05 / 06

Review: God and Necessity

William Lane Craig


A critical review of Brian Leftow's attempt to safeguard divine aseity in the face of the challenge of Platonism.

Leftow’s God and Necessity is a remarkable achievement, a major contribution to modal metaphysics, striking in its creativity, impressive in its argumentation, and mind-numbing in its thoroughness. Reading the book is somewhat reminiscent of ploughing one’s way through Aquinas’ Summa contra gentiles: not content to prove his point once, Leftow piles one argument upon another to establish his contentions five to seven times over. This can make the book tedious at times, though thought-provoking and rewarding in the end.

Unfortunately, the book is somewhat hamstrung by Leftow’s inelegant writing style. He is especially attached to Anselmian turns of phrase like “If deity is a property, it is the property having which makes God divine” (p. 136). Why not say more simply, “If deity is a property, God is divine in virtue of having that property”? Or consider the following statement, which is the first condition on "x causally prevents state of affairs S1 at t ":

S or that S is not the case are the sort of thing to come about (p. 333).

The meaning of this sentence is prima facie obscure (and the numeral turns out to be a footnote rather than a superscript). Combine such sentences with convolutions like

I later explain at some length just how non-God-involving (henceforth secular) God or these items make such truths true (p. 83)


the only reality whatever determines the content of logical truths could have had from all eternity, consistent with (FD), was in the mind of God (p. 91),

and one is not sure whether one is confronted with a characteristic Leftowism or one of the many printer’s errors throughout the book. The combination of the two makes for a turgid mix which requires patience and perseverance (and sometimes multiple readings) in order to get through. Fortunately, the read is worth the time and effort.

The fundamental aim of the book is to meet the ostensible challenge posed by necessary truths to the claim that God is the sole ultimate reality by formulating and defending a theistic metaphysics for grounding modal truths. The basic question which the book seeks to answer is how modal truths relate to God. The book also takes up the subsidiary challenge posed by abstract objects to divine ultimacy (p. 27).

The book is commendable theologically for its robust defense of God’s status as the sole ultimate reality. Leftow takes seriously the biblical witness to God’s unique aseity and creation ex nihilo of all things outside Himself. Leftow therefore affirms the fundamental thesis that God is the Source of All that is outside Him:

GSA. For all x, if x is not God, a part, aspect, or attribute of God, or an event, God makes the creating-ex-nihilo sort of causal contribution to x’s existence as long as x exists (p. 20). [1]

Not only is (GSA) scripturally attested, but the (GSA)-property is arguably also a perfection which perfect being theology accordingly ascribes to God (pp. 21-2).

Given that some truths are absolutely necessary (true no matter what), a conflict with classical theism arises from the assumptions [2] that

9. Some strongly necessary truths are not about God and are not negative existentials, e.g., mathematical truths.

10. It is always the case that if a truth is necessary and not a negative existential, it has an ontology.

11. If a necessary truth not about God has an ontology, all of it lies outside God.

The conjunction of these assumptions implies that there always exists something ontologically outside God which supplies the ontology for mathematical truths, for example. But Leftow thinks it difficult to see how such abstracta could be created by God, which contradicts (GSA) (p. 26).

In his second chapter Leftow identifies four possible ways to deal with this apparent conflict:

(i) Deny that modal truths have an ontology.

(ii) Restrict the scope of (GSA) to exempt various abstracta.

(iii) Adopt a “safe” ontology that does not conflict with (GSA).

(iv) Make God the ontological foundation of modality.

Leftow concedes that his brief discussion of (i)-(iii) does not suffice to dispose of them conclusively, but he thinks that he has given “at least some reason to think that these will not do” (p. 71). The bulk of the book is then taken up by an examination of the competing theistic views.

Theistic views are united in their conviction, which Leftow thinks theists ought to endorse, that for any true modal proposition P God either is, contains, has, has attributes that have, or produces all truth-makers or truth-explainers for ◊P or P (p. 115). Theistic theories may be differentiated on the basis of which facet of theism they call upon to explain modal truths. An important class of theistic theories, indeed, the dominant position, is what Leftow calls deity theories, those which ground modality in God’s nature. Thomism is a prime example of such a theory. Not only does Leftow find no good reason to embrace a deity theory (chap. 6), but he also subjects them to particularly heavy criticism (chap. 8).

Instead, or in addition, to God’s nature, other theistic theories appeal to God’s activity to ground modal truths, either His contingent activity (Cartesianism), or His necessary activity, as either determined by His nature (Leibnizianism) or not so determined (Leftow’s view) (p. 136). Leftow considers Descartes’ platonism uneconomical, since it assumes a realm of dependently existing abstracta (p. 74), and incoherent, since it cannot be up to anything what its own nature is (p. 134), and regards Leibniz’s natural act theory as a needlessly elaborated deity theory, since God’s nature determines His activity (p. 144).

On Leftow’s view necessary truths of logic and mathematics, like necessary truths solely about God, have their foundation in God’s nature. Where he departs from deity theories is his handling of so-called secular modal truths, truths which provide no information about God (p. 249). [3] Leftow develops an ingenious account of how God is responsible for stipulating modal truths about creatures.

On a deity theory like Aquinas’, the divine nature includes powers to do various things, such as to create a dog, and therefore it is possible that dogs exist. One may move away from such a deity theory in two steps: (1) Agree that it belongs to God’s nature to conceive various secular states of affairs, but then hold that it is at God’s discretion to assign to them their modal status. So God by His nature conceives of things like zebras, married bachelors, round squares, and unicorns, and He freely decides which of these will be possible or not. (2) Deny that it belongs to God’s nature to conceive all the various secular states of affairs and thus restrict God’s powers to general abilities to conceive, create, and so on, in the place of determinate powers like the ability to create a dog. It is up to God to invent or “dream up” the various secular states of affairs before assigning their modal status to them. Thus, Leftow’s view, like Cartesianism, has a strong voluntaristic component: God freely thinks up secular states of affairs and then freely decides which of them are to be possible or not.

Leftow’s view leads to a bizarre modal theory. One might think that on his view God could have decided to dream up other states of affairs or could have assigned to them a modal status different from that which they have. But such modal locutions cannot be true until God has determined what is and is not possible. Modality on Leftow’s view arises only ex post facto, so that, given God’s decision, it is now impossible that God could have dreamed up different states of affairs or made round squares possible. [4] There is no possible world in which God thinks up different secular states of affairs or assigns a different modal status to them. Nevertheless, it is up to God both what secular states of affairs there are and which possible worlds there are.

Leftow struggles to find a coherent articulation of his view. “If either the stock of states of affairs or their modal status is up to God, one needs to say something like that God has the power to bring about states of affairs that are not in fact possible, without actually saying it and so suggesting that they are after all possible” (p. 253). Leftow proposes the locution that it was “in God” to think up different states of affairs and assign a different modal status to those He has invented (pp. 252ff). This notion is defined as follows:

God has it in Him to do A =df. God is intrinsically such that (God wills to have the power to do A) ⊂ (God has the power to do A).

Unfortunately, it is unclear whether the material conditional in the definiens is intended to have as its antecedent the entire preceding clause or simply the parenthetical clause. Since on Leftow’s theory God does not will to have the power to do A by His nature,  [5] the definiens must have the form: God is intrinsically such that: (pq). [6] In other words, on Leftow’s view it belongs to God’s nature to bestow powers on Himself. God does not naturally have the power to create a dog, but He has willed to have that power. In that explanatorily prior moment, it is in God to create a dog, but He does not have the power to create a dog. Similarly, it is in Him to conceive different states of affairs, but He does not have the power to conceive different states of affairs.

Explanatorily prior to God’s conceiving creatures, there are no modal facts about particular creaturely states of affairs at all. Nonetheless, because God has the general power to create creatures, it follows that God’s nature guarantees that possibly creatures exist. Since it is a secular modal truth that possibly creatures exist, Leftow concedes that his view is a very thin, partial deity theory (p. 275). God’s nature alone suffices to make it true that possibly there is something non-divine. In order for particular non-divine things to exist, however, God must first think them up and then decide which of them shall be possible.

On Leftow’s view God’s assignment of modal status to the things He thinks up is guided by His preferences. Apart from preferences concerning moral or perhaps aesthetic value, God’s preferences are not determined by His nature but are brute. In line with His preferences God decides that some things should be possible and others impossible. The former, Leftow (somewhat misleadingly) says, God permits and the others prevents. Leftow provides a nice summary of the explanatory order in the genesis of secular modality (pp. 362-4):

(i) God exists wholly alone. There are no other concreta. There is nothing abstract outside Him. God has the power to create, and so it is possible that there be some creature or other, but there are no states of affairs involving determinant creatures.

(ii) God thinks up states of affairs involving determinate creatures.

(iii) God notes any good- or bad-making features these states would have, were they to obtain.

(iv) If the states would have good- or bad-making features, God takes attitudes toward (has preferences concerning) their obtaining. If they would not have such features, God takes no attitude toward their obtaining.

(v) Given His approval, disapproval, or neutrality, God decides whether to permit or prevent the various states of affairs.

(vi) God prevents or permits the various secular states of affairs, thereby determining their modal status.

Finally Leftow provides a reductive analysis of broadly logical modality in terms of causal modality. Modalities are determined by powers plus the opportunity to employ them. So something is broadly logically possible if it is causally possible for God to produce; if God lacks the causal power to bring it about, then it is impossible (p. 391). It is important to keep in mind, of course, that on Leftow’s view God Himself freely decides which causal powers He has concerning specific secular states of affairs. They are the result of His permissions and preventions.

What shall we say to all this? To begin with, I think it is clear that Leftow’s modal theory, while impressive, is highly counterintuitive. For intuitively, if it is up to God in that explanatorily prior moment freely to invent determinate secular states of affairs and creaturely essences and freely to assign to them their modal status, then God was able to do so, had the power to do so, and could do so. Not only that, but He also was able to invent and decide differently, had the power to do so, and could have done so. This is just how these modal locutions are used. But on Leftow’s theory all that is false. God lacked the power to conceive of a dog and so also the power to make dogs possible. And on Leftow’s strange retrospective modality, it is impossible that God have done anything differently. Flouting our strong modal intuitions, Leftow’s theory is therefore highly counterintuitive.

Moreover, his theory may well be incoherent. On Leftow’s view it is “in God” to think up different secular states of affairs or creaturely essences. This locution sounds like a modal notion, to the effect that God was able to do such things. Leftow uses the locution in this way as well, as we have seen. But Leftow denies that it is a modal notion (p. 253). Being in God is defined to mean that God’s nature is such that a certain material conditional is true: if God wills to have a particular power, such as to create dogs, then He has it. Leftow’s conditional definition of what it is to be “in God” is equivalent to saying that God wills to have a particular power only if He has it. That seems to get the explanatory priority wrong, which suggests that material implication is too weak to serve the intended purpose here. The intention seems to be to make God’s willing to have a particular power explanatorily prior to His having it: He has it because He willed it; He doesn’t will it because He has it. This, however, raises the further question: can He, explanatorily prior to thinking up secular states of affairs, will to have the power to create dogs? The answer is no, for in that explanatorily prior moment, according to Leftow’s account, there is no such thing as doghood. Therefore, God at that moment is unable to will to have the power to create dogs. But if He is unable to will to have the power to create dogs, how does God manage to acquire that power?

One might answer that it is in God to will to have the power to create dogs. But if that is not a modal notion, then same problem recurs: God is unable to will to have the power to will to have the power to create dogs, since there is not yet any such thing as doghood. We are evidently embarked on an infinite regress which is truly vicious, since at every point God is powerless to will what is required. So being “in God” is either a modal notion, in which case God does have particular powers after all, per typical deity theories, or else it involves a vicious infinite regress, subverting a successful account of God’s powers.

Moreover, consider God’s assigning modal status to the secular states of affairs He conceives. According to Leftow’s account, God’s assignments were guided by His preferences, and He could have had different preferences. Nota bene that having different preferences was not merely in God; according to Leftow’s account God was able, that is, had the power, to have different preferences. [7] So why is it not possible that God’s preferences were such, for example, that dogs turned out to be reptiles rather than mammals? [8] Isn’t it thus possible, contrary to Leftow’s theory, that dogs be reptiles?

Leftow denies this, maintaining that God, whatever His preferences, must have the same permissions and preventions from eternity that He does in the actual world (p. 406). Leftow is keenly aware of the difficulty this affirmation presents:

This may seem to sit uneasily with His being able to have alternate preferences, as it implies that no matter what God had preferred, though He might have chosen a different actuality—shaping the universe’s ends in different ways, creating a different universe, or not creating—He would not have allowed different possibilities. But this is at worst only a tension, not an inconsistency, and perhaps the tension is only apparent ( p. 407).

This response seems to underestimate the difficulty. Even were it true that if God had different preferences, He would choose the same possibilities (itself a highly dubious assumption!), nevertheless, God, as a libertarian agent, still could choose differently. So there seems to be a genuine inconsistency here. [9]

As for the tension, Leftow tries to reduce it by emphasizing that God’s moral nature constrains His preferences and thus His assignment of modal status. But we have already seen how general those preferences are and that with regard to many states of affairs God is indifferent as to their modal status. It seems perfectly consistent with God’s nature that He have decided that gold have a different atomic number or that dogs be reptiles. Indeed, if we allow God’s preferences to constrain His choices too narrowly, then Leftow’s theory is in danger of collapsing into a deity theory.

At this point we should do well to re-examine the motivation for adopting so extraordinary a modal theory. Here Leftow’s subsidiary project of crafting an anti-platonist metaphysic becomes crucial. He states, “the Introduction’s ultimacy concerns . . . are met if (GSA) and (FD [i.e., God alone is beginningless]) are true, there is a level of causal explanation at which God alone explains other things’ existence, there is no going past this level in any explanation of other things’ existence, nothing other than God accounts for God’s existence, and everything other than God has/had a cause of its existence” (p. 133). So it is not necessary truth as such which threatens divine ultimacy. Rather it is platonism that is the bête noire.

It is striking, however, how independent Leftow’s anti-platonist metaphysic is of his modal theory. Leftow develops a kind of divine psychologism which replaces abstracta with thoughts in the mind of God. The theist who shares Leftow’s ultimacy concerns may adopt such a metaphysic without embracing Leftow’s modal theory. Once one has adopted divine psychologism, one need not offer any modal theory at all, for the ultimacy concerns have been satisfied. Ironically, then, the central project of the book is thus seen to be something of a red herring or addendum to the really important matter, which is defeating platonism. [10]

It lies beyond the scope of this review to delve into Leftow’s formulation and defense of divine psychologism. [11]  But it is worth noting how attenuated Leftow’s discussion of anti-platonism is. For Leftow’s psychologism is an anti-platonist realism. He takes little cognizance of anti-realist views. This omission is not explicitly acknowledged until the final paragraph of the book: “theism yields the best realist account of modality. The anti-realist options include conventionalism, fictionalism, and projectivism. . . . My full treatment of modal anti-realism must await another occasion” (p. 551). Note how incomplete Leftow’s list of anti-realist options is. Conventionalism, holding as it does that there is no fact of the matter concerning the existence of abstract objects, is really a form of arealism, not anti-realism. I am unsure what Leftow means by projectivism, but anti-realist options include in addition to fictionalism such views as figuralism, neutralism, constructibilism, modal structuralism, pretence theory, neo-Meinongianism, and so on.

Leftow refers to conventionalism and fictionalism as versions of the “no ontology” view (p. 540). That should prompt us to re-visit Leftow’s brief discussion in chapter 2 of the first way to deal with the alleged conflict between theism and necessary truth: the no ontology solution (pp. 48-59). He rejects this solution because necessary truths, even if they have no truth-makers, involve an ontological commitment to the truths themselves. But a deflationary nominalism would avoid such a commitment, taking the truth predicate to be merely a device of semantic ascent, a way of talking about a proposition P rather than asserting that P.

This raises the metaontological question of what sort of criterion of ontological commitment Leftow is presupposing throughout the book. Although he does not explicitly address the question, in a number of places it seems that he presupposes the customary view that we are committed to the existence of the values of variables bound by the first-order, existential quantifier and to the referents of singular terms in sentences we take to be true (e.g., pp. 77, 81, 96, 307, 480-1, 511). But this metaontological thesis is eminently challengeable and so cannot be merely assumed.

Against those who would challenge premise (10) in the argument above, Leftow argues that truth must have an ontology (pp. 24-5). But although he speaks freely of truth-makers throughout the book, his understanding of truth-makers is so thin that the notion of truth’s having an ontology becomes utterly obscure. At one point Leftow asks whether, if there were absolutely nothing, it would be the case that 2+2=4. If you think not, then “you accept that the latter claim has some ontology” (p. 25). What is the theist to make of this? If, per impossible, there were no God, then, I suppose, we might agree that nothing would be true. But truth’s having an ontology in this sense goes no distance toward showing that the singular terms “2+2” and “4” have real world referents, whether divine thoughts or abstract objects. To characterize anti-realist solutions as “no ontology” solutions in so thin a sense is therefore highly misleading. They might perhaps better be classed as “safe ontology” solutions—except that Leftow’s discussion of that option then fails to connect with them. In short, as Leftow himself acknowledges, much more remains to be said about anti-realist solutions to the problem of God and abstract objects. [12]

Reprinted with permission.
Copyright 2014 The Society of Christian Philosophers.

  • [1]

    The inclusion of events in the list of exceptions is a curiosity which Leftow later withdraws (pp. 76ff.).

  • [2]

    I retain Leftow’s numbering.

  • [3]

    Leftow holds that logical and mathematical truths do provide information about God, since he takes them to be universally quantified statements (p. 251).

  • [4]

    “God could not have thought up other than He did. . . . I only add that this modal character was not imposed by His nature, but instead was consequent on His thinking as He did. Whereas Platonists, and so on, will say that God thought as He did because He had to, I say that He had to only because He did” (p. 496).

  • [5]

    Leftow says, “It is in God to make dogs, but it is not by His nature in Him to make dogs, since it is not part of his nature that there should be such a property as doghood” (p. 253).

  • [6]

    This becomes clearer on p. 296.

  • [7]

    “God has the chance and power to adopt other preferences. His doing so is causally possible. So there are alternate, causally possible states for reality, in which He has these preferences ab initio” (p. 403).

  • [8]

    Leftow endorses divine conventionalism with respect to non-definitional, modal-essential truths (p. 432). On Leftow’s view it is in God to invent creaturely essences that include the properties of dogs and reptiles or the properties of dogs and mammals. Suppose that He has done so. He has preferred that the former be impossible and the latter possible. But He could have preferred otherwise. Leftow’s view leaves it undecided whether, had He done so, creatures exemplifying that essence would be reptilian dogs or would be some other sort of creature, “schmogs,” which replace dogs. In either case, the salient point is that God was able to create something that is impossible.

  • [9]

    On Leftow’s view all possible histories form a treelike structure beginning at the moment at which God thinks up secular states of affairs (pp. 403-6). God’s forming His actual preferences begins one branch. There are other possible histories branching from that moment in which God has different preferences. As each possible history continues from its preferential starting point, it branches into a tree of causally possible continuations. A path through such a tree is a possible world. Leftow holds that to occur on a branch continuing from a branch of actual history is to be possibly possible. But now consider histories continuing from different initial preferential starting points. Since it is causally possible for God to have such preferences, paths through such branches ought to be regarded as possibly possible and therefore, by S5, possible.

    Leftow rejoins that since God could not have dreamed up different secular states of affairs than He has, “God must have all and only the actual candidate histories in view” (p. 407). This rejoinder seems incorrect. Take a physically possible universe operating according to different natural laws. God could have preferred that such a world be impossible, in which case it is not one of the actual candidate histories. Of course, given that all branches originate in the moment of God’s thinking up secular states of affairs, they are branches off the actual world and so on Leftow’s own view possible, in contradiction to his theory.

  • [10]

    Leftow has reminded me that “not only Platonism counts as a bete noire for me. Possibilism is another, whether Meinongian or Lewisian” (personal communication, July 22, 2013). But neo-Meinongianism does not raise the ultimacy concerns that motivate Leftow’s project, since abstract objects do not exist on this view, making it a sort of nominalism; and Leftow himself thinks that “theism can be conjoined with Lewis-style possibilism” (Ibid.), so that again ultimacy concerns do not arise.

  • [11]

    I take this up in my review of God and Necessity in Philosophy 89 (2014): 171-6.

  • [12]

    I’m grateful to Brian Leftow for his comments on the drafts of both my reviews.