Philosophy Lexicon of Arguments

Author Item Excerpt Meta data
Heyting, A.
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Constructivism 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.
Heyting, A.

> Counter arguments in relation to Constructivism

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Ed. Martin Schulz, access date 2017-05-01