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23025
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Philosophers should be more inductive, and test results by their conclusions, not their self-evidence [Russell]
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Full Idea:
The progress of philosophy seems to demand that, like science, it should learn to practise induction, to test its premisses by the conclusions to which they lead, and not merely by their apparent self-evidence.
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From:
Bertrand Russell (Explanations in reply to Mr Bradley [1899], nr end)
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A reaction:
[from Twitter] Love this. It is 'one person's modus ponens is another person's modus tollens'. I think all philosophical conclusions, without exception, should be reached by evaluating the final result fully, and not just following a line of argument.
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8920
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Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
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Full Idea:
A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
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From:
Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
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A reaction:
So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part
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19696
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There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]
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Full Idea:
We must distinguish between something's being a 'reason for which' a creature believes something, and its being a 'reason why' a creature believes something. ...We must also distinguish a 'reason for which' from a 'reason to' believe something.
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From:
Ram Neta (The Basing Relation [2011], Intro)
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A reaction:
He doesn't spell the distinctions out clearly. I take it that 'for which' is my personal justification, 'why' is the dodgy prejudices that cause my belief. and 'to' is some actual good reasons, of which I may be unaware.
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