11 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. |
| 19718 | Indefeasibility does not imply infallibility [Grundmann] |
| Full Idea: Infallibility does not follow from indefeasibility. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: If very little evidence exists then this could clearly be the case. It is especially true of historical and archaeological evidence. |
| 19717 | Can a defeater itself be defeated? [Grundmann] |
| Full Idea: Can the original justification of a belief be regained through a successful defeat of a defeater? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeater-Defs') | |
| A reaction: [Jäger 2005 addresses this] I would have thought the answer is yes. I aspire to coherent justifications, so I don't see justifications as a chain of defeat and counter-defeat, but as collective groups of support and challenge. |
| 19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
| Full Idea: An unmodified reliabilism does not accommodate defeaters, and surely there can be defeaters against reliably produced beliefs? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeaters') | |
| A reaction: [He cites Bonjour 1980] Reliabilism has plenty of problems anyway, since a generally reliable process can obviously occasionally produce a bad result. 20:20 vision is not perfect vision. Internalist seem to like defeaters. |
| 19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
| Full Idea: There are 'rebutting' defeaters against the truth of a previously justified belief, 'undercutting' defeaters against the power of the evidence, and 'reason-defeating' defeaters against the truth of the reason for the belief. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'How') | |
| A reaction: That is (I think) that you can defeat the background, the likelihood, or the truth. He cites Pollock 1986, and implies that these are standard distinctions about defeaters. |
| 19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
| Full Idea: Advocates of the defeasibility theory have tried to exclude true pieces of information that are misleading defeaters. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: He gives as an example the genuine news of a claim that the suspect has a twin. |
| 19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
| Full Idea: The 'defeasibility theory' of knowledge claims that knowledge is only present if there are no facts that - if they were known - would be genuine defeaters of the relevant justification. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: Something not right here. A genuine defeater would ensure the proposition was false, so it would simply fail the truth test. So we need a 'defeater' for a truth, which must therefore by definition be misleading. Many qualifications have to be invoked. |
| 19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
| Full Idea: Theories that combine basic justification with the defeasibility of this justification are referred to as 'moderate' foundationalism. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: I could be more sympathetic to this sort of foundationalism. But it begins to sound more like Neurath's boat (see Quine) than like Descartes' metaphor of building foundations. |
| 7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
| Full Idea: Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius. | |
| From: report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny. |