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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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13127
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Categories can't overlap; they are either disjoint, or inclusive [Sommers, by Westerhoff]
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Full Idea:
Fred Sommers, in his treatment of types, says that two ontological categories cannot overlap; they are either disjoint, or one properly includes the other. This is sometimes referred to as Sommers' Law.
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From:
report of Fred Sommers (Types and Ontology [1963], p.355) by Jan Westerhoff - Ontological Categories §24
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A reaction:
The 'types', of course, go back to Bertrand Russell's theory of types, which is important in discussions of ontological categories. Carnap pursued it, trying to derive ontological categories from grammatical categories. 85% agree with Sommers.
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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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