6 ideas
15381 | Dyamic logics model changes between classical states, in action, belief, and computing [Uckelman] |
Full Idea: Dynamic logic gives versions of propositional, modal and predicate logics, in which the states are classical, but changes of assignments between states can be expressed, by modelling action, knowledge and belief change, and compute programs. | |
From: Sara L. Uckelman (Dynamic Logics [2010]) | |
A reaction: [compressed] |
23476 | Logical constants seem to be entities in propositions, but are actually pure form [Russell] |
Full Idea: 'Logical constants', which might seem to be entities occurring in logical propositions, are really concerned with pure form, and are not actually constituents of the propositions in the verbal expressions of which their names occur. | |
From: Bertrand Russell (The Theory of Knowledge [1913], 1.IX) | |
A reaction: This seems to entirely deny the existence of logical constants, and yet he says that they are named. Russell was obviously under pressure here from Wittgenstein. |
23477 | We use logical notions, so they must be objects - but I don't know what they really are [Russell] |
Full Idea: Such words as or, not, all, some, plainly involve logical notions; since we use these intelligently, we must be acquainted with the logical objects involved. But their isolation is difficult, and I do not know what the logical objects really are. | |
From: Bertrand Russell (The Theory of Knowledge [1913], 1.IX) | |
A reaction: See Idea 23476, from the previous page. Russell is struggling. Wittgenstein was telling him that the constants are rules (shown in truth tables), rather than objects. |
18273 | Logical truths are known by their extreme generality [Russell] |
Full Idea: A touchstone by which logical propositions may be distinguished from all others is that they result from a process of generalisation which has been carried to its utmost limits. | |
From: Bertrand Russell (The Theory of Knowledge [1913], p.129), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What' |
22315 | There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell] |
Full Idea: On Russell's pre-war conception it is obvious that a complex cannot be negative. If a complex were true, what would make it false would be its non-existence, not the existence of some other complex. | |
From: comment on Bertrand Russell (The Theory of Knowledge [1913]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 41 'Neg' | |
A reaction: It might be false because it doesn't exist, but also 'made' false by a rival complex (such as Desdemona loving Othello). |
9591 | The human intellect has not been, and cannot be, fully formalized [Nagel/Newman] |
Full Idea: The resources of the human intellect have not been, and cannot be, fully formalized. | |
From: E Nagel / JR Newman (Gödel's Proof [1958], VIII) | |
A reaction: This conclusion derives from Gödel's Theorem. Some people (e.g. Penrose) get over-excited by this discovery, and conclude that the human mind is supernatural. Imagination is the key - it is a feature of rationality that escapes mechanization. |