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The Philosophy of Gottlob Frege: Concepts and Functions
The Intersection of Logic and Mathematics in His 1891 Lecture
Introduction
According to , in a letter to (1629–1695), before the concept of “functions” it was
(…) often difficult to analyze the properties of a figure by calculation, and still more difficult to find very convenient geometrical demonstrations and constructions, even when the algebraic calculation is completed.
But this new characteristic (functions), which follows the visual figures, cannot fail to give the solution, the construction, and the geometric demonstration all at the same time, and in a natural way and in one analysis, that is, through determined procedure. (Leibniz, 1989, p. 250)
Through this new kind of construction, it would be possible to relate arithmetic expressions and geometric figures on a Cartesian plane without the need to draw these figures.
For example, a growing rectangle could be represented by a function ‘y = f(x)’. When expressed on the Cartesian plane, it might appear like this:
