A Note on the "Paradox of Analysis". Morton G. White Mind, New Series, Vol. 54, No. 213. (Jan., 1945), pp. 7172. Stable URL: http://links.jstor.org/sici?sici=00264423%28194501%292%3A54%3A213%3C71%3AANOT%22O%3E2.0.CO%3B2D Mind is currently published by Oxford University Press.
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[email protected] http://www.jstor.org Wed Jun 6 08:04:19 2007
A NOTE ON THE " PARADOX O F ANALYSIS
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PROF. MAX BLACKhas recently undertaken to show that there is no paradox of analysis even if analysis in Moore's sense is about concepts. One of the consequences of this paradox, stated by Prof. C. H. Langford 2, is that a sentence like : (1) The concept being rc brother is identical with the concept being a mule sibling. expresses the same proposition as : (2) The concept being a brother is identical with the concept being a brother. Prof. Moore believes that (1) is true but thinks i t does not express the same proposition as (2). Prof. Black tries t o show conclusively that (1) does not express the same proposition as (2). I n this note I want to show that the argument which Black offers for this view is mrong. It should be pointed out t h a t I confine myself here t o Black's argument, and that I a m not committing myself to any view on the synonymity of (1) and (2). Black argues that (1)may be regarded as expressing a relation B between the concepts brother, male, and sibling, the latter three terms abbreviated as " b ", " ))I, ", and " s " respectively. Thus (1) expresses the same proposition as : and (2) expresses the same proposition as :

where the doublebar symbolizes identity betweeEl concepts. Now, so far as I can see, Prof. Black concludes that (3) does not express the same proposition as (4) simply because the relation B is different from the relation of identity. It follows, he says, that (1) does not express the same proposition as (2),and t h a t the paradox of analysis dissolves. He says, in effect, that no plausible interpretation of being the same proposition would permit us to say that a n identity is the same proposition as one " i n which a nonidentical relation is a component ". It seems to me that Prof. Black has made an error. EIe appears to be arguing that no two sentences can express the same proposition if one expressly mentions a relation which is distinct from the relation expressly mentionpd by the other. As a counterexample consider the following. Using Prof. Black's example from arithmetic, 'MIND, no. 211, pp. 263267. .' The Notion of Analysis in Jloore's Philosophy," TZe Philosophy of G. E. Moore, pp. 319342.
suppose I choose to express the proposition that 21 = 3 x 7 by the sentence " 21 is thrice 7 ". It is obvious that the twotermed relation of being thrice is different from the threetermed relation that holds between 21, 3, and 7, nevertheless " 21 = 3 x 7 " expresses the same proposition as " 21 is thrice 7 ". And finally, let us construct a, translation of (1)which parallels the idiom in which " thrice " is used. Unfortunately there is no parallel idiom in standard English usage which can be applied to the brothermalesibling situation, but we can give a name to the relation which holds between one relation and another when the first is the second with its domain limited to males. Call this relation " C ". Then we may express (3) as follows : (5) C(b, s) It would not follow that (5) and (3) express different propositions, a false conclusion to which we are led by Prof. Black's principle. ,
The error in Black's argument is due to his failure to see that the synonymity of two sentences expressing relations depends not only on the relations expressed but also on the terms expressly said to be related.
NORTONG. WRITE.