7 ideas
| 21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
| Full Idea: The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. | |
| From: Wilfrid Sellars (Philosophy and Scientific Image of Man [1962], p.3), quoted by Owen Flanagan - The Really Hard Problem 1 'Vocation' | |
| A reaction: I'm happier with broad things than broad hanging together, but to me this sounds about right. |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
| Full Idea: The 'Principle of Reducibility' says if an object is a system of objects, then every property of the object must consist in the fact that its constituents have such and such qualities and such and such relations | |
| From: Wilfrid Sellars (Philosophy and Scientific Image of Man [1962], p.27), quoted by William Lycan - Consciousness | |
| A reaction: This sounds to me a more promising attitude to reduction than all this talk of Ernest Nagel's 'Bridge Laws'. If we ask HOW a higher level property arises because of a lower level property, we can describe a mechanism rather than a law. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |