13 ideas
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.216) | |
| A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject. |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
| A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| Full Idea: Russell's theory of types meant that features common to different levels of the hierarchy became uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (The Theory of Logical Types [1910]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: I'm not clear whether this is the main reason why type theory was abandoned. Ramsey was an important critic. |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| Full Idea: In Russell's mature 1910 theory of types classes are defined in terms of propositional functions, and functions themselves are regimented by a ramified theory of types mitigated by the axiom of reducibility. | |
| From: report of Bertrand Russell (The Theory of Logical Types [1910]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133 |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
| Full Idea: We will define a function of one variable as 'predicative' when it is of the next order above that of its arguments, i.e. of the lowest order compatible with its having an argument. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.237) | |
| A reaction: 'Predicative' just means it produces a set. This is Russell's strict restriction on which functions are predicative. |
| 17488 | Empiricist theories are sets of laws, which give explanations and reductions [Glennan] |
| Full Idea: In the empiricist tradition theories were understood to be deductive closures of sets of laws, explanations were understood as arguments from covering laws, and reduction was understood as a deductive relationship between laws of different theories. | |
| From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
| A reaction: A lovely crisp summary of the whole tradition of philosophy of science from Comte through to Hempel. Mechanism and essentialism are the new players in the game. |
| 17493 | Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan] |
| Full Idea: Modern champions of mechanisms say models should identify both the parts and their spatial, temporal and functional organisation, ...and the practical importance of diagrams in addition to or in place of linguistic representations of mechanisms. | |
| From: Stuart Glennan (Mechanisms [2008], 'Discover') | |
| A reaction: Apparently chemists obtain much more refined models by using mathematics than they did by diagrams or 3D models (let alone verbal descriptions). For that reason, I'm thinking that 'model' might be a better term than 'mechanism'. |
| 17487 | Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan] |
| Full Idea: To a significant degree, a mechanistic philosophy of science can be seen as an alternative to an earlier logical empiricist tradition in philosophy of science that gave pride of place to laws of nature. | |
| From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
| A reaction: Lovely! Someone who actually spells out what's going on here. Most philosophers are far too coy about explaining what their real game is. Mechanism is fine in chemistry and biology. How about in 'mathematical' physics, or sociology? |
| 17489 | Mechanisms are either systems of parts or sequences of activities [Glennan] |
| Full Idea: There are two sorts of mechanisms: systems consist of collections of parts that interact to produce some behaviour, and processes are sequences of activities which produce some outcome. | |
| From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
| A reaction: [compressed] The second one is important because it is more generic, and under that account all kinds the features of the world that need to be explained can be subsumed. E.g. hyperinflation in an economy is a 'mechanism'. |
| 17490 | 17th century mechanists explained everything by the kinetic physical fundamentals [Glennan] |
| Full Idea: 17th century mechanists said that interactions governed by chemical, electrical or gravitational forces would have to be explicable in terms of the operation of some atomistic (or corpuscular) kinetic mechanism. | |
| From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
| A reaction: Glennan says science has rejected this, so modern mechanists do not reduce mechanisms to anything in particular. |
| 17491 | Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan] |
| Full Idea: One of the advantages of the move from nomological to mechanistic modes of explanation is that the latter allows for explanations involving exception-ridden generalizations. | |
| From: Stuart Glennan (Mechanisms [2008], 'regular') | |
| A reaction: The lawlike approach has endless problems with 'ceteris paribus' ('all things being equal') laws, where specifying all the other 'things' seems a bit tricky. |
| 17494 | Since causal events are related by mechanisms, causation can be analysed in that way [Glennan] |
| Full Idea: Causation can be analyzed in terms of mechanisms because (except for fundamental causal interactions) causally related events will be connected by intervening mechanisms. | |
| From: Stuart Glennan (Mechanisms [2008], 'causation') | |
| A reaction: This won't give us the metaphysics of causation (which concerns the fundamentals), but this strikes me as a very coherent and interesting proposal. He mentions electron interaction as non-mechanistic causation. |