37 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] |
| 23674 | If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid] |
| 23675 | We shouldn't do to others what would be a wrong to us in similar circumstances [Reid] |
| 23672 | To be virtuous, we must care about duty [Reid] |
| 23673 | Every worthy man has a principle of honour, and knows what is honourable [Reid] |
| 20624 | Work degrades into heat, but not vice versa [Close] |
| 20623 | First Law: energy can change form, but is conserved overall [Close] |
| 20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
| 20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
| 20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
| 20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
| 20642 | Photon exchange drives the electro-magnetic force [Close] |
| 20627 | Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close] |
| 20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
| 20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
| 20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
| 20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
| 20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
| 20641 | Electrons get their mass by interaction with the Higgs field [Close] |
| 20631 | Dirac showed how electrons conform to special relativity [Close] |
| 20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
| 20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
| 20640 | Space-time is indeterminate foam over short distances [Close] |