8728
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Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
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Full Idea:
Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
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From:
Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
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A reaction:
Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!
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4761
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The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel]
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Full Idea:
Mackie's 'error theory' of ethics says that if a fact is something that corresponds to a true proposition, there are actually no moral facts, hence no knowledge of what moral statements are about.
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From:
report of J.L. Mackie (Ethics: Inventing Right and Wrong [1977]) by Pascal Engel - Truth §4.2
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A reaction:
Personally I am inclined to think that there are moral facts (about what nature shows us constitutes a good human being), based on virtue theory. Mackie is a good warning, though, against making excessive claims. You end up like a bad scientist.
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23257
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We can treat people as equals, or actually treat them equally [Dworkin, by Grayling]
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Full Idea:
Dworkin distinguishes between treating people as equals, that is, 'with equal concern and respect', and treating them equally. This latter can be unjust.
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From:
report of Ronald Dworkin (Taking Rights Seriously [1977]) by A.C. Grayling - The Good State 2
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A reaction:
The big difference I see between them is that the first is mere words, and the second is actions. Cf. 'thoughts and prayers' after US school shootings. How about equal entitlements, all things being equal?
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