|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. |
|Berka I 122
Addition/disjunction/union/Hilbert: the addition of the numbers can be traced back to the disjunction of predicates. - Are F and G incompatible predicates, and is the the number m assigned to the predicate F, and number n to the G, so the predicate F v G corresponds to the number m + n ((s)> Association).
Extended function calculus: with these, numerical equations such as 1 + 1 = 2 become purely logical, provable sentences. E.g. 1 + 1 = 2, logical form:
(F)(G)([Unv (F,G) & 1(F) & 1(G)] > 2(F v G)).(1)
1. D. Hilbert und W. Ackermann, Grundzüge der theoretischen Logik, Berlin (6. Aufl. Berlin/Göttingen/Heidelberg 1972, §§ 1,2)_____________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.
Logik Texte Berlin 1983