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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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5020
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Our thoughts are either dependent, or self-evident. All thoughts seem to end in the self-evident [Leibniz]
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Full Idea:
Whatever is thought by us is either conceived through itself, or involves the concept of another. …Thus one must proceed to infinity, or all thoughts are resolved into those which are conceived through themselves.
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From:
Gottfried Leibniz (Of Organum or Ars Magna of Thinking [1679], p.1)
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A reaction:
This seems to embody the rationalist attitude to foundations. I am sympathetic. Experiences just come to us as basic, but they don't qualify as 'thoughts', let alone knowledge. Experiences are more 'given' than 'conceptual'.
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15998
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Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard]
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Full Idea:
To love another in spite of his weaknesses and errors and imperfections is not perfect love. No, to love is to find him lovable in spite of, and together with, his weaknesses and errors and imperfections.
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From:
Søren Kierkegaard (Works of Love [1847], p.158)
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A reaction:
A true romantic at heart, Kierkegaard ideally posits perfect love as unconditional love, and not just of good attributes, predicates and conditions. However, the real question for both me and Kierkegaard is, is perfect love desirable or even possible?[SY]
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