6 ideas
| 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. |
| 6457 | Sensations are mental, but sense-data could be mind-independent [Vesey] |
| Full Idea: Whereas a sensation is by definition mental, a sense-datum might be mind-independent. | |
| From: Godfrey Vesey (Collins Dictionary of Philosophy [1990], p.266) | |
| A reaction: This seems to be what Russell is getting at in 1912, as he clearly separates sense-data from sensations. Discussions of sense-data always assume they are mental, which may make them redundant - but so might making them physical. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |