by Corry Shores
[Frege, Begriffsschrift, Chapter 1, Entry Directory]
[The following is summary. Bracketed commentary is my own. Please forgive my typos, as proofreading is incomplete.]
We express an indeterminate function of argument A as: Φ(A) and with the judgment stroke as
In order to express an indeterminate function of the argument A, we put A in brackets after a letter, as inΦ(A)SimilarlyΨ(A,B)means a function (not further determined) of the two arguments A and B. Here the places of A and B within the brackets represent the places occupied by A and B in the function (whether A and B each occupy one place in it or more). Accordingly in generalΨ(A,B) and Ψ(B,A)are different.(Frege 15)
Indeterminate functions of several arguments are expressed similarly.
may be read as ‘A has the property Φ’.
may be read as ‘B stands in the Ψ-relation to A’ or as ‘B is a result of applying the operation Ψ to the object A.’
[The next point I do not understand. Let me quote it
In the expressionΦ(A)p. 19] the symbol Φ occurs in one place; and we may imagine it replaced by other symbols Ψ, Χ, so as to express different functions of the argument A; we may thus regard Φ(A) as a function of the argument Φ. This makes it specially clear that the concept of function in Analysis, which in general I have followed, is far more restricted than the one developed here.(15)