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. |
14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition. | |
From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3 | |
A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers? |
22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
Full Idea: I am training and sharpening my appetite for those pleasures that are left. ...We must cling tooth and claw to the use of the pleasures of this life which the advancing years, one after another, rip from our grasp. | |
From: Michel de Montaigne (I.39 On Solitude [1580], p.276) | |
A reaction: That may be one of the most inspiring ideas I have read about pleasure. |