## Philosophy Dictionary of ArgumentsHome | |||

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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._____________ 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 |
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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. _____________ 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 |

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