Philosophy Dictionary of ArgumentsHome
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| Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic._____________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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Paul Lorenzen on Excluded Middle - Dictionary of Arguments
Berka I 271 Sentence of the excluded middle/Dialogical Logic/intuitionistic/logical constants/Lorenzen: If the particle is given its dialogical meaning also in the meta-language, then one can no longer generally prove the only classical valid A v i A. >Dialogical logic, >Provability, >Metalanguage, >Logical particles, >Intuitionism. Solution/Gentzen: one considers the sequences with additional infinite rules: (n)A > B(n) v C > A > (x)B(x) v C (n)A u B(n) > C > A u (Ex)B(x) > C which are allowed for derivation. Axiom: all sequences are allowed as axioms A u p > q v B for false or true constant prime formulas p or q. >G. Gentzen. LorenzenVsRecursiveness/LorenzenVsFormalism: this is no longer a formalism in the sense of a definition of a recursive enumeration, but a "semi-formalism" (concept by Schütte). >Recursion, >Recursivity. Trivially, this is consistent. Any formula that can be derived from Peano's arithmetic is it also here. >Consistency. This is a "constructive" consistency proof, if the dialogical procedure is recognized as constructive. >Constructivism. I 272 Infinity/premisses/dialogical logic/Lorenzen: one can state a step number l < e0 to each formula that can be derived in the Peano formalism with the following: e0 = ω to the power of ω to the power of ω to the power of ... P can thus first calculate an ordinal number e >Recursion. The statements that are used in the consistency proof are generally not recursive.(1) 1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200_____________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. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Lorenzen
> Counter arguments in relation to Excluded Middle
Ed. Martin Schulz, access date 2024-04-28