17697
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The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
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Full Idea:
The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
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From:
David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
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A reaction:
Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.
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15990
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Every individual thing which exists has an essence, which is its internal constitution [Locke]
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Full Idea:
I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist.
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From:
John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
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A reaction:
This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species.
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15994
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If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]
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Full Idea:
What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge.
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From:
John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
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A reaction:
I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it.
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