6 ideas
| 6409 | The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling] |
| Full Idea: The idea that there should be something like a distinction of levels among properties is captured in Ramsey's 'simple theory of types'. | |
| From: report of Frank P. Ramsey (works [1928]) by A.C. Grayling - Russell | |
| A reaction: I merely report this, though it is not immediately obvious how anyone would decide which 'level' a type belonged on. |
| 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. |
| 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. |
| 3212 | Beliefs are maps by which we steer [Ramsey] |
| Full Idea: Beliefs are maps by which we steer. | |
| From: Frank P. Ramsey (works [1928]), quoted by Georges Rey - Contemporary Philosophy of Mind p.259 n5 |
| 21799 | We just use the word 'faculty' when we don't know the psychological cause [Galen] |
| Full Idea: So long as we are ignorant of the true essence of the cause which is operating, we call it a 'faculty'. | |
| From: Galen (On the Natural Faculties [c.170], I.iv), quoted by Dominik Perler - Intro to The Faculties: a History 2 | |
| A reaction: This is probably the view of most modern neuroscientists. I want to defend the idea that we need the concept of a faculty in philosophy, even if the psychologists and neuroscientists say it is too vague for their purposes. |