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17447
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Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
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Full Idea:
In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
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From:
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
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A reaction:
This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
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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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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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