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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12434
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Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
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Full Idea:
We must distinguish between explaining particular necessities and explaining necessity in general; and we ought to distinguish between explaining, in regard to any necessary truth, why it is true, and explaining why it is necessary.
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From:
Bob Hale (The Source of Necessity [2002], p.308)
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A reaction:
Useful. The pluralist view I associate with Fine says we can explain types of necessity, but not necessity in general. If we seek truthmakers, there is a special case of what adds the necessity to the truth.
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12433
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If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
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Full Idea:
If the alleged necessity, e,g, 2+2=4, really does depend upon a convention governing the use of the words in which we state it, and the existence of that convention is merely a contingent matter, then it can't after all be necessary.
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From:
Bob Hale (The Source of Necessity [2002], p.302)
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A reaction:
[Hale is citing Blackburn for this claim] Hale suggests replies, by keeping truth and meaning separate, and involving laws of logic. Blackburn clearly has a good point.
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12436
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Concept-identities explain how we know necessities, not why they are necessary [Hale]
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Full Idea:
It seems to me that identity-relations among concepts have more to do with explaining how we know that vixens are female foxes etc., than with explaining why it is necessary, and, more generally, with explaining why some necessities are knowable a priori.
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From:
Bob Hale (The Source of Necessity [2002], P.313)
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A reaction:
Hale rejects the conceptual and conventional accounts of necessity, in favour of the essentialist view. This strikes me as a good suggestion of Hale's, since I agree with him about the essentialism.
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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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