4 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. |
| 16627 | If you remove the accidents from a horse and a lion, the intellect can't tell them apart [Francis of Marchia] |
| Full Idea: Let all accidents be removed from a lion and a horse. Nothing remains in the intellect to distinguish them. We distinguish a lion and a horse only by analogy to the accidents proper to each. The intellect does not have an essential concept of either one. | |
| From: Francis of Marchia (Commentary on Sentences [1330], I.3.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.3 | |
| A reaction: What a very nice thought experiment, and very convincing about how the mind perceives such things. But we don't believe horse and lion just consists of the surface properties of them which we experience. |
| 21650 | No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber] |
| Full Idea: For Paul Pietroski no expression in natural language is semantically referential. ....Reference to objects occurs not at the level of semantics, but at the level of thought or utterance. | |
| From: report of Paul M. Pietroski (Events and Semantic Architecture [2004]) by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 07.2 | |
| A reaction: Love this. It has always struck me that reference is what speakers do. Try taking any supposedly referential description and sticking 'so-called' in front of it. That seems to leave you with the reference even though you have denied the description. |