18247
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Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
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Full Idea:
In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
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From:
report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
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A reaction:
This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
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3285
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We may be unable to abandon personal identity, even when split-brains have undermined it [Nagel]
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Full Idea:
As a result of the evidence of split-brains, it is possible that the ordinary, simple idea of a single person will come to seem quaint some day, …but we may be unable to abandon the idea, no matter what we discover.
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From:
Thomas Nagel (Brain Bisection and Unity of Consciousness [1971], p.164)
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A reaction:
I'm not sure what grounds you can have for a claim that we can't abandon our current view of selves, even when the new reality will be utterly different. Rather conservative? I would expect future concepts to roughly match future reality.
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6608
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Strong sense, delicate sentiment, practice, comparisons, and lack of prejudice, are all needed for good taste [Hume]
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Full Idea:
Strong sense, united to delicate sentiment, improved by practice, perfected by comparison, and cleared of all prejudice, can alone entitle critics to the valuable character of having 'taste'.
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From:
David Hume (Of the standard of taste [1757]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.6
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A reaction:
I agree entirely with this, but then I am a very politically incorrect elitist when it comes to taste. It just seems screamingly obvious that professional wine-tasters have a better appreciation of wine than me, and so on for the rest of the arts.
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