C.S. Lewis at Poets’ Corner
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27. Yablo, “Does Ontology Rest on a Mistake?” 255, 259.
28. Yablo, “Paradox of Existence,” 293. By “commitment” I think Yablo means to indicate one’s commitment to the existence of the thing. Indeed, he seems to mean
“conscious commitment,” the opposite of simulation or make-believe. Cf. Yablo, “Does Ontology Rest on a Mistake?” 250; Yablo, “The Myth of the Seven,” 98.
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things called “numbers,” so as to be able to express an (other-
wise hard to express because) infinitely disjunctive fact about
relative cardinalities like so: The number of Fs is divisible by the number of Gs.29
Given our finitude, we cannot express infinite disjunctions like “There is one star and one planet, or there are two stars and one planet, or . . .” and so have no choice but to resort to number talk in order to talk, in this case, about stars and planets. “It is only by making as if to countenance numbers, that one can give expression in English to a fact having nothing to do with numbers, a fact about stars and planets and how they are numerically proportioned.”30
Yablo draws a number of very interesting parallels between talk of Platonic objects31 and figurative talk. These parallels serve as evidence that abstract object talk is a kind of figurative language.32
Yablo thinks that the decision between Platonism and figural-
ism depends upon the answers to the following questions: (1) what does 29. Yablo, “Myth of the Seven,” 98.
30. Yablo, “Paradox of Existence,” 295.
31. It should be noted that Yablo has an idiosyncratic understanding of what a Platonic object is. Objects are Platonic relative to an area of discourse if the discourse depends on how those objects behave yet the discourse is not really about those objects.
For example, someone who expresses concern about the number of starving people in the world is concerned about people, not some abstract object. Platonic objects, Yablo says, whether abstract or not, are deducible by overly easy existence proofs. He gives the following illustrations of discovering unexpected objects in statements’ truth conditions:
the truth value of:
is held to turn on:
argument A is valid
the existence of countermodels
it is possible that B
the existence of worlds
there are as many Cs as Ds
the existence of 1–1 functions
there are over five Es
the number of E’s exceeding five
he did it Fly
the event of his doing it being F
there are Gs which BLAH
there being a set of Gs which BLAH
she is H
her relation to the property H-ness
The entities denoted by the italicized terms in the right-hand column are Platonic because the sentences in the left-hand column are not really about them (Yablo, “Paradox of Existence,” 277). The expressions on the right are therefore existential metaphors. If the objects denoted by such expressions do exist, most of them are plausibly construed to be abstract objects. In fact, Yablo himself says, “the existence of abstract objects is straightforwardly deducible from premises that few would think to deny”
(ibid., 276). Since our interest is in the existence of abstract objects, we shall take Yablo’s Platonic objects to be abstract. Yablo notes that in addition to the parallels between figurative language and talk of Platonic objects, evidence for the metaphorical character of such talk is that it is the best explanation of why such overly easy existence proofs fail.
32. Yablo, “Paradox of Existence,” 302–4; cf. Yablo, “Go Figure,” 89–90; Yablo, “Abstract Objects,” 227–30.
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Platonism/figuralism help us to explain, and (2) what explanatory puzzles does Platonism/figuralism generate?
Consider first, question (2). Yablo believes that anti-Platonists have relied too heavily on the explanatory puzzles generated by Platonism, though he takes no cognizance of the theological puzzle that drives our inquiry, namely, how the putative existence of abstract objects is to be reconciled with divine aseity and creatio ex nihilo. Given our theological commitments, we know that Platonism is unacceptable. So all we need from Yablo, then, is some reason to prefer figuralism above other anti-Platonisms. Yablo has done a good job of laying out the case for taking abstract object discourse as figurative, but he does not examine the com-parative explanatory power of other anti-Platonistic views with respect to the data. So more work needs to be done.
As for explanatory puzzles generated by figuralism, Yablo considers only the objection that abstract object talk, and particularly mathematical discourse, is not plausibly a matter of make-believe. This objection, however, is really an objection to a pretense theoretical analysis of figurative language, not to the figuralist thesis that abstract object talk is figurative.
Consideration of such a puzzle is therefore better reserved for another time when discussing pretense theory.
So let us consider instead an objection that has been raised against figuralism by John Burgess and Gideon Rosen. They think that the claim that mathematical discourse is figurative is implausible. They write: Certainly in all clear cases of figurative language—and it is worth stressing that the boundary between figurative and literal
is as fuzzy as can be—the non-literal character of the linguistic
performance will be perfectly obvious as soon as the speaker is forced to turn attention to the question of whether the remark
was meant literally.
We further submit that mathematical discourse fails this
test for non-literalness.33
One is tempted to ask what evidence can be cited in support of their opening sentence, but never mind. The more important point is that this objection, if sound, at best proves that mathematical discourse is not a clear case of figurative language, a hardly surprising result.34 What does not follow 33. Rosen and Burgess, “Nominalism Reconsidered,” 533.
34. Burgess and Rosen themselves acknowledge that on Yablo’s view “an existence theorem is ambiguous between a literal and a figurative sense” (ibid., 528). I am not sure how seriously they take this ambiguity.
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is that mathematical discourse does not lie somewhere in that fuzzy area between clearly figurative and clearly literal expressions.
The second and perhaps more important point to make is that while
Yablo, like Lewis, espouses figuralism as a hermeneutic thesis about how mathematicians themselves understand their discourse, there is no reason the anti-realist has to present it as such. In the absence of linguistic and sociological studies about what the community of working mathematicians think about this question, the figuralist can remain agnostic about hermeneutical questions and present the figurative interpretation simply as one reasonable way of understanding abstract object talk. If such an interpretation is reasonable, then the Indispensability Argument has been defeated.
Turn now to question (1). What are the alleged explanatory benefits of Platonism? The principal merit claimed on behalf of Platonism is that it provides a basis for the objective truth of mathematics.35 But here the difference between fictionalism and figuralism comes clearly to the fore. Figuralism affirms the truth of mathematical sentences, for these are figurative speech and as such escape the traditional criterion of ontological commitment. Just as “It’s raining cats and dogs!” may be true without there being animals falling from the sky, so the truth that “1+1=2” does not require the reality of numbers. Of course, the theistic figuralist who does not believe in abstract objects will deny the literal truth of figurative talk about abstract objects; but he will insist on the truth of such statements when understood, not literally, but figuratively.
Still we may wonder what the objective basis of
mathematical truths is, if not the reality of the objects referred to or quantified over in such statements. Here Yablo seems to differ from Lewis, who seemed to think that we could explain mathematical metaphors only in terms of more metaphors.
Yablo maintains that the real content of mathematical truths is logical truths, which require no ontological foundation: “Arithmetic is, at the level of real content, a body of logical truths—specifically, logical truths about cardinality—while set theory consists at the level of real content, of logical truths of a combinatorial nature.”36 In short, the realist has no advantage 35. Yablo, “Go Figure,” 88; Yablo, “Paradox of Existence,” 286–90.
36. Yablo, “Myth of the Seven,” 99; Yablo, “Abstract Objects,” 230–32. The real content of arithmetical truths like 2+3=5 is the first-order logical truth ሺʹ��Ƭ͵� �
Ƭ�ሺ�Ƭ �ሻሻ՜ͷ�ሺ�� �ሻ) ®$5 u(Fu v Gu). When it comes to non-numerical
mathematical statements such as are comprised by set theory, Yablo takes the figurative language of sets to express certain combinatorial logical truths, that is, truths about what one gets when combining objects in different ways.
In his earlier work, Yablo contrasted the literal and metaphorical content of a figurative sentence (“Does Ontology Rest on a Mistake?” 248–49), but was not always consistent with his later use of terminology. For example, the existentially metaphorical
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over the anti-realist in accounting for the objectivity of mathematical truth, since the real content of metaphorical statements about such imaginary entities as numbers and sets is logical truths.
Finally, as for the explanatory benefits of figuralism, although Yablo has benefits of his own in mind, surely for the theist the most important benefit is that it explains how to reconcile mathematical truth with divine aseity. The theist has good reasons for thinking that Platonism is false and may embrace figuralism’s account of mathematics’ necessity, apriority, and absoluteness without compromising his anti-realism about abstracta.
In sum, it seems to me that figuralism is a plausible option for the theist to pursue as a means of defeating the Indispensability Argument for Platonism. It offers an interpretation of abstract object discourse that is figurative, not literal, thereby avoiding ontological commitment while preserv-ing truth. Figuralism has the additional advantage of being a very plausible interpretation of mathematical discourse in view of the striking similarities of such discourse to figurative speech.
Figuralism thus offers an attractive solution to the challenge of Platonism to God’s being the sole ultimate reality. What figuralism does leave unchallenged, though, is the Quinean metaontological criterion for ontological commitment which comes to expression in premise (I) of the Indispensability Argument. Some might see this as an advantage of figuralism, since it places figuralism on common ground concerning customary views of quantification and reference. Other anti-realists, however, will see this strategy as timid and insufficiently radical. These other anti-realists will dare to assail the sanctuary of Quinean metaontology itself.
statement “The average star has 2.4 planets” can be paraphrased as “The number of planets divided by the number of stars is 2.4.” This eliminates the average star, but only at the expense of committing us to numbers. Since numbers are not the cosmologist’s concern, says Yablo, this statement is also metaphorical. Yablo would later put it differently: numbers are therefore Platonic. Therefore, the figuralist will take the paraphrase to be metaphorical. Yablo then says that the more literal content is “There are 12 planets and 5 stars or there are 24 planets and 10 stars or . . . .” But later Yablo would realize that such a statement actually gives, not the literal content, but the real content, and does not commit its user to numbers. Because the real content is inexpressible, being an infinite disjunction, we have no recourse but to resort to metaphor, such as those used in the original statement and its paraphrase.
In his later work, Yablo tends to contrast the literal content of figurative speech with its real content (“Go Figure,” 94–95; “Abstract Objects,” 209–30). There he explains that for the figuralist “The average mother has 2.3 children, but there is no average mother”
is true because the first clause is figurative and the second literal. The real content of the first clause will be an inexpressible, infinite disjunction.
17
Remembering C. S. Lewis
Walter Hooper 1
Ladies and gentlemen, besides apologising for the amount of autobiography in this talk, I must make it absolutely clear from the outset that my acquaintance with Lewis was, in comparison to that of many of his friends, a mere flea-bite. There was of course Lewis’s beloved brother, Warnie, who knew Jack Lewis more intimately than anyone. And there are so many others such as J. R. R. Tolkien who have left fascinating reminiscences of Lewis. If you had been at this banquet fifty years ago any one of those men would have been the speaker you should have invited. But as they are now in heaven, I am touched by your graciousness in inviting me here.
My introduction to Lewis’s writings goes back to May 1953 when I
was nearing my final term at the University of North Carolina at Chapel Hill. This was the time of the Korean War and all young men were worried whether they’d be allowed to finish their degree before being drafted into the army.
In that happy place during a very happy time of my life, I was introduced to J. B. Phillips’s Letters to Young Churches: A Translation of the New Testament Epistles (1947). It contained an Introduction by C. S. Lewis.2 I’d 1. Walter Hooper is Trustee of and Literary Adviser to the estate of C. S. Lewis and has edited many collections of Lewis’s writings, most notably the three-volume Collected Letters. In 1974, with Roger Lancelyn Green, he wrote the first biography of C. S. Lewis, which he revised and expanded in 2002. He is also the author of C. S. Lewis, A Companion and Guide (HarperCollins, 1996). In 1963 he served as Lewis’s private secretary when Lewis was in declining health.
2. The Introduction is published as “Modern Translations of the Bible,” in God in the Dock, ed. Hooper.
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never heard his name before, and I read the Introduction simply because it was there. It made a total conquest of me. It was not so much what he said, but the way he said it. What came through the Introduction was not simply information about the Epistles but something about Lewis. I knew I’d stumbled upon someone whose faith was as certain as that of the apostles.
Thereafter I wanted passionately to read anything I could find by
Lewis. After a number of deferments by the draft board, I finally finished my degree—and it was then straight into the army and Fort Jackson, South Carolina. I had meanwhile discovered a little bookshop in Greensboro run by two elderly ladies who, the day before I went to Fort Jackson, put into my hands a copy of Lewis’s Miracles, which went with me into the army. During basic training I kept Miracles hidden beneath my shirt, which made for a good deal of discomfort during callisthenics and bayonet practice. However, in those little ten-minute breaks between firing bazookas and throwing grenades, I managed to read a page or so. If a book can hold your interest during all that excitement, and while you’re crawling under barbed wire in a muddy trench, it is a very, very good book.
Because Lewis wrote in so many genres—fairy tales, theology, science fiction, literary criticism—he sometimes appears to be half a dozen different authors, especially if you only discover his fairy tales after having exhausted his theology, or only discover his science fiction after having worked your way through his literary criticism. But that was not my experience. During the next two years at Fort Jackson and Fort Bragg I received all my Lewis books from the ladies in Greensboro, and I simply read them in the order they sent them to me, which was not at all systematic: Miracles, then English Literature in the Sixteenth Century, then The Lion, the Witch an
d the Wardrobe, and so forth. This turned out to be very important because I never imagined Lewis to be several different compartmentalised authors, but rather one author of several geniuses.
By November 1954 I was working for some chaplains at Fort Bragg,
and they arranged for me to talk to the first person to come my way who had met Lewis. It was Dr. Bob Jones Jr., President of Bob Jones University, who was known as the hottest of all hot-gospellers. He was coming to preach at Fort Bragg, and I was given the job of looking after him. When he was alone, I went into his little office to see if there was anything he needed. Of course I couldn’t resist asking what he thought of C. S. Lewis. He became very serious. “That man,” he said—there was a pause—“that man smokes a pipe, and that man drinks liquor—but I do believe he’s a Christian!”
I began corresponding with Lewis shortly after this. In my first letter from Lewis, dated 30 November 1954, he made it clear he didn’t want me to think too highly of him for he began by saying, “I am glad if I have been the
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instrument of Our Lord’s help to you: in His Hands almost any instrument will do, otherwise none.”3
We continued to correspond, and it was while I was lecturing on English Literature at the University of Kentucky in Lexington in the early 1960s that I began writing an academic book about Lewis—never completed. This led Lewis to invite me to come and see him. I went to Oxford in June 1963.
I had an appointment with Lewis at the house—The Kilns, Kiln Lane in Headington Quarry—on Monday the 10th June. However, I’d been warned that his house, some five miles from Oxford, was very difficult to find, and on the previous Friday afternoon, the 7th June, almost as soon as I’d arrived in Oxford, I went out to see if I could find his house. No one in Kiln Lane could tell me where he lived, but someone showed me where his housekeeper lived, and I went there. The housekeeper, Mrs. Miller, said she’d just seen him arrive back from Cambridge, and she urged me to go and call on him.