73 ideas
18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
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] |
18948 | There is an object for every set of properties (some of which exist, and others don't) [Parsons,T, by Sawyer] |
18570 | There may be several ways to individuate things like concepts [Machery] |
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] |
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] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
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] |
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] |
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] |