8 ideas
| 13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
| Full Idea: Russell's Paradox is a stripped-down version of Cantor's Paradox. | |
| From: comment on Bertrand Russell (Letters to Frege [1902]) by Graham Priest - The Structure of Paradoxes of Self-Reference §2 |
| 10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
| Full Idea: Russell's paradox showed that we cannot consistently assume what is sometimes called the 'naïve comprehension principle', namely that every property is collectivizing. | |
| From: comment on Bertrand Russell (Letters to Frege [1902]) by Michael Potter - Set Theory and Its Philosophy 03.6 |
| 9127 | Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen] |
| Full Idea: Russell refuted Frege's principle that there is a set for each property. | |
| From: report of Bertrand Russell (Letters to Frege [1902], 1904.12.12) by Roy Sorensen - Vagueness and Contradiction 6.1 | |
| A reaction: This is the principle stumbling block to any attempt to explain properties purely in terms of sets. I would say that Russell proved there couldn't be a set for each predicate. You can't glibly equate proper properties with predicates. |
| 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
| Full Idea: Ramsey suggested that 'if', 'given that' and 'on the supposition that' come to the same thing, and that the degrees of belief in the antecedent should then conform to probability theory. | |
| From: report of Frank P. Ramsey (Truth and Probability [1926]) by Frank P. Ramsey - Law and Causality B | |
| A reaction: [compressed] |
| 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
| Full Idea: Ramsey gave an axiomatic treatment of preference in the face of uncertainty, when applied to a particular agent. | |
| From: report of Frank P. Ramsey (Truth and Probability [1926]) by Donald Davidson - Truth and Predication 2 | |
| A reaction: This is evidently the beginnings of Bayesian decision theory. |
| 7531 | We don't assert private thoughts; the objects are part of what we assert [Russell] |
| Full Idea: I believe Mont Blanc itself is a component part of what is actually asserted in the proposition 'Mont Blanc is more than 4000 metres high'; we do not assert the thought, which is a private psychological matter, but the object of the thought. | |
| From: Bertrand Russell (Letters to Frege [1902], 1904.12.12), quoted by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: This would appear to be pretty much externalism about concepts, given that Russell would accept that other people know much more about Mont Blanc than he does, and their knowledge is included in what he asserts. |
| 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. |