36 ideas
7791 | The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle] |
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] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
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] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
11002 | Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |