176 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 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] |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| 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] |
| 10840 | We must be able to specify truths in a precise language, like winning moves in a game [Dummett] |
| 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] |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| 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] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 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] |
| 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] |
| 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] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 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] |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
| 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] |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| 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] |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 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] |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| 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] |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 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] |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| 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] |
| 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] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 10532 | We can understand universals by studying predication [Dummett] |
| 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] |
| 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] |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by 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] |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| 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] |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
| 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] |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 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] |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 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] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 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] |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| 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] |
| 7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| 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] |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| 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] |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| 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] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |