By Richard Gaskin
This publication is a scientific and ancient exploration of the philosophical value of grammar. within the first 1/2 the 20 th century, and particularly within the writings of Frege, Husserl, Russell, Carnap and Wittgenstein, there has been sustained philosophical mirrored image at the nature of grammar, and at the relevance of grammar to metaphysics, common sense and technological know-how.
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Extra resources for Grammar in Early Twentieth-Century Philosophy (Routledge Studies in Twentieth Century Philosophy)
Since that which John said is true and that which Tom said is not true, then by (6), it cannot be that that which John said is the same thing as that which Tom said. Since each uttered the very same sentence, then on at least one of these two occasions, that which was said was not the sentence, and so on at least one of these two occasions, it was something other than the sentence that was said either to be true or to be false. This argument is commonly invoked by Propositionalists. 32 Richard Mendelsohn 1 1 1 11 11 Note that in each of the above arguments it was assumed that the property x was said to possess was the same property as the property y was said to lack.
3) confusedly connected the reference of the parts with the sense of the whole. Frege’s solution (1892a) was to reject (3), and to split it into two substitution principles, one for reference,4 0111 5111 The evening star = the evening star (4) If r(␣) = r(␤), then S␣ and S␣ /␤ have the same truth-value, and one for sense, (5) If e(␣) = e (␤), then S␣ and S␣ /␤ have the same cognitive value 30 1 Richard Mendelsohn (where e( ) abbreviates the sense expressed by ( ) ). In this essay, we will be dealing only with the development of the ﬁrst of these substitution principles, (4).
Functions But let us get back to Frege, who did not speak of properties and predicates, but rather of functions and function expressions. For any non-empty sets, S and S ′ (not necessarily distinct), a function f from S to S ′ correlates elements of S (the domain of f ) with elements of S ′ (the range of f ) in an orderly fashion. If x ∈ S, then f (x) ∈ S ′ and f(x) is the value of the function f for the argument x. We are justiﬁed in speaking of the value of the function for a given argument because of the fundamental property of functions: for any x, y in the domain of f , 34 1 1 1 11 Richard Mendelsohn (16) If x = y, then f (x) = f (y).