|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 human with black hair and that and that appearance. In the case of the human, it would be possible to complete the description more and more without being able to find one. I would not have the human yet.
In the construction it is so: as long as the construction is not completely described, I cannot be sure whether what I am looking for is logically correct, so can be described at all.
The imperfect description leaves just out what would be necessary for something to be sought. It is thus only an apparant description of the person sought.
E.g. Proof of the Goldbach theorem. P. 76. E.g. The proof of induction has been rediscovered and it is not just a combination of simpler conclusions.
To what extent is the searched contained in the process of searching?
E.g. North Pole: someone shows a point on the map, that is the specification of the target.
E.g. When searching the pentagon with a circle and a ruler, the question is: does the concept 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 concepts of construction (a layman concept of the pupil and a mathematical one).
The space is, in reality, only seemingly 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.
Intuitionism: An Introduction (Study in Logic & Mathematics) 1971