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Introduction
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.
An equation merely marks the point of view from which I consider
the two expressions: it marks their equivalence in meaning.
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.
We do not have an a priori belief in a law of conservation, but
rather a priori knowledge of the possibility of a logical
form.
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Logic
meaning, I must know their meaning, and I cannot know their meaning
without knowing whether what they mean is the same or
different.
An equation merely marks the point of view from which I consider
the two expressions: it marks their equivalence in meaning.
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.
We do not have an a priori belief in a law of conservation, but
rather a priori knowledge of the possibility of a logical
form.