|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correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn.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.|
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Ravenparadox/Poundstone: "This herring is red" supports both contra positions: a) "All non-black things are non-ravens" and "all non-white things are non-ravens" (contra position of "All ravens are white") - it follows:. black is white - that is the paradox.
Does not need to be a paradox if the number of objects is finite.
Knowledge paradox/prisoners paradox/Poundstone: (unexpected execution) only works if the other thinks about the situation and draws wrong conclusions.
Knowledge paradox/prisoners paradox/Quine/Poundstone: (unexpected execution) the "knowledge" here is an illusion - the first conclusion, after which the prisoners cannot be executed on the last day is not valid - the illogical is better off: he can suspect the right - the assumption of a specific day causes that the execution can take place on any day - N.B./Poundstone: error: the assumption when the impossible is excluded, there should remain something possible - if the prisoner assumes the impossibility, he can be executed on any day.
Thomson's lamp/Poundstone: light turns on for 1/2 minutes, then off for 1/4 minutes, then on for 1/8 ... Total: 1 - question: is it on or off after 1 min? (Sum of infinite elements) - wrong question - analog: if the greatest number is odd/even.
Ultimately physical limit: frequency, energy, switchers.
Zenon/Achilles/Poundstone: Solution: overtaking after 111,111 ... cm - the "infinity" lies in Zenon's analysis, not in physics - Arrow paradox: even in the relativity theory the moment remains blurry - also here we believe in cause and effect: the present determines the future - how does the arrow know, where it must go? - No physical problem, row term no solution.
Olbers Paradox: four times the area balances four times weaker radiation - it would heat up on earth to the average temperature of stars - solution: redshift.
Tristram Shandy paradox/Russell/Poundstone: if he lived infinitly long, there would remain no day undescribed because there could be no day mentioned, for which it would be impossible - one-to-one allocation is possible - but never completed - but not at reversal infinite past: you cannot make an unambiguous assignment of certain days to certain years - in the last year he cannot have written about one day of this year - infinitly long incomplete manuscript.
Paradox/antinomy/Poundstone: general form: the illusion that all truth is also recognizable - unexpected execution: the victim is wrong because it thinks it can achieve something through logical reasoning, which is impossible to achieve in that way - Newcomb's paradox: the one who makes the prediction, cannot know his own thoughts.
I W. Poundstone Im Labyrinth des Denkens, Reinbek 1995