Reply to D. A. Martin W. V. Quine The Journal of Philosophy, Vol. 67, No. 8. (Apr. 23, 1970), pp. 247-248. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819700423%2967%3A8%3C247%3ARTDAM%3E2.0.CO%3B2-N The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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e47
COMMENTS AND CRITICISM
ments about their properties need not be construed as presupposing Platonism or else reduced to statements about things. Of course, the philosopher may refuse to accept our untidy ordinary language, which makes constant use of four different ontologies. H e may, rather, adopt an ideal language, trying to use everywhere the ontology he favors most. I n principle there is nothing wrong with this strategy, as long as the philosopher who adopts it realizes that the English phrases he "analyses" into the ontological framework of his choice can also be differently construed. That is, he should remember that the resolutions he offers for such philosophical puzzles can be matched by (at least three) other solutions, which, given the whole ontology they presuppose, can handle those problems equally well. EDDY M. ZEMACH
State University of New York at Stony Brook
COMMENTS AND CRITICISM REPLY TO D. A. MARTIN
I
N Donald A. Martin's review*' of my Set Theory and Its Logic there are some wrong or questionable statements which, because of their authoritative tone and because of the mathematical nature of their subject matter, could easily pass unquestioned. I t is this danger that prompts me to break, for once, my habit of not answering reviews (a habit which is shared, I understand, by the Journal of Philosophy). An example is this: Quine adopts the axiom of replacement applied to (von Neumann) ordinals. In the presence of the axiom of choice, this is equivalent to the axiom of replacement (111).
Presumably Martin's reasoning is that the axiom of choice implies the numeration theorem, and the numeration theorem together with my axiom schema of ordinal replacement gives the general axiom schema of replacement. But what he overlooks is that you can get the numeration theorem from the axiom of choice only with the help of various comprehension premisses which are not implied by my axioms. T h e comprehension premisses that I invoked for my own proof of the numeration theorem (p. 226) were quite substantial. l o I wish to thank my friend Eric Walther for the many helpful comments he made on an earlier version of this paper. This JOURNAL, LXVII, 4 (Feb. 26, 1970): 111-114.
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THE JOURNAL OF PHILOSOPHY
Martin stresses that my main system is not neutral in the sense of being compatible with all or most of the systems surveyed in the last part of my book. I made this point too, in various places-e.g. in pp. 50f, in treating of my exclusion of ultimate classes. Reading Martin, however, one tends to forget how weak my main system is. It yields no infinite classes, nor even the power-set axiom. Let it not be supposed, moreover, that systems are easily weakened by just conditionalizing the desired theorems with the missing axioms as antecedents. I t is in the missing axiom schemata that the rub comes. This is why I gained so much simplification when in the revised edition I let down the bars to the axiom schema of ordinal replacement (23.12). When Martin writes that Quine cites only very minor applications of Fundierung . . . and then makes the absurd statement that there is no a priori reason for this fundamental axiom to be adopted (113)
he is basing his estimate of absurdity on a difference of opinion over what to regard as natural or intuitive in the matter of class existence. This difference of opinion is a main theme in his review. Elsewhere in his review Martin brands one and another technical formulation as erroneous. But these allegations are strictly ex cathedra, giving us readers little to go 0n.l W. V. QUINE
Harvard University
BOOK REVIEWS Wissenschaftliche Erklurung und Begrundung. WOLFGANG STEGYork: Springer-Verlag, 1969. xxvii, 812 p. M ~ ~ L L E RBerlin-Heidelberg-New .
I n this superbly lucid, admirably complete, and thoroughly workedout book the author deals in elaborate detail with practically all the important issues that have been under discussion (particularly in 1 Let me touch incidentally on a less substantive point: Martin's complaint of my copious use of symbolic logic. Some of us are helped by the semi-mechanical character of a rather explicit proof, and these were my intended readers. Others will be warned off by the formulas on the dust jacket. But I am puzzled when he says I use "a very large collection of very small symbols." I was conservative in my choice of notations and, I thought, sparing in the multiplication of them. Moreover I detect no tendency toward smaller than usual sizes. Unfortunately some of the pages in the revised edition came through faint because of bad printing; I wonder if this is the trouble.
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[Footnotes] *
Review: [Untitled] Reviewed Work(s): Set Theory and Its Logic by Willard van Orman Quine Donald A. Martin The Journal of Philosophy, Vol. 67, No. 4. (Feb. 26, 1970), pp. 111-114. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819700226%2967%3A4%3C111%3ASTAIL%3E2.0.CO%3B2-M
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