From Lagrange to Frege: Functions and Expressions

When one is concerned with specifying the original reference [Bedeutung ] of the word ‘function’ in its mathematical usage, it is easy to fall into calling function of x an expression [Ausdruck ] formed from ‘x’ and particular numbers by means of the notations [Bezeichnungen] for sum, product, power, difference, and so on. This is inappropriate [unzutreffend ] because in this way a function is depicted [hingestellt ] as an expression—that is, as a concatenation of signs [Verbindung von Zeichen]—not as what is designated [Bezeichnete] thereby. Hence, instead of ‘expression’, one should say ‘reference of an expression’.