|Method: a method is a procedure agreed on by participants of a discussion or research project. In the case of violations of a method, the comparability of the results is in particular questioned, since these no longer come from a set with uniformly defined properties of the elements._____________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. |
|Friedrich Waismann Suchen und Finden in der Mathematik 1938 in Kursbuch 8 Mathematik 1967
Method/Search/Find/Waismann: Can you describe exactly what you are looking for? For example, a student is looking for the construction of a regular pentagon. Caution: the construction does not depend on accuracy, because also an inaccurately designed construction can be correct!
From this it can already be seen that the construction has no necessary connection with the concept of a figure which has five equal sides when it is measured.
In reality, we have quite different concepts of pentagons, which correspond to each other roughly the same as physical geometry to the mathematical one. We can speak of a measured and a constructed pentagon. (The constructed is, of course, not an ideal being, which stands beside the measured, but a concept which is determined by the method of construction.)
E.g. Let us search for the root of 436. Let us assume that I randomly extract numbers, multiply them by themselves, and compare with 436.
How can it been seen that I was looking for it? This was not to be seen in my computing operations.
How can I recognize my search? Probably only because I have a feeling of disappointment at the end.
Let us suppose that I calculate root 436 according to the usual calculation method, then I will not get into having to speak of my feelings.
For the process is what is called the search of the root, while the other is not a search for this root. One and the other can only be called searching in a very different sense.
Find/Mathematics/Waismann: If a description is complete, the object is found. This is not the case in the life situation.
The activity does not yet contain the objective. Some will not call it searching. For the search in mathematics it is characteristic that one cannot describe the searched before or only seemingly._____________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