Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/129

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(Thus in the "Principia Mathematica" of Russell and Whitehead there occur definitions and primitive propositions in words. Why suddenly words here? This would need a justification. There was none, and can be none for the process is actually not allowed.)

But if the introduction of a new expedient has proved necessary in one place, we must immediately ask: Where is this expedient always to be used? Its position in logic must be made clear.

5.453 All numbers in logic must be capable of justification.

Or rather it must become plain that there are no numbers in logic.

There are no pre-eminent numbers.

5.454 In logic there is no side by side, there can be no classification.

In logic there cannot be a more general and a more special.

5.4541 The solution of logical problems must be neat for they set the standard of neatness.

Men have always thought that there must be a sphere of questions whose answers—a priori—are symmetrical and united into a closed regular structure.

A sphere in which the proposition, simplex sigillum veri, is valid.

5.46 When we have rightly introduced the logical signs, the sense of all their combinations has been already introduced with them: therefore not only "pvq" butalso "~(pv~q)", etc. etc. We should then already have introduced the effect of all possible combinations of brackets ; and it would then have become clear that the proper general

primitive signs are not "pvq", "", etc.,