‘modally stable existence,’ in addition to its temporally stable existence, seems too weak. Where does the stronger kind of necessity enter, which ensures that God must exist regardless of what the world is like? On Dvořák’s interpretation of Aquinas, God just exists, and due to his superior nature, he cannot be brought out of existence by anything that exists alongside of him (or by himself, for that matter). This does not seem to preclude the possibility that, had things been different, God might have failed to exist in the first place.

Similarly, Forgie’s take, although suggesting that God exists necessarily despite the a posteriori character of this truth, leaves it open that God does not exist in virtue of the fact that we can conceive of scenarios where God does not exist. The non-existence of God is possible in the same sense that it is possible that the brightest celestial body we see in the morning (de dicto) could have been different from the brightest one in the evening. Or that the clear liquid flowing from my tap could have been constituted by something different than H2O. The necessity of God’s existence, to sum it up, is conditional on the fact that he happens to exist, just like the necessity of the fluid that actually flows from our taps being constituted by H2O is conditional on this fluid actually being H2O.

In the end, it seems that ‘God exists’ is broadly logically necessary in one sense while remaining contingent in another. Given that God is uncaused, eternal, and indestructible, there are no possibilities where he could fail to exist, if he exists. If he exists, he cannot not exist. In the same way, Hesperus cannot fail to be identical to Phosphorus given that we, in our actual world, have (unknowingly at first) fixed those two names upon the same celestial body. Yet, at the same time, it remains conceivable that God does not exist, and that it could have been the case that he did not exist, even if he happens to exist. In some other, or even higher, regard, then, God’s existence is still contingent. Viewed this way, there appears to be no substantive difference between factual necessity and broad logical necessity. Therefore, as a conclusion of the Third Way, God as a factum brutum or as a logically necessary being in Forgie’s and Dvořák’s sense are both equally unsatisfying (or equally satisfying).

Is this congruent with Aquinas’ own views? Apparently not. The problem is that God’s existence fails to be necessary enough. The Third Way and its precursor in the Summa Contra Gentiles quoted above require a stronger kind of necessity. This is because it would be arbitrary to stop the ascendance from contingent being to necessary being at an entity whose existence still reasonably requires an explanation. As John Knasas succinctly puts it: ‘If the Christian God is understood simply in terms of real, or factual, necessity, then he is unapproachable by the cosmological argument’ (1978, 379). Counting Aquinas’ Third Way and related arguments as articulations of the cosmological argument, this pertains to these arguments on Forgie’s and Dvořák’s interpretations of Aquinas as well, since their accounts yield nothing more than factual necessity, as argued above.

This represents a real problem for those who wish to remain committed to the more than factual necessity of God’s existence but accept Aquinas’ claim that no a priori corroboration of God’s existence is possible. The Kripkean approach exemplified by Forgie and Dvořák cannot dispel this problem.

The task of the rest of this paper is to find a coherent picture where the a posteriori character of God’s existence is combined with its broad logical necessity. As one would expect, Aquinas provides the ultimate solution himself in his treatment of self-evident propositions. But in order to appreciate the force of his solution, some groundwork has to be done first, in particular with respect to the nature of modality.

This brings us to our next part. We need to examine more thoroughly what conceivability can tell us about possibility. Does the conceivability of God’s non-existence, which perhaps might hold even if God does in fact exist, really imply the possibility of his non-existence?

Conceivability as a guide to possibility

Let us expand on the basic Kripke-inspired thinking introduced in the last two parts with the help of one of its most elaborate followers, David Chalmers. Chalmers’ account of modality entails one less controversial thesis about the integration of Kripke-cases, and one more substantial, and more controversial, thesis regarding the nature of modality. The less controversial (though not universally accepted) aspect of Chalmers’ account is his way of accommodating Kripke-style a posteriori necessities, namely, his two-dimensionalism.Footnote 14 According to Chalmers’ two-dimensionalism, concepts have two intensions (functions from possible worlds to referents/extensions). The primary intension fixes reference in the actual world, while a secondary intension fixes reference in counterfactual worlds relative to the actual world. The primary intension of ‘water’ consists in some superficially describable features of water. The secondary intension, by contrast, is determined indexically by the actual nature of the stuff that ‘water’ is being applied to in the actual world. Thus, the secondary intension is derived from the primary together with the context in which the term is being introduced. Corresponding to these two intensions, two dimensions of modality ensue: primary and secondary possibility (and necessity). According to its primary intension, ‘water’ might consist of something other than H2O, whereas this is impossible if ‘water’ is being considered according to its secondary intension.Footnote 15

This framework is relatively easy to accept.Footnote 16 More controversial is Chalmers’ substantial claim, argued for on the basis of this approach to Kripke’s a posteriori necessities, that possibility and (ideal) conceivability converge. According to Chalmers, the much-celebrated discovery that some conceptually possible states of affairs are metaphysically impossible turns out to be an imprecise rendering of the fact that some statements express states of affairs that are possible according to the statement’s primary intension while being impossible if evaluated according to its secondary intension. The actual range of possible worlds, moreover, corresponds to the range of conceivable scenarios according to the primary intension. This is not as easy to accept as the purely procedural-terminological approach to Kripke-cases.

This mirrors a general tension between two prevalent intuitions concerning the relationship between modality and conceivability. First, why should possibility depend in any way on a human being’s ability to fathom certain scenarios? Indeed, isn’t one of the most important lessons from Kripke that the notion of possibility ought not to be conflated with epistemic notions? It certainly is but, at the same time, possibility does seem to be intimately connected to conceivability. (Otherwise, nobody would have conflated a priori and necessity in the first place, before Kripke.) After having integrated Kripke’s plausible counterexamples – maybe by reducing a posteriori necessity to necessity according to a secondary intension—it seems highly plausible to assume that the range of conceivable scenarios and the range of (metaphysically) possible worlds are identical, given some constraints on what should count as conceivable.

As to those constraints, Chalmers stresses that the notion of conceivability in question must be ideal conceivability, i.e., conceivability on ideal rational reflection. Furthermore, positive conceivability, where the scenario in question is being imagined in some kind of objectual or conceptual way, is a better guide to possibility than negative conceivability. Negative conceivability occurs when a scenario cannot be ruled out a priori, which is less telling than positive conceptions of a scenario.

Without further argument, I will adopt Chalmers’ framework in its less controversial aspects—the treatment of Kripke-cases—and address the tension shortly. At this point in our inquiry, it is clear that there is no secondary possibility that God does not exist, if he exists. Considered as a counterfactual world to the actual world, where God ex hypothesi exists, there is no possible world in which there is no God. The open question is whether there is a primary possibility of God’s non-existence, i.e., a conceptual possibility of God’s non-existence, which, given Chalmers’ premises, entails the metaphysical possibility (or broad logical possibility) of his non-existence. Following Forgie, we could think of ‘God’ as a term that has been fixed upon God and refers rigidly to him. Because of his nature, moreover, God cannot not exist. It is a metaphysical necessity that God exists and that the proposition ‘God exists,’ since it refers to this necessarily existing being, is a necessarily true proposition. However, according to a primary intension, which encapsulates the conceptual content of ‘God,’ there is a conceivable possibility that ‘God’ could fail to have any referent at all. This would presumably once more raise the question why God exists, if his existence is contingent in terms of primary possibility. Ultimately, this would undermine the line of reasoning in the Third Way and in the argument from contingency in Summa Contra Gentiles, as described above, at least on our interpretation of it.

This part will end with the concession that God could have failed to exist (even if he happens to exist), if we can conceive ideally of scenarios where he does not exist. The path towards this result lays the groundworks for my ultimate conclusion, presented in the next part, that God’s non-existence is ideally inconceivable, which, again, makes God’s existence necessary in the highest possible sense.

To enter on this path, let us first ask whether there are conceivable scenarios that fail to determine possible worlds. Are there what Chalmers (2002) calls ‘strong necessities,’ that is, ideally conceivable scenarios that are not possible? The decisive point, then, is the transfer from conceived scenarios to possible worlds. This is the tension referred to above: To what extent are we entitled to draw conclusions about modalities based on what we can conceive of? That we are entitled to this to some extent, or even to a very large extent, is agreed upon by all. What is controversial are the more challenging examples where a case can be made that our intuitions of conceivability are being misled and become untrustworthy.

One of those challenging cases, which helped trigger an intense debate about the relationship between possibility and conceivability (going on for some thirty years now), is a scenario where all physical facts of our world remain the same but there is no consciousness in the world—the possibility or impossibility of zombie worlds. Reviewing Chalmers’ conceivability argument for the possibility of such worlds, Stephen Yablo raises the issue of conceivable but non-possible worlds. He argues:

Suppose for example that E is P& ¬ C, where P = ‘everything is physically like so’ and C = ‘there is consciousness.’ To understand E, it’s enough to understand its conjuncts, that is, to know that P is verified by the worlds that are physically like so, and that C is verified by the worlds where there is consciousness. Obviously though to know in these sorts of ways the truth-conditions of P and C does not even begin to tell me whether a world verifying the first can avoid verifying the second. Understanding is knowing what a world has to be like to verify a statement; how easy or difficult it may be for worlds like that to exist is another matter entirely. (Yablo 1999, 461)

It is trivially true that it is entirely different for a possible world to exist in the sense of becoming/being actual than it is for a possible world to be thought of. On the other hand, for a possible world to exist as a possible world—to reflect a real possibility—is not obviously an entirely different matter than being a possible object of (consistent) thought.

Yet Yablo’s line of reasoning has something to it. On Chalmers’ account, a conceptually coherent thought implies that there is at least one possible world picked out by the primary intension. But is this really so? Why couldn’t a conceptually coherent thought, considered as a primary intension, determine an empty extension, a null set of possible worlds?

Here is how Yablo thinks an answer could go (1999, 460): Understanding a proposition is knowing under what circumstances it would be true, or conceiving of it as true as opposed to false. Given that we understand a certain proposition, like P& ¬ C from above, we grasp those circumstances. But circumstances under which a proposition is true are nothing other than those possible worlds at which that very proposition is true – the proposition maps possible worlds to truth values. If we succeed in grasping the truth conditions of a proposition, this implies that there are possible worlds that are mapped onto the value ‘true.’ Some propositions are true at every possible world, while some fail to map any world to the value ‘true.’ Arguably, the latter are propositions we fail to grasp.

There remains a question about what it is to understand a proposition like P& ¬ C apart from the formal description of it as ‘grasping truth-conditions,’ which is why Yablo himself ultimately rejects this suggestion. It is not entirely clear what it is to conceive of worlds without consciousness. For example, how do we conceive of a person having no consciousness while behaving just like a person with consciousness? It is extremely difficult to tell zombies apart from non-zombies. As Yablo remarks, we might end up in a situation where the physicalists fail to imagine a world where P& ¬ C holds, while the non-physicalists are perfectly able to do so, since their respective conceptions are essentially informed by their metaphysical presuppositions.

Apart from these worries connected to this particular proposition, however, there are strong reasons for assuming that (a sufficiently qualified) conceivability implies possibility. What are those reasons? If we were not to accept this relation of implication, we would be committed to what Chalmers calls an ‘extreme modal-realist view (even stronger than David Lewis’s) on which possible worlds are simply “out there”…’ (1999, 481), making our modal judgments true or false independently of our capacity to conceive of different scenarios. We would, in effect, decouple our modal concepts from the domain of rational thought.

Chalmers enunciates why this would be an undesirable outcome. He considers and rejects the position of those who claim that some scenarios – for example, those where the laws of nature are different form our actual laws of nature – while conceivable, might still be metaphysically impossible and thus fail to correspond to any possible world:

Think of the reasons why “possible worlds” talk is introduced into philosophy in the first place. Possible worlds are introduced to deal with counterfactual thought, the semantics of counterfactual language, rational inference, and the contents of belief, among other reasons. A scientist can think counterfactually (and rationally) about scenarios with different laws, and can make true utterances about these scenarios. If we are to use possible-worlds talk to characterize the contents of her beliefs in discovering laws, we will need to appeal to counternomic worlds. Without counternomic worlds, we will not be able to use worlds to make sense of her inference processes. And so on. Ruling out counternomic worlds will make possible worlds useless for many or most standard purposes. Even if someone insists that such worlds are not metaphysically possible, we need logically possible counternomic worlds. (Chalmers, 1999, 481)

This argument draws on our understanding of what role our modal concepts are supposed to play. Furthermore, the reason for accepting this role is that it is hard to make sense of modal concepts otherwise. A special realm of metaphysical modality, where the ties to our capacity to conceive are severed, seems incomprehensible or even mysterious. Even more, it seems useless. In the end, ‘breaking the link between conceivability and possibility breaks the link between rationality and modality’ (Chalmers, 1999, 490).

Maybe there are ‘metaphysical’ modalities which, in every respect, elude our capacities to conceive. But, if so, it is hard to understand what those notions are about. We could still use a concept of possibility that is more permissive and only excludes scenarios that are not ideally conceivable and includes all scenarios that are ideally conceivable. And why should the former notion of possibility, the ‘metaphysical’ notion, be better, more useful, or truer to reality, in any regard, than the latter? To state that the notion of ‘metaphysical’ possibility/necessity conveys a brute fact about the way things are, converts the notion of possibility/necessity into a non-modal notion, it seems. It has some matter-of-factness about it that is incongruous with talk about modality in the first place.

For our concerns, the problem of decoupling possibility from conceivability is the fact that it renders Aquinas’s proofs involving modality, most prominently the Third Way, much less convincing. The point about these proofs is that they initiate a chain of explanations that cries out for a non-contingent, ultimate explanation. This is why a necessary being at the end of the chain is being postulated. However, it appears we cannot grasp the way in which or in virtue of what this being exists necessarily if we find ourselves able to conceive of scenarios where this being does not exist. In effect, we postulate a ‘necessary’ being without really grasping the sense in which the necessary being exists necessarily. This fails in providing us with an ultimate explanation. We are simply told that there is a being in whom the chain of explanations finds an end, and that this being exists by ‘necessity,’ although its non-existence is conceivable. From our perspective, the necessarily existing being is indiscernible from an ultimate brute fact, from Swinburne’s factually necessary God. It seems that the notion of necessity has lost its content.

As an intermediate conclusion, let us state that Chalmers is right. Ideal conceivability, if understood correctly, yields possibility. If it is ideally conceivable that God does not exist, then it is possible that God does not exist. As shown in the last part, God’s non-existence appears to be conceivable in a two-dimensional approach, which indicates that there are possible worlds in which there is no God. Still, the possibility remains that our seeming ability to conceive of godless worlds is ultimately due to some kind of ignorance on our part. Accordingly, it might still be the case that our alleged conceptions of worlds where God does not exist are not instances of ideal conceivability.

This brings us to Aquinas’ own contention, namely, that our assumed ability to conceive of God’s non-existence is ultimately a product of our inability to grasp God’s nature. Thus, following Aquinas, there are reasons for assuming that the apparent conceivability of godless worlds fails to point to a possible world. At the same time, there are intelligent beings who are able to grasp God’s nature. Can they conceive of possible scenarios where God does not exist? In that case, the two-dimensional thinking is being reiterated and we end up, again, with possible worlds entailing no God. Addressing all of this will be our focus in what remains.

The self-evidence of God’s existence

According to Aquinas, a self-evident proposition is one where the property ascribed to the subject by the predicate is included in the essence of the subject. However, some self-evident propositions are self-evident in themselves while failing to be self-evident to us because we do not understand the subject’s essence sufficiently.Footnote 17 This is the case for God and the self-evidence of God’s existence:

Just as it is evident to us that a whole is greater than a part of itself, so to those seeing the divine essence in itself it is supremely self-evident that God exists because His essence is His being. But, because we are not able to see His essence, we arrive at the knowledge of His being, not through God Himself, but through His effects. (Aquinas 1975, I, 11)

In Part Two, I argued that God’s existence is necessary in a broad logical sense for Aquinas, as opposed to being merely factually necessary. After that, the claim was made that this gives rise to a tension in his account due to his rejection of a priori arguments for God’s existence. Here, Aquinas does claim that God’s existence is indeed self-evident and a priori appraisable by mere knowledge of the divine essence, but only for those who are actually able to grasp this essence. From this position, we could claim that we are unable to grasp God’s nature and this is the reason why we are seemingly able to conceive of God’s non-existence, even though the latter is impossible.

What should we make of this claim? What reasons do we have for thinking that our apprehension of God is insufficient for assessing whether God’s non-existence is possible? A blunt claim that we cannot conceive ideally of God’s non-existence because we cannot grasp God’s nature is not immediately reasonable. After all, it seems that we can conceive of worlds without God irrespective of what the actual nature of God is. In other words, we do not necessarily need to understand God in any depth to imagine God not existing. Likewise, we can conceive of the non-existence of other objects, the natures of which we do not fully comprehend (Bigfoot, say). It is sufficient that we have some grasp of God, one would assume.

At this juncture, we must examine what it means to think about God according to Aquinas. How do we, who are not in a position to grasp God’s nature, conceive of God’s existence? As described in Part Two, in a Thomistic framework, we conceive of God as an ultimate cause of the world. We arrive by way of argument—the Five Ways—at an uncaused cause and at a source of the existence of everything else. Since we cannot grasp the nature of God, we have cognitive access to God only through God’s effects. For a thing to exist is for it to receive being (esse) from the source of all being, which is God. But, conversely, for a thing to be God from our perspective, that is, to serve as the referent of our expression ‘God,’ is for it to be the ultimate cause of everything existing and the source of everything’s existence. Thus, our access to God is granted by the fact that non-divine things that we do grasp very well can be thought of as God’s effects. The Five Ways to God are not only demonstrations of God’s existence but are also ways for us to give content to the notion of God.

To conceive of God’s non-existence for us, accordingly, would be to conceive of the world lacking this kind of ultimate cause and source of existence. How do we do that? Perhaps we can grant that God is the cause of everything and the source of existence as a matter of fact, and still conceive of existence as having nothing to do with God, i.e., with subsistent being. Maybe we can imagine things existing without receiving their being from God and without having an ultimate cause. Alternatively, instead of imagining everything being as it is minus God, we could maybe conceive of total nothingness, a totally empty possible world. If nothingness in this sense is ideally conceivable, then it is possible, according to the remarks in Part Five on conceivability and modality, which means that God exists contingently in the broad logical sense.

Remember, we do not want to rely on any mysterious notion of ‘metaphysical’ necessity which has no link whatsoever to conceivability. Thus, even if things actually do receive their being from God, we could perhaps conceive of scenarios where those things just exist, independently of any source of being. Moreover, even if a totally empty world is impossible due to God’s ‘necessary’ existence, we can perhaps conceive of scenarios where the ‘necessarily’ existing God does not exist. Again, pounding the table and emphatically insisting on the ‘metaphysical’ impossibility of these scenarios should not be counted as a satisfying response.Footnote 18 The only option, therefore, is to argue that the presumed conceivability of God’s non-existence on our part is not a case of ideal conceivability.

Aquinas on being

The Thomistic way into this is to focus on being. For those creatures who see the divine essence, God’s existence is self-evident, Aquinas claims. But God’s essence is exactly that: being, although in the qualified sense of subsistent being. What kind of thing is being? How do we apprehend being? What is it that we do when we ascribe being to things? What exactly is it that we conceive of when we conceive of something as existing, or as not existing?

In what follows, I will review and endorse Aquinas’ position on this. Without arguing exhaustively for it, I hope to present it as a reasonable option. As such, it would corroborate the claim that the necessity of God’s existence can be coherently and sensibly combined with its a posteriori character on a Thomistic account. This is what I aim to demonstrate.

To make a very long story very short, Aquinas views being as act.Footnote 19 The notion of being in Aquinas does not refer to the existential quantifier, nor to some kind of property. Instead, it refers to the actualization of an essence; the moment of actuality as opposed to potentiality. For a thing to exist is for its essence to be actualized, and this is what it means to be. In Aquinas, this signals a peculiar kind of dependence where all things existing remain dependent on an efficient cause bringing about their act of existing by actualizing their forms. This kind of dependence, moreover, is the driving force behind the argument for God’s existence in De Ente: the actuality of objects receiving their being from an external cause raises the question of an ultimate source of being where the transmission of being through actualization comes to rest.Footnote 20

For our concerns, the important thing about this is what repercussions it has for our ability to grasp what it is to exist. According to Aquinas, being is the proper object of what he calls the second operation of the intellect, which is judgment. In its first operation, by contrast, the intellect grasps the nature of a thing, its real definition. The result of the first operation is a concept, while the second operation brings forth a proposition. An assertion about existence belongs to this second operation where it is said of a thing that it exists. We do not consider things as having existence as part of what they are. We do not attribute existence to them as one more property that they possess; rather, we judge that they exist or fail to exist as the things they are and with the properties they have. Here is how Aquinas describes the dual operations of the intellect:

We must realize that, as the Philosopher says, the intellect has two operations, one called the ‘understanding of indivisibles’ by which it knows what a thing is, and another by which it joins and divides, that is to say, by forming affirmative and negative statements. Now these two operations correspond to two principles in things. The first operation concerns the nature itself of a thing, in virtue of which the object known holds a certain rank among beings, whether it be a complete thing, like some whole, or an incomplete thing, like a part or an accident. The second operation has to do with a thing’s being (esse), which results from the union of the principles of a thing in composite substances, or, as in the case of simple substances, accompanies the thing’s simple nature. (Aquinas 1963, V, 3c)

If we follow Aquinas, while gently eliding the details of his account, the decisive insight related to this is that our grasp of existence is not conceptual.Footnote 21 We do not have a concept of existence which we understand separately, and with which we construct a proposition. Instead, our grasp of existence is a concomitant feature of our act of judging. Existence is something we grasp indirectly. This is ultimately the reason why Anselm-style arguments for the existence of God are doomed from the outset. No matter how much perfection we ascribe to a being, we will never be able to derive its existence from its perfections.Footnote 22 This is because existence cannot be a feature of a thing which we grasp together with its further features. Being categorically different from the essence of a thing, and from its accidental traits, existence is the object of a different intellectual operation than a thing’s essential and accidental properties. At the end of the Third Way, or, more explicitly, at the final step of the ascendance in De Ente, we realise that a being must exist whose existence is subsistent, whose existence is its essence. This step, however, is still within the range of judgment. The notion of subsistent existence lacks a conceptual content from our perspective. Instead, the notion draws its content from arguments for the existence of such a being.

How, then, can we conceive of godless worlds against this background? Remember that, in a Thomistic framework, conceiving of a scenario where there is no God amounts to conceiving of a scenario where the empirical world has no ultimate source or cause of its existence, or, alternatively, where absolutely nothing exists.

Here is how I believe the above exposition of Aquinas’ account of conceptualisation and judgment bears on that question. It seems that we must grasp what it is to exist in order to conceive of a thing’s existence as independent of a source of existence. We have to conceive not only of that particular thing but of its existence as well, in order to conceive of that existence itself as independent of a higher source of being and independent of an ultimate cause. Now, conceiving of things as existing, and in a second step, as existing independently of any source of existence, is different from merely judging that they exist. In order to do the former, we have to grasp their act of existing. In Aquinas’ terminology, we must understand what it is for an object not only to be what it is (its essence), but also what it is for it to be what it is, to be actualized. Furthermore, we must view this moment of being actualized as holding independently of any ultimate source of actualization. Or, in less Thomistically charged vocabulary: we have to grasp the difference between being the mere product of an act of conceiving and actually being out there, and that the content of this difference—the very existing itself—is independent of any ultimate source of existence. But it is simply not clear what it is that we need to think in order to be able to say that we conceive of things existing without an ultimate source of their existence or actualization. If we conceive of those things, what kind of difference does it make to this conception if we augment it by conceiving of them as lacking a source of their existence? To be able to do that in an intelligible way, we would have to comprehend what it is for them to exist, but that is something we have no direct understanding of, as explained above. The transfer from a conception of a thing to a conception of its act of existing remains elusive. The difference between a picture I have in my head of things existing out there and the picture I have in my head of things existing out there, as opposed to merely being part of a picture in my head, is nothing I can conceive of in a direct manner.

To substantiate and clarify this line of thought, consider the following statement from Elisabeth Anscombe commenting on Hume’s views on causality (causality being intimately related to existence on a Thomistic account) and the implications of our alleged ability to imagine causeless events:

But what am I to imagine if I imagine a rabbit coming into being without a cause? Well, I just imagine a rabbit coming into being. That this is the imagination of a rabbit coming into being without a cause is nothing but, as it were, the title of the picture. Indeed I can form an image and give my picture that title. But from my being able to do that, nothing whatever follows about what is possible to suppose “without contradiction or absurdity” as holding in reality. (1974, 150)Footnote 23

Of course, just like existence, causation is something we grasp very well in terms of judging that some things or events cause other things or events. But conceiving of causation in itself is a different matter. We can clearly imagine scenarios without any rabbits and scenarios entailing rabbits. Accordingly, we can shift between those scenarios—we just picture a location where no rabbit is present and then put a rabbit into the picture by means of our imagination. That a rabbit being imagined in this way could represent a picture of something coming-into-being without being preceded by something else causing it, however, is not part of the picture itself. It is an additional assumption, or, indeed, a title of the picture. Analogically, existence is something we have a rather good grasp of in terms of judgment. We notice that some things exist, and we can infer the existence of some things based on evidence making the existence of those things probable. But existence itself, just like causation (and related to causation), eludes us. We cannot conceive of things existing in addition to, and as distinct from, our conceiving of the properties of those things. To put it bluntly: considered in itself, our conceiving of existence—as opposed to judging that things exist—is exhausted by our capacity to associate the term ‘exists’ with our conceptions of things. Like the rabbit in Anscombe’s example: far from being conceived of as a causeless rabbit, it is really a normal rabbit declared to be without a cause.

I take it that this poses a strong reason for assuming that our alleged conception of things existing without having an explanation of their existence in terms of a transmission of existence from an ultimate source of existence is moot. This applies to our efforts to conceive of a completely empty world as well. How do we conceive of an empty world? Presumably, by removing existence from all things that do exist in the actual world. Thus, we have to think that all familiar objects and properties are not actualized. Yet the difference between things that lack actualization and things that are actualized is nothing we can conceive of in a direct way. It seems the best conception we can produce of a completely empty world is simply a mental picture of emptiness paired with a description of it as being empty. Supposedly, emptiness means that the world is lacking actualized things. Since we do not grasp what it is for a thing to be actualized (that is, to exist), however, we cannot give any content to this conception. Thus, while I can judge that this or that thing does not exist, or conceive of scenarios where some things do not exist by re-arranging objects in my imagination, I cannot give any conceptual (or otherwise intelligible) content to the notion that all things I know of would lack existence.

Provided that Aquinas’ views on being are correct, this suggests that our efforts to conceive of God’s non-existence is not an example of ideal conceivability. Our inability to conceptualise existence is a strong reason for concluding that we cannot conceive of God’s non-existence in an ideal way on a Thomistic account. If our apparent ability to conceive of godless worlds is not an example of ideal conceivability, it is not a good guide to the modality of God’s existence either. Therefore, it might be the case that God exists by broad logical necessity even given Chalmers’ plausible views on conceivability and possibility.

God’s necessary existence from the perspective of the blessed: What is it that we know that we don’t know?

For this approach to succeed, it is clear that for those creatures who grasp God’s essence, and for God himself, the non-existence of God must be incomprehensible and remain an inconceivable scenario. Otherwise, we would end up in the grinder of the two-dimensional machinery once again and there would still be possible worlds where God fails to exist. If angels and the blessed were able to conceive of God’s non-existence while denying the metaphysical possibility of his non-existence, this would just look like a modal re-branding of the fact that God exists. Thus, for the Thomist, the plausible assumption that angels and the blessed, who apprehend God’s essence,Footnote 24 could still conceive of his non-existence in an ideal way, must be rejected.

How can we reject this? How can we think our way into this without having to think thoughts that we are unable to think for principal reasons? I believe the best we can do is this: creatures grasping God’s nature as subsistent being do not understand existence only indirectly in the synthesizing act of judgment, like we do. Instead, they derive the meaning of the term ‘exist’ from a deeper understanding of existence. In contrast to our existence-involving judgments about reality, they apprehend the inner structure of reality and how reality depends on a source of being. Rather than ascending intellectually to God by means of judgments concerning created things, they take the opposite route and intuit the nature of existence of all created things as derived from this source of existence.

If this is true, the apparently plausible idea that even angels and the blessed could conceive of God’s non-existence is mistaken. It stems from the error of viewing their understanding of existence in accordance with our practice of judgment – where existence is only grasped concomitantly. From their perspective, the very question of the existence or non-existence of things can only be asked against the backdrop of the source of all existence, which gives content to their thoughts about existence. Entertaining the proposition ‘God does not exist’, while having this understanding of God as subsistent being is not possible, since the very nature of the state or activity that is expressed by the term ‘exist,’ thus understood, is nothing other than what is expressed by the subject term. Footnote 25 A scenario where God does not exist is inconceivable from this standpoint – not because the stability and incorruptibility of God make him factually necessary, but because the very question of whether God exists already involves a notion of existence that ultimately flows from the nature of God.