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18244
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I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
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Full Idea:
Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.
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From:
Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4
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A reaction:
Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.
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9382
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Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
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Full Idea:
I call 'entitlement' (as opposed to justification) the epistemic rights or warrants that need not be understood by or even be accessible to the subject.
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From:
Tyler Burge (Content Preservation [1993]), quoted by Paul Boghossian - Analyticity Reconsidered §III
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A reaction:
I espouse a coherentism that has both internal and external components, and is mediated socially. In Burge's sense, animals will sometimes have 'entitlement'. I prefer, though, not to call this 'knowledge'. 'Entitled true belief' is good.
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