31 ideas
| 23889 | Among the Greeks Aristotle is the only philosopher in the modern style [Weil] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 20457 | Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli] |
| 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] |
| 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] |
| 20468 | Quantum mechanics deals with processes, rather than with things [Rovelli] |
| 20467 | Quantum mechanics describes the world entirely as events [Rovelli] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 20469 | There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli] |
| 20461 | The basic ideas of fields and particles are merged in quantum mechanics [Rovelli] |
| 20462 | Because it is quantised, a field behaves like a set of packets of energy [Rovelli] |
| 20463 | There are about fifteen particles fields, plus a few force fields [Rovelli] |
| 20464 | The world consists of quantum fields, with elementary events happening in spacetime [Rovelli] |
| 20459 | Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli] |
| 20460 | Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli] |
| 20466 | Quantum Theory describes events and possible interactions - not how things are [Rovelli] |
| 20465 | Nature has three aspects: granularity, indeterminacy, and relations [Rovelli] |
| 20458 | The world is just particles plus fields; space is the gravitational field [Rovelli] |
| 20470 | Only heat distinguishes past from future [Rovelli] |
| 23892 | The only legitimate proof of God by order derives from beauty [Weil] |