74 ideas
| 18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
| 4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| 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] |
| 15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
| 18570 | There may be several ways to individuate things like concepts [Machery] |
| 4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 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] |
| 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] |
| 4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |