81 ideas
8605 | In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis] |
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] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
16324 | Any definition of truth requires a metalanguage [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] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [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] |
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] |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [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] |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [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] |
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] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [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] |
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] |
8607 | Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
8606 | A supervenience thesis is a denial of independent variation [Lewis] |
8580 | Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis] |
8571 | Universals are wholly present in their instances, whereas properties are spread around [Lewis] |
10717 | Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver] |
16217 | Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley] |
8613 | Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis] |
8585 | Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis] |
8586 | Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis] |
8589 | For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis] |
15460 | All perfectly natural properties are intrinsic [Lewis, by Lewis] |
15726 | Natural properties fix resemblance and powers, and are picked out by universals [Lewis] |
7031 | Lewis says properties are sets of actual and possible objects [Lewis, by Heil] |
8572 | Any class of things is a property, no matter how whimsical or irrelevant [Lewis] |
18433 | There are far more properties than any brain could ever encodify [Lewis] |
8604 | We need properties as semantic values for linguistic expressions [Lewis] |
14499 | Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki] |
15120 | Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne] |
8573 | Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis] |
8569 | I suspend judgements about universals, but their work must be done [Lewis] |
21961 | Physics aims to discover which universals actually exist [Lewis, by Moore,AW] |
8576 | The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis] |
8570 | To have a property is to be a member of a class, usually a class of things [Lewis] |
8574 | Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
8579 | Psychophysical identity implies the possibility of idealism or panpsychism [Lewis] |
9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
8614 | A sophisticated principle of charity sometimes imputes error as well as truth [Lewis] |
8615 | We need natural properties in order to motivate the principle of charity [Lewis] |
8608 | Counterfactuals 'backtrack' if a different present implies a different past [Lewis] |
8584 | Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis] |
8581 | Physics discovers laws and causal explanations, and also the natural properties required [Lewis] |
15727 | Physics aims for a list of natural properties [Lewis] |
8611 | A law of nature is any regularity that earns inclusion in the ideal system [Lewis] |