9123
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Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
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Full Idea:
Priest says there is room for contradictions. He gives the example of someone in a doorway; is he in or out of the room. Given that in and out are mutually exclusive and exhaustive, and neither is the default, he seems to be both in and not in.
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From:
report of Graham Priest (What is so bad about Contradictions? [1998]) by Roy Sorensen - Vagueness and Contradiction 4.3
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A reaction:
Priest is a clever lad, but I don't think I can go with this. It just seems to be an equivocation on the word 'in' when applied to rooms. First tell me the criteria for being 'in' a room. What is the proposition expressed in 'he is in the room'?
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9987
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An aggregate in which order does not matter I call a 'set' [Bolzano]
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Full Idea:
An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.
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From:
Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
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A reaction:
The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.
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12735
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Everything has a fixed power, as required by God, and by the possibility of reasoning [Leibniz]
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Full Idea:
It follows from the nature of God that there is a fixed power of a definite magnitude [non vagam] in anything whatsoever, otherwise there would be no reasonings about those things.
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From:
Gottfried Leibniz (De aequopollentia causae et effectus [1679], A6.4.1964), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6
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A reaction:
This is double-edged. On the one hand there is the grand claim that the principle derives from divine nature, but on the other it derives from our capacity to reason and explain. No one doubts that powers are 'fixed'.
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