117 ideas
| 19199 | Some say metaphysics is a highly generalised empirical study of objects [Tarski] |
| 19193 | Disputes that fail to use precise scientific terminology are all meaningless [Tarski] |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
| 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] |
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| 19178 | Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski] |
| 19177 | A definition of truth should be materially adequate and formally correct [Tarski] |
| 19186 | A rigorous definition of truth is only possible in an exactly specified language [Tarski] |
| 19194 | We may eventually need to split the word 'true' into several less ambiguous terms [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] |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| 19180 | It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski] |
| 19181 | In the classical concept of truth, 'snow is white' is true if snow is white [Tarski] |
| 19196 | Scheme (T) is not a definition of truth [Tarski] |
| 19183 | Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski] |
| 19182 | Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski] |
| 19198 | We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski] |
| 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] |
| 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] |
| 19184 | The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski] |
| 19191 | Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski] |
| 19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski] |
| 19189 | The metalanguage must contain the object language, logic, and defined semantics [Tarski] |
| 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] |
| 10824 | If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski] |
| 16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
| 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] |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| 19190 | We need an undefined term 'true' in the meta-language, specified by axioms [Tarski] |
| 19197 | Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski] |
| 19185 | Semantics is a very modest discipline which solves no real problems [Tarski] |
| 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| 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] |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| 19187 | The Liar makes us assert a false sentence, so it must be taken seriously [Tarski] |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |