77 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] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
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] |
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] |
17957 | Maybe possibility is constituted by potentiality [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] |
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] |
19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [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] |
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] |