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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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9152
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If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K]
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Full Idea:
In traditional abstraction, the colour green merely has the intrinsic property of being green, other properties of things being abstracted away. But why should that be regarded as a type? It must be because the property is common to the instances.
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From:
Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §5)
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A reaction:
A nice question which shows that the much-derided single act of abstraction is not sufficient to arrive at a concept, so that abstraction is a more complex matter (perhaps even a rational one) than simple empiricists believe.
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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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9146
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After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
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Full Idea:
In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}!
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From:
Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1)
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A reaction:
Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets.
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21924
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As the subject of willing I am wretched, but absorption in knowledge is bliss [Schopenhauer]
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Full Idea:
As the subject of willing I am an exceedingly wretched being, and all our suffering consistd in willing, ...but as soon as I am absorbed in knowledge, I am blissfully happy and nothing can assail me.
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From:
Arthur Schopenhauer (Manuscript remains [1855], I p.137), quoted by Peter B. Lewis - Schopenhauer 4
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A reaction:
So the source of his pessimism is subjection to his own will. However, since becoming absorbed in knowledge is an easy task for a scholar, he has little to grumble about. Nietzsche mocked the great pessimist for playing the flute every day.
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