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10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
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A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
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A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
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10527
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An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
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Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
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A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
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22454
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We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot]
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Full Idea:
Williams argued that we can tolerate inconsistency in moral principles though not in assertions, and that this is explained by the fact that it is the concern of the latter but not of the former to reflect an 'independent order of things'.
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From:
report of Bernard Williams (Consistency and realism (with 1972 note) [1966]) by Philippa Foot - Moral Realism and Moral Dilemma p.37
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A reaction:
Put like this, Williams seems to beg the question, which is whether there is an independent moral order to things. There seems to be an easy answer, which is that we are only intolerant of inconsistency when we are confident about it.
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7830
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A talking triangle would say God is triangular [Spinoza]
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Full Idea:
If a triangle could speak it would say that God is eminently triangular.
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From:
Baruch de Spinoza (Letters to Blijenburgh [1665], 1665), quoted by Matthew Stewart - The Courtier and the Heretic Ch.10
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A reaction:
Spinoza had a rather appealing waspish wit. This nicely dramatises an ancient idea (Idea 407). You can, of course, if you believe in God, infer some of His characteristics from His creation. But then see Hume: Ideas 1439, 6960, 6967, 1440.
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