86 ideas
12274 | Begin examination with basics, and subdivide till you can go no further [Aristotle] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
12260 | Dialectic starts from generally accepted opinions [Aristotle] |
12291 | There can't be one definition of two things, or two definitions of the same thing [Aristotle] |
12292 | Definitions are easily destroyed, since they can contain very many assertions [Aristotle] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
12261 | Differentia are generic, and belong with genus [Aristotle] |
12263 | 'Genus' is part of the essence shared among several things [Aristotle] |
12272 | We describe the essence of a particular thing by means of its differentiae [Aristotle] |
12279 | The differentia indicate the qualities, but not the essence [Aristotle] |
12283 | In definitions the first term to be assigned ought to be the genus [Aristotle] |
12289 | The genera and the differentiae are part of the essence [Aristotle] |
12285 | The definition is peculiar to one thing, not common to many [Aristotle] |
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] |
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] |
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] |
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] |
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] |
11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
12273 | Unit is the starting point of number [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] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
12267 | There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle] |
12282 | An individual property has to exist (in past, present or future) [Aristotle] |
12264 | An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle] |
12280 | Genus gives the essence better than the differentiae do [Aristotle] |
13269 | In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle] |
12284 | Everything that is has one single essence [Aristotle] |
12262 | An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle] |
12290 | Destruction is dissolution of essence [Aristotle] |
12286 | If two things are the same, they must have the same source and origin [Aristotle] |
12266 | 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle] |
12287 | Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle] |
12288 | Numerical sameness and generic sameness are not the same [Aristotle] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
12259 | Reasoning is when some results follow necessarily from certain claims [Aristotle] |
12271 | Induction is the progress from particulars to universals [Aristotle] |
12293 | We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
12276 | Justice and self-control are better than courage, because they are always useful [Aristotle] |
12277 | Friendship is preferable to money, since its excess is preferable [Aristotle] |
12275 | We value friendship just for its own sake [Aristotle] |
12281 | Man is intrinsically a civilized animal [Aristotle] |
21733 | The right-wing conception of freedom is based on the idea of self-ownership [Cohen,GA] |
21739 | Plenty of people have self-ownership, but still lack autonomy [Cohen,GA] |
21736 | It is doubtful whether any private property was originally acquired legitimately [Cohen,GA] |
21734 | It is plausible that no one has an initial right to own land and natural resources [Cohen,GA] |
21735 | Every thing which is now private started out as unowned [Cohen,GA] |
12265 | All water is the same, because of a certain similarity [Aristotle] |
12278 | 'Being' and 'oneness' are predicated of everything which exists [Aristotle] |