7 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. |
| 18088 | Intentionality is the mark of dispositions, not of the mental [Place] |
| Full Idea: My thesis is that intentionality is the mark, not of the mental, but of the dispositional. | |
| From: Ullin T. Place (Intentionality and the Physical: reply to Mumford [1999], 1) | |
| A reaction: An idea with few friends, but I really like it, because it offers the prospect of a unified account of physical nature and the mind/brain. It seems reasonable to say my mind is essentially a bunch of dispositions. Mind is representations + dispositions. |
| 18089 | Dispositions are not general laws, but laws of the natures of individual entities [Place] |
| Full Idea: Dispositions are the substantive laws, not, as for Armstrong, of nature in general, but of the nature of individual entities whose dispositional properties they are. | |
| From: Ullin T. Place (Intentionality and the Physical: reply to Mumford [1999], 6) | |
| A reaction: [He notes that Nancy Cartwright 1989 agrees with him] I like this a lot. I tend to denegrate 'laws', because of their dubious ontological status, but this restores laws to the picture, in the place where they belong, in the stuff of the world. |
| 21236 | Instead of gravitational force, we now have a pervasive gravitational field [Farmelo] |
| Full Idea: Physics replaced the notion that bodies exert gravitational force on each other by the more effective picture that the bodies in the universe give rise to a pervasive gravitational field which exerts a force on each particle. | |
| From: Graham Farmelo (The Strangest Man [2009], 08) | |
| A reaction: This still uses the word 'force'. I sometimes get the impression that gravity is the curvature of space, but gravity needs more. Which direction along the curvature are particles attracted? The bottom line is the power of the bodies. |
| 21235 | The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo] |
| Full Idea: Dirac showed that the Schrödinger waves were simply the mathematical quantities involved in transforming the description of a quantum based on its energy values to one based on possible values of its position. | |
| From: Graham Farmelo (The Strangest Man [2009], 08) | |
| A reaction: Does this eliminate actual physical 'waves' from the theory? |
| 21234 | Experiments show that fundamental particles of one type are identical [Farmelo] |
| Full Idea: It is an established experimental fact ...that every single fundamental particle in the universe is the same and identical to all other particles of the same type. | |
| From: Graham Farmelo (The Strangest Man [2009], 07) | |
| A reaction: A loud groan is heard from the tomb of Leibniz. I'm unclear how experiments can establish this. If electrons have internal structure (which is not ruled out) then uniformity is highly unlikely. |