7 ideas
| 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. |
| 10650 | In the military, persons are parts of parts of large units, but not parts of those large units [Rescher] |
| Full Idea: In military usage, persons can be parts of small units, and small units parts of large ones; but persons are never parts of large units. | |
| From: Nicholas Rescher (Axioms for the Part Relation [1955]), quoted by Achille Varzi - Mereology 2.1 | |
| A reaction: This much-cited objection to the transitivity of the 'part' relation seems very odd. There could hardly be an army or a regiment if there weren't soldiers to make up parts of it. |
| 17503 | Theories can never represent accurately, because their components are abstract [Cartwright,N, by Portides] |
| Full Idea: Cartwright objects that the claim that theories represent what happens in actual situations is to overlook that the concepts used in them (such as 'force functions' and 'Hamiltonians') are abstract. | |
| From: report of Nancy Cartwright (The Dappled World [1999]) by Demetris Portides - Models 'Current' | |
| A reaction: I'm not convinced by this. The term 'abstract' is too loose. In a sense most words are abstract because they are universals. If I say 'that's a cat', that is a very accurate remark, despite the generality of 'cat'. |