5 ideas
| 21563 | The 'no classes' theory says the propositions just refer to the members [Russell] |
| Full Idea: The contention of the 'no classes' theory is that all significant propositions concerning classes can be regarded as propositions about all or some of their members. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.200) | |
| A reaction: Apparently this theory has not found favour with later generations of theorists. I see it in terms of Russell trying to get ontology down to the minimum, in the spirit of Goodman and Quine. |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 21565 | Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell] |
| Full Idea: In Richard's puzzle, we use the notion of 'definition', and this, oddly enough, is not definable, and is indeed not a definite notion at all. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.209) | |
| A reaction: The background for this claim is his type theory, which renders certain forms of circular reference meaningless. |
| 21564 | Vicious Circle: what involves ALL must not be one of those ALL [Russell] |
| Full Idea: The 'vicious-circle principle' says 'whatever involves an apparent variable must not be among the possible values of that variable', or (less exactly) 'whatever involves ALL must not be one of ALL which it involves. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.204) | |
| A reaction: He offers this as a parallel to his 'no classes' principle. That referred to classes, but this refers to propositions, and specifically the Liar Paradox (which he calls the 'Epimenedes'). |
| 5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
| Full Idea: The soul, when it has partaken of intelligence and reason and concord, is not merely a work but also a part of god and has come to be not by his agency but both from him as source and out of his substance. | |
| From: Plutarch (67: Platonic Questions [c.85], II.1001) | |
| A reaction: A most intriguing shift of view from earlier concepts of the psuché. How did this come about? This man is a pagan. The history is in the evolution of Platonism. See 'The Middle Platonists' by John Dillon. Davidson is also very impressed by reason. |