39 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] |
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] |
17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
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] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
17545 | Quantum theory shows that exact science does not need dogmatic realism [Heisenberg] |
17538 | Quantum theory does not introduce minds into atomic events [Heisenberg] |
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] |
17534 | A 'probability wave' is a quantitative version of Aristotle's potential, a mid-way type of reality [Heisenberg] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
17553 | We can retain the idea of 'substance', as indestructible mass or energy [Heisenberg] |
17544 | Basic particles have a mathematical form, which is more important than their substance [Heisenberg] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
17550 | We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
17549 | Seven theories in science: mechanics, heat, electricity, quantum, particles, relativity, life [Heisenberg, by PG] |
17540 | Energy is that which moves, and is the substance from which everything is made [Heisenberg] |
17541 | Energy is an unchanging substance, having many forms, and causing all change [Heisenberg] |
17548 | Maxwell introduced real fields, which transferred forces from point to point [Heisenberg] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
17533 | Radiation interference needs waves, but radiation photoelectric effects needs particles [Heisenberg] |
17532 | An atom's stability after collisions needs explaining (which Newton's mechanics can't do) [Heisenberg] |
17537 | Position is complementary to velocity or momentum, so the whole system is indeterminate [Heisenberg] |
17551 | It was formerly assumed that electromagnetic waves could not be a reality in themselves [Heisenberg] |
17543 | So-called 'empty' space is the carrier of geometry and kinematics [Heisenberg] |
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] |
17552 | In relativity the length of the 'present moment' is relative to distance from the observer [Heisenberg] |