|Intuitionism: A) intuitionism in mathematics assumes that the objects to be inspected, e.g. numbers are only constructed in the process of the investigation and are therefore not finished objects, which are discovered. This has an effect on the double negation and the sentence of the excluded middle.|
B) Intuitionism of ethics assumes that moral principles are fixed and are immediately (or intuitively) knowable.
_____________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
Intuitionism/formalism/d'Abro: The intuitionist is a rigorist, insofar as he considers definitions and proofs accepted by the formalist to be inadequate. It should be admitted that they are not given by logic, but by intuition.
E.g. Zermelo's (formalist) proof that the continuum is an ordered set. I.e., that the points can be placed one after the other, with a successor for each point.
PoincaréVsZermelo: he invented a typical argument: the pragmatist rejected Zermelo's proof because it would take too much time to carry it out, and the number of operations to be performed would be even greater than Aleph zero, it cannot be expressed with a finite number of words. The pragmatist will conclude that the theorem is pointless.
Groups: Formalists: Cantor, Hilbert, Zermelo, Russell - Intuitionists: Poincaré, Weyl
According to Weyl, the concept of the irrational number must either be abandoned, or thoroughly modified.
Brouwer: when dealing with infinite quantities, the sentence of the excluded middle does not apply.
The intuitionists assert with Poincaré that antinomies without any infinity 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.