121 ideas
18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
6123 | Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
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] |
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] |
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] |
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] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
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] |
18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
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] |
6143 | Prolonged events don't seem to endure or exist at any particular time [Merricks] |
6135 | A crumbling statue can't become vague, because vagueness is incoherent [Merricks] |
18564 | Do categories store causal knowledge, or typical properties, or knowledge of individuals? [Machery] |
18604 | Are quick and slow categorisation the same process, or quite different? [Machery] |
18573 | For each category of objects (such as 'dog') an individual seems to have several concepts [Machery] |
18602 | A thing is classified if its features are likely to be generated by that category's causal laws [Machery] |
18565 | There may be ad hoc categories, such as the things to pack in your suitcase for a trip [Machery] |
6145 | Intrinsic properties are those an object still has even if only that object exists [Merricks] |
6124 | I say that most of the objects of folk ontology do not exist [Merricks] |
6134 | Is swimming pool water an object, composed of its mass or parts? [Merricks] |
6125 | We can eliminate objects without a commitment to simples [Merricks] |
18570 | There may be several ways to individuate things like concepts [Machery] |
14229 | Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins] |
6142 | The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks] |
14472 | If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson] |
14469 | Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks] |
6137 | Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks] |
6127 | 'Unrestricted composition' says any two things can make up a third thing [Merricks] |
6131 | Composition as identity is false, as identity is never between a single thing and many things [Merricks] |
6132 | Composition as identity is false, as it implies that things never change their parts [Merricks] |
6141 | There is no visible difference between statues, and atoms arranged statuewise [Merricks] |
6130 | 'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks] |
6138 | It seems wrong that constitution entails that two objects are wholly co-located [Merricks] |
6128 | Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks] |
6136 | Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks] |
6133 | If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks] |
6150 | The 'warrant' for a belief is what turns a true belief into knowledge [Merricks] |
18616 | If a term doesn't pick out a kind, keeping it may block improvements in classification [Machery] |
18614 | Vertical arguments say eliminate a term if it picks out different natural kinds in different theories [Machery] |
18615 | Horizontal arguments say eliminate a term if it fails to pick out a natural kind [Machery] |
18609 | Psychologists use 'induction' as generalising a property from one category to another [Machery] |
18610 | 'Ampliative' induction infers that all members of a category have a feature found in some of them [Machery] |
6144 | You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks] |
6140 | Maybe the word 'I' can only refer to persons [Merricks] |
6149 | Free will and determinism are incompatible, since determinism destroys human choice [Merricks] |
6148 | Human organisms can exercise downward causation [Merricks] |
18562 | Connectionists cannot distinguish concept-memories from their background, or the processes [Machery] |
18561 | We can identify a set of cognitive capacities which are 'higher order' [Machery] |
6146 | Before Creation it is assumed that God still had many many mental properties [Merricks] |
6147 | The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks] |
18574 | Concepts for categorisation and for induction may be quite different [Machery] |
18588 | Concept theories aim at their knowledge, processes, format, acquisition, and location [Machery] |
18611 | We should abandon 'concept', and just use 'prototype', 'exemplar' and 'theory' [Machery] |
8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
18567 | In the philosophy of psychology, concepts are usually introduced as constituents of thoughts [Machery] |
18569 | In philosophy theories of concepts explain how our propositional attitudes have content [Machery] |
18563 | By 'concept' psychologists mean various sorts of representation or structure [Machery] |
18558 | Concept theorists examine their knowledge, format, processes, acquisition and location [Machery] |
18557 | Psychologists treat concepts as long-term knowledge bodies which lead to judgements [Machery] |
18560 | Psychologist treat concepts as categories [Machery] |
18592 | The concepts OBJECT or AGENT may be innate [Machery] |
18566 | Concepts should contain working memory, not long-term, because they control behaviour [Machery] |
18584 | One hybrid theory combines a core definition with a prototype for identification [Machery] |
18585 | Heterogeneous concepts might have conflicting judgements, where hybrid theories will not [Machery] |
18578 | Concepts as definitions was rejected, and concepts as prototypes, exemplars or theories proposed [Machery] |
18575 | The concepts for a class typically include prototypes, and exemplars, and theories [Machery] |
18591 | Classical theory can't explain facts like typical examples being categorised quicker [Machery] |
18583 | Many categories don't seem to have a definition [Machery] |
18590 | Classical theory implies variety in processing times, but this does not generally occur [Machery] |
18594 | Knowing typical properties of things is especially useful in induction [Machery] |
18593 | The term 'prototype' is used for both typical category members, and the representation [Machery] |
18595 | Prototype theories are based on computation of similarities with the prototype [Machery] |
18596 | Prototype theorists don't tell us how we select the appropriate prototype [Machery] |
18603 | Maybe concepts are not the typical properties, but the ideal properties [Machery] |
18605 | It is more efficient to remember the prototype, than repeatedly create it from exemplars [Machery] |
18606 | The prototype view predicts that typical members are easier to categorise [Machery] |
18597 | Concepts as exemplars are based on the knowledge of properties of each particular [Machery] |
18598 | Exemplar theories need to explain how the relevant properties are selected from a multitude of them [Machery] |
18599 | In practice, known examples take priority over the rest of the set of exemplars [Machery] |
18600 | Theory Theory says category concepts are knowledge stores explaining membership [Machery] |
18601 | Theory Theory says concepts are explanatory knowledge, and concepts form domains [Machery] |
18607 | Theory theorists rely on best explanation, rather than on similarities [Machery] |
18608 | If categorisation is not by similarity, it seems to rely on what properties things might have [Machery] |
18587 | The theory account is sometimes labelled as 'knowledge' or 'explanation' in approach [Machery] |
18577 | The word 'grandmother' may be two concepts, with a prototype and a definition [Machery] |
18589 | For behaviourists concepts are dispositions to link category members to names [Machery] |
13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
18612 | Americans are more inclined to refer causally than the Chinese are [Machery] |
18613 | Artifacts can be natural kinds, when they are the object of historical enquiry [Machery] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |