80 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 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] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 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] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 19024 | A determinate property must be a unique instance of the determinable class [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] |
| 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] |
| 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] |
| 19028 | Possibilities are potentialities of actual things, but abstracted from their location [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] |
| 19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [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] |
| 19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [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] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 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] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
| 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] |
| 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] |