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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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19891
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Rule of law is superior to autonomy, because citizens can see what is expected [Hooker,R]
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Full Idea:
Men saw that to live by one man's will became the cause of all men's misery. This contrained them to come unto laws wherein all men might see their duty beforehand, and know the penalties of transgressing them.
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From:
Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], I s.10), quoted by John Locke - Second Treatise of Government 111 n1
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A reaction:
One British school has a single rule, that pupils 'shall always treat other people with respect'. Presumably the rulers, as well as the pupils, must decide when this is transgressed. The rule of law may be preferable.
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17005
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Natural things observe certain laws, and things cannot do otherwise if they retain their forms [Hooker,R]
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Full Idea:
Things natural …do so necessarily observe their certain laws, that as long as they keep those forms which give them their being they cannot possibly be apt or inclinable to do otherwise than they do.
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From:
Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], 1.3.4), quoted by Marc Lange - Laws and Lawmakers 1.2
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A reaction:
Cited by some as the beginnings of the idea of 'laws of nature', but it is striking that Hooker says the laws are controlled by 'forms' (which are Aristotelian essences). This is an essentialist view of laws, not a regularity or divine power one.
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