Philosophy Dictionary of Arguments

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Basic Concept: theories differ in what terms they choose as the basic concepts, which are not further defined. A definition of these concepts within the theory would be circular and may cause > paradoxes. E.g. The theory of mind by G. Ryle is based on the concept of disposition, other theories presuppose mental objects. See also paradoxes, theories, terms, definitions, definability, systems, explanations.
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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 Basic Concepts - Dictionary of Arguments

Berka I 59
Axioms/Logic/Berka: for methodological reasons, systems with at least two basic concepts are preferred (e.g. the pairs of functors N C, A N, or K N).
In general, one uses the one by Hilbert and Bernays (1934)(1) today, with five basic concepts. N.B.: because of the 5 basic concepts it works without definitions.

I. Formulas of implication:

CpCqp - CCpCCpqCpq - CCpqCCqrCpr


II. Formulas of conjunction:

CKpqp - CKpqq - CCpqCCprCpKqr


III. Formulas of alternatives (disjunction):

CpApq - CqApq - CCprCCqrCApqr


IV. Formulas of equivalence:

CEpqCpq - CEpqCqp - CCpqCCqpEpq

I 60

V. Formulas of negation

CCpqCNqNp - CPNNp - CNNpp

>Systems (mathematics)
, >Implication, >Conjunction, >Disjunction,
>Equivalence, >Negation, >Definitions, >Definability.

1. D. Hilbert & P. Bernays: Grundlagen der Mathematik, Vol. 1. Berlin 1934, Julius Springer Verlag.

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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


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Ed. Martin Schulz, access date 2024-02-27
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