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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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22132
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Species and genera are individual concepts which naturally signify many individuals [William of Ockham]
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Full Idea:
In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals.
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From:
William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056
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A reaction:
'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist.
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21091
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It would be absurd if even a free constitution did not impose restraints, for the public good [Hume]
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Full Idea:
A republican and free form of government would be an obvious absurdity, if the particular checks and controls, provided by the constitution, had really no influence, and made it not the interest, even of bad men, to act for the public good.
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From:
David Hume (That Politics may be reduced to a Science [1750], p.14)
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A reaction:
Presumably if you attain absolute power you can write any old constitution you like (Clause 1: the presidency is for life). But there does seem much point in doing it - unless it is to facilitate the use of the law for persecutions.
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21092
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Nobility either share in the power of the whole, or they compose the power of the whole [Hume]
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Full Idea:
A nobility may possess power in two different ways. Either every nobleman shares the power as part of the whole body, or the whole body enjoys the power as composed of parts, which each have a distinct power and authority.
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From:
David Hume (That Politics may be reduced to a Science [1750], p.15)
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A reaction:
He says the first type is found in Venice, and is preferable to the second type, which is found in Poland. Presumably in the shared version there is some restraint on depraved nobles. The danger is each noble being an autocrat.
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19381
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The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham]
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Full Idea:
Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist.
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From:
William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist'
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A reaction:
I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all.
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