15 ideas
8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
10245 | One geometry cannot be more true than another [Poincaré] |
15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
18203 | Avoid non-predicative classifications and definitions [Poincaré] |
8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
7401 | Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck] |
5454 | Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo] |
16560 | Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver] |
8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
3645 | To understand the universe mathematics is essential [Galileo] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
19673 | Galileo mathematised movement, and revealed its invariable component - acceleration [Galileo, by Meillassoux] |