34 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 17545 | Quantum theory shows that exact science does not need dogmatic realism [Heisenberg] |
| 17538 | Quantum theory does not introduce minds into atomic events [Heisenberg] |
| 17534 | A 'probability wave' is a quantitative version of Aristotle's potential, a mid-way type of reality [Heisenberg] |
| 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] |
| 16473 | Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker] |
| 19258 | Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 17550 | We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg] |
| 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] |
| 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] |
| 17552 | In relativity the length of the 'present moment' is relative to distance from the observer [Heisenberg] |