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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.
Gist of Idea
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment
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.95
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.
Related Ideas
Idea 9223 My Proceduralism has one simple rule, and four complex rules [Fine,K]
Idea 9222 The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
| 21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |