6 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory. | |
| From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1 | |
| A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises. |
| 12314 | Audience-relative explanation, or metaphysical explanation based on information? [Stanford] |
| Full Idea: Rather than an 'interest-relative' notion of explanation (Putnam), it can be informational content which makes an explanation, which is an 'audience-invariant' contraint, which is not pragmatic, but mainly epistemological and also partly metaphysical. | |
| From: Michael Stanford (Explanation: the state of play [1991], p.172) | |
| A reaction: [compressed summary of Ruben 1990] Examples given are that Rome burning explains Nero fiddling, even if no one ever says so, and learning that George III had porphyria explains his madness. |
| 12313 | Explanation is for curiosity, control, understanding, to make meaningful, or to give authority [Stanford] |
| Full Idea: There are a number of reasons why we explain: out of sheer curiosity, to increase our control of a situation, to help understanding by simplifying or making familiar, to confer meaning or significance, and to give scientific authority to some statement. | |
| From: Michael Stanford (Explanation: the state of play [1991], p.172) |
| 12315 | We can explain by showing constitution, as well as showing causes [Stanford] |
| Full Idea: The powerful engine of my car can be explained by an examination of each of its parts, but it is not caused by them. They do not cause the engine; they constitute it. | |
| From: Michael Stanford (Explanation: the state of play [1991], p.174) | |
| A reaction: [example from Ruben 1990:221] This could be challenged, since there is clearly a causal connection between the constitution and the whole. We distinguish engine parts which contribute to the power from those which do not. |