|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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|A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967
The sentence of the excluded middle/VsBrouwer: the sentence of the excluded middle speaks for the fact that the antinomies occur not only in connection with infinite quantities.
E.g. Liar Paradox. Here, too, the principle of the logically excluded middle did not seem to apply.
E.g. Russell's barber's paradox, with the barber shaving everyone in town except those who shave themselves. Here, too, the sentence of the excluded middle does not apply without infinite quantities.
The intuitionists assert with Poincaré that antinomies without any infinities are lopish.
Poincaré: The antinomies of certain logicians are simply circular._____________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.