@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 18 Dec 2017},
author = {Logic Texts},
subject = {Paradoxes},
note = {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.
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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.
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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.
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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.
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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.
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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.
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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.
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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)},