9 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. |
| 15464 | The distinction between dispositional and 'categorical' properties leads to confusion [Lewis] |
| Full Idea: To avoid the danger of claiming that dispositions are their own categorical bases, we do better to eschew the alleged distinction between dispositional and 'categorical' properties altogether. | |
| From: David Lewis (Finkish dispositions [1997], II) | |
| A reaction: Since I have been unable to form any intuitive notion of what a 'categorical' property is, I like this, though not necessarily for his reason. |
| 15463 | All dispositions must have causal bases [Lewis] |
| Full Idea: Prior, Pargetter and Jackson have argued convincingly for the thesis that all dispositions must have causal bases. | |
| From: David Lewis (Finkish dispositions [1997], II) | |
| A reaction: [Their paper is 1982] This key thesis is tackled by modern defenders of powers. The question is not who has the best arguments, but who offers the most coherent picture. What is a 'causal basis'? What sort of thing could be primitive or fundamental? |
| 15461 | A 'finkish' disposition is real, but disappears when the stimulus occurs [Lewis] |
| Full Idea: A disposition which would straight away vanish if put to the test is called 'finkish'. A finkishly fragile thing is fragile so long as it is not struck. But if it were struck, it would straight away cease to be fragile, and it would not break. | |
| From: David Lewis (Finkish dispositions [1997], I) | |
| A reaction: There are also 'antidotes'. Finks kill the disposition, antidotes kill the effect. These cases are problems for the simple conditional analysis of a disposition - because we never achieved the consequent. |
| 15462 | Backtracking counterfactuals go from supposed events to their required causal antecedents [Lewis] |
| Full Idea: 'Backtracking' counterfactual reasoning runs from a counterfactually supposed event to the causal antecedents it would have to have had. | |
| From: David Lewis (Finkish dispositions [1997], I) | |
| A reaction: Why not call it a 'transcendental' counterfactual? Presumably you go thisworld>> counterfactualevent>> worldneededtocauseit. It conjures up two possible worlds instead of one. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |