9224
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Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
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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.
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From:
Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
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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.
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9223
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My Proceduralism has one simple rule, and four complex rules [Fine,K]
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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).
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From:
Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
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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.
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4800
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Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos]
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Full Idea:
Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction.
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From:
report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1
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A reaction:
The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms.
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