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An Introduction To Non-aristotelian Systems And General Semantics.

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SUPPLEMENT II
THE THEORY OF TYPES1 by Paul Weiss*
It would seem from the interpretation that Whitehead and Russell put on the theory of types, that it is impossible or meaningless to state propositions which have an unrestricted possible range of values, or which, in any sense, are arguments to themselves. Thus on the acceptance of the principle that statements about all propositions are meaningless,2 it would be illegitimate to say, "all propositions are representable by symbols," "all propositions involve judgment," "all propositions are elementary or not elementary," and if no statement could be made about all the members of a set,3 it would be impossible to say, "all meanings are limited by a context," "all ideas are psychologically conditioned," "all significant assertions have grammatical structures," etc., all of which are intended to apply to themselves as well. The theory seems also to make ineffective a familiar form of refutation. General propositions are frequently denied because their enunciation or acknowledgment depends on the tacit supposition of the truth of a contradictory or contrary proposition. Such refutations assume that the general proposition should be capable of being an argument of the same type and to the same function as its own arguments, so that according to Whitehead and Russell, they fallaciously refute "by an argument which involves a vicious circle fallacy".4
That these limitations on the scope of assertions or on the validity of refutations are rarely heeded is apparent even from a cursory examination of philosophical writings since 1910. Thus Russell, apropos to Bergson's attempt to state a formula for the comic says,6 "it would seem to be impossible to find any such formula as M. Bergson seeks. Every formula treats what is living as if it were mechanical, and is therefore by his own rules a fitting object of laughter." The characterisation of all formulae, even though it refers to a totality, seems to Mr. Russell to be of the same type as the formulae characterised.
x Chap. II., Principia Mathematica.
*[Reprinted from Mind: a Quarterly Review of Psychology and Philosophy. Vol. XXXVII., N.S., No. 147; with minor corrections.]
*P. 37, ibid, (second edition).                'P. 37, ibid.                * P. 38, ibid.
' "Prof. Guide to Laughter," Cambridge Review, Vol. 32, 1912, and Jourdain's Philosophy of Mr. B*tr*nd R*ss*ll, pp. 86-7.
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