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Ideas for 'Three-Dimensionalism v Four-Dimensionalism', 'On Note L to Bayle's 'Rorarius'' and 'The Limits of Abstraction'

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6 ideas

18. Thought / E. Abstraction / 1. Abstract Thought

9144	Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
	Full Idea: Fine says creative definitions can found mathematics. His 'procedural postulationism' says one stipulates not truths, but certain procedures for extending a domain. The procedures can be stated without invoking an abstract ontology.
	From: report of Kit Fine (The Limits of Abstraction [2002], 100) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 4
	A reaction: (For creative definitions, see Idea 9143) This sounds close in spirit to fictionalism, but with the emphasis on the procedure (which can presumably be formalized) rather than a pure act of imaginative creation.

18. Thought / E. Abstraction / 2. Abstracta by Selection

10141	Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
	Full Idea: Many different kinds of mathematical objects (natural numbers, the reals, points, lines, figures, groups) can be regarded as forms of abstraction, with special theories having their basis in a general theory of abstraction.
	From: Kit Fine (The Limits of Abstraction [2002], I.4)
	A reaction: This result, if persuasive, would be just the sort of unified account which the whole problem of abstact ideas requires.

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

10135	We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
	Full Idea: A principle of abstraction is 'conceptual' when the items upon which it abstracts are concepts (e.g. a one-one correspondence associated with a number), and 'objectual' if they are objects (parallel lines associated with a direction).
	From: Kit Fine (The Limits of Abstraction [2002], I)

9142	Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
	Full Idea: Fine considers abstraction principles as instances of reconceptualization (rather than implicit definition, or using the Context Principle). This centres not on reference, but on new senses emerging from analysis of a given sense.
	From: report of Kit Fine (The Limits of Abstraction [2002], 035) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 2
	A reaction: Fine develops an argument against this view, because (roughly) the procedure does not end in a unique result. Intuitively, the idea that abstraction is 'reconceptualization' sounds quite promising to me.

10137	Abstractionism can be regarded as an alternative to set theory [Fine,K]
	Full Idea: The uncompromising abstractionist rejects set theory, seeing the theory of abstractions as an alternative, rather than as a supplement, to the standard theory of sets.
	From: Kit Fine (The Limits of Abstraction [2002], I.1)
	A reaction: There is also a 'compromising' version. Presumably you still have equivalence classes to categorise the objects, which are defined by their origin rather than by what they are members of... Cf. Idea 10145.

10138	An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
	Full Idea: We can see an object as being the abstract of a concept with respect to a relation on concepts. For example, we may say that 0 is the abstract of the empty concept with respect to the relation of one-one correspondence.
	From: Kit Fine (The Limits of Abstraction [2002], I.2)
	A reaction: This is Fine's attempt to give a modified account of the Fregean approach to abstraction. He says that the reference to a relation will solve the problem of identity between abstractions.