Philosophy Dictionary of Arguments

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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.

Author Item Summary Meta data
I 312
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.
I 312/313
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.

Chr. Thiel
Philosophie und Mathematik Darmstadt 1995

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Ed. Martin Schulz, access date 2019-07-23
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