Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/139

Thus in Russell's notation also it appears evident that "$q:p\lor \sim p$" says the same as "$q$"; that "$p\lor \sim p$" says nothing.

5.514 If a notation is fixed, there is in it a rule according to which all the propositions denying $p$ are constructed, a rule according to which all the propositions asserting $p$ are constructed, a rule according to which all the propositions asserting $p$ or $q$ are constructed, and so on. These rules are equivalent to the symbols and in them their sense is mirrored.

5.515 It must be recognized in our symbols that what is connected by "$\lor$", "$.$", etc., must be propositions.

And this is the case, for the symbols "$p$" and "$q$" presuppose "$\lor$", "$~$", etc. If the sign "$p$" in "$p\lor q$" does not stand for a complex sign, then by itself it cannot have sense; but then also the signs "$p\lor p$", "$p.p$" etc. which have the same sense as "$p$" have no sense. If, however, "$p\lor p$" has no sense, then also "$p\lor q$" can have no sense.

5.5151 Must the sign of the negative proposition be constructed by means of the sign of the positive? Why should one not be able to express the negative proposition by means of a negative fact? (Like: if "$a$" does not stand in a certain relation to "$b$", it could express that "$aRb$" is not the case.)

But here also the negative proposition is indirectly constructed with the positive.

The positive proposition must presuppose the existence of the negative proposition and conversely.

5.52 If the values of $\xi$ are the total values of a function $fx$ for all values of $x$, then $N{\bar {\xi }}=\sim (\exists x).fx$.

5.521 I separate the concept all from the truth-function.

Frege and Russell have introduced generality

in connexion with the logical product or the logical