Philosophy Dictionary of ArgumentsHome
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Kurt Gödel on Universal Validity - Dictionary of Arguments
Berka I 314 Universal Validity/Goedel: universal validity leads to universal quantification: for formulas with free individual variables A(x,y,...w) this means the general validity of (x)(y)...(w) A(x,y,...w). >Universal quantification, >Quantification, >Existential quantification. Def Satisfiability/Goedel: "satisfiability" leads to >existence quantification. ((s)"there is a model".) This is then correspondingly the fulfillability of (Ex)(Ey)...(Ew) A. Then one can say: "A is universally valid" means: "~A is not fulfillable". >Satisfaction, >Satisfiability.Refutability: refutability is the provability of negation. >Negation, >Proofs, >Provability. I 310 Provability/universal validity/Goedel:... here we have proved the equivalence between "universally valid" and "provable". Over-countable/Goedel: N.B.: this equivalence contains a reduction of the over-countable to the countable for the decision problem because "generally valid" refers to the over-countable totality of the functions, while "provable" presupposes only the countable totality of the proof figures.(1) >Decision problem, >Countability, >Overcountable. 1. K. Gödel: Die Vollständighkeit der Axiome des logischen Funktionenkalküls, in: Mh, Math. Phys. 37 (1930), pp. 349-360._____________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. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Gödel
> Counter arguments in relation to Universal Validity
Ed. Martin Schulz, access date 2024-04-27