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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20544
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Berlin distinguishes 'negative' and 'positive' liberty, and rejects the latter [Berlin, by Swift]
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Full Idea:
Isaiah Berlin draws a famous distinction between 'negative' and 'positive' concepts of liberty, and argues that the latter should be seen as a wrong turning (because totalitarian regimes have invoked it).
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From:
report of Isaiah Berlin (Two Concepts of Liberty [1958]) by Adam Swift - Political Philosophy (3rd ed) 2 'Intro'
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A reaction:
Swift argues against him, saying that positive liberty is not a single concept (it's three), and has aspects that should be defended. I think I'm with Swift on that. Is religious freedom a freedom 'from' something, or a freedom 'to do' something?
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