90 ideas
16241 | The metaphysics of nature should focus on physics [Maudlin] |
16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
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] |
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] |
15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [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] |
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] |
15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [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] |
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] |
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] |
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] |
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] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
16259 | Naďve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
5833 | Education is the greatest of human goods [Xenophon] |
16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
16270 | If laws are just regularities, then there have to be laws [Maudlin] |
16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
16265 | If time passes, presumably it passes at one second per second [Maudlin] |
16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |