Combining Texts

All the ideas for 'Purifications (frags)', 'Our Knowledge of Mathematical Objects' and 'Clitophon'

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4 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

9224	Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
	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

9222	The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
	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.

9223	My Proceduralism has one simple rule, and four complex rules [Fine,K]
	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.

22. Metaethics / B. Value / 2. Values / f. Altruism

1590	The just man does not harm his enemies, but benefits everyone [Plato]
	Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone.
	From: Plato (Clitophon [c.372 BCE], 410b)
	A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus.