194 ideas
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] |
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] |
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] |
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] |
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] |
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] |
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] |
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] |
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] |
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] |
18658 | The 'Kantian' self steps back from commitment to its social situation [Kymlicka] |
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] |
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] |
18650 | Teleological theories give the good priority over concern for people [Kymlicka] |
18664 | Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka] |
16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
18624 | Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka] |
18626 | One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka] |
18627 | A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka] |
18625 | To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka] |
18638 | The difference principles says we must subsidise the costs of other people's choices [Kymlicka] |
23418 | Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka] |
18635 | Social contract theories are usually rejected because there never was such a contract [Kymlicka] |
23369 | Some liberals thinks checks and balances are enough, without virtuous citizens [Kymlicka] |
23370 | Good citizens need civic virtues of loyalty, independence, diligence, respect, etc. [Kymlicka] |
23373 | Liberals accept that people need society, but Aristotelians must show that they need political activity [Kymlicka] |
23375 | Minimal liberal citizenship needs common civility, as well as mere non-interference [Kymlicka] |
23376 | Modern non-discrimination obliges modern citizens to treat each other as equals [Kymlicka] |
23377 | The right wing sees citizenship in terms of responsibility to earn a living, rather than rights [Kymlicka] |
23414 | Liberals say state intervention in culture restricts people's autonomy [Kymlicka] |
18630 | Utilitarianism is no longer a distinctive political position [Kymlicka] |
18623 | The quest of the general good is partly undermined by people's past entitlements [Kymlicka] |
18628 | We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka] |
18629 | Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka] |
18637 | Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka] |
23371 | Modern democratic theory focuses on talk, not votes, because we need consensus or compromise [Kymlicka] |
23390 | In a liberal democracy all subjects of authority have a right to determine the authority [Kymlicka] |
18663 | Modern liberalism has added personal privacy to our personal social lives [Kymlicka] |
23374 | We have become attached to private life because that has become greatly enriched [Kymlicka] |
18632 | Liberalism tends to give priority to basic liberties [Kymlicka] |
22818 | Liberals are not too individualistic, because people recognise and value social relations [Kymlicka] |
23410 | Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka] |
23387 | Liberals must avoid an official culture, as well as an official religion [Kymlicka] |
23388 | Liberals need more than freedom; they must build a nation, through a language and institutions [Kymlicka] |
23380 | Some individuals can gain citizenship as part of a group, rather than as mere individuals [Kymlicka] |
23381 | The status hierarchy is independent of the economic hierarchy [Kymlicka] |
23383 | Some multiculturalists defended the rights of cohesive minorities against liberal individualism [Kymlicka] |
23384 | 'Culturalist' liberals say that even liberal individuals may need minority rights [Kymlicka] |
23385 | Multiculturalism may entail men dominating women in minority groups [Kymlicka] |
23386 | Liberals must prefer minority right which are freedoms, not restrictions [Kymlicka] |
23389 | Why shouldn't national minorities have their own right to nation-build? [Kymlicka] |
23391 | Multiculturalism is liberal if it challenges inequality, conservative if it emphasises common good [Kymlicka] |
18656 | Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka] |
23409 | Community can focus on class or citizenship or ethnicity or culture [Kymlicka] |
18659 | The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka] |
18660 | Communitarians say we should pay more attention to our history [Kymlicka] |
23419 | Communitarianism struggles with excluded marginalised groups [Kymlicka] |
18657 | Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka] |
23413 | Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka] |
23415 | Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka] |
18649 | If everyone owned himself, that would prevent slavery [Kymlicka] |
18640 | Libertarians like the free market, but they also think that the free market is just [Kymlicka] |
18651 | The most valuable liberties to us need not be the ones with the most freedom [Kymlicka] |
18661 | Ancient freedom was free participation in politics, not private independence of life [Kymlicka] |
18633 | Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka] |
18634 | Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka] |
18654 | Marxists say justice is unneeded in the truly good community [Kymlicka] |
18652 | The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka] |
23379 | Rights are a part of nation-building, to build a common national identity and culture [Kymlicka] |
23382 | Rights derived from group membership are opposed to the idea of state citizenship [Kymlicka] |
18655 | Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka] |
23411 | Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka] |
23412 | Justice resolves conflicts, but may also provoke them [Kymlicka] |
23378 | The welfare state helps to integrate the working classes into a national culture [Kymlicka] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |