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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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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7563
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The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley]
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Full Idea:
The 'influx' model of causation says that causes involve a process of contagion, as it were; when the kettle boils, the gas infects the water inside the kettle with its own 'individual accident' of heat, which literally flows from one to the other.
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From:
report of Francisco Suárez (works [1588]) by Nicholas Jolley - Leibniz Ch.2
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A reaction:
This nicely captures the scholastic target of Hume's sceptical thinking on the subject. However, see Idea 2542, where the idea of influx has had a revival. It is hard to see how the water could change if it didn't 'catch' something from the gas.
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15314
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Faraday's single field of variable forces introduces a criterion of Unity into what is ultimate [Faraday, by Harré/Madden]
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Full Idea:
In Faraday lines of force picture the directional structure of powers,...so the fundamental entity is a single, unified field. ...A new criterion of the ultimate has stepped in: Unity. The universal field is still the final explanation, but not invariant.
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From:
report of Michael Faraday (Experimental Researches in Electricity [1859]) by Harré,R./Madden,E.H. - Causal Powers 9.II.B
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A reaction:
Almost Parmenides, except that the field is not invariant. But that was always the ancient objection to the One - that it offered no explanation of change.
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