10 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. |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 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. |
| 23366 | We see nature's will in the ways all people are the same [Epictetus] |
| Full Idea: The will of nature may be learned from those things in which we do not differ from one another. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 26) | |
| A reaction: There you go! This is the rule for anthropologists on field trips. And it guides us towards a core of essential human nature. But it neglects the way that nature is expressed in different cultures, which is also important. |
| 4022 | Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C] |
| Full Idea: The injunction of Epictetus is well known, that in commiserating with another for his misfortune, we ought to talk consolingly, but not be moved by pity. | |
| From: report of Epictetus (The Handbook [Encheiridion] [c.58], §16) by Charles Taylor - Sources of the Self §15.1 | |
| A reaction: This goes strongly against the grain of the Christian tradition, but strikes me as an appealing attitude (even if I am the sufferer). |
| 23365 | If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus] |
| Full Idea: When you see someone weeping is sorrow …do not shrink from sympathising with him, and even groaning with him, but be careful not to groan inwardly too. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 16) | |
| A reaction: The point is that the person's suffering is an 'indifferent' because nothing can be done about it, and we should only really care about what we are able to choose. He is not opposed to the man's suffering, or his need for support. |
| 23368 | Perhaps we should persuade culprits that their punishment is just? [Epictetus] |
| Full Idea: The governor Agrippinus would try to persuade those whom he sentenced that it was proper for them to be sentenced, …just as the physician persuades a patient to accept their treatment. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 22) | |
| A reaction: This resembles the Contractualism of T.H. Scanlon (that actions are good if you can justify them to those involved). It may be possible to persuade people by the use of sophistry and lies. Nevertheless, a fairly civilise proposal. |