|Aspect: perspective from which an object or a problem is considered. Problematic when aspects, views, perspectives are objectified. They are not part of the object, but consist in the relation to the object._____________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
Aspect/Waismann: The fact that an aspect is possible can only be seen when it is there. You can simply underline the newly discovered, so you give a new sign.
The formulas with the underlinings do something different than those without underlining, they make the new structure visible.
For example, suppose there is a tribe of people who owns our decimal system, and calculates exactly as we do, but infinite decimal fractions remain unknown to them. People stop the division, e.g. at the 5th place.
1/3 = 0.333333.
The periodicity would not be noticeable to them, they would not have to think that this always goes on like this.
After the discovery of the infinite decimal fractions one "sees" the calculation differently! This is the discovery that one sees the infinite possibility of progression into the calculation._____________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