Tractatus Logico-Philosophicus by Ludwig Wittgenstein
page 61 of 101 (60%)
page 61 of 101 (60%)
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5.32 All truth-functions are results of successive applications to elementary propositions of a finite number of truth-operations. 5.4 At this point it becomes manifest that there are no 'logical objects' or 'logical constants' (in Frege's and Russell's sense). 5.41 The reason is that the results of truth-operations on truth-functions are always identical whenever they are one and the same truth-function of elementary propositions. 5.42 It is self-evident that C, z, etc. are not relations in the sense in which right and left etc. are relations. The interdefinability of Frege's and Russell's 'primitive signs' of logic is enough to show that they are not primitive signs, still less signs for relations. And it is obvious that the 'z' defined by means of 'P' and 'C' is identical with the one that figures with 'P' in the definition of 'C'; and that the second 'C' is identical with the first one; and so on. 5.43 Even at first sight it seems scarcely credible that there should follow from one fact p infinitely many others , namely PPp, PPPPp, etc. And it is no less remarkable that the infinite number of propositions of logic (mathematics) follow from half a dozen 'primitive propositions'. But in fact all the propositions of logic say the same thing, to wit nothing. |
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