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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7880
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If a blind persons suddenly sees a kestrel, that doesn't make visual and theoretical kestrels different [Papineau on Jackson]
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Full Idea:
An ornithological Mary might know everything theoretical about kestrels, but be blind from birth, then have her sight restored. She now knows "That bird eats mice", so visual kestrels must be ontologically distinct from theoretical ones.
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From:
comment on Frank Jackson (Epiphenomenal Qualia [1982]) by David Papineau - Thinking about Consciousness 6.3
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A reaction:
A nice reductio, and I think this pinpoints best what is wrong with the knowledge argument. Knowledge, and the means of acquiring it, are two distinct things. When I see x, I don't acquire knowledge of x, AND knowledge of my seeing x.
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7377
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Mary learns when she sees colour, so her complete physical information had missed something [Jackson]
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Full Idea:
It seems obvious that Mary will learn something about the world when she is released from her black-and-white room; but then it is inescapable that her previous knowledge was incomplete; she had all the physical information, so there is more to have.
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From:
Frank Jackson (Epiphenomenal Qualia [1982], §1)
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A reaction:
This is Jackson's famous 'knowledge argument', which seems to me misconceived. Since I don't think phenomenal colours are properties of objects (Idea 5456), Mary learns more about herself, and about her means of acquiring knowledge.
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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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