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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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22762
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Some properties are inseparable from a thing, such as the length, breadth and depth of a body [Sext.Empiricus]
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Full Idea:
Some properties are inseparable from the things to which they belong - as are length, breadth and depth from bodies, for without their presence it is impossible to perceive Body.
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From:
Sextus Empiricus (Against the Logicians (two books) [c.180], I.270)
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A reaction:
For the opposite case he suggests a man running, talking or sleeping. He doesn't mention essential natures, but this is clearly correct. We might say that they are properties which need to be mentioned in a full definition.
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12729
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The cause of a change is not the real influence, but whatever gives a reason for the change [Leibniz]
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Full Idea:
That thing from whose state a reason for the changes is most readily provided is adjudged to be the cause. ...Causes are not derived from a real influence, but from the providing of a reason.
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From:
Gottfried Leibniz (Specimen inventorum [1689], A6.4.1620), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5
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A reaction:
Leibniz is not denying that there are real influences. He seems to be offering the thesis which I am pursuing, that the need for explanation is the crucial factor in shaping the structure of our metaphysics.
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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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