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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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7024
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Properties are universals, which are always instantiated [Armstrong, by Heil]
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Full Idea:
Armstrong takes properties to be universals, and believes there are no 'uninstantiated' universals.
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From:
report of David M. Armstrong (A Theory of Universals [1978]) by John Heil - From an Ontological Point of View §9.3
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A reaction:
At first glance this, like many theories of universals, seems to invite Ockham's Razor. If they are always instantiated, perhaps we should perhaps just try to talk about the instantiations (i.e. tropes), and skip the universal?
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9478
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Even if all properties are categorical, they may be denoted by dispositional predicates [Armstrong, by Bird]
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Full Idea:
Armstrong says all properties are categorical, but a dispositional predicate may denote such a property; the dispositional predicate denotes the categorical property in virtue of the dispositional role it happens, contingently, to play in this world.
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From:
report of David M. Armstrong (A Theory of Universals [1978]) by Alexander Bird - Nature's Metaphysics 3.1
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A reaction:
I favour the fundamentality of the dispositional rather than the categorical. The world consists of powers, and we find ourselves amidst their categorical expressions. I could be persuaded otherwise, though!
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10728
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A thing's self-identity can't be a universal, since we can know it a priori [Armstrong, by Oliver]
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Full Idea:
Armstrong says that if it can be proved a priori that a thing falls under a certain universal, then there is no such universal - and hence there is no universal of a thing being identical with itself.
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From:
report of David M. Armstrong (A Theory of Universals [1978], II p.11) by Alex Oliver - The Metaphysics of Properties 11
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A reaction:
This is a distinctively Armstrongian view, based on his belief that universals must be instantiated, and must be discoverable a posteriori, as part of science. I'm baffled by self-identity, but I don't think this argument does the job.
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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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