6 ideas
21560 | Any linguistic expression may lack meaning when taken out of context [Russell] |
Full Idea: Any sentence, a single word, or a single component phrase, may often be quite devoid of meaning when separated from its context. | |
From: Bertrand Russell (Substitutional Classes and Relations [1906], p.165) | |
A reaction: Contextualism is now extremely fashionable, in philosophy of language and in epistemology. Here Russell is looking for a contextual way to define classes [so says Lackey, the editor]. |
21561 | 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell] |
Full Idea: 'The number one is bald' or 'the number one is fond of cream cheese' are, I maintain, not merely silly remarks, but totally devoid of meaning. | |
From: Bertrand Russell (Substitutional Classes and Relations [1906], p.166) | |
A reaction: He connects this to paradoxes in set theory, such as the assertion that 'the class of human beings is a human being' (which is the fallacy of composition). |
8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'. | |
From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9) | |
A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part |
18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
Full Idea: Russell's Axiom of Reducibility states that to any propositional function of any order in a given level, there corresponds another which is of the lowest possible order in the level. There corresponds what he calls a 'predicative' function of that level. | |
From: report of Bertrand Russell (Substitutional Classes and Relations [1906]) by David Bostock - Philosophy of Mathematics 8.2 |
21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
Full Idea: Relations in intension are of the utmost importance to philosophy and philosophical logic, since they are essential to complexity, and thence to propositions, and thence to the possibility of truth and falsehood. | |
From: Bertrand Russell (Substitutional Classes and Relations [1906], p.174) | |
A reaction: Should we able to specify the whole of reality, if we have available to us objects, properties and relations? There remains indeterminate 'stuff', when it does not compose objects. There are relations between pure ideas. |
6171 | Beliefs are states of the head that explain behaviour, and also items with referential truth-conditions [McGinn] |
Full Idea: We view beliefs both as states of the head explanatory of behaviour, and as items possessed of referential truth-conditions. | |
From: Colin McGinn (The Structure of Content [1982]), quoted by Mark Rowlands - Externalism Ch.6 | |
A reaction: McGinn wants to build a two-part account of meaning on this point, which Rowlands resists. Hume just wanted to define belief by a feeling, but it seems obvious that truth must also be involved. |