76 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] |
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| 9912 | There are no such things as numbers [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| 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] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 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] |
| 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] |
| 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] |
| 19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [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] |
| 19025 | Potentialities may be too weak to count as 'dispositions' [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] |
| 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] |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| 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] |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |