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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4577
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There is no necessity higher than natural necessity, and that is just regularity [Quine]
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Full Idea:
In principle I see no higher or more austere necessity than natural necessity; and in natural necessity, or our attribution of it, I see only Hume's regularities
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From:
Willard Quine (Necessary Truth [1963], p.76)
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A reaction:
Presumably this allows logical necessity as a 'lower' necessity, but denies 'metaphysical' necessity, in line with Hume and other tough empiricists. Personally I adore metaphysical necessities, but they are a bit hard to establish conclusively.
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21497
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If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing]
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Full Idea:
Without a detailed account, coherence is reduced to the mere muttering of the word 'coherence', which can be interpreted so as to cover all arguments, but only by making its meaning so wide as to rob it of almost all significance.
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From:
A.C. Ewing (Idealism: a critical survey [1934], p.246), quoted by Erik J. Olsson - Against Coherence 2.2
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A reaction:
I'm a fan of coherence, but it is a placeholder, involving no intrinsic or detailed theory. I just think it points to the reality of how we make judgements, especially practical ones. We can categorise the inputs, and explain the required virtues.
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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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