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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15643
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Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle]
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Full Idea:
Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does.
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From:
Antony Eagle (Locke on Essences and Kinds [2005], IV)
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A reaction:
This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about.
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23282
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If all that matters in morality is motive and intention, that makes moral luck irrelevant [Williams,B]
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Full Idea:
The idea that one's whole life can be immune to luck has not prevailed (e.g. in Christianity), …but its place has been taken by the idea that moral value can be immune, …if it is motive that counts, and in actions it is not worldly changes but intention.
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From:
Bernard Williams (Moral Luck [1976], p.20)
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A reaction:
[compressed] That is, that Kant offers a way to make luck irrelevant to morality. Williams disagrees, but says at least Kant offers 'solace to a sense of the world's unfairness'.
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