Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/175

Rh  Frege says that these expressions have the same meaning but different senses.

But what is essential about equation is that it is not necessary in order to show that both expressions, which are connected by the sign of equality, have the same meaning: for this can be perceived from the two expressions themselves.

And, that the propositions of mathematics can be proved means nothing else than that their correctness can be seen without our having to compare what they express with the facts as regards correctness.

The identity of the meaning of two expressions cannot be asserted. For in order to be able to assert anything about their meaning, I must know their meaning, and if I know their meaning, I know whether they mean the same or something different.

The equation characterizes only the standpoint from which I consider the two expressions, that is to say the standpoint of their equality of meaning.

To the question whether we need intuition for the solution of mathematical problems it must be answered that language itself here supplies the necessary intuition.

The process of calculation brings about just this intuition.

Calculation is not an experiment.

Mathematics is a method of logic.

The essential of mathematical method is working with equations. On this method depends the fact that every proposition of mathematics must be self-evident.

The method by which mathematics arrives at its equations is the method of substitution.

For equations express the substitutability of two expressions, and we proceed from a number Rh