13 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. |
| 20475 | Maybe modal sentences cannot be true or false [Casullo] |
| Full Idea: Some people claim that modal sentences do not express truths or falsehoods. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: I can only imagine this coming from a narrow hardline empiricist. It seems to me obvious that we make true or false statements about what is possible or impossible. |
| 20476 | If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo] |
| Full Idea: If one can only know a priori that a proposition is necessary, then one can know only a priori that a proposition is contingent. The evidence relevant to determining the latter is the same as that relevant to determining the former. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: This seems a telling point, but I suppose it is obvious. If you see that the cat is on the mat, nothing in the situation tells you whether this is contingent or necessary. We assume it is contingent, but that may be an a priori assumption. |
| 20471 | Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo] |
| Full Idea: There are three suggested epistemic conditions on a priori knowledge: the first regards the source of justification, the second regards the defeasibility of justification, and the third appeals to the strength of justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2) | |
| A reaction: [compressed] He says these are all inspired by Kant. The non-epistemic suggested condition involve necessity or analyticity. The source would have to be entirely mental; the defeasibly could not be experiential; the strength would be certainty. |
| 20477 | The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo] |
| Full Idea: The leading claim of proponents of the a priori is that sources of justification are of two significantly different types: experiential and nonexperiential. Initially this difference is marked at the phenomenological level. | |
| From: Albert Casullo (A Priori Knowledge [2002], 5) | |
| A reaction: He cites Plantinga and Bealer for the phenomenological starting point (that some knowledge just seems rationally obvious, certain, and perhaps necessary). |
| 20472 | Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo] |
| Full Idea: There is reason to view non-epistemic analyses of a priori knowledge (in terms of necessity or analyticity) with suspicion. The a priori concerns justification. Analysis by necessity or analyticity concerns the proposition rather than the justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2.1) | |
| A reaction: [compressed] The fact that the a priori is entirely a mode of justification, rather than a type of truth, is the modern view, influenced by Kripke. Given that assumption, this is a good objection. |
| 20474 | 'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo] |
| Full Idea: A justified belief that a proposition is not true is an 'overriding' defeater, ...and the belief that a justification is inadequate or defective is an 'undermining' defeater. | |
| From: Albert Casullo (A Priori Knowledge [2002], n 40) | |
| A reaction: Sounds more like a sliding scale than a binary option. Quite useful, though. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |