The Analytic Tradition in Philosophy, Volume 1 by Soames Scott

Author:Soames, Scott
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2014-08-10T16:00:00+00:00

Here the notion “C (x) is always true” is taken as ultimate and indefinable, and the others are defined by means of it. Everything, nothing, and something, are not assumed to have any meaning in isolation, but a meaning is assigned to every proposition in which they occur. This is the principle of the theory of denoting I wish to advocate: that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expressing they occur has a meaning.3

According to Russell, ⌈Everything is F⌉ expresses the proposition that predicates the property being always true of the propositional function for which the formula ⌈x is F⌉ stands. In the above passage, as well as in much of the rest of “On Denoting,” he uses the word ‘proposition’ very loosely, sometimes when speaking of sentences, and sometimes when he has their meanings—propositions proper—in mind. A similar looseness accompanies his use of ‘propositional function’ for a formula, or for its meaning. Since, at this stage of his career, Russell was still a believer in fully fledged propositions, I will reconstruct his remarks in those terms. At this stage, he was still a realist of sorts about propositional functions as well—which I will continue to characterize as genuine functions taking entities as arguments and assigning propositions containing those entities as values.4 So understood, ⌈Everything is F⌉ expresses the proposition that pF is always true—e.g., when F = ‘human’, (i) pF is the function that assigns to any object o the proposition that o is human, and (ii) pF is always true iff it assigns a true proposition as value to every object o as argument (e.g., for every object o, the proposition that o is human is true). Similarly, ⌈Nothing is F⌉ and ⌈Something is F⌉ mean, (something equivalent to) respectively, that pF is never true, and pF is sometimes true.

At this point a serious foundational issue must be faced. Although it is, of course, taken for granted that a propositional function that is always true is one that assigns a true proposition to every object, Russell does not take this to be a definition of that notion. Rather, he takes the property of being always true to be primitive. From his perspective, it is the quantifier ‘every’ that is defined in terms of the unexplicated and antecedently understood notion of a propositional function being always true. In this way he avoids the problem we had (in section 1 of chapter 2) in making sense of Frege’s analysis of quantification as the predication of a higher-order concept (expressed by the quantifier) of a lower-order concept (expressed by the grammatical predicate). Our problem came from using the very quantifier being analyzed to explain the higher-order concept it expressed—thereby generating the need for still further analysis in terms of a yet higher-order concept. In the end, we were left with an unending hierarchy of logically equivalent, but structurally different, propositions each with an equal claim on being “the proposition expressed by the original sentence.

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