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Lewis E. Hahn and Paul A. Schilpp eds., The Philosophy of W. V. Quine. La Salle, IL: Open Court 1986. Pp. xvi+705.
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Lewis E. Hahn and Paul A. Schilpp eds., The Philosophy of W. V. Quine. La Salle, IL: Open Court 1986. Pp. xvi+705.
Published online by Cambridge University Press: 01 January 2020
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1 The ‘Princeton interpretation,’ ensuing from Harman, Gilbert ‘Quine on Meaning and Existence,’ Part I of the Review of Metaphysics, XII (September, 1967), 124-51Google Scholar; Part II of the Review of Metaphysics (December, 1967), 343-67. See also Boorse, Christopher ‘The Origin of the Indeterminacy Thesis,’ Journal of Philosophy 72 (1975), 369-87CrossRefGoogle Scholar.
2 Quine, W.V. The Roots of Reference (LaSalle, IL: Open Court 1973), 4Google Scholar
3 Quine, W. V. ‘Epistemology Naturalized’ in Ontological Relativity and Other Essays (New York: Columbia University Press 1969), 82-3CrossRefGoogle Scholar
4 Ibid. 83
5 Charlton, William Weakness of the Will (Oxford: Basil Blackwell 1988), 10Google Scholar
6 The Philosophy of W. V. Quine, vol. 18 of the Library of Living Philosophers, Lewis E. Hahn and Paul A. Schilpp, eds. (La Salle, IL: Open Court 1986). Page references to this work I shall furnish in the main text in parentheses.
7 From Alston to White.
8 Quine, W.V. The Time of My Life: An Autobiography (Cambridge: MIT Press 1985)Google Scholar
9 Quine, W.V. Theories and Things (Cambridge, MA: Harvard Univesity Press 1981)Google Scholar
10 In like fashion, Quine suggests that Thompson’s piece, received in 1973, might have benefited from a reading of ‘Mind and Verbal Dispositions,’ which appeared in 1975 (Reply to Manley Thompson, 565), and Smart’s, received in 1974, from a reading of ‘Whither Physical Objects?’, by Quine, W. V. Boston Studies in Philosophy of Science 39 (1975) 497-504.CrossRefGoogle Scholar
11 Similarly, The Web of Belief, written with Joseph Ullian, is cited by Quine as the principal source of his views about scientific method (493). Another problem for the editors is Quine’s huge popularity. There is no more, or more carefully, scrutinized living philosopher than he. Several British Columbia forests have been sacrificed to the production of paper sufficient to sustain the Quinean commentary industry over the decades. Then, too, there have been earlier Festschrifte, not necessarily called such, most notably Words and Objections, Donald Davidson and Jaakko Hintikka, eds. (Dordrecht: Reidel 1969) and Essays on the Philosophy of W. V. Quine, Robert W. Shahan and Chris Swoyer, eds. (Norman, OK: University of Oklahoma Press 1979); and Quine himself has never been stingy about replying to his critics carefully and at length. Since 1975, at least a half a dozen books have appeared, all but two earlier than PQ. Cf. Paul Gochet, Ascent to Truth: A Critical Examination of Quine’s Philosophy (Munich & Vienna: Philosophia Verlag 1986), 13. The post-PQ titles are Roger Gibson’s Enlightened Empiricism: An Examination of W. V. Quine’s Theory of Knowledge (Tampa, FL: University of South Florida Press 1988), and Hookway’s, Christopher Quine: Language, Experience and Reality (Oxford: Polity Press 1988Google Scholar). Thus, unlike the state of the critical commentary surrounding the publication in 1963 of the Schilpp volume on Carnap, which permitted that book to take a commanding and central place in Carnapian criticism, for all its substantial virtues, the sheer mass of retrospective critical giveand- take on Quine makes it tougher for the present work to stand out.
12 ‘I began [in 1951] working toward a philosophy book that proved, nine years later, to be Word and Object’ (W.V.Quine, The Time of My Life, 228).
13 I owe this point to a conversation with Jeanne Peijnenburg of the University of Groningen.
14 Cf. Arnold Levison: ‘A curious feature of Quine’s discussion of this topic [=sense data) is that he allows approximately 230 largely unrelated pages to intervene between the beginning and the end of a connected line of argument’ (323).
15 Quine, W.V. Word and Object (Cambridge, MA: MIT Press 1960), 78Google Scholar, and ‘Reply to Chomsky,’ in Words and Objections, 302-3.
16 Gilbert Harman, ‘An Introduction to “Translation and Meaning,”’ Chapter Two of Word and Object, in Words and Objections, 14-15. Received favorably by Quine in his Reply to Harman (ibid., 296).
17 This is Kripke’s formulation, discussed approvingly by Quine in ‘First General Discussion Session,’ Synthese 27 (1974), 471-508, at 480 and 482.
18 Quine, W.V. ‘On the Reasons for the Indeterminacy of Translation,’ Journal of Philosophy 67 (1970), 178-83CrossRefGoogle Scholar, at 181.
19 Ibid.; emphasis added.
20 Ibid., 179-80
21 Ontological Relativity and Other Essays, 89
22 Ibid., 86-7
23 Gilbert Harman, ‘First General Discussion Session: 494. Jaakko Hintikka, ‘Behavioral Criteria of Radical Translation: in Words and Objections, 79-80. Harman persists with this theme in his contribution to PQ, ‘Quine’s Grammar’:’ … if Quine is right about ordinary translation between languages, it is unclear what interest such translation could have for scientific theory’ (168). And ‘Quine’s argument [that there is no fact of the matter concerning the grammar of one’s language] is simply invalid in its present form …. What Quine has yet to show is that the alternative theories of language that he envisions are real alternatives … he must show that currently accepted substantive and methodological principles in linguistics (and psychology) do not sufficiently anchor the meanings of the relevant grammatical hypotheses. I do not see that he will be able to do this, given the current situation in linguistics’ (175).
24 Quine, W.V. The Ways of Paradox and Other Essays (New York: Random House 1966), 233-41Google Scholar, at 233-4.
25 Ibid., 235-7
26 Ibid., 216; emphasis added.
27 Ontological Relativity and Othere Essays, 97; emphasis added. Other Quinean tests do, however, suggest a more austere conception of evidence: ‘whatever evidence there is for science is sensory evidence’ (Ontological Relativity, 75).
28 Quoted from Ellman, Richard James Joyce, 2nd rev. ed. (New York: Oxford University Press 1982), 601-2Google Scholar. In the end, the French Ulysses emerged from this artful tangle of analytical hypotheses and bore on its title page: ‘Traduit de I’angláis par M. Auguste Morel assisté par M. Stuart Gilbert. Traduction entièrement revue par M. Valéry Larbaud avec la collaboration de I’auteur.’
29 And of the kind that Quine himself has done: ‘I dictated a translation of my Portuguese to an English stenographer in Sao Paulo under the title “Notes on Existence and Necessity“’ (PQ, 24). Later, in making his own French translation of The Philosophy of Logic he ‘luxuriated in the freedom that a self-translator enjoys. If a sentence is sticky, he is free to say something else to the same long-run purpose’ (PQ, 37). To the same long-run purpose, is it? By the way, though Quine used his French text to re-work the English for the American publisher, the French edition of the book is in a translation by Professor Largault. Is it relevant for the assessment of the thesis of the indeterminacy of translation that Quine himself is an experienced hand?
30 The Ways of Paradox, 66; emphasis in the original.
31 From a Logical Point of View, 103
32 Harold N. Lee shows some indication of smudging the distinction between values of a theory’s variables and objects semantically indispensable to theory (’Discourse and Event,’ 295-314). Though he cites the quotation of the previous note, he also quotes Quine as saying, entirely correctly, that the values of a variable refer’ … to the objects in the universe of discourse over which a quantifier ranges’ (The Ways of Paradox 154) and he adds, without pause, that ‘it is the values of the variables in a quantified formula that make the formula … true or false’ (298). Fair enough, but this is not ontological commitment; this is reference. Objects making sentences true aren’t the objects of ontological commitment, the objects of ontological commitment are the objects necessary for making sentences true. I notice, however, that in his Reply, Quine does not correct Lee on this point, so it is possible that I may have misunderstood the exposition.
33 Cartwright, Richard ‘Ontology and the Theory of Meaning,’ Philosophy of Science 21 (1954), 316-25CrossRefGoogle Scholar; reprinted in Cartwright, Richard Philosophical Essays (Cambridge, MA: MIT Press 1987), 1-13Google Scholar; references herein to the 1987 reprint.
34 ‘Ontology and the Theory of Meaning,’ 10 (I retain Cartwright’s numbering).
35 Ibid., 11
36 Ibid., emphasis added. Cf. James Corman: ‘By his criterion logicism is ontologically committed to whatever certain abstract terms denote …. But he cannot get from this premise to the conclusion that logicism is committed to abstract enties unless he provides another premise about what abstract terms denote’ (Metaphysics, Reference and Language (New Haven: Yale University Press 1966], 150).
37 Quine’s confidence in the intelligibility of the theory of reference has varied with his subsequent views about reference, brought to important modification in The Roots of Reference. A fundamental question arises. How, given the inscrutability of reference, can the legitimate core concepts of semantics, reference and satisfaction, be made to behave? (Cf. Roth, 434ff. and 443ff.)
38 In fact, translation is not a problem by analogy with the problem of ontological commitment; it is also directly a problem for ontological commitment.
39 Theories and Things 21-2; quoted in Gibson, 152. But see Gibson’s n. 2 (153) and Quine tidying remarks (156). See also three paragraphs below.
40 Theories and Things, 23; emphases added.
41 One such ‘demonstration’ would isolate small, rudimentary fragments, F1 and F2, of two grown-up languages L1 and L2. It could be established that translation between F1 and F2 is not indeterminate, because in their simplicity they are embedded in publically ascertainable contexts. Given the lack of indeterminacy between F1 and F2, there will be no indeterminacy between F1x and F2x, slight complexity-extensions of F1 and F2. Whence, by mathematical induction there is no indeterminacy between L1 and L2 (of course, the problem is that mathematical induction is not really operating here).
42 Kirk, Robert Translation Determined (Oxford: Clarendon Press 1986)Google Scholar
43 Valuable insights into the semantic linkages between and among these theses are also supplied by Gochet, Paul ‘Five Tenets of Quine,’ Monist 65 (1982), 13-24CrossRefGoogle Scholar.
44 Romanos, George D. Quine and Analytic Philosophy (Cambridge, MA: MIT Press 1983) 181-3Google Scholar
45 Words and Objections, 302ff.
46 I owe this point to Roger Gibson, who develops it in detail in his able book The Philosophy of W. V. Quine (Tampa, FL: University of South Florida Press 1982).
47 In fact that we ever get anything right is, given Quine’s austere constraints, miraculous, and anthropic principle arguments tum out to be no more complex and vexing than our accounting for the flotation of ice!;
48 Ontological Relativity and Other Essays, 83
49 Word and Object, 2
50 Ibid., 1
51 Ibid.
52 The Roots of Reference, 1
53 Word and Object, 5
54 The Roots of Reference, 3-4
55 Ibid., 2
56 Word and Object, 23
57 Ibid., 22
58 Ibid., 4
59 W.V. Quine (From a Logical Point of View), 44
60 Ontological Relativity and Other Essays, 71
61 Ibid., 75-6
62 The Roots of Reference, 2
63 W.V. Quine, ‘The Nature of Natural Knowledge,’ in Guttenplan, Samuel ed., Mind and Language (Oxford: Clarendon Press 1975), 8Google Scholar
64 The Roots of Reference, 3; italics added.
65 Ontological Relativity and Other Essays, 82-3
66 Ibid., 83; emphases added.
67 Barry Stroud, The Significance of Naturalized Epistemology,’ Midwest Studies in Philosophy 1 (1981), 455-71; reprinted in Kornblith, Hilary ed., Naturalizing Epistemology (Cambridge, MA: The MIT Press 1985), 71-89Google Scholar, at 82. References herein to the 1985 reprint.
68 Ibid., 77
69 The Ways of Paradox, 216. And: ‘[i]llusions are illusions only relative to a prior acceptance of genuine bodies with which to contrast them …. The positing of bodies is already rudimentary physical science; and it is only after that stage that the sceptic’s invidious distinctions can make sense’ (The Nature of Natural Knowledge,’ 67).
70 Arnold Levison makes a similar point:’ … Quine seems to be working with two [conflicting] criteria for positing objects …. The first criterion is “comparative directness of association with sensory stimulation” … The second criterion is “utility for theory”’ (‘Indeterminacy and the Mind-Body Problem,’ 328).
71 Theories and Things, 16
72 Ibid., 17
73 ‘Equivalently: any sum or aggregates of point-events’ (Theories and Things, 124).
74 Ibid., 17; emphases added. So now our ontology is thorough-goingly abstract, at least it would be if we had any reassurance that a commitment to sets is a commitment to abstract entities. ‘ … I pondered … Carnap’ s expedient of spatiotemporal coordinates, as [a] possible [avenue] to a Pythagorean ontology of natural numbers. I was not deeply stirred by such a prospect …. Twelve years later still, however, … I recognized that developments in particle physics itself lent some support to a wholly abstract ontology’ (31).
75 Theory and Things, 20
76 Ibid., 97
77 Ibid.
78 Ibid.; emphasis added.
79 Theories and Things, 98
80 In fact, ‘a humiliating demotion’ (Quine, ‘Ontology and Ideology Revisited,’ Journal of Philosophy 80 [1983], 499-502, at 501) and ‘an ontological debacle’ (’Whither Physical Objects?’ 503).
81 Cushing, James ‘Models and Methodologies in Current Theoretical High Energy Physics,’ Synthese 50 (1982), 78CrossRefGoogle Scholar; cf. C.A. Hooker: ‘[Quantum] theory is strikingly empirically adequate, well understood mathematically but poorly understood conceptually and ontologically’ (’Surface Dazzle, Ghostly Depths,’ in Churchland, Paul M. and Hooker, Clifford A. eds. Images of Science [Chicago: University of Chicago Press 1985), 183)Google Scholar.
82 And: ‘[r]evision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle’ (From a Logical Point of View, 43).
83 Hilary Putnam, ‘Is Logic Empirical?’ in Boston Studies in the Philosophy of Science 5, R. Cohen and M. Wartofsky, eds. (Dordrecht: Reidel 1968). Reprinted as ‘The Logic of Quantum Mechanics’ in Putnam, Hilary Mathematics, Matter and Method: Philosophical Papers, Vol. I (Cambridge: Cambridge University Press 1975), 174-97Google Scholar, at 174. References herein to the 1975 reprint. Cf. Bas C. van Fraassen: ’what is shown (by the situation in quantum physics] is that standard logic has a limited domain of application’ (The Labyrinth of Quantum Logics,’ in C.A. Hooker, ed. (Dordrecht: Reidel 1975] 577-607, at 603).
84 Quine, W.V. The Philosophy of Logic (Englewood Cliffs, NJ: Prentice-Hall 1970) 86Google Scholar; emphases added.
85 Carnap, Rudolf The Logical Syntax of language (London: Routledge and Kegan Paul 1937) 319Google Scholar
86 The Philosophy of Logic, 86
87 ‘The Logic of Quantum Mechanics,’ 178
88 Ibid., 179
89 ‘The Labyrinth of Quantum Logics: 580-1
90 Ibid., 600
91 Philosophy of Logic, 85; cf. the attempt by Birkhoff and von Neumann to save the modularity of disjunction by tinkering with the physics. Birkhoff, G. ‘Lattices in Applied Mathematics,’ American Mathematical Society, Proceedings of Symposia in Pure Mathematics 2 (1961), 155-84.CrossRefGoogle Scholar
92 Priest, Graham and Routley, Richard On Paraconsistency (Canberra: Australian National University Press 1984), 192-3Google Scholar. Quine’s enthusiasm for paraconsistent approaches is, shall we say, bated. ‘To turn to a popular extravaganza, what if someone were to reject the law of non-contradiction and so accept an occasional sentence and its negation both as true? An answer one hears is that this would vitiate all science. Any conjunction of the form “p· ∼p” logically implies every sentence whatever …. In answer to this answer, one hears that such a full-width trivialization could perhaps be staved off by making compensatory adjustments to block this indiscriminate deducibility … Perhaps it is suggested, we can so rig our new logic that it will isolate contradictions and contain them … My view of this dialogue is that neither party knows what he’s talking about’ (Philosophy of Logic, 81; emphasis added).
93 On Paraconsistency, 192-3. I acknowledge, by the way, that the cumulative hierarchy is not the way of Quine’s own treatment of sets. This is another story to which I tum in the next section.
94 For more of this, see John Woods, The Groningen Lectures on Paraconsistent Logic, forthcoming.
95 Philosophy of Logic, 81
96 ‘It is at the limits of the classical logic of quantification, then, that I would continue to draw the line between logic and mathematics’ (Philosophy of Logic, 91).
97 Cf. what Russell was about in his Lowell Lectures of 1914, reprinted as Our Knowledge of the External world (London: Allen and Unwin 1914): “’A proposition of pure logic” is one such as this: If a thing has a certain property, and whatever has this property has a certain other property, then the thing in question also has that other property’ (67). Note the exclusion of ‘empirical terms.’ Logical truths stand aside from ‘mathematical truth [which for Quine] … as Dreben has put it … is not sui generis’ (UIIian, 584).
98 Philosophy of Logic, 97-8
99 Ibid., 87
100 ‘The Logic of Quantum Mechanics,’ 190
101 Philosophy of Logic, 95
102 Ibid., 61; emphasis added.
103 Ibid.
104 Ibid, 60; emphasis added.
105 Any such proposal, to define validity or logical truth in terms of a proof procedure, tends to call forth a clamor of protest. It is protested that the property of being provable by the chosen proof procedure is intrinsically uninteresting’ (54). But, no, formulating the completeness theorem [=’if a schema is satisfied by every model, it can be proved’] ‘is independent of how we define logical truth … .’ So, after all’ … we can define logical truth by mere description of a proof procedure, without loss of any of the traits that may have made logical truth interesting to us in the first place’ (Philosophy of Logic, 57).
106 Richard Cartwright, Philosophical Essays, 235
107 van Fraassen, Bas C. ‘Meaning Relations Among Predicates,’ Nôus 2 (1967), 161-79Google Scholar
108 Philosophy of Logic, 50
109 Ibid., 59; emphasis added.
110 Ibid., 35
111 Ibid., 49
112 Philosophy of Logic, 102
113 ‘Quine thinks that to do logic solely by analyzing ordinary language would be like doing physics by analyzing the opinions of the men in the street’ (169).
114 The Ways of Paradox, 150; emphasis added.
115 The utter importance of what I’ve been calling Quine’s logical ‘naturalism’ is highlighted by Hintikka’s stern rebuke: ‘Quine’s [rooting of the formal language of logic in the mother tongue] exemplifies what seems to me one of the most pervasive and pernicious mistakes in contemporary philosophy of logic and philosophical logic …. [T]he greater semantical clarity of suitable formal languages … implies that [they] can … be understood and mastered independently of the messy ways in which the same things are expressed in natural languages and independently of the even messier ways in which natural languages are translated into logician’s (sic) standardized discourse’ (’Quine on Who’s Who,’ 213). This is a touchy point, which Quine does not take up in his Reply to Hintikka. Still, one has the impression that if Quine yielded to Hintikka here, logic would have lost or anyhow compromised its naturalistic foundation.
116 Church, Alonzo Review of Quine’s ‘Whitehead and the Rise of Modern Logic,’ Journal of Symbolic Logic 7 (1942), 100-1Google Scholar
117 Referential Opacity and Modal Logic, 98
118 Ullian reminds us (578) of ‘an ingenious proof’ of Scott: if NF is consistent it cannot be decided whether there are any individuals (Dana Scott, ‘Quine’s Individuals,’ in ernest Nagel, , et al., eds., Logic, Methodology, and the Philosophy of Science [Stanford: Stanford University Press 1962), 111-15Google Scholar). Cf. Quine: ‘A third drawback philosophically may be seen in the rejection by NF and ML of the axiom of regularity, or Fundierung, for … ungrounded classes have an individuation problem. The celebrated principle of individuation of classes, namely that they are identical if and only if their members are identical, serves to individuate them only insofar as their members are already individuated; and on this score an ungrounded class totters over an infinite regress’ (Reply to Joseph S. Ullian, 590).
119 Thus Cartwright, Richard ‘Classes and Attributes,’ in Philosophical Essays, 161-70Google Scholar.
120 From a Logical Point of View, 107
121 ‘Classes and Attributes,’ 162
122 Quine, W.V. Set Theory and Its Logic (Cambridge, MA: Harvard University Press 1963) 1-2Google Scholar; quoted in Cartwright at 164.
123 ‘Classes and Attributes: 165
124 Details in ‘Classes and Attributes: 167
125 Ibid., 167-8
126 Ibid., 169
127 Ibid.; emphasis added.
128 A necessary condition of specifying a difference between K-things and K*;-things is to reveal something true of all K-things and of none of the K*;-things. In showing that various of Quine’s attempts to fulfil this condition don’t work, we do not, of course, show that K and K*; don’t differ. Nor do we show that their difference is hopelessly obscure. But, still it is fair to press the question, ‘If this, that and the other thing don’t reveal the difference between classes and attributes, then what does?’ An obvious answer to this question seems to be this: that having members is true of all classes and false of all attributes. But it won’t do. It is over-severe with the null class; and what is said to be false of all attributes is also false of all non-classes. The not-having members of attributes is thus not a distinctive difference between classes and attributes.
129 Cf. Skolem, Lectures on Set Theory, 52: ‘The reason for this [lack of influence] is presumably the existence of such sets … as V which are elements of themselves, pathological sets as they are called …. I don’t think, however, that this circumstance ought to worry mathematicians because it is not necessary to take these abnormal sets into account in the development of the ordinary mathematical theories’ (quoted in Ullian at 589, n. 68).
130 Hailperin, Theodore ‘Sets of Axioms for Logic’ (Journal of Symbolic Logic 9 [1944], 1-19CrossRefGoogle Scholar). Here I follow the standard citations convention for the JSL.
131 George Berry, Review of ‘Sets of Axioms for Logic’ (1944: 73)
132 J. Barkley Rosser, ‘The Burali-Forti Paradox’ (1942: 1-17)
133 Hailperin, ‘Sets of Axioms for Logic’
134 J. Barkley Rosser and Hao Wang, ‘Non-standard Models for Formal Logics’ (1950: 113-29)
135 Wang (1950: 113-29)
136 Ibid.
137 Both proved by Specker, E.P. ‘The Axiom of Choice in Quine’s New Foundations for Mathematical Logic,’ Proceedings of the National Academy of Science 39 (1953), 972-5CrossRefGoogle ScholarPubMed.
138 C. Ward Henson, Review of Ronald Bjoom Jensen: ‘On the Consistency of a Slight (?) Modification of Quine’s New Foundations’ (1975: 241-2)
139 ‘[This] is ruled out by the axiom of counting, which seems a recommendation for that axiom’ (Ullian, 578).
140 Ibid.
141 Ullian, 578ff.
142 Ullian, 578
143 W.V. Quine, ‘Element and Number,’ 135-49; Ullian, 578-9
144 Black, Max ‘A Critical Review of Mathematical Logic (Quine’s Mathematical logic)’ Mind 52 [1943) 264-75CrossRefGoogle Scholar; quoted in Ullian at 579)
145 Mathematical Logic, revised ed. (Cambridge, MA: Harvard University Press 1981), iv
146 For want of space, I shall restrict my remarks about STL. It is, as Ullian rightly avers, ‘a real tour de force on set theory’ (582). It carefully examines what in addition to quantification theory is minimally necessary for mathematics. Its virtual classes are smooth and powerful and (largely) neutral. Its axioms are stingy. And it ‘plump[s] for the primacy of the iterative concept’ of sethood (Reply to Hao Wang, 646).
147 Donald Martin, ‘Review of: From Frege to Gödel,’ Jean van Heijenoort, expositionary ed., Journal of Philosophy 67 (1970), 113
148 Drake, F. Set Theory (Amsterdam: North-Holland 1974)Google Scholar, 19f.; quoted in Ullian at 585.
149 Shoenfield, Joseph Mathematical Logic (Reading, MA: Addison-Wesley 1967), 238fGoogle Scholar.
150 Donald Martin, 113
151 Ullian adds: ‘Dreben observes that whereas contemporary work in set theory exhibits both consideration of “intuitive models” and concern with systematic construction and proof, only the latter is discernible in Quine, for whom the syntactic aspect is the subject’ (588-9, n. 56).
152 Quine, W.V. Selected Logical Papers (New York: Random House 1966), 27Google Scholar
153 Theories and Things, 10
154 Selected Logical Papers, 49; quoted by Ullian (585). Here Wang is unregenerate. ‘True,’ he says, ‘Quine still emphasizes the “real” advantages of [NF’s and ML’s] “convenience and elegance.” But this is a debatable point in view of in view of the lack of an intuitive picture comparable to the iterative concept and the necessity to add ad hoc axioms and concepts to actually develop mathematics in them’ (639). Wang seems to miss Quine’s point. All theories, ninety-nine parts conceptualization, are inherently ad hoc!;
155 W. V. Quine, Review of Geach, ‘Subject and Predicate’ (138); quoted in Ullian at 585.
156 Set Theory and its Logic, 329; emphasis added.
157 Portions of earlier drafts of this paper were exposed to the watchful scrutiny of helpful colleagues at the University of Amsterdam, the University of Groningen and the University of Lethbridge. My thanks are due to E.M. Barth, Jeanne Peijnenburg, Frans H. van Eemeren, Rob Grootendorst, Ronald Yoshida, Brent Hudak and Bryson Brown. Later versions have benefited from advice from Jonathan Bennett, Roger Gibson, J.J. Macintosh, Cheryl Misak, Graham Priest, W.M. Scheltens, Richard Sylvan, and Joseph Ullian, to whom all my thanks.