Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'Holism: a Shopper's Guide' and 'Our Knowledge of Mathematical Objects'

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6 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.
13. Knowledge Criteria / C. External Justification / 7. Testimony
7458 The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
     Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite.
     From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8
     A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
3441 If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
     Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes.
     From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
9381 If some inferences are needed to fix meaning, but we don't know which, they are all relevant [Fodor/Lepore, by Boghossian]
     Full Idea: The Master Argument for linguistic holism is: Some of an expression's inferences are relevant to fixing its meaning; there is no way to distinguish the inferences that are constitutive (from Quine); so all inferences are relevant to fixing meaning.
     From: report of J Fodor / E Lepore (Holism: a Shopper's Guide [1993], §III) by Paul Boghossian - Analyticity Reconsidered
     A reaction: This would only be if you thought that the pattern of inferences is what fixes the meanings, but how can you derive inferences before you have meanings? The underlying language of thought generates the inferences? Meanings are involved!