5 ideas
18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
Full Idea: The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems, | |
From: Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
A reaction: The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted? |
14742 | It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N] |
Full Idea: Insofar as identity seems vague, it is provably mistaken. If it is vague whether x and y are identical (as in the Ship of Theseus), then x,y is definitely not the same as x,x, since the first pair is indeterminate and the second pair isn't. | |
From: Nathan Salmon (Reference and Essence: seven appendices [2005], App I) | |
A reaction: [compressed; Gareth Evans 1978 made a similar point] This strikes me as begging the question in the Ship case, since we are shoehorning the new ship into either the slot for x or the slot for y, but that was what we couldn’t decide. No rough identity? |
18885 | Kripke and Putnam made false claims that direct reference implies essentialism [Salmon,N] |
Full Idea: Kripke and Putnam made unsubstantiated claims, indeed false claims, to the effect that the theory of direct reference has nontrivial essentialist import. | |
From: Nathan Salmon (Reference and Essence: seven appendices [2005], Pref to Exp Ed) | |
A reaction: Kripke made very few claims, and is probably innocent of the charge. Most people agree with Salmon that you can't derive metaphysics from a theory of reference. |
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. |
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. |