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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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8375
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'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
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Full Idea:
'Necessary' is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments. Thus 'If x is a man, x is mortal' is necessary, because it is true for any possible value of x.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.175)
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A reaction:
This is presumably the intermediate definition of necessity, prior to modern talk of possible worlds. Since it is a predicate about functions, it is presumably a metalinguistic concept, like the semantic concept of truth.
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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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4396
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The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
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Full Idea:
The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.173)
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A reaction:
A bold proposal which should be taken seriously. However, if we drop it from scientific explanation, we may well find ourselves permanently stuck with it in 'folk' explanation. What is the alternative?
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8379
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In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell]
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Full Idea:
An 'event' (in a statement of the 'law of causation') is intended to be something that is likely to recur, since otherwise the law becomes trivial. It follows that an 'event' is not some particular, but a universal of which there may be many instances.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.179)
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A reaction:
I am very struck by this. It may be a key insight into understanding what a law of nature actually is. It doesn't follow that we must be realists about universals, but the process of abstraction from particulars is at the heart of generalisation.
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