236 ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 15209 | Like disastrous small errors in navigation, small misunderstandings can wreck intellectual life [Harré/Madden] |
| 15215 | Philosophy devises and assesses conceptual schemes in the service of worldviews [Harré/Madden] |
| 10838 | To explain a concept, we need its purpose, not just its rules of usage [Dummett] |
| 15212 | Analysis of concepts based neither on formalism nor psychology can arise from examining what we know [Harré/Madden] |
| 15210 | Humeans see analysis in terms of formal logic, because necessities are fundamentally logical relations [Harré/Madden] |
| 15236 | Positivism says science only refers to immediate experiences [Harré/Madden] |
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| 15227 | Logically, definitions have a subject, and a set of necessary predicates [Harré/Madden] |
| 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] |
| 15273 | Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden] |
| 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] |
| 15274 | Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden] |
| 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] |
| 15211 | There is not an exclusive dichotomy between the formal and the logical [Harré/Madden] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 15261 | Humeans can only explain change with continuity as successive replacement [Harré/Madden] |
| 15268 | Humeans construct their objects from events, but we construct events from objects [Harré/Madden] |
| 15257 | The induction problem fades if you work with things, rather than with events [Harré/Madden] |
| 15300 | Fundamental particulars can't change [Harré/Madden] |
| 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] |
| 15319 | Hard individual blocks don't fix what 'things' are; fluids are no less material things [Harré/Madden] |
| 15320 | Magnetic and gravity fields can occupy the same place without merging [Harré/Madden] |
| 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] |
| 15318 | Gravitational and electrical fields are, for a materialist, distressingly empty of material [Harré/Madden] |
| 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] |
| 15267 | Events are changes in states of affairs (which consist of structured particulars, with powers and relations) [Harré/Madden] |
| 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] |
| 15281 | Humeans see predicates as independent, but science says they are connected [Harré/Madden] |
| 15279 | Energy was introduced to physics to refer to the 'store of potency' of a moving ball [Harré/Madden] |
| 15276 | Some powers need a stimulus, but others are just released [Harré/Madden] |
| 15305 | Some powers are variable, others cannot change (without destroying an identity) [Harré/Madden] |
| 15218 | Scientists define copper almost entirely (bar atomic number) in terms of its dispositions [Harré/Madden] |
| 15302 | We explain powers by the natures of things, but explanations end in inexplicable powers [Harré/Madden] |
| 15303 | Maybe a physical field qualifies as ultimate, if its nature is identical with its powers [Harré/Madden] |
| 15258 | Powers are not qualities; they just point to directions of empirical investigation [Harré/Madden] |
| 15315 | What is a field of potentials, if it only consists of possible events? [Harré/Madden] |
| 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] |
| 15272 | The good criticism of substance by Humeans also loses them the vital concept of a thing [Harré/Madden] |
| 15304 | We can escape substance and its properties, if we take fields of pure powers as ultimate [Harré/Madden] |
| 15309 | The assumption that shape and solidity are fundamental implies dubious 'substance' in bodies [Harré/Madden] |
| 15264 | The notorious substratum results from substance-with-qualities; individuals-with-powers solves this [Harré/Madden] |
| 15262 | In logic the nature of a kind, substance or individual is the essence which is inseparable from what it is [Harré/Madden] |
| 15297 | We can infer a new property of a thing from its other properties, via its essential nature [Harré/Madden] |
| 15266 | We say the essence of particles is energy, but only so we can tell a story about the nature of things [Harré/Madden] |
| 15220 | To say something remains the same but lacks its capacities and powers seems a contradiction [Harré/Madden] |
| 15222 | Some individuals can gain or lose capacities or powers, without losing their identity [Harré/Madden] |
| 15296 | A particular might change all of its characteristics, retaining mere numerical identity [Harré/Madden] |
| 15275 | 'Dense' time raises doubts about continuous objects, so they need 'continuous' time [Harré/Madden] |
| 15271 | If things are successive instantaneous events, nothing requires those events to resemble one another [Harré/Madden] |
| 15256 | Humeans cannot step in the same river twice, because they cannot strictly form the concept of 'river' [Harré/Madden] |
| 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] |
| 15290 | What reduces the field of the possible is a step towards necessity [Harré/Madden] |
| 15291 | There is 'absolute' necessity (implied by all propositions) and 'relative' necessity (from what is given) [Harré/Madden] |
| 15230 | Logical necessity is grounded in the logical form of a statement [Harré/Madden] |
| 15214 | Natural necessity is not logical necessity or empirical contingency in disguise [Harré/Madden] |
| 15221 | The relation between what a thing is and what it can do or undergo relate by natural necessity [Harré/Madden] |
| 15224 | A necessity corresponds to the nature of the actual [Harré/Madden] |
| 15232 | Natural necessity is when powerful particulars must produce certain results in a situation [Harré/Madden] |
| 15288 | People doubt science because if it isn't logically necessary it seems to be absolutely contingent [Harré/Madden] |
| 15289 | Property or event relations are naturally necessary if generated by essential mechanisms [Harré/Madden] |
| 15231 | Transcendental necessity is conditions of a world required for a rational being to know its nature [Harré/Madden] |
| 15234 | There is a transcendental necessity for each logical necessity, but the transcendental extends further [Harré/Madden] |
| 15260 | Counterfactuals are just right for analysing statements about the powers which things have [Harré/Madden] |
| 15233 | If natural necessity is used to include or exclude some predicate, the predicate is conceptually necessary [Harré/Madden] |
| 15242 | Having a child is contingent for a 'man', necessary for a 'father'; the latter reflects a necessity of nature [Harré/Madden] |
| 15216 | Is conceptual necessity just conventional, or does it mirror something about nature? [Harré/Madden] |
| 15235 | There is a conceptual necessity when properties become a standard part of a nominal essence [Harré/Madden] |
| 15228 | Necessity and contingency are separate from the a priori and the a posteriori [Harré/Madden] |
| 15252 | If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite [Harré/Madden] |
| 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] |
| 15245 | It is silly to say that direct experience must be justified, either by reason, or by more experience [Harré/Madden] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 15244 | We experience qualities as of objects, not on their own [Harré/Madden] |
| 15248 | Inference in perception is unconvincingly defended as non-conscious and almost instantaneous [Harré/Madden] |
| 15269 | Humean impressions are too instantaneous and simple to have structure or relations [Harré/Madden] |
| 8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
| 15286 | Clavius's Paradox: purely syntactic entailment theories won't explain, because they are too profuse [Harré/Madden] |
| 15283 | Simplicity can sort theories out, but still leaves an infinity of possibilities [Harré/Madden] |
| 15316 | The powers/natures approach has been so successful (for electricity, magnetism, gravity) it may be universal [Harré/Madden] |
| 15298 | We prefer the theory which explains and predicts the powers and capacities of particulars [Harré/Madden] |
| 15225 | Science investigates the nature and constitution of things or substances [Harré/Madden] |
| 15255 | Conjunctions explain nothing, and so do not give a reason for confidence in inductions [Harré/Madden] |
| 15270 | Hume's atomic events makes properties independent, and leads to problems with induction [Harré/Madden] |
| 15284 | Contraposition may be equivalent in truth, but not true in nature, because of irrelevant predicates [Harré/Madden] |
| 15285 | The items put forward by the contraposition belong within different natural clusters [Harré/Madden] |
| 15287 | The possibility that all ravens are black is a law depends on a mechanism producing the blackness [Harré/Madden] |
| 15306 | Only changes require explanation [Harré/Madden] |
| 15293 | If explanation is by entailment, that lacks a causal direction, unlike natural necessity [Harré/Madden] |
| 15294 | Powers can explain the direction of causality, and make it a natural necessity [Harré/Madden] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 15254 | If the nature of particulars explains their powers, it also explains their relations and behaviour [Harré/Madden] |
| 15317 | Powers and natures lead us to hypothesise underlying mechanisms, which may be real [Harré/Madden] |
| 15310 | Solidity comes from the power of repulsion, and shape from the power of attraction [Harré/Madden] |
| 15219 | Essence explains passive capacities as well as active powers [Harré/Madden] |
| 15301 | The very concepts of a particular power or nature imply the possibility of being generalised [Harré/Madden] |
| 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] |
| 15226 | What properties a thing must have to be a type of substance can be laid down a priori [Harré/Madden] |
| 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] |
| 15229 | We say there is 'no alternative' in all sorts of contexts, and there are many different grounds for it [Harré/Madden] |
| 5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| 5833 | Education is the greatest of human goods [Xenophon] |
| 15292 | We can base the idea of a natural kind on the mechanisms that produce natural necessity [Harré/Madden] |
| 16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
| 15299 | Species do not have enough constancy to be natural kinds [Harré/Madden] |
| 15253 | If the concept of a cause includes its usual effects, we call it a 'power' [Harré/Madden] |
| 15278 | Humean accounts of causal direction by time fail, because cause and effect can occur together [Harré/Madden] |
| 15246 | Active causal power is just objects at work, not something existing in itself [Harré/Madden] |
| 15213 | Causation always involves particular productive things [Harré/Madden] |
| 15217 | Efficient causes combine stimulus to individuals, absence of contraints on activity [Harré/Madden] |
| 15277 | The cause (or part of it) is what stimulates or releases the powerful particular thing involved [Harré/Madden] |
| 15237 | Originally Humeans based lawlike statements on pure qualities, without particulars [Harré/Madden] |
| 15238 | Being lawlike seems to resist formal analysis, because there are always counter-examples [Harré/Madden] |
| 15223 | Necessary effects will follow from some general theory specifying powers and structure of a world [Harré/Madden] |
| 15241 | Humeans say there is no necessity in causation, because denying an effect is never self-contradictory [Harré/Madden] |
| 15240 | In lawful universal statements (unlike accidental ones) we see why the regularity holds [Harré/Madden] |
| 15239 | We could call any generalisation a law, if it had reasonable support and no counter-evidence [Harré/Madden] |
| 15243 | We perceive motion, and not just successive occupations of different positions [Harré/Madden] |
| 15265 | 'Energy' is a quasi-substance invented as the bearer of change during interactions [Harré/Madden] |
| 15280 | 'Kinetic energy' is used to explain the effects of moving things when they are stopped [Harré/Madden] |
| 15321 | Space can't be an individual (in space), but it is present in all places [Harré/Madden] |
| 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] |
| 15259 | Chemical atoms have two powers: to enter certain combinations, and to emit a particular spectrum [Harré/Madden] |
| 15263 | Chemistry is not purely structural; CO2 is not the same as SO2 [Harré/Madden] |
| 15295 | Theism is supposed to make the world more intelligible - and should offer results [Harré/Madden] |