7 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. |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
| From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
| A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |
| 22331 | Moral statements are imperatives rather than the avowals of emotion - but universalisable [Hare, by Glock] |
| Full Idea: According to Hare's universal prescriptivism, moral statements are closer to imperatives than to avowals of emotion; their purpose is to guide action. But unlike imeperatives they are universalisable. | |
| From: report of Richard M. Hare (Freedom and Reason [1963]) by Hans-Johann Glock - What is Analytic Philosophy? 2.9 | |
| A reaction: Why isn't 'everyone ought to support West Ham' a moral judgement? |
| 22484 | Universalised prescriptivism could be seen as implying utilitarianism [Hare, by Foot] |
| Full Idea: Hare has suggested that a fairly tight form of utilitarianism can be obtained from universalised prescriptivism. | |
| From: report of Richard M. Hare (Freedom and Reason [1963]) by Philippa Foot - Does Moral Subjectivism Rest on a Mistake? p.191 | |
| A reaction: All the benefits of Bentham, Kant and Hume, in one neat package! Since I take all three of them to be wrong about ethics, that counts against this idea. |
| 6449 | The categorical imperative leads to utilitarianism [Hare, by Nagel] |
| Full Idea: Hare has proposed that utilitarianism is the ultimate standard to which we are led by the categorical imperative. | |
| From: report of Richard M. Hare (Freedom and Reason [1963], p.123-4) by Thomas Nagel - Equality and Partiality | |
| A reaction: It seems to me better to say that Kant starts (unwittingly) from something like utilitarianism, that is, an assumption that human happiness and welfare have some sort of intrinsic value that cannot be demonstrated. Otherwise evil can be universalised. |