35 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] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| 21202 | The strong force has a considerably greater range than the weak force [Martin,BR] |
| 21211 | If an expected reaction does not occur, that implies a conservation law [Martin,BR] |
| 21209 | Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR] |
| 21201 | A 'field' is just a region to which points can be assigned in space and time [Martin,BR] |
| 21212 | The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR] |
| 21205 | Many physicists believe particles have further structure, if only we could see it [Martin,BR] |
| 21203 | Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR] |
| 21207 | The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR] |
| 21204 | The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR] |
| 21208 | Eletrons don't literally 'spin', because they are point-like [Martin,BR] |
| 21210 | Virtual particles surround any charged particle [Martin,BR] |
| 21206 | The properties of a particle are determined by its quantum numbers and its mass [Martin,BR] |
| 21213 | String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR] |
| 21200 | An 'element' is what cannot be decomposed by chemistry [Martin,BR] |