6.232 Frege says that the two expressions have the same meaning but
different senses. But the essential point about an equation is that it is
not necessary in order to show that the two expressions connected by the
sign of equality have the same meaning, since this can be seen from the two
expressions themselves.
6.2321 And the possibility of proving the propositions of mathematics means
simply that their correctness can be perceived without its being necessary
that what they express should itself be compared with the facts in order to
determine its correctness.
6.2322 It is impossible to assert the identity of meaning of two
expressions. For in order to be able to assert anything about their
meaning, I must know their meaning, and I cannot know their meaning without
knowing whether what they mean is the same or different.
6.2323 An equation merely marks the point of view from which I consider the
two expressions: it marks their equivalence in meaning.
6.233 The question whether intuition is needed for the solution of
mathematical problems must be given the answer that in this case language
itself provides the necessary intuition.
6.2331 The process of calculating serves to bring about that intuition.
Calculation is not an experiment.
6.234 Mathematics is a method of logic.
6.2341 It is the essential characteristic of mathematical method that it
employs equations.
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