74 ideas
21360 | Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle] |
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] |
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] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [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] |
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] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [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] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [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] |
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] |
16320 | Some say deflationism is axioms which are conservative over the base theory [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] |
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] |
13212 | Infinity is only potential, never actual [Aristotle] |
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] |
13221 | Existence is either potential or actual [Aristotle] |
16100 | True change is in a thing's logos or its matter, not in its qualities [Aristotle] |
16101 | A change in qualities is mere alteration, not true change [Aristotle] |
12133 | If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle] |
13213 | All comings-to-be are passings-away, and vice versa [Aristotle] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
12134 | Matter is the substratum, which supports both coming-to-be and alteration [Aristotle] |
16572 | Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle] |
16573 | Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle] |
13214 | The substratum changing to a contrary is the material cause of coming-to-be [Aristotle] |
13215 | If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
16717 | Which of the contrary features of a body are basic to it? [Aristotle] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
13216 | Matter is the limit of points and lines, and must always have quality and form [Aristotle] |
17994 | The primary matter is the substratum for the contraries like hot and cold [Aristotle] |
13224 | There couldn't be just one element, which was both water and air at the same time [Aristotle] |
16594 | The Four Elements must change into one another, or else alteration is impossible [Aristotle] |
13223 | Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle] |
13210 | Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle] |
13220 | Bodies are endlessly divisible [Aristotle] |
13211 | If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle] |
13228 | There is no time without movement [Aristotle] |
16595 | If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
13227 | Being is better than not-being [Aristotle] |
13226 | An Order controls all things [Aristotle] |