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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.
Gist of Idea
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology
Source
report of Kit Fine (The Limits of Abstraction [2002], 100) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 4
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.799
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.
Related Idea
Idea 9143 Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
| 9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
| 9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
| 9144 | Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert] |
| 10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
| 10136 | Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K] |
| 10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
| 10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
| 10141 | Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K] |
| 10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |
| 10144 | Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K] |
| 10145 | Abstracts cannot be identified with sets [Fine,K] |