15927
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Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine]
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Full Idea:
For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain.
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From:
report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3
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A reaction:
Lavine summarises this as 'first-order logic with parameters'.
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14742
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It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N]
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Full Idea:
Insofar as identity seems vague, it is provably mistaken. If it is vague whether x and y are identical (as in the Ship of Theseus), then x,y is definitely not the same as x,x, since the first pair is indeterminate and the second pair isn't.
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From:
Nathan Salmon (Reference and Essence: seven appendices [2005], App I)
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A reaction:
[compressed; Gareth Evans 1978 made a similar point] This strikes me as begging the question in the Ship case, since we are shoehorning the new ship into either the slot for x or the slot for y, but that was what we couldn’t decide. No rough identity?
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5121
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Basing ethics on flourishing makes it consequentialist, as actions are judged by contributing to it [Harman]
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Full Idea:
Basing ethics on human flourishing tends towards utilitarianism or consequentialism; actions, character traits, laws, and so on are to be assessed with reference to their contributions to human flourishing.
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From:
Gilbert Harman (Human Flourishing, Ethics and Liberty [1983], 9.2.2)
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A reaction:
This raises the question of whether only virtue can contribute to flourishing, or whether a bit of vice might be helpful. This problem presumably pushed the Stoics to say that virtue itself is the good, rather than the resulting flourishing.
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