Ideas from 'Our Knowledge of Mathematical Objects' by Kit Fine [2005], by Theme Structure

[found in 'Oxford Studies in Epistemology Vol. 1' (ed/tr Gendler,R/Hawthorne,J) [OUP 2004,978-0-19-928590-7]].

green numbers give full details    |     back to texts     |     unexpand these ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment
                        Full Idea: My Proceduralism offers axiom-free foundations for mathematics. Axioms give way to the stipulation of procedures. We obtain a form of logicism, but with a procedural twist, and with a logic which is ontologically neutral, and no assumption of objects.
                        From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
                        A reaction: [See Ideas 9222 and 9223 for his Proceduralism] Sounds like philosophical heaven. We get to take charge of mathematics, without the embarrassment of declaring ourselves to be platonists. Someone, not me, should evaluate this.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
The objects and truths of mathematics are imperative procedures for their construction
                        Full Idea: I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction.
                        From: Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro)
                        A reaction: I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism.
My Proceduralism has one simple rule, and four complex rules
                        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).
                        From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
                        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.