Philosophy Dictionary of ArgumentsHome
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| 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correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn.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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Logic Texts on Paradoxes - Dictionary of Arguments
Read III 187f Paradoxes: Hierarchy (Tarski)-problem: the Cretan 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. >Self-reference. 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. III 196 Semantically complete: is a language that contains its own truth predicates. Avoidance of paradox: is done by separation of the truth conditions from fallacy conditions. >Richness of a language, >Meta language, >Object language. --- Sainsbury 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. >Limits, >Motion. V 19 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. 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. >Zeno. SainsburyVsAristoteles: today: we are constantly trying to allow points of time: E.g. acceleration at a point, etc. V 39 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. V 184 Sentence/Statement: a sentence is only circular at a certain occasion. - The paradox is therefore not in the meaning, but in the occasion. >Circular reasoning, >Utterance._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Logic Texts 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 Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Sai I R.M. Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 German Edition: Paradoxien Stuttgart 1993 |
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> Counter arguments against Logic Texts
> Counter arguments in relation to Paradoxes
Ed. Martin Schulz, access date 2024-04-28