Abstract
A new version of the ontological argument for the existence of God is outlined and examined. After giving a brief account of some traditional ontological arguments for the existence of God, where their defects are identified, it is explained how this new argument is built upon their foundations and surmounts their defects. In particular, this version uses the resources of impossible worlds to plug the common escape route from standard modal versions of the ontological argument. After outlining the nature of impossible worlds, and motivating the need for positing them, the new argument is delineated and its premises justified. It is taken for granted that the argument cannot be sound, since it would prove too much. However, its premises are all plausible, and their denial promises to have significant ramifications. Several intuitive lines of objections are then explored in order to illuminate their shortcomings. The puzzle that the argument poses is therefore not whether the argument is sound, for it clearly cannot be. Rather, it is to place pressure on its plausible premises, so some plausible account of how the argument fails can be identified, and that the devising of such an account promises to be insightful. In the process, we should gain an improved understanding of how such ontological arguments work.
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Notes
In particular, see his Prosologion (1077–1078, Chap. II–III). It is unclear to me that the argument I present in the text is in fact the one Anselm makes. But my concern here is not exegesis, and it is a version of the argument that is at least sometimes attributed to him (cf. Le Poidevin, 1996, Chap. 2).
This version of the argument also avoids the cross-hairs of the renowned Kantian retort, that existence is not a property.
Throughout I am at pains to avoid naming God. Doing so would have risked begging the question of theism by presupposing an entity that answers to that name. Instead, the arguments run from the mere concept God, to its being satisfied by an actual existent. I apologise for the cumbersome, and perhaps at times clunky, prose that results from this decision.
Roughly, a concept, C, is satisfied by a being, x, iff the ascription of C to x expresses a true proposition.
Plantinga bemoans, rather than advocates, this intuition.
Or at the very least, one cannot build bridges from the conceptual world to the “concrete” world. Many in fact do seem happy to build bridges from the conceptual world to the “abstract” world. This would leave the door open for the theist to claim that God is an abstract entity (see Leftow 1990, for a discussion of this proposal). Indeed, on some conceptions of what it is to be an “abstract” entity, God would likely fall into that class. Take for example the construal of “abstract” entities as non-spatial and non-temporal. If God is conceived as transcending space and time, as many do, then God would be one of the abstracta.
It is not clear to me that there is any natural distinction between concrete and abstract entities. For those who hold a disparate attitude towards whether conceptual bridges can be built towards the abstract, compared to the concrete, world, some good reason(s) for treating the abstract and the concrete differently will need to be given. Otherwise, it will be evident that their differential treatment will be resting upon an unprincipled bias. I doubt that a principled way of distinguishing the two kinds of entities, a way that justifies a differential attitude towards building bridges from the conceptual world, can be had.
Though, of course, this is controversial. For example, we might be mistaken about what it is we are in fact conceiving of, thus creating the illusion of possibility.
In Chalmers’ (2002) terminology, it might be claimed that it is ‘ideal conceivability’, as opposed to ‘prima facie conceivability’, that entails possibility.
Consider also the prima facie conceivability of certain time travel stories that are popular in the science fiction literature, but upon closer inspection are revealed to be incoherent.
It only ‘may’ seem too strict, since some might be happy to assign this level of strictness to conceivability for the entailment at a cost of delimiting the number of cases we can conceive of in sufficient detail, such that the conceiving entails the possibility of the conceived. This would add a, perhaps insurmountable, barrier to our ability to acquire knowledge of what is merely possible by using our faculty of conceiving.
The ‘perhaps’ here is because it is plausible that there could be some things that are possible, but not conceivable. And maybe a God is such a thing.
The ‘◊’ and ‘
’ are modal operators on sentences or propositions ‘p’, to be interpreted respectively as ‘It is possible that…’ and ‘It is necessary that…’.If you believe in transworld identity, and as such do not think that the ‘our’ in ‘our world’ helps us, then the demonstrative ‘this’ can do the important work of singling out the actual world in the expression ‘this world’, by this or that utterance or inscription by us of that demonstrative expression.
It will not rely on an actuality operator, since I am treating the property of being an actually necessary existent as a brute extrinsic first-order property of things. Though I do not think that it will affect the argument much if we were to analyse the property of being an actually necessary existent as a complex property accordingly: ‘λx.@
E!x’. Of course, this will rely on using lambda-abstractions to analyse the complexity of the predicate, as well as both an actuality operator and an existence predicate. I prefer not to analyse the property this way to keep the argument simpler and making as few commitments, and hence targets, as possible.Perhaps, it might be thought, that some sense could be made of ‘greatest conceivable being’ if like Plato, Plotinus, Descartes, or more recently Quentin Smith (2002), you believed in varying degrees of being. However, it seems intuitive to many that being simply does not permit degrees; it is a categorical notion. Something either is, or it is not (though, see McDaniel 2013). But even if we grant that there are degrees of being, it remains to be explained why unqualified greatness should be positively, rather than negatively, correlated with higher degrees of being. Any pull in either direction seems more like prejudice that privileges one qualifying determinate that relativises greatness in one directed-ordering rather than its opposite.
I imagine that some might retort that one qualifying determinate for greatness, one directed-ordering of things, simply is privileged. Maybe so, but then we lack any epistemology for this hidden structure of reality. Nor is it clear what a privileged directed-ordering would need to be like for it to be a directed-ordering of unqualified greatness, rather than some other privilege. The simple fact is that there seems to be no non-redundant theoretical role for greatness to play, whether or not greatness is taken to be reductively analysable or primitive. And this leaves little room for understanding. I should like to emphasise that the target of my criticism here is perfect being theology.
Though, as we shall later see, there is an important upshot for these criticisms for my version of the ontological argument.
“Maximal” here means that for every p, ‘p v ¬p’ is true in all worlds. This does not of course rule out it being the case that for some p, ‘p & ¬p’ is true at a world, though, given the falsity of dialetheism, those worlds would be impossible worlds. Though, there is a worry here that a contradiction at an impossible world would infect the actual world (cf. Stalnaker 2002). Some might want to drop this “maximality” constraint on impossible worlds, perhaps because they think that such worlds can have gaps, as well as gluts. Nothing that follows will hang on this matter.
By “the world” I mean the world from which the possibility/impossibility of another world is being considered, i.e. the world which other worlds need to be accessible from to be possible relative to that world. This world would be non-rigidly actual relative to itself.
The examples are not crucial. If you think these scenarios are possible—Mackie (2006) is an example of this contention—then pick your own ways that things cannot be.
Roughly, a world w′ is closer than a world w″ to a world w, if, and only if, there are fewer differences in what propositions are true between w′ and w, than between w″ and w. There are clearly problems with this account of ‘closeness’, such as, for any slight difference between worlds w and w′, there would seem to be infinitely many propositions that have a different truth-value. So for example, if p is true in w, and false in w′, then there will be another proposition p*, that is the proposition that p is true, and yet another proposition p**, that is the proposition that p* is true, ad infinitum… that will all be true in w, but false in w′. But then there would appear to be infinitely many differences between every possible world. Hopefully, the intuitive idea of ‘closeness’ should be reasonably clear, or clear enough for present purposes, that we can set aside such tangential issues here.
The situation, as presented, is not quite as straightforward as I have made it seem. For the more attentive reader might complain that the closest world to the actual world where an impossible antecedent is true is just a world which is otherwise exactly like the actual world. Usually, when assessing the closeness of two possible worlds where the antecedent of a counterfactual is true, we can appeal to the preservation of certain important dependencies or laws to trump brute similarity. After all, brute similarity between worlds on its own would not yield an interesting analysis of counterfactuals. The counterfactuals are meant to be getting at some sort of dependency of the consequent on the antecedent.
However, let us assume an absolute notion of possibility (perhaps metaphysical possibility) where relative possibilities (e.g. nomic possibility) place extra constraints, or dependencies, on the constituents of the worlds than occur in the merely absolutely possible worlds. Each kind of relative possibility corresponds to the obtaining of some extra dependency relations, not contained in merely absolutely possible worlds, between the constituents of that world. We then take the common assumption that the relatively possible worlds are a mere subset of the absolutely possible. That is, that those extra dependencies only hold at worlds within that subset of the absolutely possible worlds. A problem then arises when we leave the domain of the absolutely possible worlds, as happens when consider counterpossible conditionals. It seems like no dependency relations obtain to trump brute similarity. And as a result, the closest worlds with an impossible antecedent would just be those that are otherwise exactly like the actual world. Accordingly, the impossible world theorist, not implausibly, needs to give up this picture. They must contend that the relative possibilities are not subsets of the absolutely possible. Indeed, Yagisawa (2010) does reject absolute possibility, opting only for relative possibilities, perhaps precisely for this reason.
Indeed, this picture is intuitive. For example, it gives a nice explanation of certain inconsistent time travel stories, such as in the Grandfather’s Paradox, as being nomically possible, even though absolutely impossible. This is the reverse of Lewis’s (1976) consistent time travel stories that are absolutely possible, even if nomically impossible. Our unease about the consistent time travel cases is that it seems like nomic dependencies do hold in those worlds, and that they would determine the changing of what happens at a time. That is, they would seem to permit the occurrence of contradictions. The obvious explanation is that they do. But all this means is that the nomically possible is not a subset of the logically or absolutely possible.
This is not to suggest that all possible and impossible things are conceivable. Indeed, many impossible things will surely not be conceivable, like circular-squares, and other analytic impossibilities. Nor am I suggesting that all that is inconceivable is neither possible nor impossible.
Indeed, part of what makes theism so difficult to assess is that there is really a cluster of, more or less, closely related God concepts in the vicinity, such that a charge against one often fails to spread to all others. As a result, a common move for the theist to escape criticism is to slink about between the concepts in that cluster. Though, it is unclear to me that this is in fact a defect of the dialectic, or as philosophical manoeuvre, illegitimate, it does make the ensuing debate particularly tough on atheists. I have tried to leave the concept God employed in IMPOSSIBLE relatively unspecified so that the reader may swap and change, within limits, as they please.
See Fine (1994) for a criticism of this view of essence.
Note, for those that find P9 suspect, it is an insufficient answer to the challenge that I am presenting merely to reject this premise. You need to explain how you can permissibly reject this premise given the justification it has received.
I am thinking here of those who like certain paraconsistent logics, such as relevantist logics. My guess is that such logics will be quite popular amongst those accepting impossible worlds. Though, the commitment to impossible worlds does not in itself entail a commitment to such logical systems.
By ‘impossible beings’ and ‘impossibilia’, I mean beings that do not exist at any possible world and whose existence is impossible. Impossible beings should be contrasted firstly with beings that do not exist at any possible world, but are also not impossible—perhaps because the notion of that being is incoherent (That is not to suggest that there are beings of this kind). And secondly, with beings which exist at an impossible world, but also exist at a possible world.
Some might think that this is fine for certain abstract entities, like numbers or sets, as long as those entities in fact exist. But you might be dissatisfied even if those abstract entities did exist, for the same reason that a theist might be dissatisfied with an argument for God’s existence that rest purely upon conceptual grounds (see fn. 6).
As Stalnaker notes, ‘[Some] have defended impossible worlds as a dialectical move, agreeing with Lycan that possibilities and impossibilities stand or fall together, but tying them to each other only to lend weight to the rejection of both.’ (2002, p. 55).
A plausible speculative diagnosis, I suggest, is that worlds bear an inextricable tie to actuality, and modal space at large—a relation that situates worlds in modal space, and thus making them worldly. And that it is this definitive relation between worlds that makes them wholly unsuited for capturing the entire illimitable scope of the impossible. I hope that these, somewhat cryptic, remarks become clearer in the light of the proceeding examination of responses.
This principle is underwritten by the more general ubiquity principle, Ubiquity*, that: For every proposition p, p represents something that is either possible or impossible. However, P6 only requires the weaker principle, Ubiquity.
Yagisawa (2010, p. 213) seems to have reached a similar conclusion.
Importantly, this is not to claim that our concept God is incoherent, but rather that whilst the concept is coherent, modal notions are not applicable to an entity’s satisfaction of this concept. Perhaps to do so would be a category mistake. However, it is doubtful that this proposal of the non-applicability of modal notions to our modally loaded concept God, in particular, can be made sense of. But let us ignore here this fact that the concept God that I have been employing throughout this essay is such that it is constitutively the case that specific modal predications must be applicable to all entities that satisfy that concept, lest they fail to satisfy the concept.
The distinction here between these competing conceptions of the impossible resembles the debate in philosophy of perception between positive and negative disjunctivism, and their characterisations of hallucinatory perceptual experiences (cf. Martin 2004).
Or, more generally, in accordance with Ubiquity* (see fn. 32).
This would also require rejecting certain commonly held inference rules of modal systems, at least in an unrestricted domain, such as: ‘¬◊¬p →
p’.This is potentially a point of disanalogy between modality and tense. Certain things have been thought to be atemporal. If this possibility is accepted, then one might deny the corresponding principle to Ubiquity for tense. Alternatively, one might state that such atemporal entities always obtain, in the same way that a moral error theorist might claim that everything is permissible. This would allow the preservation of the corresponding Ubiquity principles. However, the temporal connotation to “always” and the moral connotation to “permissible” puts a strain on these reconciliations.
For example, Lowe (1998, Chap. 6) seems to be relying on a notion of identity stronger than necessity when he gives his hyperintensional account of ontological dependence between things as the identity of depended entity/entities metaphysically determining the identity of the depending entity/entities. He calls this kind of dependence ‘identity dependence’. Importantly, this metaphysical determination of the identities is not something that can be captured modally. So Socrates’ singleton ontological depends on Socrates, but not vice versa, even though they are necessarily co-extensive.
Alternatively, if like Gallois (1998, Chap. 6) you think that the identity relation holds contingently between entities, then motivation for the claim that ‘Hesperus and Phosphorus being non-identical is neither possible nor impossible’, would be undercut.
In Kripke’s (1980) terminology, this amounts to the claim that there can be different epistemic counterparts of the individuals that actually satisfy our concepts Hesperus and Phosphorus.
A fortiori, self-identity is surely a constitutive property of a thing. To say of a thing, x, that it is not identical to itself, is to say that it is not that thing, that x is not x. But this is just to assert that what was initially claimed to be the subject of the proposition, namely x, is not the subject of that proposition. If x is not the subject of the proposition, then it seems that nothing is. As such, the statement that ‘x is not identical to itself’ does not even appear to express a proposition. And accordingly, interpretation 1 does not even seem to mount a challenge to Ubiquity* (see fn. 32). If I am mistaken about the inconceivability of 1, then it is Proposition, not Ubiquity that should be rejected.
Indeed, this outcome would appear to undercut most, if not all, reasons for believing in impossible worlds.
A reviewer for this journal has pushed this line of reasoning further, asking: ‘What should we say when asked about the "conceivability" of our different models of modal space?’ This is an excellent question. One of the reasons for introducing impossible worlds was so that modal space provides enough room to adequately accommodate all our thoughts, rather than appealing to strategies—such as Stalnaker’s (1999) diagonalisation strategy—to explain away supposed misapprehensions about what we think. But pressing this line of thought seems to suggest that those advocating impossible worlds can never fully escape the need for such reinterpretation strategies. For instance, what should be made of our ability to conceive of modal space (possible and impossible worlds included) differently from how it in fact is? Perhaps we can introduce higher-order ‘meta-modalities’ that capture possibilities and impossibilities of different lower-level modal spaces. Yet, if we can have rigid thoughts about this world (our world) being different, that world will not be located in those other modal spaces—it is located in our modal space. Rather, the best that can be achieved is to think of relevantly similar worlds in relevantly similar modal spaces, and explain away illusions that our modal space meta-can be different as confusing it for one of those relevantly similar modal spaces. This relates to our forthcoming point about misrepresentation.
Perhaps this might be seen as grounds for rejecting P6—that conceivability entails either possibility or impossibility—since what is conceived of is neither possible Should be ‘nor’. impossible in our modal space, but rather in some meta-possible or meta-impossible modal space. But all that really matters for the argument is that what is conceived of be at some world, possible or impossible, in the entirety of modal space (including all higher-levels of modality, with alternative representations of lower-level modal space). If this cannot be achieved—either because of a failure of Proposition or a broader version of Ubiquity locating propositions at least somewhere within the entirety of modal space—, then again, as promised, we have learnt something important and interesting about modal space.
See, for example, Plantinga’s discussion of world-indexed truths: ‘Indeed, for any proposition p and world W, if there is a world in which p is true-in-W, then p is true-in-W in every world. Propositions of the form p is true in α and p is true in W are non-contingent, either necessarily true or necessarily false.’ (1974, p. 55). Similarly, see Yagisawa’s discussion of α-transforms: ‘The α-transform of a property is the same property as indexed to @: for example, the α-transform of being a philosopher is being a philosopher at @. It is almost universally accepted that the operation of α-transformation produces necessity out of contingency, i.e. if a thing has a property contingently, it has the α-transform of that property necessarily. The widely accepted reason is that if x is F at @, then for any possible world w, x is F at @ at w, and vice versa.’ (2010, p. 59).
Yagisawa (2010) is perhaps an exception here, since he treats worlds as metaphysical indices, like times, or spatial points. Yet, on Yagisawa’s view, our standard modal notions are not applicable to worlds (pp. 52 and 90)—or propositions for that matter (p. 57). Instead, whilst rejecting Divers’ (1999) ‘redundancy account’ of advanced modalizing (see Yagisawa 2010, p. 203, n. 41), Yagisawa introduces what appears to be an infinite hierarchy of ‘über modal’ or ‘meta-modal’ notions to deal with advanced modalizing claims involving the existence and nature of worlds (i.e. modal claims about metaphysical/modal spaces). But as will soon be explained, Yagisawa’s proposal is ultimately of no help to our fictional objector.
He can do this because he treats worlds as entities, or as he calls them, ‘metaphysical indices’, analogous to the substantival treatment of times or spaces. That allows that a world is defined independently of its members. This is an interesting, but unusual, characterisation of worlds.
The ‘is m ’ here is a ‘modal tense’ that Yagisawa introduces to linking verbs in order to make clear what their relative domain of quantification is. This particular modal tense restricts the quantificational domain to what obtains at any particular metaphysical/modal space.
Or perhaps, it will be insisted that It is part of the concept God that it is satisfied by a being, x, only if x has the constitutive property of satisfying the concept God in the every, or every possible, world. Both of these options would entail P10. But the weaker claim, P10, would seem to yield the desired result on its own.
’ are modal operators on sentences or propositions ‘p’, to be interpreted respectively as ‘It is possible that…’ and ‘It is necessary that…’.
E!x’. Of course, this will rely on using lambda-abstractions to analyse the complexity of the predicate, as well as both an actuality operator and an existence predicate. I prefer not to analyse the property this way to keep the argument simpler and making as few commitments, and hence targets, as possible.
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Acknowledgements
Thanks are due to Sarah Adams, Michael Bench-Capon, and Jason Turner for providing helpful feedback on earlier drafts of this work. Also to audiences at the Universities of Birmingham and Leeds, where I presented this work, and to fruitful conversations about this paper, again with Michael Bench-Capon, but also Richard Caves. The paper is better as a result of their generous feedback.
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Pezet, R.E. An impossible proof of God. Int J Philos Relig 83, 57–83 (2018). https://doi.org/10.1007/s11153-016-9591-0
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DOI: https://doi.org/10.1007/s11153-016-9591-0