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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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14508
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A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM]
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Full Idea:
A thisness is the property of being identical with a certain particular individual - not the property that we all share, of being identical with some individual, but my property of being identical with me, your property of being identical with you etc.
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From:
Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1)
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A reaction:
These philosophers tell you that a thisness 'is' so-and-so, and don't admit that he (and Plantinga) are putting forward a new theory about haecceities, and one I find implausible. I just don't believe in the property of 'being-identical-to-me'.
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12034
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If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM]
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Full Idea:
There is a temporal argument for the possibility of non-identical indiscernibles, if there could be a cyclical universe, in which each event was preceded and followed by infinitely many other events qualitatively indiscernible from itself.
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From:
Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3)
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A reaction:
The argument is a parallel to Max Black's indiscernible spheres in space. Adams offers the reply that time might be tightly 'curved', so that the repetition was indeed the same event again.
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14510
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Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM]
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Full Idea:
Similar to the argument from spatial dispersal, we can argue against the Identity of Indiscernibles from temporal dispersal. It seems there could be a cyclic universe, ..and thus there could be distinct but indiscernible events, separated temporally.
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From:
Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3)
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A reaction:
See Idea 14509 for spatial dispersal. If cosmologists decided that a cyclical universe was incoherent, would that ruin the argument? Presumably there might even be indistinguishable events in the one universe (in principle!).
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16455
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Black's two globes might be one globe in highly curved space [Adams,RM]
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Full Idea:
If God creates a globe reached by travelling two diameters in a straight line from another globe, this can be described as two globes in Euclidean space, or a single globe in a tightly curved non-Euclidean space.
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From:
Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3)
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A reaction:
[my compression of Adams's version of Hacking's response to Black, as spotted by Stalnaker] Hence we save the identity of indiscernibles, by saying we can't be sure that two indiscernibles are not one thing, unusually described.
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11901
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Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P]
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Full Idea:
Moderate Haecceitism says that thisnesses and transworld identities are primitive, but logically connected with suchnesses. ..Extreme Haecceitism involves the rejection of all logical connections between suchness and thisness, for persons.
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From:
report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Penelope Mackie - How Things Might Have Been
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A reaction:
I am coming to the conclusion that they are not linked. That thisness is a feature of our conceptual thinking, and is utterly atomistic and content-free, while suchness is rich and a feature of reality.
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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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12032
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Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM]
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Full Idea:
Direct reference is commonly effected by the use of proper names and indexical expressions, and sometimes by what has been called (by Donnellan) the 'referential' use of descriptions.
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From:
Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 2)
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A reaction:
One might enquire whether the third usage should be described as 'direct', but then I am not sure that there is much of a distinction between references which are or are not 'direct'. Either you (or a sentence) refer or you (or it) don't.
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