6 ideas
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another. | |
From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6 | |
A reaction: Lake suggests that it should therefore be called CZF. |
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. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |