On Not Learning to Quantify W. V. Quine The Journal of Philosophy, Vol. 76, No. 8. (Aug., 1979), pp. 429-430. Stable URL: http://links.jstor.org/sici?sici=0022-362X%28197908%2976%3A8%3C429%3AONLTQ%3E2.0.CO%3B2-8 The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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ON NOT LEARNING T O Q U A N l I F Y
429
What its semantics are, thus freed of the pretence that it is how we say (3) in the vernacular, is the subject of another paper. THOMAS J. RICHARDS
LaTrobe University
ON N O T LE'4RNING T O QUANTIFY
N T h e Roots of Reference" I ventured a speculative reconstruction of steps that might plausibly lead a child of our culture to a mastery of our apparatus of reference. I have hoped to see other minds drawn into this speculation and even to see it rendered less speculative by empirical admixtures. So I am glad of Thomas J. Richards' sympathetic interest in the venture.+ I agree with him on his substantive points. Where he is off the mark is in his estimate of our disagreement. His crucial mistake occurs simultaneously with his first formula (421), where he writes: Quine holds that absolute objectual quantification (I) (x)Fx
is learned (98) as a n abbreviation of
(x) (if not Fx then Fx)
(2) (I follow Quine's notation t o the letter.)
I-Iis reference to page 98 is to T h e Roots of Reference, and he does indeed follow my notation to the letter, but he follows my text less assiduously. For my very next sentence was this: These derivations are artificial, but their existence suffices to dull one's interest i n what the actual learning process may have been.
So I did not think that (1) was thus learned. Richards marshals a substantial argument to show that it was not. My own reason for not thinking so was just that it would be so absurdly unrealistic. I was not interested in how people learn our actual quantifiers. Few do, statistically speaking. Truly unrestricted quantification is rare outside logic. Idiomatic uses of 'everything', as in 'Everything seemed to go wrong today', are categoricals with a tacit first term; thus 'Everything that I undertook today seemed to go wrong'.
" La Salle, 111.: Open
t "How
Court, 1974. Quine Didn't Learn to Quantify," this JOURNAL, this issue, 421-429.
0022-362X/79/7608/0429.$00.50
O 1979 The Journal of Philosophy, Inc.
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THE JOURNAL OF PHILOSOPHY
If we care to speculate on how people would most naturally progress to unrestricted quantification if they were to do so, Richards' proposal strikes me as the reasonable line. My own interest was merely in how the child might progress to an adequate apparatus of reference. I suggested steps whereby he might plausibly arrive at the construction: (3) Every thing x such that Gx is a thing x such that F x or a vernacular variant using nouns. So much for the child. his (3) is indeed an adequate show how w e can paraphrase quantification into that idiom. the form: (4)
ordinary relative clauses and proI t was only in order to show that apparatus that I then went on to our canonical general form (1) of (1) is equivalent to (2), which is of
(x)(if Gx then F x )
which is equivalent to (3). Such was the tacit rationale of pages 97 f. of T h e Roots of Reference, and I regret that it did not shine through-though surely the sentence quoted above from page 98 was forthright enough. At any rate the misunderstanding runs deeper than thus far indicated. Richards supposes also that I am representing the child as progressing from (3) directly to (4), and he is at pains to argue the implausibility of such a step, rightly enough, by contrasting the roles of the bound variables in (3) and (4). Actually I meant to leave the child content with (3), which does the work of (4). If the child were to progress to the actual (4), he would have to get there by an arduous route through (1); not vice versa. I n view of my unconcern over the learning of quantifiers, one may wonder at my concern, later in T h e Roots of Reference, over the learner's progress to high levels of set theory; for the achievement i n either case is rather the exception than the rule. T h e answer is that the latter case opens up new and irreducible domains of reference, whereas the former case involves only intertranslatable notations. W. V. QUINE
Harvard University
