|Limits, philosophy: here we are concerned with the classification of knowledge domains or the identification of possibilities for thought. We need to determine what belongs to a domain and what does not. Problems arise wherever something is to be described beyond an area by the means of this area itself ('impracticability', 'unthinkability','inconceivability'), as well as where an area is solely covered by means originating from this area itself ( Circularity)._____________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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|Sai V 15ff
Race track/movement/Zenon/Paradox/Sainsbury: should prove that nothing can begin to move, to get to a point after one meter, one has to come up to the half first, etc.
Problem: the correspondence of physical space and mathematical series - For example, a point divides a distance, the two distance parts have no common point. Does the division point belong to one or the other?
(It cannot belong to both, since they have no point in common, otherwise they would not be divided.) It is necessary to regulate this by determination - but physically nothing can depend on a determination - logically: we need the concept of a limit which itself does not take up space.
Solution: passing the distance is sufficient, since the boundary point Z* does not belong to the series of Z-points, but Z* belongs to the area of the space corresponding to the Z-series (the preceding points) Problem: we have to assume that we have coherent concepts of space, but we get these only through these mathematical structures. Conclusion: Zenon demands a more careful elaboration of our spatial concepts.
Corresponds essentially to Achilles/turtle._____________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.
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001