29 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
| 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] |
| 17550 | We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg] |
| 22307 | Propositions don't name facts, because two opposed propositions can match one fact [Russell] |
| 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] |
| 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] |
| 17532 | An atom's stability after collisions needs explaining (which Newton's mechanics can't do) [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] |