6 ideas
9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
Full Idea: Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space. | |
From: Tyler Burge (Frege on Apriority [2000], IV) | |
A reaction: This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics. |
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. |
9423 | If simplicity and strength are criteria for laws of nature, that introduces a subjective element [Mumford on Lewis] |
Full Idea: Lewis's simplicity and strength criteria introduce an element of subjectivity into the laws, because the best system seems to be determined by what we take to be simple and strong in a system. | |
From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
A reaction: [Mumford cites Armstrong 1983:67 for this] |
9424 | A number of systematizations might tie as the best and most coherent system [Mumford on Lewis] |
Full Idea: Since the best system view is a coherence theory, the possibility could not be ruled out that a number of different systematizations of the same history might be tied for first place as equally best. | |
From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
A reaction: [Mumord cites Armstrong 1983:70] Personally I am a fan of coherence theories, and this problem doesn't bother me. |
9409 | Laws are the best axiomatization of the total history of world events or facts [Lewis, by Mumford] |
Full Idea: The Mill-Ramsey-Lewis theory takes laws to be axioms (or theorems) of the best possible systematizations of the world's total history, where such a history is a history of events or facts. | |
From: report of David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 1.3 |
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. |