23539
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Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
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Full Idea:
A precise language is often assigned a classical semantics, in which the semantic value of a name is its referent, the semantic value of a predicate is its extension (the objects of which it is true), and the value of a sentence is True or False.
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From:
Kit Fine (Vagueness: a global approach [2020], 1)
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A reaction:
Helpful to have this clear statement of how predicates are treated. This extensionalism in logic causes trouble when it creeps into philosophy, and people say that 'red' just means all the red things. No it doesn't.
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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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3425
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Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim]
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Full Idea:
Ernest Nagel defines reduction as the possibility of deriving all laws of one theory by logic and mathematics to another theory, with appropriate 'bridging principles' (either definitions, or empirical laws) connecting the expressions of the two theories.
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From:
report of Ernest Nagel (The Structure of Science [1961]) by Jaegwon Kim - Philosophy of Mind p.213
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A reaction:
This has been labelled as 'weak' reduction, where 'strong' reduction would be identity, as when lightning is reduced to electrical discharge. You reduce x by showing that it is y in disguise.
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23540
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Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
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Full Idea:
If 'P is red' and 'P is orange' are indefinite, then 'P is red and P is orange' seems false, because red and orange are exclusive. But if two conjoined indefinite sentences are false, that makes 'P is red and P is red' false, when it should be indefinite.
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From:
Kit Fine (Vagueness: a global approach [2020], 1)
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A reaction:
[compressed] This is the problem of 'penumbral connection', where two indefinite values are still logically related, by excluding one another. Presumably 'P is red and P is of indefinite shape' can be true? Doubtful about this argument.
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23546
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Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
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Full Idea:
Standard notions of vagueness all accept borderline cases, and presuppose a higher standpoint from which a judgement of being borderline F, rather than simply being F or being not F, can be made.
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From:
Kit Fine (Vagueness: a global approach [2020], 3)
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A reaction:
He says that the concept of borderline cases is an impediment to understanding vagueness. Proposing a third group when you are struggling to separate two other groups doesn't seem helpful, come to think of it. Limbo cases.
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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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