Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


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Theses I
Theses II

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I 131
Abstraction/Mathematics/Frege/Thiel: Abstraction is a purely logical process, an operating with statements whose logical character is revealed by the change from the structure of the complicated initial statement to the structure of the new statement.
>Abstraction, >Structures.
Frege was the first to understand this. Statements not only about numbers, but also about quantities, functions, concepts, state of affairs, meaning and truth value of a statement, about structures.
I 133
Numbers/Numerals/Number Names/Names/Mathematics/Thiel: The philosophical point of the transition from general statements about numerals to arithmetical statements lies in the fact that, although we have introduced speech about numerals in addition to speech about numbers, we have introduced speech about numbers as a way of speaking, as a facon de parler, the possibility of which does not depend on there being abstract objects beyond the concrete numerals, which we call "numbers".
>Numbers, >Mathematical entities.
I 134
We also had no reason to regard the numerals as "names" of numbers, so that about 4, IV, and |||| would denote the same number Four, as probably assumed in the traditional philosophy of numbers.

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