37 ideas
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 17867 | If a concept is not compact, it will not be presentable to finite minds [Almog] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 17872 | Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog] |
| 17871 | Fregean meanings are analogous to conceptual essence, defining a kind [Almog] |
| 17866 | Essential definition aims at existence conditions and structural truths [Almog] |
| 17868 | Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog] |
| 17870 | Alien 'tigers' can't be tigers if they are not related to our tigers [Almog] |
| 17869 | Kripke and Putnam offer an intermediary between real and nominal essences [Almog] |
| 17876 | Individual essences are just cobbled together classificatory predicates [Almog] |
| 17873 | Water must be related to water, just as tigers must be related to tigers [Almog] |
| 22594 | In 1794 France all individual and legal rights were suppressed by the general will [Dunt] |
| 22602 | Over several centuries a set of eight main liberal values was established [Dunt] |
| 22596 | No government, or the whole nation, can control an individual beyond legitimate scope [Dunt] |
| 22603 | Laissez-faire liberalism failed to give people the protections and freedoms needed for a good life [Dunt] |
| 22592 | Nationalism pretends that we can only have a single identity [Dunt] |
| 17864 | Defining an essence comes no where near giving a thing's nature [Almog] |
| 17863 | Essences promise to reveal reality, but actually drive us away from it [Almog] |