|Paradoxes: are contradictions within formally correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn. Paradoxes are not errors, but challenges that may lead to a re-formulation of the prerequisites and assumptions, or to a change in the language, the subject domain, and the logical system. See also Russellian paradox, contradictions, range, consistency._____________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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|Re III 187f
Paradoxes: Hierarchy (Tarski)-problem: Kreter does not know which level his own statement assumes - it is only meaningful if truth attribution takes place at a lower level - it requires knowledge! (> Knowledge/understanding).
Self-reference: is not always bad or faulty.
Re III 192f
Curry paradox: If A and if A. then B, then B - If this conditional sentence is true, then snow is black - ponendo ponens - solution: contraction: two applications are replaced by one - change of logic. Example:
If this (conditional) theorem is true, then snow is black.
Consequentia mirabilis: If A, then ~ A, thus ~ A - contraction: If A, then if A, then 0 = 1; So if A, then 0 = 1 - contraction leads to triviality: it makes every statement from the curry paradox true.
Re III 196
Semantically completed: language contains its own truth predicates - avoidance of paradox: is done by separation of the truth conditions from fallacy conditions.
Sai V 17
Zenon/Sainsbury: Zenon's thesis: no area of space is infinitely divisible, so that it has an infinite number of parts, if each part has a certain extent, for then the sum is infinitly large - Zenon tried to show with this, that not really many things exist - overall, no object can have parts, for then it must be infinitely large.
Sainsbury: infinite division goes only mentally. - Problem: then no composition to space - in the composition, however, the space does not have to grow indefinitely. - e.g. sequences with limit.
Sai V 38f
Arrow/Paradox/Zenon: at any time, the flying arrow takes a space that is identical to it. The arrow cannot move in a moment because movement requires a period of time and a moment is seen as a point - this also applies to everything else: nothing moves. Time/AristotelesVsZenon: Time does not consist of points - SainsburyVsAristoteles: today: we are constantly trying to allow points of time: E.g. acceleration at a point, etc.
The question of whether the arrow is moving or resting in a moment is also related to other moments - Defininition rest/Sainsbury: an object rests under the condition that it is also at the same point in all nearby moments - no information about the individual moment can determine whether the arrow is moving - the premise is acceptable: no movement at the moment - but the conclusion is unacceptable.
Sai V 184
Sentence/Statement: is only circular at a certain occasion - paradox is therefore not in the meaning, but in the occasion - ((s)> usage theory)_____________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