156 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] |
| 12667 | Metaphysics aims at the simplest explanation, without regard to testability [Ellis] |
| 13567 | Ontology should give insight into or an explanation of the world revealed by science [Ellis] |
| 5486 | Essentialism says metaphysics can't be done by analysing unreliable language [Ellis] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 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] |
| 13604 | Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis] |
| 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] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [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] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [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] |
| 12666 | We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [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] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 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] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [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] |
| 12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
| 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] |
| 12683 | Objects and substances are a subcategory of the natural kinds of processes [Ellis] |
| 12670 | A physical event is any change of distribution of energy [Ellis] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 13584 | The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis] |
| 5468 | Properties are 'dispositional', or 'categorical' (the latter as 'block' or 'intrinsic' structures) [Ellis, by PG] |
| 13587 | There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis] |
| 12673 | Physical properties are those relevant to how a physical system might act [Ellis] |
| 13577 | Typical 'categorical' properties are spatio-temporal, such as shape [Ellis] |
| 9436 | The property of 'being an electron' is not of anything, and only electrons could have it [Ellis] |
| 5469 | The passive view of nature says categorical properties are basic, but others say dispositions [Ellis] |
| 12665 | I support categorical properties, although most people only want causal powers [Ellis] |
| 12682 | Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis] |
| 12684 | Spatial, temporal and numerical relations have causal roles, without being causal [Ellis] |
| 13582 | 'Being a methane molecule' is not a property - it is just a predicate [Ellis] |
| 12672 | Properties and relations are discovered, so they can't be mere sets of individuals [Ellis] |
| 5456 | Redness is not a property as it is not mind-independent [Ellis] |
| 18398 | Space, time, and some other basics, are not causal powers [Ellis] |
| 13580 | Causal powers must necessarily act the way they do [Ellis] |
| 13598 | Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis] |
| 12676 | Causal powers can't rest on things which lack causal power [Ellis] |
| 13568 | Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis] |
| 13586 | Maybe dispositions can be explained by intrinsic properties or structures [Ellis] |
| 5481 | Properties have powers; they aren't just ways for logicians to classify objects [Ellis] |
| 23781 | Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE] |
| 13585 | The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis] |
| 5458 | Nearly all fundamental properties of physics are dispositional [Ellis] |
| 13596 | A causal power is a disposition to produce forces [Ellis] |
| 13599 | Powers are dispositions of the essences of kinds that involve them in causation [Ellis] |
| 12686 | Causal powers are a proper subset of the dispositional properties [Ellis] |
| 13572 | There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis] |
| 13573 | Universals are all types of natural kind [Ellis] |
| 12685 | Categorical properties depend only on the structures they represent [Ellis] |
| 5443 | Kripke and others have made essentialism once again respectable [Ellis] |
| 5444 | 'Individual essences' fix a particular individual, and 'kind essences' fix the kind it belongs to [Ellis] |
| 13571 | Scientific essentialism doesn't really need Kripkean individual essences [Ellis] |
| 12679 | A real essence is a kind's distinctive properties [Ellis] |
| 5462 | Essential properties are usually quantitatively determinate [Ellis] |
| 5448 | 'Real essence' makes it what it is; 'nominal essence' makes us categorise it a certain way [Ellis] |
| 13578 | The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis] |
| 5477 | One thing can look like something else, without being the something else [Ellis] |
| 13576 | Necessities are distinguished by their grounds, not their different modalities [Ellis] |
| 12668 | Metaphysical necessity holds between things in the world and things they make true [Ellis] |
| 5479 | Scientific essentialists say science should define the limits of the possible [Ellis] |
| 12687 | Metaphysical necessities are those depending on the essential nature of things [Ellis] |
| 5483 | Essentialists deny possible worlds, and say possibilities are what is compatible with the actual world [Ellis] |
| 13570 | Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis] |
| 5447 | Metaphysical necessities are true in virtue of the essences of things [Ellis] |
| 5476 | Essentialists say natural laws are in a new category: necessary a posteriori [Ellis] |
| 5478 | Imagination tests what is possible for all we know, not true possibility [Ellis] |
| 5482 | Possible worlds realism is only needed to give truth conditions for modals and conditionals [Ellis] |
| 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] |
| 5453 | Essentialists mostly accept the primary/secondary qualities distinction [Ellis] |
| 5466 | Primary qualities are number, figure, size, texture, motion, configuration, impenetrability and (?) mass [Ellis] |
| 12669 | Science aims to explain things, not just describe them [Ellis] |
| 13607 | If events are unconnected, then induction cannot be solved [Ellis] |
| 5485 | Emeralds are naturally green, and only an external force could turn them blue [Ellis] |
| 13597 | Good explanations unify [Ellis] |
| 5484 | Essentialists don't infer from some to all, but from essences to necessary behaviour [Ellis] |
| 13601 | Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis] |
| 13569 | To give essentialist explanations there have to be natural kinds [Ellis] |
| 13600 | The point of models in theories is not to idealise, but to focus on what is essential [Ellis] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 5457 | Predicates assert properties, values, denials, relations, conventions, existence and fabrications [Ellis, by PG] |
| 5488 | Regularity theories of causation cannot give an account of human agency [Ellis] |
| 5489 | Humans have variable dispositions, and also power to change their dispositions [Ellis] |
| 5490 | Essentialism fits in with Darwinism, but not with extreme politics of left or right [Ellis] |
| 5472 | Natural kinds are of objects/substances, or events/processes, or intrinsic natures [Ellis] |
| 6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
| 12681 | There are natural kinds of processes [Ellis] |
| 13583 | There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis] |
| 13574 | Natural kinds are distinguished by resting on essences [Ellis] |
| 5471 | Essentialism says natural kinds are fundamental to nature, and determine the laws [Ellis] |
| 12680 | Natural kind structures go right down to the bottom level [Ellis] |
| 5446 | For essentialists two members of a natural kind must be identical [Ellis] |
| 5480 | The whole of our world is a natural kind, so all worlds like it necessarily have the same laws [Ellis] |
| 13575 | If there are borderline cases between natural kinds, that makes them superficial [Ellis] |
| 5445 | Essentialists regard inanimate objects as genuine causal agents [Ellis] |
| 5463 | Essentialists believe causation is necessary, resulting from dispositions and circumstances [Ellis] |
| 5491 | A general theory of causation is only possible in an area if natural kinds are involved [Ellis] |
| 5442 | For 'passivists' behaviour is imposed on things from outside [Ellis] |
| 5473 | The laws of nature imitate the hierarchy of natural kinds [Ellis] |
| 5474 | Laws of nature tend to describe ideal things, or ideal circumstances [Ellis] |
| 5475 | We must explain the necessity, idealisation, ontology and structure of natural laws [Ellis] |
| 13595 | Laws don't exist in the world; they are true of the world [Ellis] |
| 6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
| 12675 | Laws of nature are just descriptions of how things are disposed to behave [Ellis] |
| 5460 | Causal relations cannot be reduced to regularities, as they could occur just once [Ellis] |
| 13566 | A proton must have its causal role, because without it it wouldn't be a proton [Ellis] |
| 13579 | What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis] |
| 13581 | Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis] |
| 13594 | The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis] |
| 5459 | Essentialists say dispositions are basic, rather than supervenient on matter and natural laws [Ellis] |
| 5461 | The essence of uranium is its atomic number and its electron shell [Ellis] |
| 6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
| 13603 | A primary aim of science is to show the limits of the possible [Ellis] |
| 5464 | For essentialists, laws of nature are metaphysically necessary, being based on essences of natural kinds [Ellis] |
| 6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
| 5487 | Essentialism requires a clear separation of semantics, epistemology and ontology [Ellis] |
| 6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |
| 12671 | I deny forces as entities that intervene in causation, but are not themselves causal [Ellis] |
| 12674 | Energy is the key multi-valued property, vital to scientific realism [Ellis] |
| 12689 | Simultaneity can be temporal equidistance from the Big Bang [Ellis] |
| 12690 | The present is the collapse of the light wavefront from the Big Bang [Ellis] |