109 ideas
18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16324 | Any definition of truth requires a metalanguage [Halbach] |
15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
16309 | Every attempt at formal rigour uses some set theory [Halbach] |
16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
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] |
18570 | There may be several ways to individuate things like concepts [Machery] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
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] |
18616 | If a term doesn't pick out a kind, keeping it may block improvements in classification [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] |
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] |
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] |
18566 | Concepts should contain working memory, not long-term, because they control behaviour [Machery] |
18575 | The concepts for a class typically include prototypes, and exemplars, and theories [Machery] |
18583 | Many categories don't seem to have a definition [Machery] |
18591 | Classical theory can't explain facts like typical examples being categorised quicker [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] |
18587 | The theory account is sometimes labelled as 'knowledge' or 'explanation' in approach [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] |
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] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
16591 | Prime matter is nothing but its parts [Vanini] |
18613 | Artifacts can be natural kinds, when they are the object of historical enquiry [Machery] |