49 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
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] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20589 | Maybe a person's true self is their second-order desires [Tuckness/Wolf] |
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] |