Nagasawa's Maximal God and the Ontological Argument

Abstract

Yujin Nagasawa has recently defended two reformulated Ontological Arguments, one adapted from Anselm's ‘Classical’ version and one from Plantinga's ‘Modal’ version. This article explains in detail why both of them fail, and then goes on to present general objections to any Ontological Argument.

Yujin Nagasawa's ambitious and ingenious book, Maximal God: A New Defence of Perfect Being Theism (2017), culminates in defences of two different versions of the Ontological Argument, based respectively on the ‘Classical’ version of Saint Anselm (in chapters 5 and 6) and the ‘Modal’ version of Alvin Plantinga (in chapter 7). Nagasawa's approach to both of these is novel and interesting, but in both cases, I shall argue, his attempted defence fails – the Ontological Argument remains powerless to give any support whatever to the claim that a ‘perfect being’ exists. Having presented objections against each of his arguments individually, I shall end by drawing some general – and highly negative – conclusions regarding the prospects for any successful Ontological Argument.

Nagasawa's Classical Ontological Argument

Nagasawa's discussion of Anselm's ‘Classical’ Ontological Argument does not attempt to defend it from all, or even most, of the objections that have been made to it over the years. His more limited aim is to show that ‘no matter how one approaches it, one cannot refute it without making a significant metaphysical or epistemic assumption, one that is often contentious in its own right’ (Nagasawa (2017), 132). Thus, for example, he sidesteps Kant's famous doctrine that existence is not a predicate – ‘probably the most widely supported objection to the ontological argument’ – on the basis that it has indeed been seriously disputed, for example by Colin McGinn (2000) and Barry Miller (2002), and hence cannot be considered a decisive or uncontroversial refutation (Nagasawa (2017), 132–133).

Chapters 5 and 6 of Nagasawa's book are accordingly directed against my own claim – made first in Millican (2004) – that (in his words) ‘there are two types of objection that do not raise deep philosophical issues . . . Millican's own new objection and the so-called “parody objection”, which was originally introduced by Anselm's contemporary Gaunilo’ (Nagasawa (2017), 134). Nagasawa's aim is to show that, on the contrary, both of these objections involve making ‘a deep metaphysical or epistemic assumption . . . that is . . . contentious in its own right’, and hence ‘there is no obvious or uncontroversial objection to the argument’ (Nagasawa (2017), 150, 132). Here I shall dispute this claim only in respect of my own ‘new objection’ against Anselm's argument.

Concepts, instantiation, and greatness

Nagasawa starts his chapter 5 by sketching the ‘theory of natures’ that I developed in the 2004 article, though he remarks (Nagasawa (2017), 136 n. 5) that the argument might as well be expressed in terms of concepts. I agree, and that is what I shall do here, silently amending relevant quotations accordingly.¹

To explain my objection below, I shall mainly follow the presentation in Millican (2018), whose aim was to highlight why the argument fails (rather than its ability to survive standard objections). There I made a point of spelling out familiar difficulties with the notion of ‘existence in the mind’, how easily one can fall into paradox if this is taken too literally, and why ‘thinking of an x’ cannot always be understood in terms of there being some x of which one is thinking (Millican (2018), 21–22). I also highlighted issues with the identity of ‘mental objects’, given that a single thing can be thought of in multiple ways, and that thoughts can have indeterminate reference (Millican (2018), 23–25). All this demands careful use of terminology and the drawing of appropriate distinctions, especially given that Anselm's argument operates by reductio ad absurdum to convict the atheist so-called ‘Fool’ of contradiction. For such an argument to be persuasive, it is obviously essential that the framework within which the argument is couched is not itself inconsistent, for if it is, the Fool's contradiction cannot reliably be attributed to his atheist premise, rather than to the framework.

These considerations are fundamentally logical, focused on the avoidance of evident incoherence and contradiction; so they should be neither metaphysically nor epistemically controversial. And they suggest that Anselm's argument – rather than being put in terms of ‘objects in the mind’ – is indeed best understood in terms of concepts, interpreting his notion of ‘existence in reality’ as instantiation of the relevant concept, and the greatness of a concept as a measure of both the impressiveness of its defining properties, and its instantiation (or not).² Anselm's notion of greatness embraces ‘whatever it is better to be than not to be’ (Anselm (1077–1078/1998), Proslogion V), but both Nagasawa and I have generally been content to focus on just three measures of impressiveness – in power, wisdom (or knowledge), and benevolence (or goodness) – and just two levels of ‘reality’ – either instantiated or not.³ Thus the highest possible degree of greatness will be achieved by the concept of an omnipotent, omniscient, omnibenevolent being which is instantiated, in other words the concept of an omniperfect God in a universe where such a God really exists. How exactly the scale of greatness works below this ideal of perfection, however, is as yet indeterminate.

Some examples, and an important distinction

Before we proceed further, it will be helpful to consider some specific examples, and to emphasize a distinction which can easily be overlooked or misunderstood, between two different ways in which a concept might be thought to have a property. Consider, for instance, the following three concepts:

God: {omnipotent, omniscient, omnibenevolent}

Laika: {first dog to be sent into space}

Lassie: {dog, catches villains, rescues victims, portrayed in film and on television}

In each case the name of the concept is specified in italic small capitals at the left,⁴ while at the right, in curly brackets, we have the concept's characteristic or internal properties – the properties in terms of which it is defined, and which make it the concept that it is. Note, however, that the latter are not properties of the concept itself, but are properties of whatever instantiates the concept – for example, the concepts Laika and Lassie are not themselves dogs (but the Moscow mongrel named ‘Laika’ who instantiated Laika was indeed a dog). On the other hand, when we say that the concept Laika is instantiated, or has a certain degree of Anselmian greatness, we are describing the concept itself – ascribing an external property to it – rather than defining it. Similar comments apply to the concept God, which is not itself omnipotent or omniscient, but is – according to the theist – both instantiated and supremely great.

To emphasize further this crucial distinction between characteristic (internal) and descriptive (external) properties of concepts, it can be helpful to think of examples in which a concept is either correctly or incorrectly described by its own characteristic properties. For example, the concept Dog is not a dog,⁵ the concept Funny is not funny, and the concept Rare is not rare. On the other hand, the concept Widely Shared is itself widely shared, the concept Abstract is itself abstract, and the concept Sophisticated is itself sophisticated. The latter auto-descriptive concepts are relatively unusual, however, and in general, there is no reason to expect that a concept will itself possess (i.e. be correctly described by) its own characteristic properties.⁶

If we focus now on the notion of greatness – understood here exclusively as an external property of concepts – it is not obvious in what order the three concepts above should be ranked. If all three were instantiated, or all three uninstantiated, then their greatness ordering would depend purely on their internal properties, in which case the ordering would clearly be:

God > Lassie > Laika

because omniperfection involves more power, wisdom, and benevolence than being a dog that catches villains (etc.), which in turn outscores being merely a dog sent into space. But the external property of instantiation weighs in the opposite direction as regards Lassie and Laika, with the former being purely fictional while the latter became really instantiated when that mongrel was sent into space in November 1957. This presumably increases the greatness of the concept Laika, but whether by enough to enable it to overtake the internally more impressive Lassie is not entirely clear. Let us suppose that it is indeed agreed to be enough, in which case a theist would take the overall greatness ordering to be:

God > Laika > Lassie

An atheist, however, might want to attribute even more importance to instantiation, to the extent of insisting that the internally modest Laika – on account of its real instantiation – would even outscore what he takes to be the uninstantiated (though internally unsurpassable) God :

Laika > God > Lassie

Such an atheist might well take the view that any really instantiated concept should count as greater than any really uninstantiated concept. We shall see later that Nagasawa contests this principle, but let us adopt it for the moment as a simplifying assumption. From this perspective, and if there are no gods or other supernatural beings, then it is not obvious what the actually greatest concept would be. It would presumably have to be one whose internal qualities include considerable power, wisdom, and benevolence, and which has in fact been instantiated in the human world (leaving aside the possibility of alien life). Unfortunately, however, these criteria pull in different directions, because human absolute rulers have tended to fall conspicuously short in terms of wisdom and especially benevolence. Among this dubious company, the Roman Emperor and Stoic philosopher Marcus Aurelius stands out, so let us for convenience suppose that the actually greatest ‘non-divine’ concept would be:⁷

Aurelius: {absolute Emperor of the Roman Empire, wise, just, beneficent}

Whether or not this choice is ultimately the best available does not matter for our purpose, which is simply to have a plausible illustrative example to hand in the discussion that follows.

The Kantian critique and Anselm's argument

Kant's famous critique of the Ontological Argument has been extremely influential, but is nevertheless somewhat obscure:

‘Being’ is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing. It is merely the positing of a thing . . . If . . . we . . . say ‘God is’, we attach no new predicate to the concept of God, but only posit the subject in itself with all its predicates, and indeed posit it as being an object that stands in relation to my concept. . . . Whatever, therefore, and however much, our concept of an object may contain, we must go outside it, if we are to ascribe existence to the object. (Kant (1781/1933), 504–506)

Leaving aside its potentially controversial first clause, this passage seems to express awareness of the following two genuine insights:

1. (a) There is a distinction between the internal and external properties of a concept.

2. (b) Real instantiation is an external property, and hence cannot be used to define a concept.

Thus real instantiation – the ‘being’ or ‘positing’ of something – is not a property ‘which could be added to the concept of a thing’ to change the concept's internal definition. And accordingly, a concept's real instantiation cannot (at least in general) be determined by mere analysis of the concept's internal or characteristic properties: ‘we must go outside’ the concept and investigate external circumstances ‘if we are to ascribe’ real instantiation to it.⁸

These insights tell strongly against Descartes's version of the Ontological Argument, since he clearly does treat real existence as one of the divine perfections, and hence as an internal, defining property of his idea of God: ‘the idea of God [is that of] a supremely perfect being . . .  Hence it is . . . a contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection)’ (Meditation 5, in Descartes (1641/1984), 45–46). In the light of our earlier discussion, however, the Kantian objection can be seen to have no force against the strongest form of the Anselmian argument, because this interprets the key quality of greatness not as an internal, characteristic property of the relevant divine concept, but rather, as an external, descriptive property. Thus understood, and spelling out the inference to ‘God’ (in the final two stages), the argument goes roughly like this:

1. (1) Let us here use Twng as a shorthand name for that concept (whichever it may be) than which no greater concept can be thought.⁹

2. (2) If Twng were not instantiated [as the atheist Fool of the Psalms claims], then it would be possible to think of some (instantiated) concept that is greater than Twng.

3. (3) But this would be an obvious contradiction, given that Twng is that concept than which no greater concept can be thought.

4. (4) Hence Twng must indeed be instantiated.

5. (5) Since Twng is that concept than which no greater concept can be thought, it must be a concept with supreme defining qualities in terms of power, wisdom, and benevolence.

6. (6) And since Twng is instantiated, as already proved, there must really exist a being – which we call ‘God’ – possessing these supreme qualities.¹⁰

Up to here, I believe, Nagasawa and I are broadly in agreement: the Anselmian argument, taking roughly the form above, can evade Kantian objections. But our key disagreement will soon emerge.

Questioning Anselm's formula

The argument just spelled out contains three seductive but questionable moves, at stages (2), (3), and (5). All look independently plausible, based on the apparent supreme greatness of the concept Twng as secured by the italicized description at stage (1), but taken together they must be opposed by the atheist:

1. (2) If Twng were not instantiated, then it would be possible to think of some (instantiated) concept that is greater than Twng.

2. (3) But this would be an obvious contradiction, given that Twng is that concept than which no greater concept can be thought.

3. (4) Since Twng is that concept than which no greater concept can be thought, it must be a concept with supreme defining qualities in terms of power, wisdom, and benevolence.

Stages (2) and (3) together claim a contradiction if Twng is not instantiated; (5) requires that Twng be defined in terms of supreme power, wisdom, and benevolence. So, if these are accepted, the existence of God (understood as a supremely powerful, wise, and benevolent being) immediately follows.

To refute all this, the atheist must interrogate the original identifying description of Twng at stage (1). But this need not involve any ‘deep’ Kantian style of objection which claims that there is something illegitimate about framing a definition in terms of greatness (e.g. on the grounds that instantiation implicitly ‘treats existence as a predicate’). Instead, the theist can effectively be challenged at a far ‘shallower’ level, to clarify key ambiguities of syntactic scope that are hidden within the Anselmian formula:

that concept than which no greater concept can be thought

When we investigate which concept exactly this formula is supposed to designate, we find that the answer is more complicated than it initially appears.

The most straightforward interpretation of Twng understands it to be referring to:

1. (i) whichever [thinkable] concept is, in fact, the greatest of all (i.e. whichever concept enjoys the highest actual degree of greatness).¹¹

But note that on this interpretation, there is no obvious guarantee that the concept in question will be supremely great. For in a world containing no supremely powerful, wise, and benevolent being, no concept will actually reach the level of greatness that would be achieved if the concept God were to be actually instantiated. On this interpretation of the Anselmian formula, therefore, the argument fails at stage (5): the concept than which no greater concept can be thought need not be a concept with supreme defining qualities in terms of power, wisdom, and benevolence. From the atheist perspective we considered earlier, for example, the referent of Twng would be the concept Aurelius.

In reaction to this, the theist will probably prefer to understand the formula in a different way, so that Twng picks out:

1. (a) whichever concept can be thought to reach the highest possible degree of greatness (i.e. a degree of greatness so high that no concept could even be thought to exceed it).

On this interpretation, Twng does indeed refer to the concept God, because this can be thought to achieve supreme greatness, simply by thinking of it as instantiated. But this raises a different potential problem with the argument, for if God – that is, Twng on this interpretation – is not actually instantiated, then Twng will not in fact reach that supreme level of greatness. So now the argument is in danger of failing at stage (3) – it is not obviously contradictory for some other concept (for example, the instantiated Aurelius) to exceed Twng in actual greatness.

A third interpretation of Anselm's formula is also worth mentioning here, though it does not feature in my debate with Nagasawa:

1. (iii) whichever concept actually reaches the highest possible degree of greatness (i.e. a degree of greatness so high that no concept could even be thought to exceed it).

The atheist should never accept that Twng, thus interpreted, achieves reference to any concept at all, since he denies that any concept actually reaches that supreme degree of greatness.¹² So to proceed with the argument under interpretation (iii) is simply begging the question in favour of theism. Nor is it plausible to consider this situation a ‘draw’ or ‘stand-off’, with the atheist denying that (iii) succeeds in reference while the theist – equally reasonably – asserts that it does refer. For the context was supposed to be an argument for God's existence, which moreover was supposed to operate by demonstrating an inconsistency in the atheist's position. In setting out to present such an argument, the theist was explicitly taking on the onus of proof, and if the atheist is able to reject the proffered argument by simply denying that (iii) refers, without falling foul of any contradiction or other difficulty, then the would-be proof has clearly failed.

In Millican (2004), I described this threefold ambiguity as ‘the one fatal flaw in Anselm's argument’, highlighting how it could be seen as arising from a double ambiguity of scope on the ‘can be thought’ operator – clearly a ‘shallow syntactic’ rather than ‘deep metaphysical’ flaw:

Interpretation (i) chooses ‘is’ at both choice-points, yielding ‘A concept which is so great that no concept is greater’ (i.e. the actually greatest concept). Interpretation (ii) chooses ‘can-be-thought’ both times, yielding ‘A concept which can be thought so great that no concept can be thought greater’ (i.e. the hypothetically greatest concept). Interpretation (iii) chooses ‘is’ and then ‘can-be-thought’, yielding ‘A concept which is so great that no concept can be thought greater’.¹³ It is then easy to see why interpretation (iii) makes an unacceptable assumption that the others do not. In the case of (i), we can imagine ordering all thinkable concepts in terms of their actual greatness, and selecting the one that comes top. In the case of (ii), we can imagine ordering all thinkable concepts in terms of their hypothetical greatness (i.e. the greatness they would achieve if instantiated), and again selecting the one that comes top. Assuming that the notion of greatness can be coherently defined, both of these seem to be unexceptionable in principle. (iii) is far more problematic, however, because here we are apparently selecting the thinkable concept that comes top in the actual ordering, and then taking for granted that this will reach a level that also puts it top in the hypothetical ordering. But unless God really exists – thus ensuring that supreme actual and hypothetical greatness coincide – this assumption will be mistaken.

The Principle of the Superiority of Existence

In Millican (2004), I attributed to Anselm a principle which Nagasawa later dubbed ‘the Principle of the Superiority of Existence’ (Nagasawa (2007), 1029; (2017), 136):

(PSE) Any concept which is instantiated is greater than any concept which is not instantiated.

This would imply that among the four criteria for greatness – power, wisdom, benevolence, and instantiation – the last ‘trumps’ the others. I introduced this principle as ‘a simplifying assumption’ and acknowledged that it was ‘not unquestionably Anselmian’ (Millican (2004), 451), though I adduced some reasons for suggesting that Anselm might have accepted it. These reasons were challenged by Nagasawa (2007, 1032–1034; 2017, 140–142), and I have since accepted that they are not compelling.¹⁴ But I disagree with Nagasawa's claim that ‘giving up’ PSE can strengthen Anselm's argument (2007, 1034; 2017, 142).

To see how PSE can simplify the logic of Anselm's argument, suppose that we are interpreting Twng as in (ii) above, thus referring to whichever concept can be thought to reach the highest possible degree of greatness. This is the interpretation that Nagasawa favours, claiming that it can yield a successful Ontological Argument,¹⁵ and as explained already, it implies that Twng refers to God, since by thinking of God as instantiated, we are thinking of it as achieving supreme greatness. With all this understood, consider again stages (2) and (3):

(2) If Twng were not instantiated, then it would be possible to think of some (instantiated) concept that is greater than Twng.

(3) But this would be an obvious contradiction, given that Twng is that concept than which no greater concept can be thought.

If PSE is accepted, then (2) trivially follows, because PSE implies that if Twng were not instantiated, then any instantiated concept – even one as humble as Dog – would be greater than Twng. Thus PSE simplifies the argument, yielding complete determinacy at stage (2). But since we are interpreting Anselm's formula as (ii) above, stage (3) – as already noted – then becomes problematic, because on this interpretation Twng succeeds in referring to God whether or not the latter is instantiated, and hence (assuming PSE) whether or not God is exceeded in actual greatness. Thus (3) fails: on this interpretation, the atheist is not guilty of any contradiction in claiming to think of a concept (e.g. Dog) that is actually greater than Twng. The key point here is that on interpretation (ii) – which is Nagasawa's own declared preference – Twng has been descriptively identified in terms of the greatness that it would achieve if it were instantiated, not in terms of its actual greatness.

Faced with this problem, Nagasawa recommends that we deny PSE. This changes the logic of the argument – at least under interpretation (ii) which we continue to presuppose here – because if PSE is rejected, then the assessment of stage (2) becomes less clear-cut. Since instantiation is no longer a ‘trump’, it follows that it can be – at least in some cases – outweighed by the three internal criteria of power, wisdom, and benevolence. And since the concept God includes all three of these internal properties to an infinite degree, it looks likely that God – even if uninstantiated – will now turn out to be greater than the instantiated Dog. Indeed, Nagasawa goes further, implying that under this interpretation, the concept God – even if uninstantiated – will exceed in actual greatness any rival concept, whether that rival concept is actually instantiated or not. And he draws the conclusion that the argument can accordingly go on to prove the actual instantiation of Twng, namely God.¹⁶

But this is much too fast, for two reasons. First, under this interpretation, stage (2) of the argument looks likely to fail. For if Twng refers to God, and God is greater than any other concept whether it is instantiated or not, then it is clearly not the case that Twng's non-instantiation would make it possible to think of some other concept that is (actually) greater than Twng. And moreover, stage (3) also risks failing, because even if we accept that God, though uninstantiated, would still be actually greater than any rival concept, it does not follow that its being exceeded in greatness would be a contradiction, because hypothetical situations in which it would be thus exceeded might at least be imaginable. Suppose, for example, that we take a demigod to be an immaterial agent which is omniscient, omnibenevolent, and extremely powerful, though limited in some way (e.g. by physical laws). Clearly God will be greater than Demigod if both are instantiated, or if both are uninstantiated. But given that a demigod, though lacking omnipotence, is a seriously impressive being – far more impressive than a mere dog or even Marcus Aurelius – it looks plausible that if Demigod were to be instantiated, and God uninstantiated, then Demigod would be greater than God. If this is even a possibility, then there is no ‘obvious contradiction’ as alleged at stage (3). This vindicates my claim that under interpretation (ii) of Anselm's formula, PSE simplifies the logic of the argument without weakening it. For with PSE asserted, the argument is completely secure at stage (2) but fails at stage (3). With PSE denied, on the other hand, stages (2) and (3) both become seriously problematic, and assessments of relative greatness become indeterminate unless further clarification is given (e.g. regarding the relative greatness of God and concepts such as Demigod in the situation just described).

Nagasawa's Defence of the Classical Ontological Argument

I have suggested that under Nagasawa's preferred reading (and with PSE accordingly rejected), stage (2) of the Anselmian argument fails because on his principles, even if Twng is not instantiated, it is not possible to think of any concept that is greater than Twng. At the corresponding stage of his own version, however, Nagasawa denies this, apparently on the basis that it would be possible to think of the concept Twng itself as instantiated in reality. His version of my (2) is accordingly as follows:

(2n) If a-concept-than-which-no-greater-concept-can-be-thought were not instantiated in reality, then it would be possible to think of a concept that is greater; namely, a-concept-than-which-no-greater-concept-can-be-thought that is instantiated in reality. (Nagasawa (2017), 144 – this is stage (4m′) in his presentation)

We can simplify this statement, given that under interpretation (ii) of Anselm's formula – which Nagasawa favours – ‘a-concept-than-which-no-greater-concept-can-be-thought’ (i.e. Twng) is agreed between us as unambiguously referring to God, because this is the concept which can be thought to reach the highest possible degree of greatness. So with interpretation (ii) assumed, (2n) – which Nagasawa asserts – can equally well be written as:

(2n′) If God were not instantiated in reality, then it would be possible to think of a concept that is greater; namely, God that is instantiated in reality.

On the same basis, (2) – which I deny as holding on Nagasawa's principles regarding PSE – can equally well be written as:

(2′) If God were not instantiated, then it would be possible to think of some (instantiated) concept that is greater than God.

It might look as though we are straightforwardly disagreeing here, but this appearance is misleading, as becomes apparent in Nagasawa's discussion (2017, 145–150) of an earlier debate between us.

Nagasawa first proposed his defence of Anselm's argument, responding to my 2004 critique, in Nagasawa (2007). There, his reconstructed argument – containing (2n) at 1035–1036 – starts from what he takes to be a fundamental claim that ‘Anselm needs to justify’:

if there were God that is instantiated in reality and God that is conceived only in the mind, then the former would be greater than the latter. (Nagasawa (2007), 1034)

My rejoinder, in the same volume of Mind, objected:

This conditional may sound plausible, but in fact it is deeply muddled because its antecedent does not describe any possible situation: the concept God – which Nagasawa takes to be the referent of Anselm's key phrase – is either instantiated in reality or it is not, and it cannot be both. (Millican (2007), 1051)

After quoting this in his book, however, and acknowledging ‘that the same being cannot be both existent and non-existent simultaneously’ (2017, 148), Nagasawa suggests that I have misunderstood his point, and draws the conclusion that my objection to his position is based on a reluctance to allow comparisons of greatness between existent and non-existent things. This would count as a relatively ‘deep’ objection to the Ontological Argument, identified as such in Millican (2004, 443), where I called it ‘the comparison difficulty’ and attributed it to Broad (1953, 181) and Charlesworth (1965, 63–65). Nagasawa accordingly accuses me of inconsistency:

Millican thinks that the comparison of greatness between uninstantiated x and instantiated x does not make sense because if x is not instantiated in reality, there is no such thing as x that is instantiated in reality. . . . this means that Millican commits himself, implicitly, to a version of the comparison difficulty, which says . . . that ‘[t]here seems to be something logically odd about purporting to compare something that exists only “in the mind” with something existing in reality’ (Millican 2004, 443). Thus, Millican's objection . . . is not as metaphysically neutral as he thinks it is. The comparison difficulty, to which Millican does not allow opponents of the classical ontological argument to commit themselves, is hidden in his own theory . . . (Nagasawa (2017), 148–149)

In the light of these comments, I now plead guilty to the charge of having previously misunderstood Nagasawa's argument, but innocent to the accusation of having based my critique on anything like the alleged comparison difficulty – I am entirely happy to allow whatever comparisons of greatness he wishes to make between concepts, whether instantiated or not (and either actually or hypothetically).

Nagasawa's latest discussion indicates that he and I have been understanding (2) in different ways. My own intended interpretation focused exclusively on actual instantiation and greatness:

(2″) If God were not actually instantiated, then it would be possible to think of some (actually instantiated) concept that is actually greater than God.

When asserting (2n′), however, Nagasawa appears to have been intending something like:

(2n″) If God were not actually instantiated, then it would be possible to think of some concept (namely God itself) that can be thought of as greater than God actually is (by thinking of that concept as instantiated).

I took Nagasawa's rejection of PSE, combined with his assertion that the concept God is greater than any other even if it is not instantiated, to imply the falsehood of (2″). But (2n″) remains very obviously true whether PSE is accepted or denied, because any coherent but not actually instantiated concept can be thought of as potentially greater than it actually is, just by thinking of it as instantiated.

Nagasawa's defence of stage (2) of the argument is therefore successful under interpretation (2n″). But this victory is Pyrrhic, because thus interpreted, the argument clearly fails at stage (3):

1. (3) But this would be an obvious contradiction, given that God is that concept than which no greater concept can be thought.

Indeed, the very logic that creates the possibility asserted by (2n″) ensures that the fulfilment of that possibility is not ‘an obvious contradiction’ (nor even false). For if God is not actually instantiated – as the atheist claims – then we can certainly think of a concept – namely God itself – which is potentially greater than God actually is (with or without PSE). So there is no contradiction in the atheist's position, and the Anselmian would-be reductio fails.

I believe that Nagasawa overlooks this problem because he tackles the two crucial stages of the argument separately, and does not bring them together to spell out exactly how he sees the overall logic working under his preferred interpretation (ii). I had maintained that – under this interpretation – the argument fails at stage (3), owing to the possibility asserted in (2″) which means that there is no contradiction in the (uninstantiated) concept God being exceeded in actual greatness. In response to this initial objection, as we have seen, Nagasawa denies PSE and takes God's greatness, even when uninstantiated, to exceed that of any other concept:

According to this interpretation, it is indeed impossible for atheists to think of a concept that is greater than a-concept-than-which-no-greater-concept-can-be-thought. (Nagasawa (2017), 144)¹⁷

This initially seems to secure the contradiction at stage (3), but Nagasawa also has to make sense of stage (2), which requires it to be possible for God to be exceeded in greatness if it is uninstantiated. Again as we have seen, he secures this possibility (2017, 148) through the interpretation (2n″):

(2n″) If God were not actually instantiated, then it would be possible to think of some concept (namely God itself) that can be thought of as greater than God actually is (by thinking of that concept as instantiated).

But he then apparently fails to appreciate that the very possibility he has just opened up through his reinterpretation at stage (2) now makes it impossible to convict the atheist of contradiction at stage (3).

Thus Nagasawa's defence of the Classical Ontological Argument depends on a crucial equivocation between actual and hypothetical greatness. His denial of PSE might indeed make it impossible for atheists to think of a concept which is actually greater than they take God to be (because on his principles, God is greater than any other concept even if it is not instantiated). But this does not make it impossible for them to think of a concept – namely God itself – which they take to be hypothetically greater than God actually is. The argument only seems to go through if we adopt the latter (hypothetical) interpretation at stage (2) of the argument, and then convict the former (non-hypothetical) interpretation of contradiction at stage (3).

I conclude that Nagasawa's attempted defence of the Classical Ontological Argument is unsuccessful. If we are careful to avoid confusion by the scope ambiguities within Anselm's ingenious formula, and to observe the distinctions between the internal and external properties of a concept and between actual and hypothetical greatness, then there is no way that the existence of God can plausibly be inferred by this sort of reasoning. And this critique seems to me to be logically solid and secure, with no dependence whatever on any ‘deep’ metaphysical commitments. In short, Nagasawa's favoured interpretation of Anselm's argument fails not because of any supposed ‘comparison difficulty’, but simply because it fails to identify any contradiction in the atheist's position. Nor should this be in the least surprising, for – as I shall argue in detail later – the evident consistency of atheism implies that any would-be argument of this kind is bound to be fallacious, deriving any plausibility that it possesses from equivocation and ambiguity.

Nagasawa's Modal Ontological Argument

The central theme of Nagasawa's book is the idea that ‘perfect being theism’ need not be committed to the traditional ‘omni God thesis’, according to which ‘God is the omniscient, omnipotent, and omnibenevolent being’. Rather, the essence of perfect being theism should be seen as the ‘perfect being thesis’ that ‘God is the being than which no greater is metaphysically possible’, which can be comfortably combined with the ‘maximal God thesis’ that ‘God is the being that has the maximal consistent set of knowledge, power, and benevolence’.¹⁸ Thus the perfect being theist can evade familiar objections to the coherence or metaphysical possibility of the omni God, by adopting instead a concept of God that is guaranteed by definition to be consistent. This general strategy sets the background for Nagasawa's approach to the Modal Ontological Argument, as we shall see shortly.

The maximal God strategy, and some initial concerns

The omni God thesis encounters many familiar objections, which Nagasawa divides into three types. ‘Type A’ are ‘arguments that purport to show the internal incoherence of God's individual properties’ (Nagasawa (2017), 82). These include such examples as the famous ‘paradox of the stone’, which asks whether God can create a stone that He cannot lift (Nagasawa (2017), 83);¹⁹ Patrick Grim's Cantorian argument that there is no set of all truths, thus challenging the notion of omniscience (Nagasawa (2017), 83); and the ‘argument from moral admiration’, which questions whether a being incapable of acting wrongly can be morally admirable (Nagasawa (2017), 83–84). ‘Type B’ are ‘arguments that purport to show the mutual inconsistency between God's properties’ (Nagasawa (2017), 84). These include the ‘argument from God's inability to sin’, which highlights a tension between omnipotence and moral perfection (Nagasawa (2017), 84); and the ‘argument from experience’ which denies that an omnipotent being can understand fear and frustration, or that a morally perfect being can understand what it is like to be evil (Nagasawa (2017), 84–85). Finally, ‘Type C’ are ‘arguments that purport to show the mutual inconsistency between the set of God's properties and a certain fact about the actual world’ (Nagasawa (2017), 85). The most familiar argument of this kind is the Problem of Evil (Nagasawa (2017), 85–86); but others are ‘the argument from divine hiddenness’ (Nagasawa (2017), 86–87) and ‘the argument from the imperfection of the actual world’ focusing on imperfections other than evil (Nagasawa (2017), 87).

A considerable literature has built up around these various objections, both urging them and attempting to answer them. But Nagasawa's ‘maximal God’ thesis aims to cut through this tangle, ‘to eliminate the force of the existing arguments against [perfect being theism] all at once and block any further arguments’, by understanding God not in the traditional ‘omni’ terms, but rather as ‘the being that has the maximal consistent set of knowledge, power, and benevolence’ (Nagasawa (2017), 90). But this formula, repeated many times,²⁰ does not mention maximal consistency with contingent facts about the empirical world, and hence it seems that that Nagasawa is not really intending his thesis simply to eliminate by definition all Type C arguments such as the Problem of Evil. Such an aspiration would anyway be unrealistic, not least because the most persuasive versions of the Problem of Evil focus on arguing that the evils of the world make the existence of God unlikely rather than logically impossible.²¹ But also, in a context where Nagasawa ultimately wants to claim that his maximal God is a necessary existent, it would be highly implausible to define that maximal God as relative to our contingent experience (implying, say, that in the wake of Auschwitz, our understanding of God's maximality might be changed because a greater potential for evil in His creation has now become apparent). Nagasawa's repeated formula indicates that he is not taking this dubious path, but is instead defining maximal God by absolute rather than contingent standards, and hence is not attempting to rule out the Problem of Evil by definition. Accordingly, his later more detailed discussion of evil (Nagasawa (2017), 113–120) suggests that he understands the maximal God thesis as merely weakening the evidential threat from evil. I am personally unconvinced even of this, but we can leave that question aside here.

Although the main point of the maximal God thesis is to circumvent objections to the coherence of the omni God thesis, Nagasawa is careful to avoid committing himself on the strength of those objections, presenting maximal God as a strategic substitute for omni God rather than a theoretical replacement. Thus he emphasizes that he is ‘not rejecting’ the omni God thesis, but rather ‘saying . . . that perfect being theists do not need to worry about [its] cogency’ – they can suspend judgement on the issue, without any threat to their perfect being theism. For if, on the one hand, the omni God thesis is coherent despite all the various objections to it, then maximal God and omni God will be one and the same. But if, on the other hand, it turns out that the omni God thesis is indeed incoherent, then the maximal God thesis nevertheless remains intact, allowing perfect being theists to ‘retain their view that God, as the being than which no greater is metaphysically possible, exists’ (Nagasawa (2017), 93). So either way, maximal God theists can achieve the best of all possible theistic beliefs.

This is a clever strategy for avoiding the threat of divine incoherence, though it raises various problems of its own, notably how to ensure that the maximal God thesis itself is well defined. For if the omni God thesis is in fact inconsistent, and one (or more) of the ‘omni-properties’ has to be weakened to avoid contradiction, there might be no clear and uniquely best way of doing so. One issue here concerns the mutual commensurability (or otherwise) of the various great-making properties. If they are not mutually commensurable, then it is hard to see how the loss of greatness that would be incurred by weakening one of them (e.g. power) can be compared against the loss that would be incurred by weakening another (e.g. benevolence), and we might then be left with a number of possible less-than-omni-gods, none of which is unambiguously surpassed by any other. But if, on the other hand, the various great-making properties are mutually commensurable, then there might be multiple possible trade-offs that could lead to an equal overall level of greatness, and again there is a threat of some kind of polytheism, owing to the loss of uniqueness. Nagasawa addresses the commensurability issue at length in his second chapter (Nagasawa (2017), 40–76), and the potential conflict with monotheism in part of his fourth chapter (Nagasawa (2017), 109–113). These discussions are rich and interesting, but do not pretend to be decisive. Indeed, Nagasawa's ultimate response is that such considerations can generate no decisive objection to his view, on the basis that for all we can tell, there might be just one maximal consistent set of great-making attributes. Thus ‘even if we accept the possibility that God does not possess omniscience, omnipotence, and omnibenevolence, we do not have to commit ourselves to the possibility that another being reaches the same axiological value as God by having a different combination of knowledge, power, and benevolence’ (Nagasawa (2017), 112).

Nagasawa's response here seems intended to put the burden of proof onto his opponent, thus apparently presuming that the maximal God thesis is to be considered acceptable unless it can be positively refuted.²² Such a presumption is in line with familiar debates involving the various Type A, B and C objections, in which the atheist aspires to refute theism, whereas the theist's primary task is merely to defend theism as possible despite the atheist's objections. But the atheist might reasonably be reluctant to accept this burden of proof when dealing with a novel thesis which has already been acknowledged to be subject to a fair range of prima facie difficulties, and whose definition is not only vague but also crucially dependent on a notion of objective axiological value which he is unlikely to accept. Before he is expected to engage seriously with that thesis, he might say, it is up to Nagasawa to specify it with sufficient clarity to give confidence that it is coherent and determinate.

Nagasawa could probably do more to address this concern, if he felt the need to do so. For example, rather than relying on a vague overall assessment of axiological value, he could maximize the individual divine attributes in turn, preserving consistency on the way. Thus maximal God might be defined as being unconditionally omnibenevolent, then as powerful as an omnibenevolent being can possibly be (hence arguably unable to sin), and finally as knowledgeable as such an omnibenevolent and powerful being can possibly be (hence arguably unable to know what it is like to be evil or frustrated). That would significantly improve the determinacy of the theory in the face of the Type B arguments, without obvious loss to its plausibility or religious value.²³ At any rate, let us assume here that the determinacy concern can either be put to one side or solved in some such way, and focus on the further crucial question: can Nagasawa then legitimately use his maximal God theory as the basis for a persuasive Modal Ontological Argument?

Plantinga's Modal Ontological Argument

Nagasawa bases his Modal Ontological Argument on the well-known version of Plantinga (1974), so I shall start by sketching this briefly, together with a few comments of my own. The argument is embedded within a possible worlds framework using the modal logic system S5, under which what is possible or necessary is the same in all possible worlds – this has the implication that iterated modalities all ‘collapse’ to the final one, for example Nec(Nec(Nec(Poss(P)))) is equivalent to Poss(P) and likewise Poss(Nec(Poss(Nec(P)))) is equivalent to Nec(P). S5 is attractively simple, and perhaps can claim to be the most appropriate logic for considering modality from the point of view of a divine creator ex nihilo. But it rules out any finer-grained modal structure, such as might, for example, acknowledge that the birth of a new individual opens new possibilities that would not have existed in alternative possible histories.²⁴ According to S5, all possibilities exist within all worlds, and every world is ‘modally accessible’ from every other. Thus necessary truth is simply truth in all possible worlds, possible truth is simply truth in some possible world, and the truth or falsehood of any modal proposition is the same in every possible world, rather than relative to the world in which it is assessed.

Within this framework, it is straightforward to express the existence of an omni God within some possible world. Plantinga calls such a being maximally excellent:²⁵

(PW) Necessarily, a being is maximally excellent in a given possible world only if it is omnipotent, omniscient, and omnibenevolent in that world.²⁶

Plantinga then goes on to introduce the even more impressive property of maximal greatness:

(PA) Necessarily, a being is maximally great only if it is maximally excellent in every possible world (i.e. it is necessarily maximally excellent).

From here, Plantinga's argument is essentially very simple, starting from the single premise (as presented in Nagasawa (2017), 184):

(1x) It is possible that a maximally great being exists.

Nagasawa develops the argument over five stages, unpacking the definitions and modal equivalences in turn, but I prefer to consider it as getting in a single bound to its conclusion:

(5x) An omniscient, omnipotent and omnibenevolent being exists in the actual world.

The point here is that because, within S5, what is necessary or possible does not vary from world to world, it immediately follows that any statement of necessity or possibility must itself be either necessary or impossible (because the necessity or possibility that it asserts will hold in the actual world if and only if it holds in every world). But the statement:

(E) a maximally great being exists.

is a disguised statement of necessity, because as specified by (PA), it implies that a maximally excellent being exists in every possible world, and hence that the statement there exists a maximally excellent being is necessarily true. Thus it trivially follows that (E) cannot possibly be contingent: it must be either necessary or impossible. Premise (1x) then rules out the latter, forcing the conclusion that (E) is necessarily true (and therefore also actually true).

In other words, if we start from a clear understanding of S5, then Plantinga's argument is effectively a ‘hole in one’: the premise (1x) leads trivially to its conclusion (5x), and thereby implicitly takes for granted from the start what it is purporting to prove. Many presentations of the argument hide this underlying simplicity by clothing the argument in technical guise, which can give the impression that it is far more subtle and ingenious than it actually is. But the technical mechanism belongs to the S5 framework, rather than to this argument in particular, and once that framework is in place, Plantinga's additional contribution is simply to serve up, in a suitable format, his chosen theistic application of it. Moreover, the logic of the argument has absolutely nothing specifically to do with the divine properties of omniscience, omnipotence, and omnibenevolence, and an exactly parallel argument can be made using far less exalted materials. Suppose, for example, we start from the two definitions:

(MW) A being is bunnyquin in a given possible world if and only if, in that world, it is a rabbit whose fur is naturally coloured in alternating red and yellow patches.²⁷

(MA) A being is omnibunnyquin if and only if it is bunnyquin in every possible world.

Then we can likewise move in a single bound from

It is possible that an omnibunnyquin being exists.

to the conclusion

There exists in the actual world a rabbit whose fur is naturally coloured in alternating red and yellow patches.

The magic that takes us from mere possibility to necessity, and thus on to actuality, is all provided by the S5 logical framework. Within that framework, any modal specification such as (PA) or (MA) is a potential Trojan horse, since by accepting the mere possibility of such a being – the sort of move that we habitually consider innocuous and open-minded – we are immediately committed to its inexorable necessity. Thus it is only a slight simplification to say that the overall logic of Plantinga's argument, with the concepts involved fully spelled out (rather than specified within separate definitions), has essentially the following structure:

It is possible that there exists an X which is of such a nature that, if it possibly exists, then it necessarily exists. Hence an X exists (both necessarily and actually).

Here more or less anything could be substituted for ‘X’ without affecting the logic, which is trivially valid but obviously question-begging.²⁸ This bears comparison with the attempt to persuade someone of the truth of Q using the single-premise argument:

P and (if P then Q)

∴  Q

Clearly nobody who has doubts about Q, and has their wits about them, will for a moment accept the premise offered, because it so obviously implies the truth of Q. For exactly the same reason, no atheist should for a moment consider accepting Plantinga's premise (1x).

Maximal God and the Modal Ontological Argument

Nagasawa is far more sympathetic to Plantinga's argument that I have been above, and – in stark contrast with my own discussion – is particularly attracted to it precisely because its conclusion is so closely tied to the ‘possibility premise’:

the modal ontological argument . . . shows that if the existence of God, or a maximally great being, is possible, then it is necessary, which entails that it is also actual. . . . The modal ontological argument reduces the burden on theists dramatically. They no longer need to appeal to such theistic arguments as the cosmological argument, the design argument, the moral argument, or the argument from miracles to demonstrate that God's existence is actual. All they need to do is to show somehow that the existence of God is possible. . . . Hence, the modal ontological argument places us only a half-step away from a definitive proof of the existence of God. . . . The crucial question then is whether premise (1x), the possibility premise, is indeed true. (Nagasawa (2017), 185)

After explaining why five previous attempts to justify the possibility premise are unconvincing,²⁹ Nagasawa ingeniously suggests that the key might be supplied by his maximal God thesis, which he has already wielded to establish possibility in other cases – notably against the Type A and Type B objections discussed earlier. If his maximal God strategy can secure possibility here also, then the Modal Ontological Argument will go through and theism will be proved.

Nagasawa indeed seems to assume that this strategy can operate in much the same way here as it did with those earlier objections:

once we accept the maximal God thesis and the perfect being thesis, we can automatically derive that it is possible that God exists because here God is understood as the being that has the maximal consistent set of knowledge, power, and benevolence. In other words, the maximal concept of God is by definition internally coherent because its components are mutually consistent (and internally coherent). This guarantees the possibility of the existence of God. That is, the possibility of God's existence comes with perfect being theism for free given the maximal God thesis. (Nagasawa (2017), 204)

Accordingly, he suggests that Plantinga's Modal Ontological Argument can straightforwardly be given a secure possibility premise, simply by replacing (PW) and (PA) above with (Nagasawa (2017), 205):

• (NW) Necessarily, a being is really maximally excellent in a given possible world only if it has the maximal consistent set of knowledge, power, and benevolence in that world.

• (NA) Necessarily, a being is really maximally great only if it is really maximally excellent in every possible world.

Immediately after providing these two definitions, Nagasawa ends his discussion of the Modal Ontological Argument with the following passage:

Once we accept that the real maximal excellence thesis and the real maximal greatness thesis apply to God, then the consistency between God's knowledge, power, and benevolence is given and there is no need to provide an additional argument for the possibility premise. In other words, the possibility of the existence of God is automatically given once we accept the maximal God thesis and the perfect being thesis. So, somewhat ironically, the sixth (and my own) argument for the possibility premise is that we do not need any argument for it. In this way, the possibility premise, arguably the only controversial premise of the modal ontological argument, is established and the argument successfully derives the existence of God. (Nagasawa (2017), 205)

But as we shall now see, Nagasawa is being too complacent here – it is not at all clear that his strategy can be so easily extrapolated from the Type A and Type B objections to apply in this way to the possibility premise of a Modal Ontological Argument.

To illustrate the problem, consider my earlier parody argument, which purported to prove the existence of a naturally harlequin-patterned rabbit, starting from the definition:

• (MW) A being is bunnyquin in a given possible world if and only if, in that world, it is a rabbit whose fur is naturally coloured in alternating red and yellow patches.

This appears to be a coherent property: if naturalists somewhere reported that they had found a colony of rabbits patterned in this way, we might be extremely surprised but would not accuse their report of inconsistency. The subsequent definition, however, is far more problematic:

• (MA) A being is omnibunnyquin if and only if it is bunnyquin in every possible world.

Most philosophers, I believe, would deny outright that this alleged property is coherent: rabbits just are not a type of being that can be necessarily existent. And it would be of no help whatever for the proponent of this argument to ‘weaken’ its conclusion, for example by allowing the rabbit's colours to be brown and white instead of red and yellow. These changes might make the actual existence of such a rabbit more plausible, but they would do nothing to make its necessary existence more plausible.

In exactly the same way, I am prepared to accept that Nagasawa has made a reasonable case for the coherence of the property of real maximal excellence (i.e. having the maximal consistent set of knowledge, power, and benevolence). In that respect, indeed, he might reasonably claim to have strengthened Plantinga's argument by avoiding Type A and B objections. But nothing that he has said in defence of his maximal God thesis has provided any reason for accepting that a being could have this property in every possible world. Just as in the case of my imagined rabbit, the obvious objection is that gods just are not a type of being that can be necessarily existent. Moreover, I believe it is this thought – rather than worries about the coherence of the omni God concept – that fundamentally motivates most atheists in opposing Plantinga's Modal Ontological Argument. They are far more likely, in other words, to object to Plantinga's definition of maximal greatness than to his definition of maximal excellence. And although Nagasawa's maximal God thesis might help to secure a coherent account of the latter, it does nothing whatever to assuage doubts about the coherence of the former.

Nagasawa himself seems to evince some awareness that there are further issues to be addressed in extending his maximal God strategy from actuality to necessity. His oft-repeated definition of the maximal God thesis is silent on this modal issue: ‘God is the being that has the maximal consistent set of knowledge, power, and benevolence.’ Likewise, he defines real maximal excellence in terms of ‘the maximal consistent set of knowledge, power, and benevolence’ (Nagasawa (2017), 205). And although he occasionally mentions necessity as an important divine property, within the crucial discussion this appears as an afterthought, as we can see if we continue the quotation above from his page 204:

It is important to remind ourselves that, as I discussed in Chapter 1,³⁰ necessary existence is included in the notion of the being than which no greater is metaphysically possible. For God to be greater than all other metaphysically possible beings, He has to be ontologically superior to all other metaphysically possible beings. No being can be ontologically superior to all other metaphysically possible beings if it is a merely contingent being. (Nagasawa (2017), 204)

But in consideration of the Modal Ontological Argument, there is all the difference in the world (well, in every possible world but one!) between ‘the maximal consistent set of knowledge, power, and benevolence’ and ‘the maximal consistent set of knowledge, power, benevolence, and necessary existence’. Everyone will agree that some positive degrees of knowledge, power, and benevolence are mutually consistent, since nearly every adult human exhibits these properties for themselves. And therefore it plausibly follows – if we are prepared to put aside worries about commensurability – that there will be some maximally consistent combination of these properties. But adding necessary existence into the mix changes things entirely. For we cannot find even one uncontroversial example that clearly exhibits all four qualities to any positive degree whatever, since no thinking agent that we know of is a necessary existent. Moreover, there is a widespread philosophical consensus (at least among atheist philosophers) that necessary existence is confined to abstract entities such as numbers, and hence that no causally active agent can possibly be a necessary existent. Hence the claim that there is any consistent positive combination of knowledge, power, benevolence, and necessary existence – let alone a maximal consistent combination – is extremely dubious, and one that most atheists will immediately reject. Thus Nagasawa's attempt to establish the possibility premise of his Modal Ontological Argument fails.

A general critique of Ontological Arguments

At the end of his final main chapter, Nagasawa describes himself as ‘a counterexample to the common perception that no one subscribes to perfect [being] theism because of the ontological argument’, adding ‘it seems to me that the argument is no less compelling than many other philosophical arguments that are widely considered persuasive’ (Nagasawa (2017), 206). By contrast, I feel quite certain that the quest for a successful Ontological Argument is as futile as the search for a geometrical method of trisecting angles or squaring circles, certain enough to make this one of the relatively few philosophical theses on which I would be fully prepared to bet my house! Here I shall conclude by drawing on points made earlier in this article to present a strongly sceptical general position on both the Classical and Modal arguments.³¹

Dismissing the Classical Ontological Argument

To take the ‘classical’ argument first, it seems evidently hopeless to attempt to define, or to identify descriptively, some concept G which simultaneously satisfies all three of the following constraints:

1. (a) The rational atheist must accept that the definition or identifying description succeeds in coherently specifying a concept G.

2. (b) The rational atheist must accept that the concept G thus specified is instantiated.

3. (c) It must be provable that anything instantiating concept G has divine qualities (e.g. infinite or maximal knowledge, power, and benevolence).

No definition or identifying description could possibly achieve all three together, unless atheism is provably inconsistent (in which case, as I will argue shortly, that should be provable more directly). Different versions of the Ontological Argument fail in different ways, but Anselm's – thanks to his cleverly ambiguous formula – has the distinction of failing in all three! Interpretation (i) discussed earlier fails in respect of (c): it picks out the actually greatest concept, whichever that may be, but without any guarantee that this will be the concept of a divine being. Interpretation (ii), which Nagasawa favours, fails in respect of (b): the atheist is given no reason to suppose that the concept is instantiated, because the way in which the concept is descriptively identified guarantees only that it is hypothetically supreme, not actually supreme. Finally, interpretation (iii) fails in respect of (a): the rational atheist can simply deny that any concept at all meets the standard of actual unsurpassable greatness that would be required to satisfy the identifying description of G under this interpretation.

The exceptional cleverness of Anselm's version of the argument lies precisely in its use of this ambiguous formula, which, through the hint of interpretation (iii), gives the illusion of combining the solidity of interpretation (i) with the ambition of interpretation (ii). But although this ambiguity makes it quite tricky to show in detail how the argument fails (as we saw earlier), it is much easier to make a persuasive case that it must fail – under any interpretation – in its attempt to frame a concept that can ground a successful Classical Ontological Argument. For the gap between the premises of any such argument (confined to the a priori) and its very substantial conclusion (a massive claim about the real world) cannot plausibly be bridged by pure logic, no matter how ingenious the theist might be. Any two of the three constraints (a), (b), and (c) are mutually achievable, but if in fact there is no God, then attempting to identify a concept that satisfies all three constraints simultaneously is as hopeless as the attempt to cover the floor of a room with a carpet that is too small: any individual corner of the room can be covered, but moving the carpet to fit one corner inevitably exposes another.

Cruder versions of the Classical Ontological Argument such as Descartes's, which explicitly include the standard divine properties within the definition of the relevant concept, satisfy constraint (c) trivially, but consequently fail more straightforwardly by violating either (a) or (b). This is usually easy to see, as long as we keep clearly in view the important distinction explained earlier, between internal (or characteristic) and external (or descriptive) properties of a concept. The former define the concept, and hence can usually be chosen as desired by the proponent of the argument when specifying which concept is to play the key role within it. By contrast, the external properties of a concept – notably its instantiation or otherwise – are properties of the concept thus defined, which often depend on external factors that cannot be determined by definition, and so cannot be arbitrarily specified. Descartes, as we saw, wishes to include ‘existence’ as a defining quality of his concept of God, and we can indeed allow him to do this – thus satisfying constraint (a) – as long as this internal notion of ‘existence’ is understood to be quite distinct from instantiation.³² But then the atheist can simply continue to deny that the concept is instantiated – thus violating constraint (b). If, on the other hand, Descartes wishes to ensure that the relevant concept is instantiated by including that property in his specification (e.g. ‘the concept of God includes all perfections as internal qualities, and it is, besides, instantiated’), then the atheist can simply deny that this succeeds in identifying any concept at all – thus violating constraint (a). Descartes cannot reasonably expect both to be able to define a concept's internal properties as he pleases and at the same time insist that the concept is instantiated.³³ To allow such arbitrary ‘definition’ would, indeed, quickly lead to wildly unacceptable conclusions, as numerous parodies of Descartes have illustrated (e.g. ‘I hereby define the concept Bunnyquin as that concept which applies only to red and yellow harlequin patterned rabbits, and which is, besides, instantiated’).³⁴

Dismissing the Modal Ontological Argument

Plantinga's Ontological Argument is far less ingenious than Anselm's, though it has been surprisingly influential, prompting John Mackie's ironic comment that Plantinga's achievement ‘in subverting (as Hume would say) all the principles of the understanding of so many intelligent readers’ could satisfy the miracle-working requirement for canonization as a saint (Mackie (1982), 55)! Plantinga devised his argument at a propitious time, benefiting both from a post-Kripkean wave of enthusiasm for modal logic, and a disproportionate respect for formalism that is still evident in academic philosophy. Strip away the technical veneer, however, and as we saw earlier, the argument is very simple. First, it defines terms in such a way as to ensure by definition that the relevant theistic notion is either necessary or impossible (and hence cannot possibly be contingent). Then it adds the premise that the notion is not impossible. The conclusion then trivially follows that God – so defined – is necessary and hence actual. The fact that the argument can be spelled out through several additional steps, unpacking the relevant definitions, should not mislead us into supposing that its logic is subtle or sophisticated: shorn of its technical garb, it is almost as simple as any philosophical argument can be.

Moreover, if we leave aside the supposed divine necessity which plays such a key role, and in sharp contrast with Anselm's Ontological Argument, the logical mechanism of Plantinga's version has absolutely nothing specifically to do with any of the standard divine attributes. As we saw, any non-modal attributes at all – including red-and-yellow-patterned rabbithood – could be plugged into the structure with exactly the same kind of logical outcome. So the fact that Plantinga has chosen to frame his argument in terms of omniscience, omnipotence, and omnibenevolence purely reflects his traditional theistic assumptions, rather than anything specifically sanctioned by the logic or by any evidential considerations. Once this has been recognized, it becomes obviously implausible to claim that this form of argument can provide any genuine warrant for the particular belief which happens – apparently quite arbitrarily – to have been chosen as its conclusion.

All this can be said without even considering any deeper metaphysical objections to the argument or the framework within which is couched.³⁵ But as pointed out earlier, I believe that the vast majority of atheist philosophers will want to deny that the concept of necessity – at least in the strong metaphysical S5 sense relevant here – can coherently be applied to a proposition asserting the existence of any concrete being, such as might potentially be capable of knowledge, power, or benevolence.³⁶ In Hume's terms, any such proposition is in the domain of ‘matter of fact and existence’ rather than abstract ‘relations of ideas’ (Hume (1748/2007), 4.1–4.2),³⁷ and accordingly must inevitably be contingent (and provable, if at all, only a posteriori). From this point of view, therefore – which many would consider philosophical common sense – not only does Plantinga's argument fail to give any evidential support whatever to theism; worse, it even defines theism in a way which guarantees its falsehood, by building into it the demand for necessity where that is not to be had.

Bringing the objections together: a double-pronged challenge

Such appeals to philosophical common-sense are, no doubt, debatable: atheists may inherit theirs from Hume, but Plantinga and others of his ilk will look to different sources, not least Anselm himself. Moreover, putting essential weight on any deep metaphysical theses would obviously jeopardize my claim – against Nagasawa – that the Ontological Argument can be defeated by objections that appeal to relatively ‘shallow’ logical considerations. So instead, I shall end by emphasizing how both the Classical and Modal versions can indeed be defeated by such shallow logical objections, which moreover can be seen as playing complementary roles within an overall broader structure.

Anselm's argument aims to prove the existence of God by finding a contradiction in the atheism of the Fool of the Psalms, who ‘has said in his heart, there is no God’. Plantinga's argument, by contrast, claims no such contradiction, but aims to establish God's existence without demonstrably refuting atheism. This suggests a two-pronged challenge to any advocate of an Ontological Argument, to explain in outline either (i) how atheism could plausibly be considered self-contradictory; or (ii) how any such argument could possibly work epistemologically without convicting atheism of contradiction. In presenting this challenge, I am again following in Hume's elegant footsteps:

there is an evident absurdity in pretending to demonstrate [the existence of God], or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable. (Hume (1779/1947), 9.5; cf. Hume (1748/2007), 12.28)

Hume's line of thought can be developed further using the terminology and insights of contemporary logic. Contradictions arise when a set of propositions involves a logical inconsistency, and when this occurs, the inconsistency may be resolved by removing propositions from the set, but never by adding new propositions to it. Accordingly, complex ambitious theories are generally far more likely to contain inconsistencies than simple modest theories, and indeed it is hard to see how an absolutely minimal theory – which does no more than deny some type of concrete object's existence without making any other assertion – could possibly be contradictory. With respect to potential self-contradiction, therefore, theism and atheism are in an entirely different position. Theism claims that several very substantial qualities (each in itself of questionable coherence) are all instantiated, and moreover that they all coincide. This gives plenty of material for potential inconsistency, as Nagasawa's discussion of the Type A and Type B objections amply illustrates. Atheism, by contrast, simply denies any such coincidence, so it is hard to see how it could possibly contain enough distinct commitments to generate an inconsistency.³⁸

Thus the first part of my challenge to the proponent of the Ontological Argument is to explain clearly and explicitly how such an internal inconsistency might be supposed to arise from atheism, given the prima facie implausibility of such an outcome. If Anselm were correct, then this could presumably be done, though his method of attempting to demonstrate such inconsistency – by proffering a slippery formula of his own that supposedly leads the atheist into contradiction – sheds little light on the source of the alleged inconsistency, and strongly suggests sleight of hand rather than genuine insight into the logic of the atheist's position. Suspecting sleight of hand here is indeed entirely rational, especially given my earlier argument that the three constraints (a), (b), and (c) cannot all be jointly achieved by any unambiguous formula. But this suspicion would be reasonable even without any such specific reason for doubt, and even if we ourselves had no clue as to how the trick takes place. For if the theist genuinely believes that atheism is internally inconsistent, then instead of cunning riddles, he owes us a straightforward account of how this surprising claim can plausibly be true.

The second part of my challenge, directed to any proponent of the Ontological Argument who declines to accuse the atheist of inconsistency, is to explain – again, clearly and explicitly – how such an argument could possibly work epistemologically without implying such inconsistency. Here we come close to Plantinga's territory, with his apparatus of possible worlds which seems to allow for truths that are necessary without their negations being self-contradictory. Plantinga never satisfactorily explains how this could the case, so here too we have every right to be suspicious.³⁹

Suppose, however, we allow for the sake of argument that there can indeed be hidden metaphysical necessities that somehow constrain what is possible, without manifesting themselves in any outright contradiction. In that case, something like Plantinga's Modal Ontological Argument (or Nagasawa's potentially weaker variant of it) might indeed perhaps track the truth, by postulating such a hidden necessity that happens to obtain. But for the reasons we saw earlier, this optimistic speculation does nothing whatever to get us close to a persuasive ontological proof, because we have no basis for judging that this particular arbitrarily postulated necessity has the remotest chance (epistemologically) of being true. Any number of such arguments could be proffered, for any number of quite different conclusions (including our necessarily existing red and yellow rabbit). Many of these conclusions will, moreover, conflict with each other, especially when they involve types of being (such as omnipotent agents) of which there cannot plausibly be more than one. So the choice between such conclusions becomes completely arbitrary even if one of them just happens to track the truth. Plantinga disguises this variety by posing the choice between a ‘maximality argument’ and a ‘no-maximality argument’, as though from an a priori point of view the probabilities are the same, like a coin-toss. But this is highly misleading. For even within the questionable framework of these alleged hidden metaphysical necessities (which, again, the atheist has been given no reason whatever to accept), Plantinga's ‘maximality argument’ is just one of many competing possible arguments, and in posing the issue as a choice between just two options – to accept a particular notion of God, or to reject it – he is trying to pull the same trick as Pascal in his famous wager, and is subject to a similar objection. For as explained earlier, it is quite illegitimate to claim an equivalence in prior plausibility between one highly specific theory and its negation, because the latter will occupy vastly more of the logical space. One vivid illustration of this is that whereas countless highly specific theories – for example, concerning the existence and particular nature of a supposedly unique omnipotent being – will logically conflict with each other (in such a way that at most one of them can be true), the negations of these theories will typically be entirely consistent with each other (and indeed might very reasonably all be considered true).⁴⁰ In this situation, the only possible rational attitude is to reject any such highly specific theory. Hence Plantinga's argument (and likewise Nagasawa's variant) would be quite hopeless from an epistemological point of view, even if his metaphysical framework were to be accepted, and even if in fact the argument happened to track the truth.⁴¹ So quite apart from all those significant doubts about the argument's deep and eminently disputable metaphysical underpinnings, its failure as a serious piece of natural theology is very clear at a far shallower and more straightforward level.

Conclusion

Nagasawa's Maximal God presents a powerful and ingenious case for his method of safeguarding perfect being theism against the threat of contradiction, and impressively brings a new perspective to both the Classical and Modal Ontological Arguments. But no amount of ingenuity can achieve the impossible task of vindicating the Ontological Argument in either form. Nor, in my view, does Nagasawa succeed in his more limited aim of showing that the opponent of such arguments is forced to appeal to ‘deep’ and potentially controversial philosophical theses.

Anselm's Classical argument is especially hard to pin down and refute, owing to his highly ambiguous key formula. But once this ‘shallow’ syntactic ambiguity has been exposed, each of the three main options leads to a fairly straightforward refutation, by violating one of the constraints (a), (b), or (c) set out earlier. In particular, Nagasawa's preferred interpretation of Anselm's formula fails to generate the contradiction on which Anselm's argument depends, because on this interpretation there is no inconsistency in the atheist's thinking of a hypothetical scenario in which the concept God would be greater than it actually is. The problem here is not any difficulty in making the comparison (as Nagasawa suggests), but simply the failure to generate a reductio of the Fool's atheism.

Plantinga's Modal argument is more straightforward, and its limitations are fairly well known, though in my view the philosophical literature tends to treat it far more generously than it deserves. Its technical apparatus disguises a fundamentally simple logical structure, starting from a definition of divinity which can only be either necessarily instantiated or impossible. This reduces the theist's task to establishing the corresponding ‘possibility premise’, and Nagasawa's ingenious idea is to harness his maximal God strategy to achieve this. That strategy can operate fairly convincingly in respect of the attributes of knowledge, power, and benevolence, which we know to be instantiated together – at least at modest levels – within the real world. But it falls down with divine necessity, owing to the absence of any good reason for supposing that such necessity (in the ‘broad logical’ sense) is even a coherent possibility for an active causal agent, as opposed to a mere abstract object such as a number. Hence we have no good reason for supposing that any positive co-instantiation of the four attributes is possible.

Nagasawa might reasonably argue that the point just made presents a deep and potentially controversial objection to Plantinga. But it can be combined also with a shallow attack, based on the observation that the logical structure of Plantinga's argument has no specific connection with the non-modal divine attributes. Thus exactly the same kind of logic can be applied to ‘prove’ the necessary existence of any arbitrarily invented entity – even a red and yellow harlequin-patterned rabbit – and Plantinga's argument structure in itself gives no reason whatever for preferring his chosen conclusion to any other. So even if we waive the ‘deep’ metaphysical objection to divine necessity, and allow that such a thing might perhaps obtain in reality, this shallow objection is quite enough to refute the argument from an epistemological point of view. I conclude, therefore, that both the Classical and Modal Ontological Arguments are after all, and despite Nagasawa's ingenious arguments to the contrary, straightforwardly refutable without dependence on any reasonably disputable metaphysical premises.