6 ideas
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 15150 | The properties of an electron can't be explained just as 'clustering' [Chakravartty on Boyd] |
| Full Idea: Boyd's homeostatic mechanisms are not responsible for the co-instantiation of the mass, charge and spin of an electron. | |
| From: comment on Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3 | |
| A reaction: I would have thought that no one has the foggiest idea (unless I have missed something?) about why electrons have those three properties. What is it about electrons that makes them do that? Explanations always run out somewhere. Substratum! |
| 15149 | Properties cluster together, either because of intrinsic relations, or because of an underlying process [Boyd, by Chakravartty] |
| Full Idea: Boyd analyses 'sociability' between properties in terms of 'homeostasis', as causal relations between properties that favour clustering, or underlying processes that favour coinstantiation, or both. | |
| From: report of Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3 | |
| A reaction: Chakravarty criticises this claim, by Boyd is clearly onto something. If, like me, you think natural kinds are overrated, you have to like his view. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |