235 ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 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] |
| 10838 | To explain a concept, we need its purpose, not just its rules of usage [Dummett] |
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| 4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
| 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 10837 | It is part of the concept of truth that we aim at making true statements [Dummett] |
| 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] |
| 10840 | We must be able to specify truths in a precise language, like winning moves in a game [Dummett] |
| 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] |
| 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] |
| 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] |
| 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] |
| 19171 | Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson] |
| 8166 | Truth is part of semantics, since valid inference preserves truth [Dummett] |
| 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] |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
| 16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
| 16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
| 16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
| 16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
| 16958 | In S4 the actual world has a special place [Dummett] |
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| 10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| 10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
| 11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
| 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] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 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] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 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] |
| 8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
| 7334 | Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A] |
| 8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| 18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
| 9182 | Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett] |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| 19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| 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] |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
| 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] |
| 19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
| 19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| 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] |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
| 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] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| 4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
| 22297 | Dummett saw realism as acceptance of bivalence, rather than of mind-independent entities [Dummett, by Potter] |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| 15049 | Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett] |
| 8184 | Philosophers should not presume reality, but only invoke it when language requires it [Dummett] |
| 8185 | We can't make sense of a world not apprehended by a mind [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 3303 | For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA] |
| 8163 | Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett] |
| 8161 | We know we can state facts, with true statements [Dummett] |
| 21628 | To say reality itself is vague is not properly intelligible [Dummett] |
| 8180 | 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett] |
| 10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
| 10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
| 4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
| 4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
| 4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [Moreland] |
| 10532 | We can understand universals by studying predication [Dummett] |
| 4453 | One realism is one-over-many, which may be the model/copy view, which has the Third Man problem [Moreland] |
| 4464 | Realists see properties as universals, which are single abstract entities which are multiply exemplifiable [Moreland] |
| 4451 | If properties are universals, what distinguishes two things which have identical properties? [Moreland] |
| 4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [Moreland] |
| 4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
| 4454 | The One-In-Many view says universals have abstract existence, but exist in particulars [Moreland] |
| 4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [Moreland] |
| 4452 | Maybe universals are real, if properties themselves have properties, and relate to other properties [Moreland] |
| 4467 | A naturalist and realist about universals is forced to say redness can be both moving and stationary [Moreland] |
| 4469 | There are spatial facts about red particulars, but not about redness itself [Moreland] |
| 4472 | Redness is independent of red things, can do without them, has its own properties, and has identity [Moreland] |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 4459 | Moderate nominalism attempts to embrace the existence of properties while avoiding universals [Moreland] |
| 4458 | Unlike Class Nominalism, Resemblance Nominalism can distinguish natural from unnatural classes [Moreland] |
| 4457 | There can be predicates with no property, and there are properties with no predicate [Moreland] |
| 4471 | We should abandon the concept of a property since (unlike sets) their identity conditions are unclear [Moreland] |
| 10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
| 10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| 10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
| 10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| 4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
| 16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
| 16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 4460 | Abstractions are formed by the mind when it concentrates on some, but not all, the features of a thing [Moreland] |
| 8175 | A theory of thought will include propositional attitudes as well as propositions [Dummett] |
| 8174 | The theories of meaning and understanding are the only routes to an account of thought [Dummett] |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| 4455 | It is always open to a philosopher to claim that some entity or other is unanalysable [Moreland] |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| 10839 | You can't infer a dog's abstract concepts from its behaviour [Dummett] |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| 8165 | To 'abstract from' is a logical process, as opposed to the old mental view [Dummett] |
| 19055 | Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett] |
| 19056 | If a sentence is effectively undecidable, we can never know its truth conditions [Dummett] |
| 8168 | To know the truth-conditions of a sentence, you must already know the meaning [Dummett] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8181 | A justificationist theory of meaning leads to the rejection of classical logic [Dummett] |
| 8182 | Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett] |
| 8183 | If truths about the past depend on memories and current evidence, the past will change [Dummett] |
| 19054 | Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett] |
| 8176 | We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett] |
| 8170 | Sentences are the primary semantic units, because they can say something [Dummett] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| 9181 | The causal theory of reference can't distinguish just hearing a name from knowing its use [Dummett] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 8169 | We can't distinguish a proposition from its content [Dummett] |
| 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] |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| 16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| 8186 | Time is the measure of change, so we can't speak of time before all change [Dummett] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8167 | If Presentism is correct, we cannot even say that the present changes [Dummett] |
| 4473 | 'Presentism' is the view that only the present moment exists [Moreland] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |