30 ideas
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
9576 | Multiplicity in general is just one and one and one, etc. [Husserl] |
17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
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] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
9575 | Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege] |
21214 | We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |