C.S. Lewis at Poets’ Corner
Page 28
13. Runia, Plato and the “Timaeus,” 138.
206
part five—oxford addresses
Interested as John is in the incarnation of the Logos, he does not linger over the pre-creatorial function of the Logos, but given the provenance of the Logos doctrine, he may well have been aware of the role of the Logos in grounding the intelligible realm as well as his role in creating the realm of temporal concrete objects.
However this may be, our exegetical study of John 1:1–3 leads to the conclusion that the author of the prologue of John’s Gospel conceives of God as the Creator of everything apart from Himself. There are no uncreated, independently existing, eternal objects, for God exists uniquely a se.
I could make exactly the same point from Paul’s correspondence, but time compels me to skip ahead.
The conviction that God is the Creator of everything that exists aside from God Himself eventually attained creedal status at the Council of Nicaea. In language redolent of the prologue to the fourth Gospel and of Paul, the Council affirmed:
I believe in one God, the Father, Almighty, Maker of heaven and
earth and of all things visible and invisible; And in one Lord,
Jesus Christ, the only Son of God, begotten of the Father before
all ages, light from light, true God from true God, begotten not
made, consubstantial with the Father, through whom all things
came into being.
The phrase “Maker of heaven and earth and of all things visible and invisible” is Pauline, and the expression “through whom all things came into being” Johannine. The Council thus confesses that God alone is uncreated and that all else was created by Him.
The Challenge of Platonism
The biblical theist cannot therefore be a Platonist, for Platonism denies that God is the sole ultimate reality. So how shall the classical theist best meet the challenge of Platonism? Figure 1 lays out some of the alternatives.
lane craig—god and the platonic host
207
Mathematical Objects
exist
meaningless
question
do
not
exist
(realism)
(arealism)
(anti-realism)
(conventionalism)
as abstract objects
as concrete objects
(neutralism)
(figuralism)
(fictionalism)
(neo-Meinongianism)
(constructibilism)
created
uncreated
physical objects mental objects
(modal structualism)
(absolute
(platonism)
(formalism)
(etc.)
creationism)
human divine
(psychologism)
(conceptualism)
Some options concerning the existence of mathematical objects
I have taken mathematical objects as representative of what are typically taken to be abstract objects. One cannot take Fig. 1 to be about abstract objects as such because, as you can see, one branch of realism treats these objects as concrete, not abstract. Note that what I have called anti-realism often goes under the name of nominalism; but I have avoided that label as less clear and potentially misleading.
Arealism
Consider our options. I take it that a classical theist cannot embrace arealism as his solution. As I use the term, arealism is the view that there just is no fact of the matter concerning the existence of putative abstract objects.14
Arealism is not an option for the classical theist, since, given divine aseity, God exists in every possible world and is the creator of any reality extra se in any world in which He exists. Therefore, it is a metaphysically necessary truth that no uncreated, abstract objects exist. Hence, there is, indeed, a fact of the matter whether uncreated abstract objects exist: they do not and cannot exist. Thus, arealism with respect to putative abstract objects is necessarily false.
14. Conventionalists like Rudolf Carnap held such questions to have no framework-independent answer because they are meaningless; metaontological anti-realists like Mark Balaguer take them to be meaningful but deny that such ontological disputes have objective answers. N.B. the distinction between ontological anti-realism, such as is featured in Fig. 1, and metaontological anti-realism. Penelope Maddy’s so-called arealism is really closer to pretense theory.
208
part five—oxford addresses
Realism
Now consider the realist options. The option requiring the least modification of Platonism is absolute creationism. Although there is a tendency to conflate absolute creationism with divine conceptualism, I take the absolute creationist to affirm that mathematical objects are not concrete objects, like mental events, but are causally effete objects existing in some sense apart from God, though causally dependent upon Him.15 Unfortunately, absolute creationism appears to involve a vicious circularity which has become known as the bootstrapping objection. The problem can be simply stated with respect to the creation of properties, a paradigmatic case of abstract objects. In order to create properties, God must already possess properties.
For example, in order to create the property being powerful God must already possess the property of being powerful, which involves a vicious circularity.
The only plausible way to avoid the bootstrapping problem, it seems to me, is to affirm that God can create a property without having the property of being able to create a property. But that just is to abandon Platonism in favour of nominalism, which holds that talk of properties is just a convenient façon de parler. Such a solution removes any motivation for realism.
So what about anti-Platonist forms of realism? Anti-Platonist realists hold that various objects normally thought to be abstract, such as mathematical objects, are in fact concrete. These may be taken to be either physical objects, such as marks on paper which are manipulated by mathematicians according to certain rules, or mental objects or thoughts, either in human minds or in God’s mind. The nineteenth-century German philosopher
Gottlob Frege subjected the views that mathematical objects are physical objects or human thoughts to such withering criticism that such views are scarcely taken seriously today.16 But Frege’s objections to human psychologism—such as the intersubjectivity, necessity, and plenitude of mathematical objects—do not touch divine conceptualism. That Frege could simply overlook what has historically been the mainstream theistic position with respect to putative abstract objects is perhaps testimony to how utterly detached nineteenth-century philosophical thinking had become from the historic Christian tradition. With the late twentieth-century renaissance of Christian philosophy, divine conceptualism is once more finding articulate defenders.17 According to these thinkers, putative abstract objects like 15. Thomas Morris and Christopher Menzel are ambiguous in this regard; Paul Gould and Richard Davis maintain, confusedly, I think, that God creates abstract objects but that these are divine thoughts.
16. Frege, The Foundations of Arithmetic, §I. 7, 8–11; §II. 26–27, 34–38.
17. Notably Alvin Plantinga, Brian Leftow, and Greg Welty.
lane craig—god and the platonic host
209
propositions, properties, possible worlds, and mathematical objects are, or are analyzable in terms of, God’s thoughts of various sorts.
Conceptualists can meet the bootstrapping objection by denying that prior to God’s conceiving them things like properties, propositions, and the like exist. God can be as He is without exemplifying properties or propositions’ being true logically prior to His conceiving them. But then, as noted before, the nerve of realism seems to be cut. So why not be an anti-realist?
Moreover, conceptualism is not entirely worry-free. For in many cases God’s thoughts do not seem suitable to play the roles normally ascribed to abstracta. Take propositions, for example. Conceptualism r
equires that God be constantly entertaining actual thoughts corresponding to every proposition. But conceptualists move far too hastily from the fact that God is om-niscient to the view that all that God knows is occurrent in consciousness.
God’s infinite knowledge is clearly not sufficient to guarantee that there are the actual mental events needed by the conceptualist. Indeed, Graham Oppy complains that conceptualism “threatens to lead to the attribution to God of inappropriate thoughts: bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth.”18 For example, consider propositions of the form for any real number r, r is distinct from the Taj Mahal. Why would God retain such inanities constantly in consciousness? Worse, consider false propositions of the form for any real number r, r is identical to the Taj Mahal. Why would God hold such a silly thought constantly in consciousness, knowing it to be false? Obviously, the concern is not that God would be incapable of keeping such a non-denumerable infinity of thoughts ever in consciousness, but rather why He would dwell on such trivialities.
Furthermore, what has been called the “aspectual shape” of a thought does not always correspond to the aspectual shape of the proposition expressed. For example, the thought that I am making a mess has a different aspectual shape than the proposition William Craig is making a mess. God can know the propositional content of my thought without His thought’s having the same aspectual shape as my thought. But if we identify God’s thoughts with propositions, we are no longer able to distinguish between the aspectual shape of a proposition and the aspectual shape of a divine thought having that propositional content. Since God has first-person thoughts, identifying God’s thoughts with propositions commits us to the existence of purely private propositions which are incommunicable by God to us. Personal indexical beliefs are just the proverbial camel’s nose. If propositions have the unique aspectual shape of God’s thoughts, many other dislocations in how we normally conceive things will be forced upon us.
In these and many other ways, the suitability of God’s thoughts to play successfully the roles ascribed to various abstracta is worrisome.
18. Oppy, “Response to Welty.”
210
part five—oxford addresses
Anti-Realism
Now I do not imagine that these worries constitute insuperable obstacles for conceptualism. Rather, my reason for raising them is to motivate theists to look more seriously at the cornucopia of anti-realist options that are available today. It is striking how little cognizance contemporary theists who have written on the problem of divine aseity take of anti-realism. They seem to have absorbed realism with their mother’s milk.
It is not as though there are overwhelming arguments for realism.
The principal argument offered on behalf of realism comes in the various incarnations of Willard Quine’s Indispensability Argument. Mark Balaguer succinctly formulates the Indispensability Argument as follows:
I) If a simple sentence ( i.e., a sentence of the form “a is F”) is literally true, then the objects that its singular terms denote exist. (Likewise, if an existential sentence ( e.g., “There is an F”) is literally true, then there exist objects of the relevant kinds.)
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 cold only be abstract objects.)
III) Therefore, abstract objects exist.
How might we respond to this argument? Although, to my knowl-
edge, C. S. Lewis did not interact with the Indispensability Argument for abstract objects, I think we have some idea of how he might have responded to it. In his essay “Bluspels and Flalansferes: A Semantic Nightmare,” Lewis claims that the greater part of our language is metaphorical rather than literal. Lewis argues that “Our thought is independent of the metaphors we employ in so far as these metaphors are optional: that is, in so far as we are able to have the same idea without them.”19 Lewis uses the example of trying to understand unimaginable higher-dimensional realities like curved 3-dimensional space on the basis of 2-dimensional analogies in Flatland. In so far as one understands the relevant mathematics, one may dispense with the metaphor. But then Lewis proceeds to say:
Our claim to independence of the metaphor is . . . a claim to
know the object otherwise than through that metaphor. . . . That
was what happened, you will remember, to the man who went
on and learned mathematics. He came to apprehend that of
which the Flatlanders’ sphere was only the image, and conse-
quently was free to think beyond the metaphor and to forget the
19. Lewis, “Bluspels and Flalansferes,” 258.
lane craig—god and the platonic host
211
metaphor altogether. In our previous account of him, however,
we carefully omitted to draw attention to one very remarkable
fact: namely, that when he deserted metaphor for mathematics,
he did not really pass from symbol to symbolized, but only from
one set of symbols to another. The equations and what-nots
are as unreal, as metaphorical, if you like, as the Flatlanders’
sphere.20
It is evident that Lewis is an anti-realist about mathematical discourse, taking it to be metaphorical and its objects unreal. Lewis thinks that in many fields of discourse the failure to realize that one is using dead metaphors with no understanding of their meaning leads to the meaninglessness of that discourse. He is more optimistic with respect to mathematical discourse: “the mathematician, who seldom forgets that his symbols are symbolic, may often rise for short stretches to ninety per cent of meaning and ten of verbiage.”21 Lewis thus thinks that mathematicians themselves realize that their discourse is not literal but metaphorical.
Lewis was apparently also an anti-realist about other abstract objects.
For example, with respect to universals, he opined, “the universal latent in every group and every plural inflection cannot be thought without metaphor.”22 Indeed, it is likely that he took the whole platonic host to be creatures of metaphor, for he writes, “open your Plato, and you will find yourself among the great creators of metaphor, and therefore among the masters of meaning.”23
I think that Lewis would therefore challenge premise (II) of the Indispensability Argument. He would contend that abstract object discourse is plausibly taken to be metaphorical, not literal, and therefore is non-commissive ontologically to abstract objects.
What shall we make of this response? The claim that abstract object discourse in general, and mathematical discourse in particular, is metaphorical rather than literal is championed today by Stephen Yablo, who has coined the term “figuralism” for the view that such discourse should not be understood literally but is a case of figurative language. Figurative speech, properly interpreted, may be true even if, taken literally, it is false.
For in figurative speech, such as understatement, hyperbole, and metaphor, the literal content is not what the speaker is asserting.24 If mathematical language is figurative, then it will be maladroit to ask after the ontological commitments of such discourse when construed literally.
20. Ibid., 260–61.
21. Ibid., 264.
22. Ibid.
23. Ibid., 265.
24. Yablo, “A Paradox of Existence,” 291.
212
part five—oxford addresses
Yablo observes that figurative language is a pervasive feature of ordinary discourse, so much so that we often do not realize that we are speaking figuratively. Like Lewis, Yablo believes that literal talk is actually the talk that is unusual.25 This presents a serious problem for Quine’s project of determining the ontological commitments of our discourse. Since figures of speech should not be taken literally, Quine recognized that his criterion of ontological commitment could not be
applied to such discourse. This situation is problematic because, in Yablo’s words, “To determine our ontological commitments, we have to ferret out all traces of non-literality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology.”26
Quine looked to science in order to eliminate metaphorical features of ordinary discourse: we are to count a thing as existing just in case it is a commitment of our best scientific theory. But, Yablo demands, what if our best theory itself contains metaphorical elements? Quine never argued that metaphor can be made to disappear entirely. If our best theories include metaphorical sentences, then we need a way of sequestering the metaphors.
But in order to do that, we need a criterion for identifying an expression as metaphorical, which we do not have. The boundaries of the literal, Yablo maintains, are so unclear that there is no telling, in cases of interest, whether our assertions are to be taken ontologically seriously. The more controversial of philosophical existence claims are equipoised between the literal and the figurative in a way that Quine’s method is powerless to address.27 Among these will be claims about abstract objects.
Yablo thinks that talk of abstract objects involves the use of what he calls “existential metaphors,” that is to say, metaphors “making play with a special sort of object to which the speaker is not [ontologically]
committed.”28 Numerical terms are such existential metaphors, useful, and sometimes indispensable, for expressing truths about the real world. Yablo provides the following illustration:
Much as we make as if, e.g., people have associated with them
stores of something called “luck,” so as to be able to describe
some of them metaphorically as individuals whose luck is “run-
ning out,” we make as if pluralities have associated with them
25. Yablo, “Go Figure,” 85.
26. Yablo, “Does Ontology Rest on a Mistake?” 229. Cf. Yablo, “Paradox of Existence,” 304–5.