|Constructivism, philosophy: the thesis that the objects of the external world, together with their properties and relations are constructed by the brain to other objects and their relations to us. Constructivist styles are differently strong in their assumptions about the existence and recognizability of an objective, independent reality. See also Autopoiesis, system theory, Luhmann, Maturana._____________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
Construction/Search/Mathematics/Waismann: e.g. false analogy: we are looking for a man with black hair and this and this appearance. In the case of the man, it would be possible to complete the description more and more without leading to a finding of such a man. I would not have the man yet.
In the construction it is so: as long as the construction is not completely described, I cannot be sure if what I am looking for is logically correct, so can be described at all.
The imperfect description leaves out just what would be necessary for something to be sought. It is therefore only an apparant description of the desired.
E.g. Proof of the Goldbach theorem. P. 76. e.g. the proof of induction has been rediscovered and not just a combination of simpler conclusions.
To what extent is the search contained in the process of searching?
E.g. North Pole: someone shows a point on the plan, which is the specification of the target.
E.g. When searching the pentagon with a circle and a ruler, the question is: does the term allow for the search or not?
In the case of mathematics the specification of the construction does not allow the search! We can even think of two different terms of construction (a layman concept of the student and a mathematical one).
The space is, in reality, only the one that contains what is sought._____________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.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976