A Note on 'About' Nicholas Rescher Mind, New Series, Vol. 72, No. 286. (Apr., 1963), pp. 268-270. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28196304%292%3A72%3A286%3C268%3AANO%27%3E2.0.CO%3B2-0 Mind is currently published by Oxford University Press.
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http://www.jstor.org Tue Jul 31 23:43:21 2007
A NOTE ON ' ABOUT '
INa recent study (" About ", MIND, vol. 70, 1961, pp. 1-24) Professor Nelson Goodman discusses the interesting logical question of " giving any general rule for deciding whether a given statement is or is not about a given thing ". . The prima facie plausible criterion : (C) A statement S is about the individual k if an expression designating k occurs in S. will obviously not serve. For one thing, a sentence may be about an individual without mentioning him (as "All 19th century U.S. presidents are males " is about Abraham Lincoln). For another, a sentence may mention an individual without being ' about ' him in any informative sense (as " Today is Tuesday and either Abraham Lincoln is a male or he is not " yields no information about Abraham Lincoln over and above that afforded by its truncated counterpart, " Today is Tuesday "). The criterion (C) is thus a t once too wide and too narrow, and must be dismissed. After consideration of difficulties of this nature affecting other criteria cognate to (C), Goodman puts forward a proposal of his own. The burden of the present note is to observe that Goodman's own proposal is subject to a defect of the type which invalidates the various other possible criteria examined by him. Goodman proposes to say that the statement S is ' absolutely about ' the individual k if there exists a statement T satisfying the following three conditions : (i) T contains an expression designating k ; (ii) T follows logically from S ; and (iii) The (universal)generalization of T with respect to the expression designating k (or with respect to any part of this expression) does
not follow logically from S. The shortcoming which this criterion exhibits is this : that given this criterion, we arrive a t the unacceptable consequence that any statement predicating any property r j to any individual a is absolutely about all individuals whatsoever. To show this, we shall make use of the assumption-not usual in logical studies, but certainly justified in the present context of inquiry-that the universe of discourse involved in our discussions contains more than one individual. (The customary procedure in logic is merely to assume a universe of at least one individual.) This assumption of a universe of a t least two members suffices to warrant the following rule of inference : (R) Given F(k), we may infer (3x) [(x # k*) & F(x)], where F is any
predicate, k any individual, and k* any individual different from k. We can now readily show that a statement predicating any property 4 to any individual a is (in Goodman's sense) absolutely
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about any other individual (say b). B'or consider the pair of statements : (8,) 4 a (TI) (3x)[(x f b) 38. 4x1 Observe the following : (i) TI contains an expression aesignating b ; (ii) T, follows logically from S, (in consequence of our rule (R)); (iii) The universal generalization of T, with respect to ' b ', namely, (Y) (34 [(x + Y) %' 4 XI
does not follow logically from S,, for if this did follow, then ' 4 a ' would entail ' (ax) [(x # a) & 4 x] ', which is patently not the case. 'Thus the statement predicating the property 4 to the individual a is also, on Goodman's criterion, ' absolutely about ' the individual b, or any other individual c, d, etc., rnutatis rnutandis. We have thus shown that Goodman's sense of ' (absolute) aboutness' as governed by the set of criteria laid down by him leads to the unacceptable consequence any statement of predication is ' about ' any individual whatsoever. It would seem that the only avenue of escape from this conclusion is to reject the rule of inference (R) on which step (ii) of the foregoing argument is based. But this extrication hardly seems available in the present context of discussion. Clearly any discussion of problems of aboutness is entirely trivial in a universe of population one. A theoretical logician, to be sure, may protest against the restrictiveness of assuming a universe of membership greater than one, but a philosopher concerned to analyze the logic of 'about' can hardly associate himself with this protest. He can scarcely object that rules of logic based upon assuming a universe of a t least two individuals force him to make an unacceptable sacrifice in the generality of his discussion. It does appear, however, that a simple and minor modification of the criteria proposed by Goodman suffices to overcome the particular difficulty noted above. For this difficulty is removed by modifying criterion (iii) to : (iii*) The restrictedly universal generalization of T with respect to the expression designating k, universal excepting k itself . . . does not follow logically from S. Note that now, instead of having to deal with the generalization with respect to ' b ' of (1) (3x)[(x Z b) & 4 XI, namely, (2) (y)(qx)[(x Z Y) & 4 XI, which does not follow from ' 4 a ', we have to deal only with a restricted generalization of (I), namely, (3) (Y)[YZ a 3 (3x)(IIx Z y l & 4 4 1
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N. RESCHER
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A NOTE ON
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which does follow from ' 4 a '. Consequently the modification of Goodman's (iii) to (iii*) does indeed overcome the point of difficulty we have noted above. Needless to say, there is no guarantee that this revised criterion is immune against other possible shortcomings. It appears that the problem of clarifying the notion of aboutness, whose difficulties Professor Goodman has justly stressed, stands in need of further inquiry, and is not to be laid to rest by even so subtle and intricate a set of considerations as those proposed by him.
University of Pittsburgh
NICHOLAS R ESCHER
