## Philosophy Lexicon of Arguments | |||

Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic. | |||

Author | Item | Excerpt | Meta data |
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Lorenzen, Paul Books on Amazon |
Excluded Middle | P. Lorenzen Ein dialogisches Konstruktivitätskriterium (1959) in Karel Berka/L. Kreiser Logik Texte Berlin, 1983 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. 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. 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). Trivially, this is consistent. Any formula that can be derived from Peano's arithmetic is it also here. This is a "constructive" consistency proof, if the dialogical procedure is recognized as constructive. --- 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 = w to the power of w to the power of w to the power of ... P can thus first calculate an ordinal number e The statements that are used in the consistency proof are generally not recursive. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Brk I K. Berka/L. Kreiser Logik Texte Berlin 1983 |

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Ed. Martin Schulz, access date 2017-03-28