A grounding modal ontological argument

The simplest version of the argument is as follows:

1. A1. It is possible that God exists.

2. A2. If it is possible that God exists, there is something that grounds the fact that it is possible that God exists.

3. A3. Only God, if anything, grounds the fact that it is possible that God exists.

4. A4. Therefore, God exists.

This argument needs refining, but it gets across the main thrust of the reasoning I am suggesting – God's possibility requires God's existence as a ground. Addressing why this might be, and how best to express this idea, will be two of the main tasks of this section.

The first amendment we should make to the argument is to replace the term ‘God’ with a suitable description, lest the worry arise that we are illicitly smuggling in the existence of God in our premises by using ‘God’ as a directly referential proper name. There are various possible replacements for the term ‘God’ including ‘a perfect being’, ‘something than which no greater can be conceived’, ‘something all-good, all-powerful and all-knowing’, and ‘a divine being’. I shall use the first of these.Footnote ¹ This change results in the following argument:

1. B1. It is possible that there is a perfect being.

2. B2. If it is possible that there is a perfect being, there is something that grounds the fact that it is possible that there is a perfect being.

3. B3. Only a perfect being, if anything, grounds the possibility that there is a perfect being.

4. B4. Therefore, there is a perfect being.

Though I shall address the claim that God (i.e. a perfect being) is possible later in the article, the aim of this article is neither to assert nor deny it – I am interested rather in the argument from this premise to the conclusion that God exists.

The obvious rationale for B2 (i.e. the claim that something grounds the possibility of the perfect being, if it is possible) is that all possibilities, or all possibilities that concern what exists, are grounded in what in fact exists. Indeed, Kant appeals to something very like this idea in his pre-critical ‘Only Possible’ argument for the existence of God, which tells us that the ens realissimum (i.e. the ultimately real being, which Kant considers to be God) must exist in order to ground any possibilities (Kant (Reference Kant and Walford2002); see the next section for further discussion of Kant's argument).

A schematic version of the claim upon which we might rest B2 runs as follows (we shall call it ‘PEA’ for ‘Possible Existence on Actual’):

Some examples may help illustrate the manner in which actual things may ground possible things. Consider first the most straightforward way something might ground a possibility – by being an example of it. Thus, because I am human, I ground the fact that it is possible that there are humans. In general, any F grounds the fact that it is possible that there are Fs. Similarly, something may ground the possibility that there are Fs by being disposed to become an F (or by having the categorical base for such a disposition). Some plurality of things may ground the possibility that there are Fs by having the potential to compose an F. What PEA suggests is that, whenever it is possible that there is an F, there is always something (or things) which grounds this possibility (in one of the above ways, or in some other way).

One may object that it is not things that ground what possibly exists, but facts (or states of affairs) about these things. Thus, instead of saying that an F grounds the possibility that there are Fs, we should say that this thing's being an F grounds this possibility. Rather than some potential F's grounding the possibility that there are Fs, this thing's being a potential F does. Seeing as some particular thing (call it ‘a’) may be only contingently an F, or only contingently disposed to become an F, we may question why a grounds the possibility that there are Fs.

Though this point is well taken, I see it as mainly a terminological issue. If something is an F, we may say that it's being an F grounds the possibility that there are Fs, or we may say that the thing itself grounds the possibility that there are Fs by being an F. Though ‘grounds’ may be used slightly differently in each such claim, the important point is that the thing figures in some grounding relation to the possibility that there are Fs. On one view, the thing is a constituent of the state of affairs that bears a grounding relation to the possibility that there are Fs. On the other view, the thing itself bears a grounding relation to this possibility in virtue of being a constituent of the relevant state of affairs. I shall talk throughout the article of this latter grounding relation, though everything I say could be straightforwardly translated into talking about the former grounding relation.Footnote ²

Why might we accept PEA, thus understood? I think PEA (or something near enough) will seem attractive to those who think of possibility claims as less fundamental than claims about actuality – that what possibly exists is built from what in fact exists. Note that this kind of motivation is not predicated on any prior commitment to theism, but simply the idea that possible things are possible because certain things are actual. Indeed, we may even see some versions of combinatorialism as capturing a similar thought – mere possibilities are (suitably determined) recombinations of actual things, properties, and relations (see e.g. Armstrong (Reference Armstrong1989)).

Turn now to B3 – the claim that only a perfect being grounds the possibility that there is a perfect being (if anything does). The natural case for B3 rests on two claims – a plausible general claim about what grounds the possibility of what, and a claim about the nature of a perfect being. Let us consider these in turn.

The first of the two claims that support B3 is (roughly) that the less fundamental does not ground the possibility of the more fundamental. We may express this rather modest idea with the following schema (call it the ‘Possibility Grounding Principle’ or ‘PGP’):

In other words, if something grounds the possibility that there is an F, it is at least as fundamental as the least fundamental possible F (i.e. a thing does not ground the possibility of an F if the least fundamental possible F would still be more fundamental than this thing).

PGP is a natural extension of the commonplace thought that the less fundamental cannot ground the more fundamental. Just as one thing's grounding another entails that the former is no less fundamental than the latter, one thing's grounding the possibility of another also entails that the former is no less fundamental than the latter. Thus, to take two arbitrary examples: a refrigerator cannot ground the possibility that there are electrons; an economy cannot ground the possibility of tigers. This is because refrigerators are less fundamental than any possible electrons, and economies less fundamental than any possible tigers. If the possibility of electrons is grounded in anything, it is in either something as fundamental as electrons (such as electrons themselves), or in something even more fundamental than electrons (such as, perhaps, quantum fields or superstrings).

The second claim upon which B3 rests involves the idea that a perfect being is perfectly fundamental – to fail to be perfectly fundamental is to be (to some extent) imperfect. Indeed, we may further maintain that a perfect being is uniquely perfectly fundamental. That is, if it is possible that there be a perfect being, then, of necessity, anything which is not a perfect being is thereby less fundamental than any possible perfect being. This claim expresses the idea that, not only is there nothing that surpasses God's fundamentality (if God is possible), but nothing even equals God's fundamentality. We may put the point like this (call the following ‘Perfect Being Fundamentality’ (‘PBF’)):

PBF captures the idea that, given that God (i.e. a perfect being) is possible at all, anything as fundamental as God (or more so) is God.

PGP and PBF together entail B3. An instance of PGP tells us that anything that grounds the possibility of a perfect being is at least as fundamental as some possible perfect being. According to PBF, anything which is at least as fundamental as some possible perfect being is a perfect being. Thus anything which grounds the possibility that there is a perfect being is a perfect being. This last claim is equivalent to B3.

We may incorporate PEA, PGP, and PBF into a final formulation of our grounding modal ontological argument for God:

1. C1. It is possible that there is a perfect being.

2. C2. If it is possible that there is an F, there is something that grounds the possibility that there is an F. (This is PEA)

   1. C-Lemma1: If it is possible that there is a perfect being, there is something that grounds the possibility that there is a perfect being. (Instance of C2)

   2. C-Lemma2: There is something that grounds the possibility that there is a perfect being. (From C1 and C-Lemma1)

3. C3. Anything which grounds the possibility that there is an F is at least as fundamental as some possible F. (This is PGP)

   1. C-Lemma3. Anything which grounds the possibility that there is a perfect being is at least as fundamental as some possible perfect being. (Instance of C3)

4. C4. Anything which is at least as fundamental as some possible perfect being is a perfect being. (This is PBF)

   1. C-Lemma4. Anything which grounds the possibility that there is a perfect being is itself a perfect being. (From C-Lemma3 and C4)

5. C5. Therefore, there is a perfect being. (From C-Lemma2 and C-Lemma4)

In essence, then, given (a) the possibility of a perfect being, conceived of as uniquely perfectly fundamental, and (b) the idea that all possible kinds of things are grounded in at least equally fundamental actual things, we may conclude that a perfect being exists.

Similarities to other arguments

It should be relatively clear why I call this a grounding modal ontological argument, but it is perhaps worth setting out the reasons explicitly. First, why might it be considered an ontological argument? Because it bears some of the hallmarks of several paradigmatic ontological arguments – it appeals to principles that are mainly supported a priori (rather a posteriori); it argues directly for the existence of a being many would immediately recognize as God (unlike usual cosmological arguments or design arguments, the main task of which is to try to establish a first cause, designer of the universe, or some such, and then support the idea that this thing is God);Footnote ³ and it appeals in part to what it takes for a being to be perfect (in this case, a perfect being is uniquely perfectly fundamental). These features, or closely related features, are present in the ontological arguments of Anselm (Reference Anselm, Davies and Evans1998), Descartes (Reference Descartes1984), Hartshorne (Reference Hartshorne1962), Malcolm (Reference Malcolm1960), Plantinga (Reference Plantinga1974), Nagasawa (Reference Nagasawa2017), and many others.

Second, why is it a modal ontological argument? The answer is simple: because it appeals to the possibility of God, and an idea of what God's perfection entails, in order to argue for the existence of God. All modal ontological arguments of which I am aware have these features (see, again, Malcolm (Reference Malcolm1960); Hartshorne (Reference Hartshorne1962); Plantinga (Reference Plantinga1974)). We shall explore whether this grounding modal ontological argument has any advantages over these other arguments in the next section.

Third, why is it a grounding modal ontological argument? This is because, unlike more paradigm modal ontological arguments, it appeals to the notion of grounding. One might worry that this puts the argument more in the territory of a cosmological argument, as it appeals to what God can explain (on the assumption that grounding is or underlies an explanatory relation). There is a precedent, however, for arguments involving appeal to some form of explication being deemed ontological arguments. In particular, Graham Oppy, in his (then) exhaustive Reference Oppy1995 book on ontological arguments, categorizes some ontological arguments as ‘modal arguments involving explicability’. The arguments he addresses under this heading are all variations of an argument found in Ross (Reference Ross1969). The basic idea of this argument is this: God is (by definition) unpreventable, and thus there can be no explanation of God's non-existence; but if there is no God, there can be an explanation of his non-existence; therefore, God exists. As should be clear, there is little in common here with my argument – among many other differences, the crucial move in the Ross-style argument is that the non-existence of God must lack an explanation, while mine appeals to the idea that God's possibility demands explanation.

Another argument worth mentioning in relation to mine is Kant's Only Possible argument for God (Kant (Reference Kant and Walford2002)). It would take us too far afield to look in depth at Kant's argument, but its (very) broad outline may be rendered in similar manner to my initial formulation of the grounding modal ontological argument, replacing the idea that God is possible with the idea that something is possible (the following should not, of course, be seen as an attempt at serious exegesis of Kant, but rather as a way of thinking of his argument that highlights its similarities to and differences from mine):

1. K1. Something is possible.

2. K2. If something is possible, there is something that grounds this fact.

3. K3. Only God, if anything, could ground the fact that something is possible.

4. K4. Therefore, God exists.

Just as, on my argument, God exists as a ground for God's possibility, God exists, on Kant's proof, as a ground for possibility tout court. Indeed, the natural rationale for thinking that God's possibility needs an actual ground is that possibilities in general need actual grounds (a thought I express above in PEA). In a sense, then, my argument and Kant's draw upon the same thought – possible things are grounded in actual things. Outside of this (admittedly significant) commonality, however, the arguments are otherwise quite different. Kant attempts to show, through many complex steps (steps which find no counterpart in my argument), that the existence of any possibility requires the existence of a unique and necessary being which grounds all possibilities – a being which he further argues is God. His starting point – that something is possible – is far less controversial than mine (that God is possible), but this starting point leaves him much further from his endpoint – the existence of a unique God – than I am from mine (that there is a God). For far more in-depth discussion of Kant's argument, see Chignell (Reference Chignell2009) and Stang (Reference Stang2010).Footnote ⁴

The last argument I wish to compare to mine is Descartes's first argument for God in his Third Meditation (Descartes (Reference Descartes1984), 24–36). Indeed, my argument is more similar to Descartes's argument than it is to any of those mentioned above, despite Descartes's argument not being considered an ontological argument, or a modal argument, or even a grounding argument (indeed, Descartes's argument is more often interpreted as a cosmological argument (see Dilley (Reference Dilley1970), or even a teleological argument (see Dennett (Reference Dennett2008)). As with my discussion of Kant's argument above, the following is not an exercise in serious exegesis of Descartes's argument, but an attempt to situate my argument better in relation to others that it resembles in notable ways.

The basic thought behind Descartes's argument is that only God could be the cause of our idea of God. As with Kant's argument, we can express the broad outlines of Descartes’ argument similarly to the first formulation of my argument, simply by replacing certain key notions in my argument with different key notions from Descartes. Thus, instead of the possibility of God, Descartes talks of the (clear and distinct) idea of God. Instead of grounding, Descartes talks of another relation that can underlie explanation – causation. Making these modifications to A1–A4 above results in the following argument:

1. D1. We have a clear and distinct idea of God.

2. D2. If we have a clear and distinct idea of God, there is something that causes our clear and distinct idea of God.

3. D3. Only God, if anything, could cause our clear and distinct idea of God.

4. D4. Therefore, God exists.

It is not just the basic outlines of our arguments that are similar, however. Descartes appeals to principles that resemble those in my final version of the argument (C1–C4), as we shall now investigate.

Just as we appeal to the general thesis that all possible things are grounded by actual things (an expression of which we find in PEA) to support the claim that any possible perfect being is grounded by something actual, Descartes appeals to the general claim that all clear and distinct ideas are caused by something to support the claim that any clear and distinct idea of God is caused by something. We may put this schematically as follows (we shall call the following the ‘Idea Cause Principle’ (or ICP)):

Descartes's commitments are in fact even stronger than this – he tells us that ‘something cannot arise from nothing’ (Descartes (Reference Descartes1984), 28) – that is, everything is caused by something, not just ideas. For our reconstruction of his argument, we shall appeal only to ICP, but it is worth noting that he supports it with the stronger claim.

Indeed, Descartes derives the thesis that something cannot arise from nothing from yet another, namely that ‘there must be at least much reality in the efficient and total cause as in the effect of that cause’ (Descartes (Reference Descartes1984), 28), from which he also infers that ‘what is more perfect – that is, contains in itself more reality – cannot arise from what is less perfect’ (Descartes (Reference Descartes1984), 28). Descartes embraces the thesis that things can have more or less reality; in particular, he thinks that an infinite substance is more real than a finite substance, which is more real than an attribute of a substance, which is more real than a mode of an attribute. What's more, this hierarchy of reality must have a certain causal structure – the less real cannot cause the more real. While talk of degrees of reality or being is somewhat out of philosophical fashion now, contemporary metaphysics is generally happy with a similar notion – that of degrees of fundamentality (indeed, McDaniel (Reference McDaniel2013) argues that we can spell out either notion in terms of the other). If we substitute reality for fundamentality and causation for grounding in Descartes's claim that the less real cannot cause the more real, we arrive at a claim I appealed to above: the less fundamental cannot ground the more fundamental.

I extend this latter thesis to encompass the claim that the less fundamental cannot ground even the possibility of the more fundamental – this is effectively how I arrive PGP. Descartes makes a similar move – he claims not only that the less real cannot cause the more real, but that the less real cannot cause our (clear and distinct) ideas of the more real. He expresses this thought using a distinction he draws between the formal and the objective reality of an idea. Formal reality is what we might simply deem reality – something has formal reality just in case it is real (with the added note that, for Descartes, reality is a matter of degree). The objective reality of an idea (or at least a clear and distinct idea) is a function of the formal reality of what is represented by this idea; thus, an idea of a substance and an idea of a mode, while having the same formal reality (both being ideas, which Descartes thinks of as modes), have differing degrees of objective reality, the former having more than the latter because it represents something more real. In this terminology, Descartes's view is that, if an idea has a certain degree of objective reality, this idea is caused by something which has at least that degree of formal reality. For the purposes of reconstructing his argument, we may put the point without utilizing this terminology (call the following schema ‘Idea Reality Principle’ or ‘IRP’):

IRP shares much in common with PGP – they are each plausible extensions of the thought that the less fundamental/real cannot give rise to the more fundamental/real.

Lastly, recall that the final principle we appealed to in our argument (PBF) captured the idea that a perfect being, if possible, is uniquely fundamental. Similarly, Descartes thinks of God as exactly that infinite substance which has the greatest (formal) reality. Indeed, Descartes thinks it is the only imaginable such substance. Given this, a clear and distinct idea of God has the greatest objective reality – a reality matched or surpassed only by the formal reality of God. Thus, anything that matches or surpasses the reality that our idea of God represents God as having is God. We may express this thought in the following thesis (call it ‘Perfect Being Reality’ (or ‘PBR’)):

It is clear that ICP, IRP and PBR are close analogues of PEA, PGP and PBF.

We are now in position to state (my interpretation of) Descartes's argument:

1. E1. We have a clear and distinct idea of a perfect being.

2. E2. If we have a clear and distinct idea of an F, there is something that causes our clear and distinct idea of an F. (This is ICP)

   1. E-Lemma1: If we have a clear and distinct idea of a perfect being, there is something that causes our clear and distinct idea of a perfect being. (Instance of E2)

   2. E-Lemma2: There is something that causes our clear and distinct idea of a perfect being. (From E1 and E-Lemma1)

3. E3. Anything which causes our clear and distinct idea of an F has at least the same degree of reality as our clear and distinct idea represents an F as having. (This is IRP)

   1. E-Lemma3. Anything which causes our clear and distinct idea of a perfect being has at least the same degree of reality as our clear and distinct idea represents a perfect being as having. (Instance of E3)

4. E4. Anything which has at least the same degree of reality as our clear and distinct idea of a perfect being represents a perfect being as having is itself a perfect being. (This is PBR)

   1. E-Lemma4. Anything which causes our clear and distinct idea of a perfect being is itself a perfect being. (From E-Lemma3 and E4)

5. E5. Therefore, there is a perfect being. (From E-Lemma2 and E-Lemma4)

The similarities between my argument and Descartes's are manifest. In some respects, we might see my argument as a modalized version of Descartes's argument. Just as the notion of something's existing in the understanding, as it features in Anselm's ontological argument, may fruitfully (though perhaps not accurately) be read as something's being possible (thus giving rise to a whole host of so-called modal ontological arguments), we may read Descartes's claim that we have a clear and distinct idea of something as the claim that this thing possibly exists. Doing so (and making the rather natural adjustments that such a change suggests) leads us to something very much like my grounding modal ontological argument. Rather than this meaning that Descartes's argument is really an ontological argument, or that my argument is not, I take this to show that the labels we give these arguments are somewhat arbitrary.

The main advantage of my argument over Descartes's is that his IRP (that anything which causes our clear and distinct idea of an F has at least the same degree of reality as our clear and distinct idea represents an F as having) is less plausible than my PGP (that anything which grounds the possibility of an F is at least as fundamental as some possible F). Aside from the fact that degrees of reality are less accepted now than are degrees of fundamentality, it is unclear why a clear and distinct idea's cause must match (or exceed) not just the reality of the idea itself, but of what the idea represents. Despite Descartes's protestations, it seems possible that we arrived at the idea of an infinite being by the negation of the finite (or the idea of a perfect being by a negation of the imperfect) – that is, our idea of God may not require God as a cause. There is, of course, much more that may be said about this aspect of Descartes's argument and about many other of its interesting features, but this is not the place to give it a comprehensive treatment (see Kenny (Reference Kenny1968), ch. 6, and Carriero (Reference Carriero2009), ch. 3, for more thorough examinations).Footnote ⁵

Worries with my argument

There are several criticisms of my argument that might be raised. Because my aim is not to defend the argument, but rather draw attention to it, I will not attempt conclusively to rebut all these worries. This said, I do think certain natural criticisms are not as strong as they may first appear, and I shall set out my reasons for thinking so.

First, even leaving aside the idea that a perfect being is possible (we shall address this in our next objection), one might worry that the argument rests on several questionable metaphysical claims, namely PEA, PGP, and PBF. Cannot someone easily resist the argument by rejecting any of these three principles? Or, instead of rejecting any of these principles, might not someone simply fail to see why they should be accepted, and thus fairly maintain that the argument is not rationally persuasive?

This is in some ways fair enough – there is no quick and easy argument for metaphysical principles like PEA and PGP – such metaphysical principles will be justified holistically, if at all, through cohering well with some attractive general metaphysical picture. Before I sketch such a picture, however, it is worth noting that PBF is probably not very controversial. Those who deem a perfect being to be possible are likely to deem it uniquely perfectly fundamental, in which case PBF stands, while those who deem perfection impossible will accept that PBF is trivially true (because then nothing is such that it is at least as fundamental as some possible perfect thing).

What, then, of PEA and PGP? Note first that these two theses make good bedfellows. Just as Descartes derives his IRP and ICP from a broader principle that the more perfect cannot arise from the less perfect, PEA and PGP both flow from a metaphysical picture according to which there is a hierarchy of fundamentality whereby all possible things are grounded in actual things higher in this hierarchy (where being higher corresponds to being more fundamental). Such a picture might be informed by (a) a judgement (made on the basis of considerations of simplicity, elegance, fruitfulness, or scientific credentials) that we should exclude brute possibility from our ideology and ontology, in favour of the objects, properties, and relations of the actual world, plus (b) the idea that grounding possibilities in the actual is a legitimate way of accounting for the possible – a way which does not thereby complicate our ideology or render it less elegant or fruitful. Such considerations may be supplemented by examples (such as those above concerning refrigerators and electrons, economies and tigers) that offer support to such a picture, and a suspicion of supposed possibilities that wander too far from what can plausibly be connected to how our universe, and the things in it (or potentially in it), might have turned out. We might further support this picture by trying to illustrate its power in application – perhaps such a picture can help account for relationship between phase spaces in physics and metaphysical possibility (see Williamson (Reference Williamson2018) for an examination of this connection), or in answering the question ‘why is there something rather than nothing?’ (in brief, there is something because something is possible and thus something must thus actually exist to ground this very possibility).

Such a metaphysical picture is, of course, open as much to attack as to support. Thus, sceptics of the notions of fundamentality or grounding will find little to recommend it (for a prominent attack on the notion of grounding, see Wilson (Reference Wilson2014)). Others may accept the idea that possibility is ungrounded on the basis that what is possible remains constant regardless of what is the case (for more on this point, see my reply to a rejoinder to my reply to the second and third objections). Yet others may reject the metaphysical modality that the picture seems to presuppose (e.g. Quine (Reference Quine1953)), or simply find that other metaphysical pictures do a better job at combining their preferred theoretical virtues.

The matter is thus not as simple as its being a good or bad idea to accept PEA and PGP. These principles cohere well with an attractive metaphysical picture, but it is a picture that is not without its problems. Still, if one is drawn independently to such a picture, and finds the problems with it overblown, one is but a short leap to accepting these principles. It is perhaps such people who will find most interest in the argument.

A second natural objection to the argument is that we are none of us in a position to assert or accept its first premise: that a perfect being is possible. Indeed, some might be tempted to reverse the argument. That is, such a person may accept PEA, PGP, and PBF, think that there is no perfect being, and thus conclude that a perfect being is impossible. After all, she might reason, as there is no perfect being, there is nothing to ground the possibility of a perfect being, and thus such a being must be impossible.

This kind of objection will be familiar from discussions of other modal ontological arguments. An atheist may well be convinced that necessary existence is a perfection, and thus that God must exist if he might, but conclude that, since God does not exist, he must not. Or an agnostic might complain that if God's necessary existence and his possible existence are a package deal, we have no more prior reason to accept his possible existence than his actual existence.

This objection ties in with the third natural objection to my argument, which is that, even if the argument is sound, it is superfluous because we have simpler and more compelling routes from God's possibility to God's existence – namely that necessary existence is a perfection, and thus God must exist if he might. Assuming, then, that we are justified in accepting the possibility of God, we need not accept PEA and PGP (and their accompanying metaphysical picture) in order to embrace God's existence, but rather the more straightforward claim that necessary existence is a perfection. The second and third objections form a dilemma – either we are not justified in accepting the possibility of God (independently of accepting God's existence), in which case my argument fails, or we are so justified, in which there is a less controversial route to God's existence via the usual modal ontological arguments.

The key to my response to these objections is to note that usual modal ontological arguments are open to a familiar atheistic parody. Just as the theist might assert the possibility that God exists and conclude, via the claim that necessary existence is a perfection, that God exists, the atheist may assert the possibility that God does not exist and conclude, via the claim that necessary existence is a perfection, that God does not exist. This symmetry is why it is a delicate matter for proponents of usual modal ontological arguments to appeal to the possibility of God's existence – the standard ways we might come to judge something possible, such as conceivability, logical coherence, imagination, skill at counterfactual judgement, intuition, etc., seem to speak just as much in favour of the possibility that God does not exist as the possibility that God does exist. These ways of judging what is possible, then, are thus unavailable (or at least not straightforwardly available) to those who advocate the usual modal ontological arguments.

My argument, on the other hand, is not subject to this parody (or, as far as I can tell, any other damaging parody) – it is consistent with the principles to which I appeal to allow both the possibility of God's existence and the possibility of God's non-existence. We may even provide a plausible ground for the latter possibility – perhaps any perfect being has the potential not to exist, or the potential to be imperfect. If so, a perfect being may not only be the ground for the possibility that there is a perfect being, but also for the possibility that there is no perfect being. Given this, we may more easily employ the standard ways of judging what is possible, and thus come to conclude that a perfect being is possible (such a thing being conceivable, coherent, something we can come to seemingly non-trivial counterfactual truths about, etc.). This line of reasoning lends us a response to our second and third objection – we do have justification for thinking that a perfect being is possible (independent of thinking there is such a being), and this justification is unavailable to other modal ontological arguments. The argument is thus neither superfluous, nor guilty of merely insisting upon the truth of a controversial possibility claim.

There is an important rejoinder to my reply here that I should address. I claim that my argument is consistent with claiming that the non-existence of a perfect being is possible. However, some might disagree on the basis that the premises of my argument, if true, are necessarily true, in which case the conclusion – that there is a perfect being – is also necessarily true (if true at all). In effect, then, my argument is just as much committed to non-contingency of a perfect being as other modal ontological arguments are.

In response, I concede that both PGP (i.e. anything which grounds the possibility that there is an F is at least as fundamental as some possible F) and PBF (i.e. anything at least as fundamental as some possible perfect being is a perfect being) are non-contingent. There is room to deny, however, that PEA (that if it is possible that there is an F, there is something that grounds the possibility that there is an F) is necessary even if it is true. Or, if PEA is necessary, we may maintain that the claim that it is possible that there is a perfect being is true but not necessary.

Take this latter idea first. It is commonplace to accept that what is possible is necessarily possible (this being reflected in S5 being a standard choice of modal logic for metaphysical modalities), but those who embrace the metaphysical picture sketched above have some principled motivation for rejecting this claim. This is because if what is possible depends on what there is, and what there is differs from one possible situation to another, then what is possible also differs from situation to situation. Let's say that a perfect being does indeed ground the possibility of a perfect being (and that nothing imperfect can do so). Had there been no perfect being (assuming this is possible), there would have been nothing to ground the possibility of a perfect being, and thus, given the necessity of PEA (and PGP and PBF), it would have been impossible for there to be one. Thus, while it is possible that there is a perfect being (because there is one), it is not necessarily possible that there is a perfect being. Note that taking this position is to reject the claim that what is possible remains constant regardless of what is the case. Above I mentioned this claim as a reason someone might reject the metaphysical picture behind my argument's principles, but one might equally reason the other way – from embracing the picture to rejecting the necessity of possibilities.

Perhaps this is a step too far for some. Fortunately, there is another option for those who wish to maintain that a perfect being is necessarily possible – to wit, we may deny the necessity of PEA. That is, one insists that possible things do have grounds, but denies that possible things must have grounds. Instead, one may maintain that possible things must have actual grounds. It is not PEA which is necessary but PEA*:

Let's say, again, that a perfect being grounds the possibility of a perfect being (and that nothing imperfect can do so). Had there been no perfect being (assuming this is possible), then while there would have been nothing to ground the possibility of a perfect being, there still would have actually been something that grounds the possibility of a perfect being (‘actually’ here rigidifies reference to the actual world). What's more, it is arguably PEA* which more fully expresses the view that possibility is grounded in actuality. What exists may vary from possible situation to possible situation, but what actually exists does not. Given that it is what actually exists that grounds possibilities, then what is possible does not vary either. Denying the necessity of PEA (and asserting the necessity of PEA*), then, allows us to maintain both that S5 governs metaphysical possibility, and that possibility is deeply dependent on actuality. It also allows us to accept the possible non-existence of a perfect being – my argument does not necessarily share with other usual modal ontological arguments a commitment to the non-contingency of perfection.

I do not take my responses to these criticisms to be conclusive. Rather, I hope to have shown merely that these objections are far from decisive. Other criticisms may be given of the argument (e.g. my conclusion is only that a perfect being exists, not that exactly one perfect being exists), but I hope to have covered most of the major worries one might have with the argument. I have stopped far short of claiming that the argument is sound or even rationally compelling, but I do wish to suggest that it is an argument worthy of serious consideration.

Concluding remarks

My ambitions in this article have been limited. I have set out an interesting argument for God, laid out some of its attractions and problems, and sketched how it relates to some other arguments for God, with special emphasis on its similarity to an argument of Descartes.

To conclude, I will present a non-theistic variant of the argument. Instead of arguing for a perfect being, we may use the same kind of reasoning to argue for a perfectly fundamental being. The adjustments needed to produce this argument are minor – principles PEA and PGP remain the same, and, instead of appealing to PBF, we appeal to the following (call it ‘Perfect Fundamentality Principle’ or ‘PFP’):

PFP verges on analytic – it tells us that anything at least as fundamental as some possible perfectly fundamental thing is itself perfectly fundamental. The only other change to the premises is to replace premise 1 (that a perfect being is possible) with the claim that a perfectly fundamental being is possible. The argument proceeds as follows:

1. F1. It is possible that there is a perfectly fundamental being.

2. F2. If it is possible that there is an F, there is something that grounds the possibility that there is an F. (This is PEA)

   1. F-Lemma1: If it is possible that there is a perfectly fundamental being, there is something that grounds the possibility that there is a perfectly fundamental being. (Instance of F2)

   2. F-Lemma2: There is something that grounds the possibility that there is a perfectly fundamental being. (From F1 and F-Lemma1)

3. F3. Anything which grounds the possibility that there is an F is at least as fundamental as some possible F. (This is PGP)

   1. F-Lemma3. Anything which grounds the possibility that there is a perfectly fundamental being is at least as fundamental as some possible perfectly fundamental being. (Instance of F3)

4. F4. Anything which is at least as fundamental as some possible perfectly fundamental being is a perfectly fundamental being. (This is PFP)

   1. F-Lemma4. Anything which grounds the possibility that there is a perfectly fundamental being is itself a perfectly fundamental being. (From F-Lemma3 and F4)

5. F5. Therefore, there is a perfectly fundamental being. (From F-Lemma2 and F-Lemma4)

Even if someone rejects the possibility of a perfect being, she may still accept the possibility that there is something perfectly fundamental (perhaps some physical particles or fields). If she is also sympathetic to the metaphysical picture that undergirds PEA and PGP, the above argument furnishes her with a strong reason for accepting that the perfectly fundamental is not only possible, but actual. This argument, then, is not only of interest to theists and philosophers of religion, but to metaphysicians in general. Given its similarities to Descartes's classic argument for God, it also highlights the continuing importance and fascination of his world-view.Footnote ⁶