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6007
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If you know your father, but don't recognise your father veiled, you know and don't know the same person
[Eubulides, by Dancy,R]
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Full Idea:
The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person.
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From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
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A reaction:
Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976).
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13334
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Contradictions are either purely logical or mathematical, or they involved thought and language
[Ramsey]
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Full Idea:
Group A consists of contradictions which would occur in a logical or mathematical system, involving terms such as class or number. Group B contradictions are not purely logical, and contain some reference to thought, language or symbolism.
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From:
Frank P. Ramsey (The Foundations of Mathematics [1925], p.171), quoted by Graham Priest - The Structure of Paradoxes of Self-Reference 1
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A reaction:
This has become the orthodox division of all paradoxes, but the division is challenged by Priest (Idea 13373). He suggests that we now realise (post-Tarski?) that language is more involved in logic and mathematics than we thought.
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13373
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Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong
[Priest,G]
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Full Idea:
A natural principle is the same kind of paradox will have the same kind of solution. Standardly Ramsey's first group are solved by denying the existence of some totality, and the second group are less clear. But denial of the groups sink both.
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From:
Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §5)
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A reaction:
[compressed] This sums up the argument of Priest's paper, which is that it is Ramsey's division into two kinds (see Idea 13334) which is preventing us from getting to grips with the paradoxes. Priest, notoriously, just lives with them.
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6516
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Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals?
[PG]
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Full Idea:
The Monty Hall Dilemma: Three boxes, one with a big prize; pick one to open. Monty Hall then opens one of the other two, which is empty. You may, if you wish, switch from your box to the other unopened box. Should you?
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From:
PG (Db (ideas) [2031])
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A reaction:
The other two boxes, as a pair, are more likely contain the prize than your box. Monty Hall has eliminated one of them for you, so you should choose the other one. Your intuition that the two remaining boxes are equal is incorrect!
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