more from this thinker | more from this text
Full Idea
My Proceduralism has one simple rule (introduce an object), and four complex rules: Composition (combining two procedures), Conditionality (if A, do B), Universality (do a procedure for every x), and Iteration (rule to keep doing B).
Clarification
See Idea 9222 for his Proceduralism
Gist of Idea
My Proceduralism has one simple rule, and four complex rules
Source
Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
Book Ref
'Oxford Studies in Epistemology Vol. 1', ed/tr. Gendler,R/Hawthorne,J [OUP 2004], p.91
A Reaction
It sounds like a highly artificial and private game which Fine has invented, but he claims that this is the sort of thing that practising mathematicians have always done.
Related Idea
Idea 9222 The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| 14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
| 9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 8706 | Constructivism rejects too much mathematics [Friend] |