The Gale–Pruss modal cosmological argument

GP makes several assumptions. GP employs the notions of contingent and necessary propositions. A contingent proposition is a proposition that is possibly true and possibly false (i.e. true in some possible worlds and false in others). A necessarily true proposition is true in every possible world. GP understands a possible world as ‘a maximal, compossible conjunction of abstract propositions’. It is maximal in the sense that for every proposition p, either p is a conjunct in this conjunction or ~ p is, i.e. in every possible world it is either true or not true that Richard Nixon drove an ice cream truck from 1969 to 1974. Every possible world is compossible in the sense that it is conceptually or logically possible that all of the conjuncts in the conjunction that specifies that world are true together: there can be no (contradictory) impossible worlds. There are also possible worlds that have different laws of nature than the actual world. Further, GP treats necessary truths as facts, i.e. it is a ‘fact’ that it is not both raining and not raining (at the same time in the same place).

GP grants that it would be unfair to assume Spinoza's and Leibniz's strong principle of sufficient reason which holds that there is a sufficient explanation for any fact in the world. Since, however, opponents of the cosmological argument cannot reasonably deny that it is at least possible that the facts in the world have a sufficient explanation GP only asserts the weak version of the principle of sufficient reason that it is possible that such facts have a sufficient explanation.

GP also assumes the modal axiom S5 that if it is possible that it is necessary that p then it is necessary that p. For example, since it is possible that 2 + 2 = 4 is necessarily true then, by S5, it is necessarily true that 2 + 2 = 4. Thus, the simplified skeleton of GP is this: (1) If it is possible that a necessary supernatural creator of the actual world exists, then it is necessary that it exists. But (2) it is possible that a necessary supernatural creator of the actual world exists. Therefore, (3) it is necessary that a necessary supernatural creator of the actual world exists. The first premise is an instantiation of S5. Since GP presupposes S5 this is not pursued here.Footnote ¹ The second premise is, therefore, the key and much of GP is directed towards proving it.

The argument for the second premise begins with the definition of a Big Conjunctive Fact (BCF). The BCF of a given world is the conjunction of all propositions that would be true of that world, were it actualized. The BCF of a world is a maximal compossible conjunction of propositions that would be true in that world, were it actualized. The BCF of the actual world consists in all the propositions that are actually true, including both the necessary and contingent propositions true in the actual world.

Since all possible worlds share the same set of necessary propositions the distinction between the various possible worlds resides in their different contingent propositions that would be true in those worlds, were they actualized. GP defines the Big Conjunctive Contingent Fact (BCCF), which contains the contingent propositions that would be true in a possible world, were it actualized. Since all possible worlds share the same set of necessary propositions, the different possible worlds are individuated by their different BCCFs. Since every possible world is maximal, for every contingent proposition p, either p or ~ p is a conjunct in this BCCF. Thus, no two possible worlds can have the same BCCF.

GP calls the BCCF of the actual world p (not to be confused with the variable ‘p’ used earlier), where p includes all the contingent facts in the actual world. Thus, p includes the existence and non-existence of all contingent beings in the world and the occurrence and non-occurrence of all the contingent events in the actual world, including the contingent acts of any necessary beings that may exist in the actual word.

GP argues that p has a sufficient explanation as follows: one cannot deny that there is some possible world w₁ that contains p but also contains q and the proposition that q explains p. But, GP argues, this hypothetical possible world w₁ turns out to be identical with w. For, suppose there were some difference between w and w₁. In that case, since possible worlds are maximal, there must be some proposition r true in w₁ but not true in w. But if r is true in w₁ and not in w, then, by the law of the bivalence, ~r is true in w. However, since, by hypothesis, everything actually true in w is also true in w₁, ~r is true in w₁ as well. But this means that r & ~r is true in w₁, which is a contradiction, and that cannot be because w₁ is supposed to be a possible world. Since the assumption that w₁ is a different possible world from w implies a contradiction, w₁ is the same as w – which means that w, the actual world, contains q and the proposition that q explains p. Since q is supposed to explain the totality of propositions in p, call this ‘the Necessity of a Total Explanation Thesis’ or NTE.

GP holds that there is such a q in every possible world: ‘[A]lthough our argument shows that in every possible world there exists a necessary being who freely brings about its [BCCF], there are possible worlds that are so nasty that nothing very admirable can be inferred about the qualities of their necessary explaining beings’ (GP, 468). That is, some possible worlds are so ‘nasty’ that one is not justified in interpreting the q in those worlds as referring to anything like G. It is only the grandeur of the actual world that enables one to upgrade its q into a report of the intentions of a G that approximates to the God of theism.

All attention now turns to the nature of this q. GP here departs from purely logical demonstrations and claims that the the only sorts of explanations that can be conceived are either scientific or personal or explanations, which GP describes as ‘some kind of conceptual truth’ (GP, 465). Call this the ‘Either Scientific or Personal explanations thesis’ or ESP. A scientific explanation explains why some proposition is true by reference to some conjunction of law-like propositions and at least one contingent proposition that reports a state of affairs at some time. A personal explanation explains why some proposition is true by reference to the intentional action of an agent. GP admits that there might be types of explanation that are beyond our ken, but, ‘in philosophy we ultimately must go with what we can make intelligible to ourselves after we have made our best effort’ (GP, 465). But q cannot be a scientific explanation. Since scientific propositions are contingent, this would mean that q is part of the actual worlds BCCF and that would mean that the explanation of the actual world's BCCF is a part of that BCCF. However, since ‘law-like propositions cannot explain themselves’, q can only, by disjunctive syllogism, be a personal explanation that ‘reports’ the intentional actions of some being.

The next question is whether this being is contingent or necessary. Obviously, however, q cannot report the actions of a contingent being. If q refers to a contingent being, the proposition that states that being's existence would be part of the BCCF of the actual world w and ‘q is not able to explain why the contingent being it refers to exists, since a contingent being's intentional action presupposes, and hence cannot explain, that being's existence’ (GP, 465). Thus, q must report the intentional actions of a necessary being.

One might assume that q must, therefore, be necessarily true because it reports the action of a necessary being. But appearances are deceiving. GP holds that ‘q is a contingent proposition that reports the free intentional action of a necessary being’ (GP, 466–467). This divides into two claims, first that q is a contingent proposition, and second that q reports the intentional actions of a free being. Additional analysis is possible but not necessary here.

GP provide several arguments that q is a contingent proposition but its main argument is a reductio ad absurdum. If q is necessarily true, then q is a conjunct in the BCF of all possible worlds. Since, however, q entails p, and since a possible world is individuated by its BCCF that would mean that every possible world is identical with the actual world (i.e. there is only one possible world). Since, notwithstanding vehement protestations from Spinoza and Leibniz, this is surely absurd, q is a contingent proposition.

Since G is a necessary being it satisfies one key component of the traditional notion of a theistic God, but such theistic views find it hard to account for the contingency in the world. Leibniz holds that God's choices are necessary, but that depends on certain of his other views. That is, even though, speaking momentarily with the vulgar, Leibniz condescends to call certain propositions ‘contingent’, he is committed to hold that from God's point of view (the only fully adequate one) all propositions are necessary (Russell (Reference Russell1967), 60–61). Leibniz cannot use GP because he holds that there really is no such thing as a BCCF. Unlike Leibniz, GP finds appropriate roles both for contingent and necessary truths. The actual world is created by a necessary being but the contingency in it arises from G's free choice.

A necessitist objection

NTE asserts that if w contains p then it also contains q and the proposition that q explains p. But is it really obvious that there must be some possible world that contains a q that explains p? Recall that GP holds that q ‘reports’ G's intention but does not provide this q. Since G's intention, involving, presumably, a massive detailed specification of physical constants, laws, etc., sufficient to determine the entire actual universe, is far too complex to be formulated by any human being, GP purports only to prove that there is such a q without providing it. Why, however, should one believe that such a q is even possible? Though most philosophers hold that logic is neutral with regard to metaphysical issues, the ‘permanentists’ or ‘necessitists’ hold that there is a necessary metaphysical substratum of the world that fixes the range of possibilities (Williamson (Reference Williamson2008), x, 376–422). Necessitism is controversial but it is not obvious that it is false (Uzquiano (Reference Uzquiano2014), § 4.4.3). Since ‘necessitism’ is represented by Wittgenstein's familiar view in the Tractatus (Wittgenstein (Reference Wittgenstein and Pears1961); hereafter, TLP) that it is necessary what things there are but contingent how those things are (TLP, 5.552–5.5521; Williamson (Reference Williamson2008), 1–2), a simplified TLP-model is employed to illustrate this point.

TLP (1.1, 2, 2.01–2.02) holds that the world is reducible to a totality of atomic facts where each atomic fact is the existence of a possible state of affairs, a concatenation of simple objects. Each atomic state of affairs (therefore, each atomic fact) is logically independent of all the others (5.134–5.135). Further, the set of possible states of affairs (and, therefore, possible atomic facts) is fixed by the substratum of the world (2.021). This substratum also determines the set of possible relations into which these objects can enter (2.023–2.0231). TLP also holds certain related modal views. The propositions of logic are tautologies that ‘say nothing’ (6.1–6.11, 6.37). Since the only necessity that exists is logical necessity, there is no causal nexus (5.136–5.1361, 6.3). TLP's necessitism envisions a very austere world.

Consider a simple TLP-model of the way this substratum fixes the set of possible states of affairs (and possible facts). Suppose, for heuristic purposes, that the basic substratum of the world consists in two basic objects, a and b, and one possible relation, R. All possible combinations of these objects and this relation are possible except that the objects cannot be in this relation to themselves. In this case, there are four possible states of affairs: a is R to b; a is not R to b; b is R to a; b is not R to a. Suppose now that the actual world w is one compossible actualization of one of these possibilities, namely, that a is R to b and that b is not R to a. Call this Simple TLP-world ‘w_st’. The ‘p’ that states the BCCF of w_st is ‘a is R to b and b is not R to a’. NTE claims that there is some possible world w₁ that contains some q that explains p, but, on TLP's view, there is no such possible q. Since the substratum of the world fixes the total set of possibilities there are no other possible facts in w_st. Further, even if there were other possibilities there is no causal nexus and, therefore, no possible explanation in w_st of p. On TLP's view, one can describe the distribution of facts in w_st but nothing in a TLP-world explains anything else. Thus, TLP denies that p even can be explained by the ‘laws of nature’ (6.371) – let alone by some contingent act of ‘divine intention’ (whatever that is supposed to mean).Footnote ² For there is no room in w_st for such a divine intention to ‘compel’ one set of facts rather than another (6.37). Although the real world is much more complicated than w_st, this simple TLP-model illustrates why Wittgenstein (in Wittgenstein (Reference Wittgenstein and Anscombe1966), 79; see also TLP, 6.432) states that ‘God is, how things stand’. Since God is how things stand, appeal to God's intentions cannot explain how they stand. Indeed, it is not even possible assign any meaning to such theological sentences. Call this the ‘TLP-Counterexample-Thesis’ or TCT.

One might object that TCT is a very unusual ‘counterexample’. Rather than specifying a possible world in a familiar way, e.g. sketching a world that is just like the actual world except that Richard Nixon drove an ice cream truck from 1969 to 1974 in it instead of being the president at that time, TCT merely rehearses TLP’s contentious metaphysical views.

The claim is not, however, that TLP’s necessitist view is clearly correct but that GP does not eliminate such necessitist views. NTE just assumes that there is not some basic substratum to the world that precludes the existence of NTE's q. But without a successful argument against such necessitist positions GP is not justified in assuming its basic premise that it is possible that there is some w₁ that contains a q that explains p. GP simply makes a major unjustified ‘metaphysical’ assumption.

The theistic bias

Since much of the remainder of GP is directed towards determining the nature of the q that provides the total explanation of p, and since, as argued in the previous section, GP's argument for NTE is inadequate, much of these arguments are moot because they are built on this weak foundation. However there are several additional sub-arguments in the latter part of GP that are worth considering in their own right.

GP purports to prove the existence of some being G that is quite close to Anselm's God: a necessarily existing supernatural purposeful intelligence that creates or designs the world by an intentional act (GP, 461, 469). A key premise in this sub-argument is that one can only conceive of two possible types of explanation, scientific or personal explanations (ESP). A personal explanation explains an event e as the product of an intentional act by an intelligent being: ‘Why is my car in the swimming pool?’ Answer: ‘Because your teenage daughter wants it there’. By contrast, a scientific explanation explains e by adverting to scientific laws and at least one contingent fact. ‘Why is my car in the swimming pool?’ Answer: ‘Because there is a physical law that objects in a gravitational field roll downward on an inclined plane’ and ‘There was an earthquake this morning that turned your driveway into an inclined plane aiming at your swimming pool’. GP argues that q cannot be a scientific explanation and infers, by disjunctive syllogism, that it must, therefore, be a personal explanation.

First, GP simply assumes that a personal explanation must be intentional. However, there are personal explanations that invoke voluntary rather than intentional actions, e.g. S admits he kissed N but insists that he did not do so intentionally because he mistook N for M (the latter being real object of his affection). His kissing N was voluntary because he did it willingly but not intentionally because he did not intend to kiss N. Applying this to GP's creation story, perhaps G voluntarily created the world but did not do so intentionally. If questioned why s/he created the world G might reply: ‘The creation of the world was an accidental but voluntary by-product of one of my other projects’. Recall Whitehead's (Reference Whitehead1968, 81) remark that in Greek philosophy the creation of the entire temporal universe ‘was an inferior avocation of [the] Absolute’. The creation of this imperfect world was not the Absolute's intention but a voluntary by-product of its more sublime timeless intention.

Further, GP is not justified in restricting the range of possible explanations to scientific or personal. There are other sorts of explanations that are ‘within our ken’. GP addresses a version of this objection put in private correspondence to the authors of GP by Phil Quinn.

Quinn suggests that one might explain the BCCF of w by reference to ‘an impersonal necessary being, rather like the Brahman of advaita Hinduism that generates the cosmos by means of blind but indeterministic mechanical causation’ (GP, 472). Quinn holds that this impersonal Hindu god is a necessary being so he is open to the reply, which GP does make, that this Hindu creator is not a necessary being in GP's sense of a being ‘the concept of which explains its existence’ (GP, 462, 470). Since GP's argument that G is a necessary being occurs after GP's argument that the explanation must be personal, this point concerning the status of the alleged necessary being is dealt with in the next section. The present question is only whether Quinn's advaita counterexample can be modified to address GP's assertion that all explanations must be either scientific or personal.

First, GP does not consider the kind of explanations that are proposed in connection with the ideas of chaos and self-organizing systems. These sorts of explanations are, arguably, scientific, but they do not typically appeal to scientific laws as normally understood and speak instead of the emergence of unforeseeable new patterns (Goodwin (Reference Goodwin1994), viii, 87–88, 202, 215). Further, although the question whether chaos theories provide genuine explanations of the relevant phenomena is not settled, there is a body of literature that argues that they can be explanatory (Bishop (Reference Bishop2008), 5.2–5.3). Second, Hume (Reference Hume and Popkin1998, § VII) puts forward a version of Quinn's point when he suggests that ‘the great vegetable, the world . . . produces . . . certain seeds [that] . . . vegetate into new worlds’. Similar views are also present in the Orphic tradition (West (Reference West1983), 205). These ‘organic cosmogonies’ in Orphism, Hinduism, and Hume are not ‘scientific’ because they do not appeal to the biological laws of genesis for support. One might object that such views are more mythological than scientific, but GP does not oppose Quinn's admittedly ‘interesting’ case on such grounds (GP, 472).

GP's real argument against such organic cosmogonies invokes a supplementary ‘argument from design’: ‘This cosmos displays considerable law-like regularity and simplicity, as well as remarkable fine-tuning of its physical constants, all of which goes unexplained by an impersonal explanation’ (GP, 472). It is, however, not clear why a personal explanation explains this any better than an impersonal one, especially when GP cannot supply G's intention. Recall that GP only purports to prove that there is a q that ‘reports’ the divine intention but does not provide it. But the distinction between no explanation and an explanation that human beings cannot provide (or possibly understand), is, for explanatory purposes, a distinction without a difference.Footnote ³ Second, contrary to GP, an oak tree and a blue whale also display considerable law-like regularity, simplicity, and fine tuning of their physical constants without being obviously produced by the intention of some intelligent being. It would be question-begging to insist that they must be so produced. Indeed, if Hume is right, the actual universe more resembles the product of organic generation from eggs or seeds than it does a product of intelligent intention. Thus, GP has not shown that the universe could not have sprouted or hatched impersonally from an egg or seed. Since GP unjustifiably limits the choice to personal and scientific explanations, the second of which is easily dismissed, it introduces one of the main tenets of theism into the premises without warrant – the anthropomorphism that the ‘creator’ (seed?) resembles a human person.

The inference to a necessary being

GP's sub-argument that q refers to the act of a necessary being is worth considering in its own right. First, what justifies GP in assuming that q reports the actions of a being at all? Why not a process, or even just the principles of genesis, whatever they are, in w? In fact, GP's assumption that q refers to a being is guided by its prior assumption that q, whatever it is, must refer to the acts of something that resembles the God of theism.

Second, even if one grants that q describes the actions of a being, what justifies GP's assumption that it is one being? Why could not q refer to the actions of a committee of beings? Hume makes an analogous objection against the argument from design (Russell (Reference Russell2013), § 4). Recall GP's argument in the first section of the present article that if p states the BCCF of w then w must also contain q and the proposition that q explains p. However, this formulation is ambiguous. Let it be that w contains q and that q reports an intention to create/design the world. GP just assumes that q reports a single intention by a single being. Why could not q be subdivided into q₁ that explains part of p and q₂ that explains the remainder of p? Perhaps q₁ states the contingent intention of one deity and q₂ the contingent intention of a second deity. One can construct further examples for q_n for any n. Thus, GP's q might refer to the actions of a committee, perhaps even a committee whose members change from time to time. In this case, GP's ‘necessary being’ would turn out to be a necessary committee of creator-designers where no particular member of the committee is necessarily a creator. This would not be congenial to theists, but GP gives no reason to preclude this possibility.

Third, GP's argument that G is a necessary being is too indirect. GP explains that ‘A being is a necessary being . . . if and only if it is necessary that it exists’ (GP, 466). GP's argument is that q either reports the action of a contingent or a necessary being but it cannot report the action of a contingent being because if it did then the BCCF of w would contain a conjunct asserting the existence of that being which would be non-explanatory (see the first section of the present article). Once again, GP infers, by disjunctive syllogism, that q reports the action of a necessary being.Footnote ⁴

GP does reference such a more direct argument: ‘[A necessary] being is a self-explaining being in that there is a successful ontological argument for its existence, even if we aren't up to giving it’ (GP, 462). Thus, GP purports to prove by indirect means that a self-explaining G necessarily exists without being able to provide the required ontological argument.Footnote ⁵

In fact, GP's logic here is not straightforward. Recall that there are certain ‘nasty’ possible worlds where GP proper only proves that there is some q that reports the action of some necessary being but not one that closely resembles GP's G. It is only the addition of a supplementary argument from design that this minimal necessary being gets upgraded to something approaching G. It is a cosmological argument for some minimally necessary explanatory being and it is only by adding a supplementary argument from design that GP purports to prove G's existence. There is an important sense, therefore, that GP is not really a cosmological argument for G's existence. The cosmological’ portion of the argument only purports to prove a first cause – perhaps even a ‘nasty’ one. To be fair, it is only to be expected that finite humans need to resort to such indirect sorts of proof when attempting to demonstrate supernatural theses. On the other hand, GP employs certain indirect sorts of devices that take one beyond what one can comfortably claim to know or even understand (e.g. G's complex supra-human intention). Indeed, what these problems really suggest is that such supernatural ‘theses’ are beyond the limits of human understanding and proof.Footnote ⁶

The Gale–Pruss objection to the advaita Hindu view of Creation

An additional problem with GP comes out in GP's reply to Quinn's suggestion that the advaita Hindu view offers a genuine alternative to GP's dichotomy of scientific and personal explanations. GP's first reply to Quinn's suggestion is that the Brahman of the advaita is not a necessary being in the sense that GP requires. It is true that Hindu philosophers do not make such assertions because of their basic view that such matters are unknowable by human beings (Taimni (Reference Taimni1974), 1–2). However, although advaita Hindus do not generally claim that the creator is ‘self-explainer’ in GP's sense, they do regard the Brahman as ‘Absolute’ and ‘unconditioned’ (Flood (Reference Flood1996), 84–85). There is therefore no reason why a Hindu philosopher could not claim that there is a successful ontological argument that proves the necessary existence of the Brahman ‘even if we aren't up to giving it’. Since GP admits it cannot provide the successful ontological argument proving that G is a ‘self-explainer’ the more humble advaita view appears quite sensible.

GP's second argument against Quinn's proposal is premised on the view that either this impersonal Brahmanic force acts deterministically or not. The view that it acts deterministically is rejected because that implies the implausible view that the universe could not be other than it is. Since GP's argument against the view that this Brahmanic force acts indeterministically is more interesting it is considered here. An indeterministic force ‘contradicts the conclusion of our argument that there is an explanation of the actual universe, since any such explanation will have to be a self-explainer. An indeterministic action is a self-explainer only if it is a free action’ (GP, 472). It is, however, unclear what the notion of explanation here has to do with explanation in science other than the shared word, e.g. it is not clear why Ed Kemper's statement that he freely intentionally murdered six innocent young women because he had been abused by his mother explains his actions. Borrowing an old dichotomy (von Wright (Reference von Wright2008)), one might say his statement enables one to understand his action but not to explain it: ‘OK, Ed, I get it. Your mother mistreated you. So did mine. But I never even considered killing innocent girls’. Indeed, the idea that free actions are self-explaining presupposes the old metaphysical-cosmological idea that freedom consists in an exotic kind of cause that initiates a new causal series ex nihilo. That is, GP is advanced as a ‘cosmological’ argument that proves the existence of a first cause but it actually presupposes the existence of first causes in its appeal to these miraculous self-explaining free actions. Further, if GP can assume such miraculous self-explaining free actions, why cannot advaita Hindus do the same? Indeed, advaita Hindus do speak of impersonal free and ‘self-luminous’ actions of the Brahman (Deutsch (Reference Deutsch1973), 9, 28, 41, 44, 50). It might be objected that these advaita claims are obscure but they are no more obscure than GP's suggestion that free actions are self-explaining uncaused causes. GP's argument against the advaita counterexample is inconclusive.