# Psychology Dictionary of Arguments

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Addition: elementary arithmetic, which is usually characterized by associativity and commutativity and a neutral zero element.
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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 Concept Summary/Quotes Sources

David Hilbert on Addition - Dictionary of Arguments

Berka I 122
Addition/disjunction/union/Hilbert: the addition of the numbers can be traced back to the disjunction of predicates. If F and G are incompatible predicates, and if the number m is assigned to the predicate F, and number n to G, the predicate F v G corresponds to the number m + n.
I 122
Extended function calculus: with the extended function calculus, 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)

>Natural deduction
, >G. Gentzen, >Derivation, >Derivability, >Axioms, >Axiom systems,
>Calculus, >Logic.

1. D. Hilbert & W. Ackermann: Grundzüge der Theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, §§ 1,2.

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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. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

> Counter arguments against Hilbert
> Counter arguments in relation to Addition