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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16764
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The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]
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Full Idea:
Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted.
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From:
Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5
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A reaction:
A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763.
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