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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11993
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Jones may cease to exist without some simple property, but that doesn't make it essential [Kung]
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Full Idea:
If Jones ceases to be a father, or ceases to be over eight years old, he will cease to exist, yet these properties surely do not belong essentially to him.
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From:
Joan Kung (Aristotle on Essence and Explanation [1977], II)
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A reaction:
This seems to correct, though I would doubt whether either of these count as true properties, in the causal sense I prefer. If being 'over 8' is a property, how many 'over n' or 'under m' properties does he have? One for each quantum moment?
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11992
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Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung]
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Full Idea:
Three essentialist claims are labelled 'Aristotelian': the thing would cease to exist without the property; an essential property is explanatory; and it is such that it must belong to everything to which it belongs.
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From:
Joan Kung (Aristotle on Essence and Explanation [1977], Intro)
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A reaction:
She says the second one is indispensable, and that it rules out the third one. My working assumption, like hers, is that the second one is the key part of the game, because Aristotle wanted to explain things.
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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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