[FOM] Mathematical explanation
neilt at mercutio.cohums.ohio-state.edu
Sat Oct 29 21:31:09 EDT 2005
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.
Even with that corrected grasp of how the German should be rendered, the
main points of my last posting stand. It is not the case that the word
"diese" has "Anzahlen" as a grammatical antecedent. So one should not
translate the German as
The sum of two numbers is determined by them.
A better translation would be
"The sum of two numbers is determined by this"---
the easiest way to recognize the thought behind the (formal)
sentence of our main heading [i.e., thm. 469] is by means of this
where "this" at its first occurrence is understood to be referring to the
formal sentence itself. And the referent of "this expression" is to the
expression within double quotes with which the indented passage begins.
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