|Addition: elementary arithmetic, which is usually characterized by associativity and commutativity and a neutral zero element._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
The fact that systems with categorically different objects have the same structure does not seem more surprising than the occurrence of structural similarities between areas of categorically different objects.
Thiel I 312
In modern mathematics one speaks not only of "the" addition, but of "an addition" and introduces linking signs. For example, one writes addition as "$" if it is associative and commutative, if it is not the case, one might prefer to write the operation as multiplication "§" or something else.
Ontology/object/mathematics/Thiel: the validity of such laws does not turn the subject area into a number area, just as the validity of any set-theoretical laws transforms the (ranges of) numbers into (ranges of) sets.
The registration of the possible types of operations does not provide any fundamental discipline._____________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