63 ideas
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 20589 | Maybe a person's true self is their second-order desires [Tuckness/Wolf] |
| 9073 | Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J] |
| 9074 | Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J] |
| 9072 | Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J] |
| 20583 | If maximising pleasure needs measurement, so does fulfilling desires [Tuckness/Wolf] |
| 20584 | Desire satisfaction as the ideal is confused, because we desire what we judge to be good [Tuckness/Wolf] |
| 20598 | In a democracy, which 'people' are included in the decision process? [Tuckness/Wolf] |
| 20614 | People often have greater attachment to ethnic or tribal groups than to the state [Tuckness/Wolf] |
| 20596 | For global justice, adopt rules without knowing which country you will inhabit [Tuckness/Wolf] |
| 20593 | The veil of ignorance ensures both fairness and unanimity [Tuckness/Wolf] |
| 20608 | Unjust institutions may be seen as just; are they legitimate if just but seen as unjust? [Tuckness/Wolf] |
| 20597 | If winning elections depends on wealth, we have plutocracy instead of democracy [Tuckness/Wolf] |
| 20606 | Epistemic theories defend democracy as more likely to produce the right answer [Tuckness/Wolf] |
| 20600 | Which areas of public concern should be decided democratically, and which not? [Tuckness/Wolf] |
| 20609 | If several losing groups would win if they combine, a runoff seems called for [Tuckness/Wolf] |
| 20605 | Rights as interests (unlike rights as autonomy) supports mandatory voting [Tuckness/Wolf] |
| 20599 | How should democratic votes be aggregated? Can some person's votes count for more? [Tuckness/Wolf] |
| 20601 | Discussion before voting should be an essential part of democracy [Tuckness/Wolf] |
| 20613 | We have obligations to our family, even though we didn't choose its members [Tuckness/Wolf] |
| 20586 | Free speech does not include the right to shout 'Fire!' in a crowded theatre [Tuckness/Wolf] |
| 20587 | Most people want equality because they want a flourishing life [Tuckness/Wolf] |
| 20591 | If there is no suffering, wealth inequalities don't matter much [Tuckness/Wolf] |
| 20602 | Some rights are 'claims' that other people should act in a certain way [Tuckness/Wolf] |
| 20604 | Choice theory says protecting individual autonomy is basic (but needs to cover infants and animals) [Tuckness/Wolf] |
| 20603 | One theory (fairly utilitarian) says rights protect interests (but it needs to cover trivial interests) [Tuckness/Wolf] |
| 20607 | Having a right does not entail further rights needed to implement it [Tuckness/Wolf] |
| 20612 | If being subject to the law resembles a promise, we are morally obliged to obey it [Tuckness/Wolf] |
| 20611 | If others must obey laws that we like, we must obey laws that they like? [Tuckness/Wolf] |
| 20610 | Instead of against natural law, we might assess unjust laws against the values of the culture [Tuckness/Wolf] |
| 20617 | How should the punishment fit the crime (for stealing chickens?) [Tuckness/Wolf] |
| 20615 | Just wars: resist aggression, done on just cause, proportionate, last resort, not futile, legal [Tuckness/Wolf] |
| 20616 | During wars: proportional force, fair targets, fair weapons, safe prisoners, no reprisals [Tuckness/Wolf] |
| 20620 | If minority views are accepted in debate, then religious views must be accepted [Tuckness/Wolf] |
| 20619 | Is abortion the ending of a life, or a decision not to start one? [Tuckness/Wolf] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |