God Over All
Divine Aseity and the Challenge of Platonism
The challenge of Platonism to the doctrine of divine aseity can be formulated in argumentative form as follows: (1) If God exists, then God is the sole ultimate reality. (2) If abstract entities exist, then God is not the sole ultimate reality. (3) Abstract entities exist. Therefore: (4) God does not exist. Since the truth of these premises entails the truth of the conclusion, the argument is obviously valid. But is it sound, that is, based on true premises? The intention of William Lane Craig’s God Over All is to show that the argument is not sound because there is a cornucopia of theistic ways to deal with it. Therefore, the Platonist challenge to “the doctrine of divine aseity can be met successfully” (208).
To achieve this goal, God Over All starts with an analysis of the first premise: If God exists, then God is the sole ultimate reality. By reflection on both the achievements of biblical and systematic theology, Craig shows this premise to be true: The Christian concept of God is the concept of God as the sole ultimate reality that “exists a se and is the source of all things apart from Himself” (43).
Once this is shown, Craig turns to the second premise: If abstract entities exist, then God is not the sole ultimate reality. After careful analysis of the difficulties to specify a clear-cut definition of abstract entities, he argues, in a first step that the most plausible account of abstract entities is one in which they are essentially “causally impotent and so are not related to other objects as causes to effects” (6). In a second step, Craig clarifies the thesis of Platonism that builds on this feature of abstract objects. In Platonism, abstract entities are supposed to be ontological heavyweights: they are “objects which exist necessarily, eternally, and a se” (43). If this is true, then if abstract objects such as numbers, sets, propositions, or possible worlds exist, God is not the sole ultimate reality.
The crucial premise therefore is the third one: Abstract entities exist. According to Craig, the crucial argument for the existence of abstract entities is the “indispensability argument” (45). It runs as follows: “I. If a simple sentence … is literally true, then the objects that its singular terms denote exist. Likewise, if an existential sentence is literally true, then there exist objects of the relevant kinds; (e.g., if ‘There is an F’ is true, then there exist some Fs.) II. There are literally true simple sentences containing singular terms that refer to things that could only be abstract objects. Likewise, there are literally true existential statements whose existential quantifiers range over things that could only be abstract objects. III. Therefore, abstract objects exist.” (45-46).
The overwhelming part of Craig’s God Over All is an analysis of possible theistic responses to both the sketched understanding of abstract objects, and to the argument from indispensability.
Craig begins by analyzing the doctrine of absolute creation. In this doctrine, abstract entities—although they exist eternally and necessarily—they are nevertheless perceived to be created by God (54). Craig is keen to point out that on pain of circularity, this option is only plausible if the Platonic array of things–on which properties are abstract objects that are exemplified by concrete objects (65)–is replaced by the assumption that “explanatorily prior to his creation of properties, God can be just as He is without exemplifying properties” (71).
Craig then turns to divine conceptualism. In divine conceptualism, no abstract objects exist. Instead, “mathematical objects and other allegedly abstract entities [are] concrete objects, namely, thoughts in God’s mind” (72). According to Craig, divine conceptualism, in principle, can uphold divine aseity, but is confronted with some pressing problems concerning the adequacy of identifying abstract objects with divine thoughts. “In many cases, God’s thoughts seem ill-suited in various ways to play the roles traditionally played by abstract objects” (95).
Craig analyses the argument from indispensability. He argues that the criterion of ontological commitment expressed in its first premise is not only “far from incumbent upon us” (124), but rather, “obviously false and wholly implausible. It is a meta-ontological thesis for which there is no good argument, and the linguistic evidence is overwhelmingly against it” (143). Once this is achieved, Craig continues to argue that the second premise of the indispensability argument does not fare better: “There are plausible ways of regarding such sentences [involving terms apparently referring to what could only be abstract entities] as not literally true” (144). To support this claim, Craig analyses a variety of anti-realist positions regarding the existence of abstract objects. He deals with fictionalism, figuralism, and pretence theory. According to Craig, although there is a conceptual overlap between these positions, they all provide plausible interpretations on which statements about abstract objects are not literally true, and therefore do not commit us to the existence of abstract entities. Fictionalism’s “claims about the falsehood of such statements seem not only coherent, but even plausible” (165); Figuralism is “perfectly reasonable [as an] interpretation of abstract discourse” (180); and “pretence theory is a tenable and … attractive option for theists seeking to meet Platonism’s challenge” (205). In sum, according to Craig, the challenge of Platonism to the doctrine of divine aseity can be successfully met by a cornucopia of different theistic responses, relying either on alternative interpretations of the apparent existence of abstract objects or on the denial of our commitment to their existence.
Craig’s God Over All Divine Aseity and the Challenge of Platonism is based upon his 2015 Cadbury Lectures given at the University of Birmingham, England. It is a very good book in analytic theology. It is clear in its structure, sophisticated in its justification, and up-to-date. One of the few problems I see, though, is that Craig might throw out the baby with the bathwater—his analysis of the mentioned anti-realist’s positions show that we do not have an ontological commitment to the existence of abstract entities because statements apparently referring to abstract entities are all literally false, and can be analyzed without loss of meaning in terms not demanding the existence of abstract objects. Why should we not apply anti-realist theories to genuine religious discourse? Many of Craig’s arguments for an anti-realism about abstract objects at least seem applicable to religious discourse. Perhaps talk about God need not be literally true, after all, and could be analyzed along the lines of religious fictionalism.
Benedikt Paul Göcke is on the faculty of theology and religion at the Ian Ramsey Centre for Science and Religion at the University of Oxford.
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