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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8756
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Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
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Full Idea:
Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition.
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From:
report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
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A reaction:
It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things.
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4688
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We imagine small and large objects scaled to the same size, suggesting a fixed capacity for imagination [Lavers]
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Full Idea:
If we think of a pea, and then of the Eiffel Tower, they seem to occupy the same space in our consciousness, suggesting that we scale our images to fit the available hardware, just as computer imagery is limited by the screen and memory available.
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From:
Michael Lavers (talk [2003]), quoted by PG - Db (ideas)
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A reaction:
Nice point. It is especially good because it reinforces a physicalist view of the mind from introspection, where most other evidence is external observation of brains (as Nietzsche reinforces determinism by introspection).
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