64 ideas
19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
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] |
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] |
19034 | The world is either a whole made of its parts, or a container which contains its parts [Vetter] |
19015 | Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter] |
19012 | The Humean supervenience base entirely excludes modality [Vetter] |
19024 | A determinate property must be a unique instance of the determinable class [Vetter] |
17954 | Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter] |
19021 | I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter] |
19016 | We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter] |
19017 | Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter] |
19014 | How can spatiotemporal relations be understood in dispositional terms? [Vetter] |
17953 | Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter] |
17952 | Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter] |
19030 | Why does origin matter more than development; why are some features of origin more important? [Vetter] |
19040 | We take origin to be necessary because we see possibilities as branches from actuality [Vetter] |
19008 | The modern revival of necessity and possibility treated them as special cases of quantification [Vetter] |
19029 | It is necessary that p means that nothing has the potentiality for not-p [Vetter] |
17959 | Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter] |
19010 | All possibility is anchored in the potentiality of individual objects [Vetter] |
19013 | Possibility is a generalised abstraction from the potentiality of its bearer [Vetter] |
17957 | Maybe possibility is constituted by potentiality [Vetter] |
17955 | Possible worlds allow us to talk about degrees of possibility [Vetter] |
19028 | Possibilities are potentialities of actual things, but abstracted from their location [Vetter] |
19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter] |
19025 | Potentialities may be too weak to count as 'dispositions' [Vetter] |
19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter] |
23705 | A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye] |
19009 | Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter] |
19027 | Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter] |
19031 | There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter] |
17958 | The apparently metaphysically possible may only be epistemically possible [Vetter] |
17956 | Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter] |
19011 | If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter] |
19037 | Are there possible objects which nothing has ever had the potentiality to produce? [Vetter] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
19018 | Explanations by disposition are more stable and reliable than those be external circumstances [Vetter] |
19020 | Grounding is a kind of explanation, suited to metaphysics [Vetter] |
19039 | The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter] |
19038 | Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter] |
17993 | Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter] |
19026 | If time is symmetrical between past and future, why do they look so different? [Vetter] |
19041 | Presentists explain cross-temporal relations using surrogate descriptions [Vetter] |