Divine necessity. Einar Duenger Bohn. Abstract 1 INTRODUCTION 2 STRONG AND WEAK DIVINE NECESSITY ARTICLE

Transcription

1 Received: 28 April 2017 Revised: 1 August 2017 Accepted: 7 August 2017 DOI: /phc ARTICLE Divine necessity Einar Duenger Bohn University of Agder Correspondence Einar Duenger Bohn, Department of Religion, Philosophy and History, University of Agder Postboks 422, 4604 Kristiansand, Norway. einar.d.bohn@uia.no Abstract Divine necessity is the thesis that God must exist. In this paper, I give a brief survey of what the thesis is more exactly, the main arguments for it, and the main arguments against it. 1 INTRODUCTION From the claim that God must exist, it follows that God actually exists, but from the claim that God actually exists, it doesn't follow that God must exist. So even if God were to actually exist, we should still ask: must God exist? The thesis of what I call strong divine necessity is the claim that God must exist, from which it follows that God actually exists. The thesis of what I call weak divine necessity is the claim that if God actually exists, then God must exist, from which it obviously does not follow that God actually exists. But if we for independent reasons add the claim that God actually exists, it follows by weak divine necessity that God must exist; on the flip side, if we for independent reasons add the claim that it is not the case that God must exist, it follows from weak divine necessity that God actually doesn't exist. 1 On the other hand, if we for independent reasons discover that God actually exists, but didn't have to exist, it follows that both strong and weak divine necessity are false. 2 Strong and weak divine necessity are often not clearly separated, but they should be: They are logically different theses. Strong divine necessity entails weak divine necessity, but weak divine necessity does not entail strong divine necessity, hence the labels strong and weak. In this paper, I first clarify both strong and weak divine necessity (Section 2). Then I present and discuss a version of each of what I take to be the three main kinds of arguments for strong divine necessity (Section 3). Then I present and discuss a version of each of what I take to be the two main kinds of arguments against strong divine necessity (Section 4). Throughout, I also consider some interesting retreats to weak divine necessity. In the last section, I consider an alternative to divine necessity, what we might call divine absoluteness (Section 5). 2 STRONG AND WEAK DIVINE NECESSITY Again, the thesis of strong divine necessity is the claim that God must exist, i.e. God could not have failed to exist, and the thesis of weak divine necessity is the claim that if God actually exists, then God must exist, i.e. if God exists, then God could not have failed to exist. Unless noted otherwise, by God I mean the intentional being that is the ultimate ground of reality and worthy of worship. Hopefully, that is neutral enough to capture sufficiently many interesting notions of God. The question then is whether such an ultimate ground must exist, or could have failed to exist. By must and necessarily I mean metaphysical necessity in the sense of truth in any possible world, where a possible world is (circularly) explained as Philosophy Compass. 2017;e wileyonlinelibrary.com/journal/phc3 1of10

2 2of10 BOHN a complete way the world could have been. I define metaphysical possibility and impossibility as usual: possibly p if and only if not necessarily not p and impossibly p if and only if necessarily not p. I separate metaphysical necessity, which is truth in any possible world, from logical necessity, which is truth in any model. Arguably, there is a model for any possible world, but there is not a possible world for any model. So logical necessity entails metaphysical necessity, but metaphysical necessity does not entail logical necessity. Deducing a logical contradiction from a claim, and thus showing that it is logically impossible (i.e., has no model), is sufficient to show that it is metaphysically impossible (i.e., false in any possible world), but providing a model, and thus showing that it is logically possible, is not sufficient to show that there is a possible world like that, i.e., that it is metaphysically possible; there are logical possibilities that are not metaphysical possibilities. In short, I distinguish between metaphysics, which employs talk of truth in a possible world, and model theory, or pure logic, which employs talk of truth in a model; the latter is necessary but not sufficient for the former. 3 I take it the theses of divine necessity are theses of de re necessity, not de dicto necessity. Roughly, de re necessity is necessity ascribed to an object, while de dicto necessity is necessity ascribed to a claim, or a proposition. So, for example, the thesis of strong divine necessity claims that God necessarily exists, not merely that necessarily God exists. There is a substantial difference here. The de dicto claim requires only that the claim God exists is true in any possible world, independently of what makes it true from world to world; it might be one God in one world but another God in another world. The de re claim on the other hand requires that one and the same object has the property of existing in any possible world; it cannot be one God in one world and another God in another world but must be one and the same God in any possible world. 4 Note that this might involve a non deflationary notion of modality, i.e., a notion according to which modal properties of objects are real properties of those objects. In fact, until noted otherwise, I henceforth ignore all deflationary notions of modality. 5 This de re understanding of divine necessity might be a bit stronger than some prefer. 6 But note again that if divine necessity is formulated merely as the de dicto necessity of the claim that God exists, then it might be that no particular being necessarily exists, in which case any possible God lacks necessary existence. But I'm interested in divine necessity, not the necessity of divinity. One might alternatively try to formulate divine necessity as the claim that there is something that is necessarily God, but note that even that is too weak because it does not entail that that something necessarily exists. Compare: there is something that is necessarily me; that does not entail that that something necessarily exists. I am necessarily me, but, unfortunately, I don't necessarily exist. The theses of divine necessity that I will be interested in don't merely say of a thing that it is necessarily God, but they say of God that it necessarily exists. 7 3 THE ARGUMENTS FOR DIVINE NECESSITY In this section, I will present and discuss a version of each of what I take to be three main kinds of arguments for the thesis of strong divine necessity, namely, the ontological argument, the cosmological argument, and the argument from abstracta. I also consider some retreats to weak divine necessity. 8 It goes without saying that I can here only present and all too briefly discuss one particular rough version of each kind of argument. There is of course much, much more to be said on all points considered. Consider it a mere taste of the meal intended to make you want more, rather than a substantial portion of it intended to fill you up. 3.1 The ontological argument There are many versions of the ontological argument, most of which are well discussed in the literature. 9 Here is a taste of just one version, for purposes of strong divine necessity. The idea is that we can, upon conceptual reflections, come to see that God necessarily exists, because, at least according to this kind of argument, God is the greatest being

3 BOHN 3of10 that can be, and it's greater to necessarily exist than to merely contingently exist. Here is one way of putting the argument: 1. God = the greatest being that can be Definition 2. God does not actually necessarily exist For reductio 3. God possibly necessarily exists Premise 4. If 2 and 3, God is possibly greater than God actually is Premise 5. But God is not possibly greater than God actually is 1 6. So not 2 or not 3 4,5 7. So God necessarily exists 2,3,6, RAA 10 Let me here only mention two good ways to block this particular argument. First, as I have argued elsewhere (Bohn, 2012), definition 1 is arguably incoherent: Greatness has no top level but is indefinitely extensible. For any possible great being, there is a possibly greater one, which entails that premises 1 and 3 are false. Second, premise 4 is deeply problematic because it's unclear how we can compare a possible God with an actual God given that for all assumption 2 says there might not be any God at all. (This same criticism holds of the strategy of using the ontological argument to first establish the existence of God, only to then try to establish its necessary existence.) It must be that we have a concept of God that might or might not have an extension in the actual world but has an extension in some possible world. Now, it is not the concept of God that is more or less great depending on whether it holds of some possible necessary thing or some actual non necessary thing, but it is its possible necessary extension that is greater than its actual non necessary extension. But the problem is that it might not have an actual extension at all! So instead, we must somehow compare a conceivable actual non necessary extension with a conceivable possible necessary extension, and somehow, the latter is greater than the former. But even then, how do we get from that to the conceivable actual extension actually existing? It's just unclear how there could be a sound way from merely considering a concept with a conceivable extension to that conceivable extension actually existing and equally unclear how there could be a sound way to it necessarily existing. For purposes of weak divine necessity, the idea behind the ontological argument is that it somehow follows from the concept of God that God must exist, if God actually exists. So for such purposes, we don't have to worry about whether God exists as we did in 2 above; we can simply assume it, which means that we have an argument for weak divine necessity that avoids at least the second of the above two criticisms: 1. God = the greatest being that can be Definition 2. God actually exists Assumption 3. God does not actually necessarily exist For reductio 4. God possibly necessarily exists Premise 5. If 2, 3 and 4, God is possibly greater than God actually is Premise 6. But God is not possibly greater than God actually is 1 7. So not 2 or not 3 or not 4 5,6 8. So if God exists, then God necessarily exists 2,3,4,7, RAA 11 This argument for weak divine necessity is stronger than the earlier argument for strong divine necessity, but it nonetheless has serious problems, even ignoring the previously mentioned problem with definition 1. The argument hinges on assumption 3 and premises 4 and 5. Unlike in the earlier argument 1 7 for strong divine necessity, given the assumption 2 that God exists, we can here reasonably compare God with a possible God, and in so comparing it across worlds, it even seems God is greater if it necessarily exists than if it merely contingently exists. But the problem is that when we so compare it across worlds, it seems we have equally clearly in mind a contingently existing God and a necessarily existing God, but the two are logically incompatible, so one of them is in fact impossible. That means, at best, that one of them must be merely epistemically possible, i.e., possible for (i.e., compatible with) all we know, but not in fact metaphysically possible. But which one is it: the actually contingent God of assumptions 2 and 3 or the possibly necessary God of premise 4? The argument doesn't tell. We need independent reasons to choose between 3 and 4, in order to move from 7 to 8.

4 4of10 BOHN It thus seems that neither strong nor weak divine necessity is very well supported by the above versions of the ontological argument. Of course, I have not surveyed all pros and cons here, and I must leave it to the reader to consider other versions of the ontological argument, but I dare claim that my conclusion is representative: The ontological argument does not establish divine necessity without much further ado. There is another related but independently interesting argument for strong divine necessity worth considering before we move on; let's call it the Plantinga argument (see, e.g., Plantinga, 1974). It is based on a similar idea as that in premises 3 and 4 in the previous two arguments (respectively): 1. God possibly necessarily exists Premise 2. So God necessarily exists 1, Modal Logic The argument is valid in any modal logic (e.g., S5) with the theorem that whatever is possibly necessary is necessary. In realist metaphysics, where all possible worlds can see each other, this theorem is very compelling. If all possible worlds can see each other, if something is necessarily the case in one world, it is the case in any world. But the Plantinga argument seems too good to be true. Why believe it is possible of God that it necessarily exists (see Section 4 below)? One might think that either it is possible of God that it must exist, in which case the conclusion 2 follows, or it is impossible of God that it must exist, in which case premise 1 is false. Again, which one is it? 12 One might grant that it is epistemically possible of God that it metaphysically must exist, but that does not entail that God metaphysically must exist; that is, the theorem that whatever is possibly necessary is necessary is not true if possibly is read epistemically and necessary is read metaphysically. So, of course, it all hinges on the kind of support that is given for premise 1. There are also parodies of the Plantinga argument. Here is one 13 : 1. God possibly doesn't necessarily exist Premise 2. So God doesn't necessarily exist 1, Modal Logic The argument is valid in the same modal logic as the Plantinga argument. Also, on its face, premise 1 of the parody argument seems as plausible as premise 1 of the Plantinga argument (see Section 4 below). So the next move should be to try to break the symmetry between the Plantinga argument and its parodies. I must here leave that to the reader. 3.2 The cosmological argument There are many versions of the cosmological argument, most of which are well discussed in the literature. 14 Here is a taste of just one version, for purposes of strong divine necessity. The idea is that all contingently existing things, including our universe, need a necessarily existing ground, which is God. Roughly, 1. Any contingent thing has a necessary ground Premise 2. The universe is a contingent thing Premise 3. So the universe has a necessary ground 1,2 4. That necessary ground is God 3, IBE So God necessarily exists 4 Note that we might here use ground as a generic term for any relevant explanatory relation; it might be causal (and diachronic) or non causal (and synchronic). 16 I can here only mention what I take to be the main problem with this kind of argument, namely, premise 1. Why cannot all contingent things have merely contingent grounds, i.e., why can there not be contingency all the way down, indefinitely? 17 Why believe premise 1? One kind of argument for premise 1 is that if all contingent things have merely contingent grounds, then, by subtraction of contingent things, there could have been absolutely nothing whatsoever. 18 But, or so the argument goes, there couldn't have been absolutely nothing whatsoever, so it cannot be that all contingent things have merely contingent grounds; so contingent things must have necessary grounds. But the first problem with this kind of argument is the first step from all things having contingent grounds to the possibility of absolutely nothing, because, contra this step, it might be that even though nothing must be, there must

5 BOHN 5of10 be something. In such a case, everything is contingent, but nonetheless, there couldn't have been absolutely nothing. So the problem is that the argument needs something like a last subtraction step from something contingent to nothing, which can be denied without accepting either the possibility of absolutely nothing or necessary grounds. The second problem with the argument is that even accepting something like that last subtraction step from something contingent to nothing, why is there being absolutely nothing whatsoever supposed to be impossible in the first place? To the contrary, as will be discussed in Section 4.1 below, on its face it seems possible. So the question remains: why believe premise 1? 19 Another argument in its favor might be in the form of IBE, an inference to the best explanation. 20 One might argue that, all else being equal, a theory that explains the contingent things in terms of a necessary ground is preferable to a theory that has no explanation of the contingent things. But the problem with this kind of argument for premise 1 is how to establish that the best explanation is in terms of a necessary ground. For example, I for one (Bohn, forthcoming1; see also Hume, 1776) find a theory according to which each contingent thing individually has an explanation in terms of other contingent things, with all contingent things collectively having no explanation whatsoever, 21 just as good, if not better than a theory according to which all contingent things have an explanation in terms of a necessary ground, a necessary ground which in turn itself has no further explanation in terms of anything else. 22 But, also, even if we believe that the universe has a necessary ground as per 3, why believe that ground is God as per 4? Is God really the best explanation for what that ground is? 23 Why can't some necessary natural law (or principle, or field, or whatever) be an equally good explanation? After all, that is a dream of physics: a necessary natural law (or principle, or field, or whatever) that necessitates the universe. The problem is of course that no one knows what that natural necessitator is supposed to be nor how physics is supposed to give us metaphysical as opposed to nomological necessity, but some believe they know what God is supposed to be and how it is supposed to give us metaphysical necessity. That might give the theist an upper hand as per The argument from abstracta The argument from abstracta is that God is the ground of all things outside of God, including some necessarily existing abstract things, but a contingently existing thing cannot ground necessarily existing things, so God must itself be a necessarily existing thing. Roughly, 1. Anything outside of God is grounded in God Premise 2. Any ground of necessary things is itself necessary Premise 3. Numbers are necessary and outside of God Premise 4. Numbers are grounded in God 1,3 5. God necessarily exists 2,3,4 Note that first, the notion of being outside of God is metaphorical and needs to be spelled out somehow. Let's here assume that can be done. Second, I here use numbers as examples of necessarily existing abstract objects outside of God, but any necessarily existing abstract objects outside of God would do the same job. So pick your favorite example. I find this argument to be one of the more interesting arguments for weak divine necessity. Of course, the argument is a non starter for a nominalist who believes that there are no necessarily existing abstract objects (e.g., Craig, 2014; Swinburne, 2015). But, contra nominalism, given that there are some necessarily existing abstract objects, e.g., numbers (or pure sets), the crux is premise 1, or the thesis of what I call divine foundationalism (Bohn, forthcoming2, forthcoming3). The thesis of divine foundationalism must be premised on the actual existence of God, which makes the argument from abstracta an argument for weak divine necessity: if God actually exists, then God is the ground of all things outside of God, which in turn entails that God necessarily exists as per 1 5 above. 25

6 6of10 BOHN 4 THE ARGUMENTS AGAINST DIVINE NECESSITY In this section, I present and discuss what I take to be two main kinds of arguments against the theses of divine necessity, namely, the argument from the possibility of absolutely nothing and the argument from the contingency of existence. 26 Again, consider the arguments a mere taste rather than a substantial meal. 4.1 The argument from the possibility of absolutely nothing If there could have been absolutely nothing whatsoever, nothing necessarily exists, and ipso facto God does not necessarily exist. So if there could have been absolutely nothing whatsoever, strong and weak divine necessity are both false. God is then at best a contingent being. Alternatively, if weak divine necessity is true, it follows by modus tollens there is actually no God. So could there have been absolutely nothing whatsoever? The most famous argument for the possibility of absolutely nothing is the subtraction argument (Baldwin, 1996; see also Coggins, 2010). Premise 1: there is a possible world w with only finitely many concrete objects. Premise 2: for any concrete object x in w, there is another possible world w 1 just like w except it is lacking x. Premise 3: no concrete object x in w is such that the non existence of any other concrete object y in w necessitates the existence of x. From premises 1 3, it follows by a series of n steps that there is a possible world w n in which there are no concrete objects. But the subtraction argument faces many problems. First, if the subtraction argument works, it only works to the effect that there could have been no concrete objects; it remains silent on whether there must be something beyond the concrete objects. Now, this is not too important for present purposes since presumably God is a concrete object, but if God is non concrete, the subtraction argument must be generalized beyond the concrete objects. 27 But it is not clear how that is to be done, since it would considerably weaken, if not simply refute, each one of the premises 1 3. Second, even sticking to only concrete objects, premise 2 might be true with respect to more or less ordinary objects like tables and chairs, but why think it is true with respect to the supposed ultimate ground of reality, namely, God? A theist might perfectly well accept that more or less ordinary concrete objects like tables and chairs might be metaphysically subtractable but not accept that God itself might be subtractable. There is nothing ad hoc in such a response, at least not for a theist; after all, God is supposed to be something special, unlike any other thing. It seems the subtraction argument is really a non starter for a theist who believes in divine necessity. But there is also what might be called an accumulative argument for the possibility of absolutely nothing whatsoever. Premise 1: the possibility of there being absolutely nothing whatsoever has a model and hence is logically consistent and hence is logically possible. 28 Premise 2: the possibility of there being absolutely nothing whatsoever is conceivable. Premise 3: anything that is logically possible and conceivable is by default metaphysically possible. 29 From premises 1 3, it follows that there being absolutely nothing whatsoever is by default metaphysically possible. The burden of proof is thus on anyone who claims it is metaphysically impossible. The problem with this kind of argument is that it has parodies. Here is one. 30 Premise 1: the possibility of a necessary being has a model (in modal logics) and hence is logically consistent and hence is logically possible. Premise 2: the possibility of a necessary being is conceivable. Premise 3: anything that is logically possible and conceivable is by default metaphysically possible. From premises 1 3, it follows that a necessary being is by default metaphysically possible. The burden of proof is thus on anyone who claims it is metaphysically impossible. So the question becomes which if any is the default position: the metaphysical possibility of absolutely nothing or the metaphysical possibility of a necessary being?

7 BOHN 7of The argument from the contingency of existence Some have argued that no true existence statement is necessarily true (most notably Hume, 1779), so everything that exists could have failed to exist, i.e., is contingent. If so, strong and weak divine necessity are both false; or, alternatively, if weak divine necessity is true, it follows by modus tollens that there is actually no God. The important difference between this case of the contingency of existence and the earlier case of the possibility of there being absolutely nothing whatsoever is that even if there being absolutely nothing whatsoever turns out to be impossible, it can still be possible that everything is contingent. It might simply be that even though nothing must be, there must be something. So even though the problem of nothingness and the problem of contingency both create the same problems for strong and weak divine necessity, the proponent of strong or weak divine necessity still faces the problem of the contingency of existence even if in the end she doesn't face the problem of absolute nothingness. So is every true existence statement metaphysically contingent? There is, as above, what we might call an accumulative argument for it. Premise 1: for any true existence statement of the form a exists, its negation a doesn't exist has a model and hence is logically consistent and hence is logically possible. Premise 2: for any true existence statement, its negation is conceivable. Premise 3: anything that is logically possible and conceivable is by default metaphysically possible. From premises 1 3, it follows that for any true existence statement, its negation is by default metaphysically possible. The burden of proof is thus on anyone who claims its negation is metaphysically impossible. So until shown otherwise, every true existence statement seems metaphysically contingent. A problem with this kind of argument is that the theist presumably believes that she has shown otherwise in the case of God. There are also parodies in the vicinity. Here is one. 31 Premise 1: for any true existence statement of the form a exists, its necessitation a necessarily exists has a model (in modal logics) and hence is logically consistent and hence is logically possible. Premise 2: for any true existence statement, its necessitation is conceivable. Premise 3: anything that is logically possible and conceivable is by default metaphysically possible. From premises 1 3, it follows that for any true existence statement, its necessitation is by default metaphysically possible. But, what's more, by the modal logics used in our discussion of the Plantinga argument in Section 3 above (e.g., S5), this entails that any existence is by default necessary existence, which (pace Williamson, 2013), is absurd. One might therefore question all arguments of the above accumulative form. But, of course, one might also instead question premise 2 of the last parody. Can we really conceive of the necessitation of any existence statement? So the question becomes: for any existence statement of the form a exists, is its necessitation as conceivable as its negation? Or, more generally, which if any possibility is the default position? 5 DIVINE ABSOLUTENESS Maybe the whole issue of whether God must exist in some metaphysical sense of must is simply misguided. Maybe we should instead move to a wholly different notion of must, where God must exist in some metaphysically non modal but rather fundamental and absolute sense of must ; let's call this the thesis of divine absoluteness. The idea is that metaphysical modality doesn't apply to God; perhaps God is the fundamental and absolute ground of all things outside of God, including all of metaphysical modality, including all its true talk of possible worlds, with God itself thus being fundamentally amodal. Then it ultimately makes no sense to claim that God could have failed to exist nor that God must exist, in some metaphysical sense of must, but it might still make sense to claim that God must exist in some sense of must according to which God's existence is a fundamental and absolute truth in the sense of being the ground of all things outside of God. Maybe that is all we should mean by the claim that God must exist. Is such divine absoluteness true? 32 There are at least three problems. First, it is very hard to understand exactly how God is supposed to be amodal; simply saying so doesn't make it so. The question Could God have failed to exist? seems a perfectly sensible question. For example, if the answer is yes, strong divine necessity is false; if the answer is no, strong divine necessity is true; either way there seems to be a truth about the metaphysical modal status of God. Second, relatedly, non deflationary metaphysical modality seems irreducible, including irreducible to God. Third, if God is the ground of all things outside

8 8of10 BOHN of itself, and some of those things are metaphysically necessary existents, it seems God must itself be at least a metaphysically necessary existent (cf. the argument from abstracta above), if not a logically necessary existent. 6 CONCLUDING REMARKS In this paper, I have briefly discussed strong and weak divine necessity, as well as all too briefly the alternative of divine absoluteness. The two theses of divine necessity seem hard to establish, and the thesis of divine absoluteness seems hard to make sense of. Maybe the theist is better off taking at least weak divine necessity as a metaphysical axiom to be justified holistically, by its theoretical fruits? Let me end by all too briefly mention two interesting alternative ways of trying to establish divine necessity. The first such alternative is based on Ted Sider's (2011) deflationary notion of metaphysical modality. According to Sider, the metaphysically necessary truths are, in a nutshell, simply some truths we put on a list and call metaphysically necessary. Mathematical truths are examples of such truths. Maybe, the existence of God too should be put on that list? Putting the existence of God on the list might perhaps be holistically and pragmatically justified. I believe such Siderian divine necessity is worth a serious discussion. The second alternative is based on Tim Williamson's (2013) necessitism, according to which it is necessary that all existing things are necessarily existing. 33 By such necessitism, it trivially follows that if God merely possibly exists, God necessarily exists. Note that according to the Plantinga argument discussed earlier, it follows from the possibility of God's necessary existence that God necessarily exists, but according to the Williamsonian argument I am giving here, it follows from the possibility of God's existence that God necessarily exists. 34 ENDNOTES 1 Cf. Findlay (1948), though Findlay operates with an outdated, pre Kripkean notion of necessity. 2 Cf. Swinburne (1994, 2015), though Swinburne operates with an arguably false conventional notion of necessity. Against conventionalism, see Quine (1935) and Sider (2011: section 6.5). 3 On possible worlds, see Divers (2002); on models, see Hodges (1997). What I call metaphysical necessity is sometimes called broad logical necessity, and what I call logical necessity is sometimes called narrow logical necessity; e.g., Swinburne (1994, 2015) and Leftow (2010). But I prefer speaking with the metaphysicians and logicians in terms of the metaphysicallogical distinction. Unless noted otherwise, by possible, necessary and impossible, I henceforth mean metaphysically possible, necessary and impossible. 4 Note that things are different if we employ counterpart theory, according to which nothing exists in two or more different possible worlds, but modal claims are made true or false in virtue of contextually determined counterpart relations to other things in other possible worlds. I have no space to discuss that option here. See Lewis (1968, 1986, especially ch.4). 5 The distinctions between deflationary/non deflationary and de re/de dicto might cut across each other, so there might be ways of formulating the above de re versions of divine necessity in a more deflationary manner, but I cannot and will not pursue that route here. But see Sections 5 and 6 below. 6 For example, Rasmussen (2016) discusses weak divine necessity in terms of de dicto necessity rather than de re necessity. 7 Alternatively, one might treat necessarily as a sentential operator, God as a rigid designator referring to one and the same thing in all possible worlds (assuming cross world identity) and then formulate divine necessity as follows: Necessarily, God exists. But I doubt that much is gained by this strategy for reasons I cannot go into here. On another note, I assume throughout that if God exists in a possible world, then God cannot fail to be God in any possible world. That is, I assume that it is essential to God that it is God and hence that God cannot be some other thing than God. 8 See also Pruss and Rasmussen (forthcoming) for a clear headed overview and discussion of various arguments for there being at least one necessarily existing concrete object. But note that it is an open question how to get from there to any of the two theses of divine necessity discussed in the present paper; though see Rasmussen (2010b, section 5) for some hints. See also Oppy (2014: ch.6). 9 See Oppy (1995, 2016) for an overview, discussion and references. 10 I m here assuming (among other things) that whatever is actually necessary is necessary (e.g., modal logic S5). RAA means reductio ad absurdum. 11 Assuming (among other things) that whatever is actually necessary is necessary (e.g., modal logic S5).

9 BOHN 9of10 12 See also Schrader (1991), though note that he talks about logical necessity. 13 Thanks to a referee for this journal for pointing to this particular version of the parody argument. 14 See Oppy, 2006, Chapter 3; Rasmussen, 2010b; and Reichenbach, 2016, for overview, discussion, and references. 15 IBE means inference to the best explanation. 16 Arguably, Rasmussen (2010b) puts too much emphasis on causality, though it is not clear to me what he means by causal. He does seem to use the term very broadly. For overview, discussion, and references on a non causal notion of grounding, see Bliss and Trogdon (2014) and Raven (2015). 17 Just like there can be grounding all the way down, indefinitely (Bohn, forthcoming1). 18 For an argument to this effect, see the subtraction argument in Section 4.1 below. In the diachronic case, the idea is that something would have to come from nothing. 19 One might also try to argue for it on the basis of a principle of sufficient reason. See Pruss (2006). 20 Thanks to a referee for this journal for pushing this point. 21 Or perhaps there simply is no contingent plurality of all contingent things; but rather, contingent plurality of contingent things is indefinitely extensible: for any contingent plurality of contingent things, there is a contingent thing not in that plurality. 22 For criticism of this kind of Humean idea, see, e.g., Pruss (2006:41 46). 23 See, e.g., Rasmussen (2010b, Section 5) for hints of some positive such arguments. 24 For a more general discussion of the Leibnizian Cosmological Arguments, see Pruss (2009). For another argument, see Rasmussen (2010a). 25 For more on this type of argument, see, e.g., Plantinga (1980, 1982); Leftow (1990); and Davidson (2013). 26 See also Pruss & Rasmussen (forthcoming, Chapter 9) for a clear headed overview and discussion of various arguments against there being a necessarily existing concrete object. See also Rasmussen (2016) and Adams (1971, 1983). 27 I intentionally leave concrete undefined here, but note that in any case, it is not equivalent with physical or material. Presumably, all physical things must be concrete, but not all concrete things must be physical. While being physical (or material) is opposed to being mental, being concrete is opposed to being abstract. Being concrete is more like violating the identity of indiscernibles, or being determinately either F or not F, for any property F. 28 Classical logic operates with no empty domain, but that is a mere formal convenience that is neither here nor there for our present purposes; for philosophical purposes, we can and should work with systems that include the empty domain. 29 Note that the accumulation of logical consistency and conceivability is not an infallible guide to metaphysical possibility. 30 See also Rasmussen (2016). 31 See also Rasmussen (2016). 32 Cf. Swinburne (1994, 2015) and Hick (1960); for criticism, see Leftow (2010). According to Leftow (2012), God is not fully metaphysically amodal but pretty close to it. 33 Note that according to Williamsonian necessitism, though that a thing exists is necessary, what it is need not be necessary. See Williamson (2013). 34 Thanks to Ben Caplan, Peter Forrest, Martin Jakobsen, Yujin Nagasawa, Atle Ottesen Søvik, and an anonymous referee for this journal for comments and discussions. ORCID Einar Duenger Bohn WORK CITED Adams, R. (1971). Has it been proved that all real existence is contingent? American Philosophical Quarterly, 8(3), Adams, R. (1983). Divine necessity. The Journal of Philosophy, 80(11), Baldwin, T. (1996). There might be nothing. Analysis, 56(4), Bliss, R. & Trogdon, K. (2014). Metaphysical grounding. Stanford Encyclopedia of Philosophy. Bohn, E. D. (2012). Anselmian theism and indefinitely extensible perfection. Philosophical Quarterly, 62(249), Bohn, E. D. (forthcoming1). Indefinitely descending ground. In R. Bliss, & G. Priest (Eds.), Reality and its structure. Oxford University Press. Bohn, E. D. (forthcoming2). Divine foundationalism. Philosophy Compass. Bohn, E. D. (forthcoming3). God and abstract objects. Cambridge University Press.

10 10 of 10 BOHN Coggins, G. (2010). Could there have been nothing? Palgrave Macmillan. Craig, W. L. (2014). Anti platonism. In P. Gould (Ed.), Beyond the control of God? Six views on the problem of God and abstract objects (pp. 2014). Bloomsbury Academic. Davidson, M. (2013). God and other necessary beings. Stanford Encyclopedia of Philosophy. Divers, J. (2002). Possible worlds. Routledge. Findlay, J. N. (1948). Can God's existence be disproved? Mind, 57(226), Hick, J. (1960). God as necessary being. Journal of Philosophy, 57(22/23), Hodges, W. (1997). A shorter model theory. Cambridge University Press. Hume, D. (1779). Dialogues concerning natural religion. As reprinted in. In Dialogues concerning natural religion and the natural history of religion (pp. 2008). Oxford University Press. Leftow, B. (1990). God and abstract objects. Faith and Philosophy, 7, Leftow, B. (2010). Swinburne on divine necessity. Religious Studies, 46(02), Leftow, B. (2012). God and necessity. Oxford University Press. Lewis, D. (1968). Counterpart theory and quantified modal logic. The Journal of Philosophy., 65, Lewis, D. (1986). On the plurality of worlds. Blackwell. Oppy, G. (1995). Ontological arguments and belief in God. Cambridge University Press. Oppy, G. (2006). Arguing about Gods. Cambridge University Press. Oppy, G. (2014). Describing Gods. Cambridge University Press. Oppy, G. (2016). Ontological arguments. Stanford Encyclopedia of Philosophy. Plantinga, A. (1974). The nature of necessity. Oxford: Clarendon Press. Plantinga, A. (1980). Does God have a nature? Milwaukee: Marquette University Press. Plantinga, A. (1982). How to be an anti realist. Proceedings and Addresses of the American Philosophical Association, 56, Pruss, A. R. (2006). The principle of sufficient reason. Cambridge University Press. Pruss, A.R. (2009). Leibnizian cosmological arguments. As in W.L. Craig & J.P. Moreland (eds.) Blackwell companion to natural theology. Oxford: Blackwell, Pruss, A. R., & Rasmussen, J. L. (forthcoming). Necessary existence. Oxford University Press. Quine, W.V.O. (1935). Truth by convention. As in W.V.O. Quine (1976). The ways of paradox and other essays. Harvard University Press. Rasmussen, J. L. (2010a). A new argument for a necessary being. Australasian Journal of Philosophy, 89(2), Rasmussen, J. L. (2010b). Cosmological arguments from contingency. Philosophy Compass, 5(9), Rasmussen, J. L. (2016). Could God fail to exist? European Journal for Philosophy of Religion, 8(3), Raven, M. (2015). Ground. Philosophy Compass, 10(15), Reichenbach, B. (2016). Cosmological argument. Stanford Encyclopedia of Philosophy. Schrader, D. (1991). The antinomy of divine necessity. International Journal for Philosophy of Religion, 30(1), Sider, T. (2011). Writing the book of the world. Oxford University Press. Swinburne, R. (1994). The Christian God. Oxford University Press. Swinburne, R. (2015). Could God be a necessary being? In Oxford studies in philosophy of religion. Volume 6. Oxford University Press. Williamson, T. (2013). Modal logic as metaphysics. Oxford University Press. Einar Duenger Bohn is a professor of philosophy at the University of Agder. He has a PhD from UMass Amherst (2009). His main research interests are in the philosophy of religion, metaphysics, and artificial intelligence, including the ethics of artificial intelligence. How to cite this article: Bohn ED. Divine necessity. Philosophy Compass. 2017;e /phc