"Representation"/numbers/numerals/mathematics/Thiel: in our sense a fictional relation to abstraction is the sense that we formulate arithmetic statements like statements about new objects, the numbers, and give these fictional proper names the form "The number n" (with a numeral "n"). "n" (counting sign) and the fictitious object (the number n) then stand in a fictional relation to each other.
The abstraction step is carried out only for those properties which are assigned to each digit (Def I 129) equivalent to the number mentioned. Thus, only such properties are said by the new objects, the numbers.
a) If there is no such property, e and e' are only apparently different. The proper names actually denote the same object.
b) However, we must distinguish this equality from the previously used construction equality, which refers directly to the construction rules. (WaismannVs)._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Philosophie und Mathematik Darmstadt 1995