[FOM] Mathematical explanation

[Gernot Salzer]

> Afterthought: in the Frege quote
> 	,,Die Summe von zwei Anzahlen ist durch diese bestimmt",
>         in diesem Ausdrucke ist der Gedanke des Satzes unserer
>         Haupt"uberschrift am leichtesten zu erkennen ...
> the word "diese" is probably feminine singular, in agreement with
> "...schrift", and the referent of "Haupt"uberschrift" is to the whole
> statement of (what is subsequently proved as) theorem 469, not just to its
> consequent consisting of the numerical identity at its top line.

Without knowing what comes before and after this quotation,
I'm completely convinced as a native speaker of German that "diese"
refers to "Anzahlen", i.e., the sentence has to be read as
,,Die Summe von zwei Anzahlen ist durch diese [zwei Anzahlen] bestimmt".
This is further supported by the fact that the sentence itself
is quoted: letting "diese" refer to something outside the quoted sentence
(meant as stand-alone phrase), in particular to something _following_
the sentence, would be a more than unusual, in fact improper, usage of
the German language. So an acceptable translation to English is
"The sum of two numbers is determined by them", but
"The sum of two numbers is determined by this" is not.

Gernot Salzer