Philosophy Lexicon of Arguments

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.
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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/Bernays (1934) 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

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.

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983

> Counter arguments against Hilbert

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Ed. Martin Schulz, access date 2017-06-26