91 ideas
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski] |
16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
7311 | The only genuine proper names are 'this' and 'that' [Russell] |
14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
14439 | A complex number is simply an ordered couple of real numbers [Russell] |
14421 | Discovering that 1 is a number was difficult [Russell] |
14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14425 | A number is something which characterises collections of the same size [Russell] |
14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
14449 | There is always something psychological about inference [Russell] |
14463 | Existence can only be asserted of something described, not of something named [Russell] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
14450 | All forms of implication are expressible as truth-functions [Russell] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
7413 | Without confidence in our beliefs, how should we actually live? [Tuck] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |