Philosophy Lexicon of Arguments

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Rules, philosophy: rules are restrictions of a domain of possibilities for subjects, communities or functionaries, or generally for acting individuals or groups. Rules may be implicit or explicit, and may be implemented by ordinance or by jointly developing equally authorized participants, e.g. in a discourse. In another sense, rules can be understood as actual regularities that can be discovered by observation. These rules can be discovered not only in action, but also in the nature of objects such as linguistic structures. See also norms, values, rule following, private language, language rules, discourse, ethics, morality, cognitivism, intuitionism, society, practice.

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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Friedrich Waismann Suchen und Finden in der Mathematik 1938 in Kursbuch 8 Mathematik 1967

Rules/Sense/System/Method/Calculus/Waismann: e.g. suppose, in an arithmetic in which only the multiplication is known, one can ask "Is this number decomposed?", that is, have we carried out a multiplication in which it emerged as a product? On the other hand, we cannot ask: "Is it decomposable?"
The other question must be answered only when we go over to the next calculus of the division.
But even here it is not really meaningful to speak of a possibility, but of a rule. To say, we cannot disassemble the number, makes the wrong impression, we would try and then encounter an obstacle.
In reality, we are expanding our system and are not seeing new possibilities, but have new rules.
If one wants, one can continue to search with a circle and a ruler, which is not wrong in itself and is not forbidden by the proof.
It just does not mean anymore what it used to mean.

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.

Wa I
F. Waismann
Einführung in das mathematische Denken Darmstadt 1996

F. Waismann
Logik, Sprache, Philosophie Stuttgart 1976

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Ed. Martin Schulz, access date 2017-10-20