54 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 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] |
| 12699 | A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz] |
| 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] |
| 12700 | Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz] |
| 12736 | If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber] |
| 17550 | We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg] |
| 12698 | Every body contains a kind of sense and appetite, or a soul [Leibniz] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 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] |