7 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. |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
| From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
| 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'). |
| 9354 | Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt] |
| Full Idea: Why should we accept that necessities can only be known a priori? Prima facie, some necessities are known empirically; for example, that water is necessarily H2O, and that Hesperus is necessarily Phosphorus. | |
| From: Michael Devitt (There is no a Priori [2005], §2) | |
| A reaction: An important question, whatever your view. If the only thing we can know a priori is necessities, it doesn't follow that necessities can only be known a priori. It gets interesting if we say that some necessities can never be known a priori. |
| 9353 | We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt] |
| Full Idea: We have no need to turn to an a priori explanation of our knowledge of mathematics and logic. Our intuitions that this knowledge is not justified in some direct empirical way is preserved. It is justified in an indirect holistic way. | |
| From: Michael Devitt (There is no a Priori [2005], §2) | |
| A reaction: I think this is roughly the right story, but the only way it will work is if we have some sort of theory of abstraction, which gets us up the ladder of generalisations to the ones which, it appears, are necessarily true. |
| 9356 | The idea of the a priori is so obscure that it won't explain anything [Devitt] |
| Full Idea: The whole idea of the a priori is too obscure for it to feature in a good explanation of our knowledge of anything. | |
| From: Michael Devitt (There is no a Priori [2005], §3) | |
| A reaction: I never like this style of argument. It would be nice if all the components of all our our explanations were crystal clear. Total clarity about anything is probably a hopeless dream, and we may have to settle for murky corners in all explanations. |