8 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. |
14895 | 'Superficial' contingency: false in some world; 'Deep' contingency: no obvious verification [Evans, by Macià/Garcia-Carpentiro] |
Full Idea: Evans says intuitively a sentence is 'superficially' contingent if the function from worlds to truth values assigns F to some world; it is 'deeply' contingent if understanding it does not guarantee that there is a verifying state of affairs. | |
From: report of Gareth Evans (Reference and Contingency [1979]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 2 | |
A reaction: This distinction is used by Davies and Humberstone (1980) to construct an early version of 2-D semantics (see under Language|Semantics). The point is that part comes from understanding it, and another part from assigning truth values. |
11881 | Rigid designators can be meaningful even if empty [Evans, by Mackie,P] |
Full Idea: Evans argues that there can be rigid designators that are meaningful even if empty. | |
From: report of Gareth Evans (Reference and Contingency [1979]) by Penelope Mackie - How Things Might Have Been 1.8 |
12709 | Motion is not absolute, but consists in relation [Leibniz] |
Full Idea: In reality motion is not something absolute, but consists in relation. | |
From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |