157 ideas
| 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] |
| 13604 | Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 12666 | We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis] |
| 13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 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] |
| 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] |
| 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] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
| 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] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 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] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 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] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |