If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes… - Gottlob Frege

If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root.

Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number-word occurs.

Equality gives rise to challenging questions which are not altogether easy to answer... a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.