89 ideas
| 1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
| 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] |
| 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] |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [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] |
| 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] |
| 12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
| 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] |
| 10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
| 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] |
| 8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
| 8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
| 16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
| 12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
| 16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
| 11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| 3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
| 8775 | A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach] |
| 8776 | We cannot learn relations by abstraction, because their converse must be learned too [Geach] |
| 10732 | If concepts are just recognitional, then general judgements would be impossible [Geach] |
| 2567 | You can't define real mental states in terms of behaviour that never happens [Geach] |
| 2568 | Beliefs aren't tied to particular behaviours [Geach] |
| 8781 | The mind does not lift concepts from experience; it creates them, and then applies them [Geach] |
| 10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach] |
| 8769 | If someone has aphasia but can still play chess, they clearly have concepts [Geach] |
| 8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
| 8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
| 8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
| 8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
| 8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
| 8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
| 8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
| 8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |
| 10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
| 10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| 1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
| 1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
| 1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |