5 ideas
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
| From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
| 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. |
| 4784 | Salmon says processes rather than events should be basic in a theory of physical causation [Salmon, by Psillos] |
| Full Idea: Salmon argues that processes rather than events should be the basic entities in a theory of physical causation. | |
| From: report of Wesley Salmon (Causal Connections [1984]) by Stathis Psillos - Causation and Explanation §4.2 | |
| A reaction: It increasingly strikes me that the concept of a 'process' ought to be ontologically basic. Edelman says the mind is a process. An 'event' is too loose, and a 'fact' too vague, and heaven knows what Hume meant by an 'object'. |