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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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16700
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In order to speak about time and successive entities, the 'present' must be enlarged [Wycliff]
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Full Idea:
It is clear from the way in which one must speak about time and other successive entities that talk about 'the present' must be enlarged. Otherwise it would have to be denied that any successive entity could exist, which is impossible.
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From:
John Wycliff (De ente praedicamentali [1375], 20 p.189), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
This is a lovely idea, even if it is not quite clear what it means. The mind seems to stretch out the now anyway (as the 'specious present'), so why not embrace that in language and conscious thought?
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16701
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To be successive a thing needs parts, which must therefore be lodged outside that instant [Wycliff]
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Full Idea:
If something is successive, it is successive with respect to its individual parts, which cannot exist at the same instant. Therefore it follows that many of its parts are lodged outside that instant.
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From:
John Wycliff (De ente praedicamentali [1375], 20 p.189), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
An obvious would be to say that there are therefore no successive entities, but Wycliff is appealing to our universal acceptance of them, and offering a transcendental argument. Nice move.
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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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