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. |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible. | |
| From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4 | |
| A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'. |
| 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. |
| 19813 | All legislators invoke God in support of extraordinary laws, because their justification is not obvious [Machiavelli] |
| Full Idea: There has never been a single legislator who, in proposing extraordinary laws, did not have recourse to God, for otherwise they would not be accepted, since many benefits known to a prudent man do not have evident persuasive reasons. | |
| From: Niccolo Machiavelli (The Discourses [1520], 1.11), quoted by Jean-Jacques Rousseau - The Social Contract (tr Cress) II.7 n8 | |
| A reaction: It does seem to be an important role for God and state religion, to give support to decisions and laws which might not be intrinsically popular. |
| 7126 | Rulers should preserve the foundations of religion, to ensure good behaviour and unity [Machiavelli] |
| Full Idea: It is the duty of the rulers of a republic or a kingdom to preserve the foundations of the religion they hold; if they do this, it will be an easy thing for them to keep their state religious, and consequently good and united. | |
| From: Niccolo Machiavelli (The Discourses [1520], I.12) | |
| A reaction: This is the germ of Marx's view, that the sole role of religion is political, as a tool used by the ruling classes to keep the populace in their place. The same idea can be found in Critias (Idea 542). But what is wrong with some central moral guidance? |