05 / 06

Review Article: God and Necessity by Brian Leftow

William Lane Craig


A critical review of Brian Leftow's claim to ground modality in God's will.

Brian Leftow, God and Necessity, Oxford: Oxford University Press, 2012, 575 pp., ISBN 978-0-19-926335-6

In 1974 Alvin Plantinga’s The Nature of Necessity signaled a renaissance of Christian philosophy in the Anglophone world. Brian Leftow’s new book God and Necessity epitomizes that renaissance. It is a major contribution to modal metaphysics, striking in its creativity, impressive in its argumentation, and mind-numbing in its thoroughness.

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).

An alleged conflict with classical theism’s claim of divine ultimacy arises from the assumptions 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 (9)-(11) implies that there exists something ontologically outside God which supplies the ontology for mathematical truths. But Leftow thinks it difficult to see how such abstracta could be created by God, which contradicts God’s being the sole ultimate reality.

Leftow identifies four possible ways to deal with this apparent conflict:

(i) Deny that modal truths have an ontology.

(ii) Restrict the scope of God’s ultimacy to exempt various abstracta.

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

(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.

The dominant theistic position, what Leftow calls a deity theory, grounds modality in God’s nature (Thomism). 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). 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 are solely about the world (p. 249).

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 natural 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.

At this point we should do well to re-examine the motivation for adopting so extraordinary a modal theory. [1] Here Leftow’s subsidiary project of crafting an anti-platonist metaphysic becomes crucial. For it is not necessary truth as such which threatens divine ultimacy. Rather platonism is the bête noire.

Leftow’s strategy for dealing with platonism is to dispense with abstracta nominalistically insofar as is possible and then to find truthmakers for abstract discourse in mental events in the mind of God. Leftow recognizes that the theist who shares Leftow’s ultimacy concerns may adopt such a metaphysic without embracing Leftow’s modal theory (p. 97). 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.

Leftow’s view is intended to be 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).

In providing a non-platonist ontology for modal truths, Leftow’s strategy is to “replace abstract modal ontology with one of divine mental events and powers” (p. 303). Leftow thus takes possible worlds semantics, in view of its quantification over worlds, to involve ontological commitment to possible worlds, an indication of his assumption of the customary criterion of ontological commitment. He accordingly adopts a fictionalist perspective on possible worlds semantics, commenting, “talk about possible worlds is a useful fiction” (p. 41). “On what I believe to be the correct semantics, its [i.e., ◊P’s] truth-condition is also existential. So on the standard approach or my own, possibility-claims are true because something(s) exist(s)” (p. 96).

Shunning possible worlds in favor of divine powers, Leftow holds that for any modal truth, God either is, contains, has, or produces all of its ontology (its truth makers or truth explainers) (p. 115; cf. pp. 95-6):

POSS. (P) (◊P is true &super; God is, contains, has, has attributes that have, (etc.), or produces all ◊P’s truthmakers.

NEC. (P) (P is true &super; God is, contains, has, has attributes that have, (etc.), or produces all oP’s truth-explainers.

Every truth of the form ◊P has a truthmaker, namely, some divine power, even if P does not. Truths of the form oP have no truthmakers, even if P does. For part of what explains the truth of oP is, in the jargon of possible worlds, the absence of possible worlds in which ØP is true. Translated into the terms of Leftow’s theory, a necessary truth is explained in part by the absence of a divine power to make its negation true. So oP has a truth-explainer, not a truthmaker.

On Leftow’s view, then, instead of quantifying over possible worlds, the proper semantics for modal claims quantifies over divine powers. Is Leftow therefore committed to an ontology which includes divine powers in the place of possible worlds? Such an ontology would be consistent with Leftow’s conception of God as the sole ultimate reality, for Leftow allows that entities not “outside” God, namely, parts, aspects, or attributes of God, are exceptions to the principle that God is the source of all reality other than Himself. Thus an ontological commitment to divine powers would not be inconsistent with God’s being the sole ultimate reality.

But Leftow has a strong methodological bent toward ontological parsimony, which inclines him to get rid of powers if he can. Here two routes suggest themselves. First, Leftow could paraphrase away commitment to divine powers by speaking, for example, of what God is able to do or can do. Leftow sometimes adverts unconsciously to such paraphrases (p. 263). Alternatively, Leftow could treat divine powers as attributes or properties of God and then proceed to provide a nominalistic analysis of properties. This seems to be his preferred alternative.

Leftow takes God’s natural powers to be part of the content of deity, that is, of the divine nature. With respect to the attributes constituitive of deity, Leftow holds that any such attributes depend ontologically on their instances (p. 254, cf. pp. 215, 243-4). Leftow thus endorses a nominalistic view, according to which deity is not an existent thing at all. “There just is no such thing as deity. God is the whole ontology for God is divine. There is nothing else to which He need bear some relation in order for this to be true, and so all it takes for it to be true is that He exist” (p. 307). Leftow therefore considers himself to have “eliminated God’s natural powers from our ontology” (p. 308).

What about other properties and powers not belonging to deity? Leftow will eliminate these by substituting for them God’s concepts: “If there were (say) eternally an attribute of caninity outside God, there would also be God’s concept of this attribute’s content. God’s natural omniscience guarantees that this concept would be complete in every respect. But then this concept can be put to any philosophical use to which we might put the attribute” (pp. 113-4).

Leftow’s conceptualism is not yet complete, however. For concepts are plausibly themselves abstract objects existing outside the conceiving mind (p. 299). They, too, must therefore be eliminated. Accordingly, Leftow adopts a fictionalist stance: “There are no divine concepts. All the same it is useful to talk about them” (p. 317; cf. p. 299). The reality behind talk of divine concepts is concrete mental events in the mind of God. Thus, “Theism without divine concepts can provide an account of modal truth whose ontology is just one non-physical substance and some events” (p. 300).

Leftow recognizes that “Platonists can try to turn the tables on me by appeal to God's mental content. If we need Platonist entities to make sense of this, then in the end, appeal to God’s mind leaves us as much reason to Platonize as we had originally” (p. 309). But Leftow resists the inference that because a thought is contentful, there must be some content to which that thought is related. For Leftow we should not think of God’s thoughts as involving relations to some abstract content.

Ultimately, then, for Leftow modal ontology consists simply of God and certain mental events. It is therefore arguable that Leftow is not at the end of the day a realist after all, but rather a closet fictionalist. For he endorses a fictionalist stance on possible worlds discourse because of its unacceptable existential commitments. Such discourse is useful because “beneath world-talk is a reality involving God over which we really do quantify,” namely, divine powers. . . .” (p. 445, cf. 411, 449). The difficulty is that, given the customary criterion of ontological commitment, quantification over divine powers commits one ontologically to the existence of powers, but Leftow denies that powers are existing things. Therefore world powers discourse is for Leftow just as fictional as possible worlds discourse. In order to preserve realism, Leftow needs to provide a modal semantics quantifying over no more than God and His mental events. But he provides no such a account, so far as I can tell. What Leftow offers rather is an ontology for modal discourse, an account of the truthmakers of modal claims. But this is an account with which the fictionalist can readily agree. The fictionalist who is a theist agrees that God has thoughts of what He can and cannot bring about, and nothing precludes regarding these thoughts as concrete mental events. [2] He just does not identify divine thoughts with what, by another name, is called possible worlds.

  • [1]

    I have commented in more detail on Leftow’s modal theory in my review of his book in Faith and Philosophy 30 (2013): 462-70. Here I focus on his subsidiary project.

  • [2]

    Especially congenial to the fictionalist will be Leftow’s account of possible and necessary secular truths on the basis of God’s deciding to permit or prevent that P: possibly P iff from eternity God does not prevent that P, and necessarily P iff from eternity God permits only that P (i.e., prevents that ØP) (p. 410).