110 ideas
22334 | Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock] |
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] |
15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [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] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
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] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
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] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
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] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
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] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
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] |
11016 | Would a language without vagueness be usable at all? [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
22332 | German and British idealism is not about individual ideas, but the intelligibility of reality [Glock] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
22336 | We might say that the family resemblance is just a consequence of meaning-as-use [Glock] |
22335 | The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |