17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
9941 | Science requires more than consistency of mathematics [Putnam] |
18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
8732 | It is spooky the way mathematics anticipates physics [Weinberg] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
3143 | Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey] |
10261 | The application of mathematics only needs its possibility, not its truth [Shapiro on Field,H] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
8863 | We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
14604 | If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J] |
8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |