Philosophy Dictionary of ArgumentsHome
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| Derivability: this is about the question which statements can be obtained according to the rules of a calculus. In logic, derivability refers to the ability to prove a statement from a set of premises using the rules of inference of a given logical system. A statement is said to be derivable if there is a proof of it in the system._____________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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David Hilbert on Derivability - Dictionary of Arguments
Thiel I 97 Derivability/Hilbert/Thiel: the methods used for the proof of the non-derivability of a formula from others by means of given derivation rules have been given for the first time by Bernays in the Hilbert school. They were first published by Bernays in his postdoctoral thesis on the proof of the independence of axiom systems of classical propositional logic. Neither of these axioms is to be derived from the others. Classic: ~~p > p effective: p > ~~p I 102 Axiomatic derivations of logical sentences were unrivaled up to the twenties in this form, then alternative procedure calculus of the "natural concluding" were developed, whose rule usually bring exactly one logical symbol into a conclusion chain or eliminate. The actual kind of mathematical approach is closer than the axiomatic approach. >Natural deduction, >G. Gentzen, >Derivation, >Axioms, >Axiom systems, >Calculus, >Logic._____________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. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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> Counter arguments against Hilbert
> Counter arguments in relation to Derivability
Ed. Martin Schulz, access date 2024-04-18