8 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. |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
| A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
| A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
| 23829 | National leaders want to preserve necessary order - but always the existing order [Weil] |
| Full Idea: Those in command see their duty as defending order, without which no social life can survive; and the only order they conceive is the existing one. | |
| From: Simone Weil (The Power of Words [1934], p.249) | |
| A reaction: She sympathises with them, because a new order is such an unknown. But it always struck me as weird that traditions are preserved because they are traditions, and not because they are good. (My old school, for example!). |
| 23828 | National prestige consists of behaving as if you could beat the others in a war [Weil] |
| Full Idea: What is called national prestige consists in behaving always in such a way as to demoralise other nations by giving them the impression that, if it comes to war, one would certainly defeat them. | |
| From: Simone Weil (The Power of Words [1934], p.244) | |
| A reaction: It's true. No nation gains prestige because of the happy lives of its citizens, or the creativity of its culture. |
| 23827 | Modern wars are fought in the name of empty words which are given capital letters [Weil] |
| Full Idea: For our contemporaries the role of Helen in the Trojan War is is played by words with capital letters. …When empty words are given capital letters, then, on the slightest pretext, men will begin shedding blood for them and piling up ruin in their name. | |
| From: Simone Weil (The Power of Words [1934], p.241) | |
| A reaction: This seems particularly true of the 1930s, where specific dogmatic ideologies seemed to grip and divide people. Simple aggressive nationalism seems to be the cause of current wars, now the fear of Communism has diminished. |