169 ideas
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| 18019 | People have dreams which involve category mistakes [Magidor] |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| 17998 | Category mistakes are either syntactic, semantic, or pragmatic [Magidor] |
| 18011 | Category mistakes seem to be universal across languages [Magidor] |
| 18012 | Category mistakes as syntactic needs a huge number of fine-grained rules [Magidor] |
| 18013 | Embedded (in 'he said that…') category mistakes show syntax isn't the problem [Magidor] |
| 18021 | Category mistakes are meaningful, because metaphors are meaningful category mistakes [Magidor] |
| 18015 | The normal compositional view makes category mistakes meaningful [Magidor] |
| 18017 | If a category mistake is synonymous across two languages, that implies it is meaningful [Magidor] |
| 18031 | If a category mistake has unimaginable truth-conditions, then it seems to be meaningless [Magidor] |
| 18016 | Two good sentences should combine to make a good sentence, but that might be absurd [Magidor] |
| 18030 | A good explanation of why category mistakes sound wrong is that they are meaningless [Magidor] |
| 18032 | Category mistakes are neither verifiable nor analytic, so verificationism says they are meaningless [Magidor] |
| 18034 | Category mistakes play no role in mental life, so conceptual role semantics makes them meaningless [Magidor] |
| 18037 | Maybe when you say 'two is green', the predicate somehow fails to apply? [Magidor] |
| 18039 | If category mistakes aren't syntax failure or meaningless, maybe they just lack a truth-value? [Magidor] |
| 18058 | Maybe the presuppositions of category mistakes are the abilities of things? [Magidor] |
| 18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
| 18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
| 18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
| 18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
| 18059 | The presuppositions in category mistakes reveal nothing about ontology [Magidor] |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| 18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
| 14113 | The null class is a fiction [Russell] |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| 14106 | Implication cannot be defined [Russell] |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| 14167 | The only classes are things, predicates and relations [Russell] |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 14117 | Numbers are properties of classes [Russell] |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| 19482 | Current physics says matter and antimatter should have reduced to light at the big bang [New Sci.] |
| 19483 | CP violation shows a decay imbalance in matter and antimatter, leading to matter's dominance [New Sci.] |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| 18060 | We can explain the statue/clay problem by a category mistake with a false premise [Magidor] |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 19737 | A system can infer the structure of the world by making predictions about it [New Sci.] |
| 19736 | Neural networks can extract the car-ness of a car, or the chair-ness of a chair [New Sci.] |
| 18020 | Propositional attitudes relate agents to either propositions, or meanings, or sentence/utterances [Magidor] |
| 16419 | No one has yet devised a rationality test [New Sci.] |
| 16417 | About a third of variation in human intelligence is environmental [New Sci.] |
| 16418 | People can be highly intelligent, yet very stupid [New Sci.] |
| 19484 | Psychologists measure personality along five dimensions [New Sci.] |
| 18035 | Two sentences with different meanings can, on occasion, have the same content [Magidor] |
| 18018 | To grasp 'two' and 'green', must you know that two is not green? [Magidor] |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| 18008 | Generative semantics says structure is determined by semantics as well as syntactic rules [Magidor] |
| 18010 | 'John is easy to please' and 'John is eager to please' have different deep structure [Magidor] |
| 18053 | The semantics of a sentence is its potential for changing a context [Magidor] |
| 18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [Magidor] |
| 17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
| 18014 | Understanding unlimited numbers of sentences suggests that meaning is compositional [Magidor] |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| 18001 | Are there partial propositions, lacking truth value in some possible worlds? [Magidor] |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| 18036 | A sentence can be meaningful, and yet lack a truth value [Magidor] |
| 18051 | In the pragmatic approach, presuppositions are assumed in a context, for successful assertion [Magidor] |
| 18043 | The infelicitiousness of trivial truth is explained by uninformativeness, or a static context-set [Magidor] |
| 18042 | The infelicitiousness of trivial falsity is explained by expectations, or the loss of a context-set [Magidor] |
| 18047 | A presupposition is what makes an utterance sound wrong if it is not assumed? [Magidor] |
| 18048 | A test for presupposition would be if it provoked 'hey wait a minute - I have no idea that....' [Magidor] |
| 18049 | The best tests for presupposition are projecting it to negation, conditional, conjunction, questions [Magidor] |
| 18050 | If both s and not-s entail a sentence p, then p is a presupposition [Magidor] |
| 18054 | Why do certain words trigger presuppositions? [Magidor] |
| 18024 | One theory says metaphors mean the same as the corresponding simile [Magidor] |
| 18023 | Theories of metaphor divide over whether they must have literal meanings [Magidor] |
| 18025 | The simile view of metaphors removes their magic, and won't explain why we use them [Magidor] |
| 18026 | Maybe a metaphor is just a substitute for what is intended literally, like 'icy' for 'unemotional' [Magidor] |
| 18028 | Gricean theories of metaphor involve conversational implicatures based on literal meanings [Magidor] |
| 18029 | Non-cognitivist views of metaphor says there are no metaphorical meanings, just effects of the literal [Magidor] |
| 18022 | Metaphors tend to involve category mistakes, by joining disjoint domains [Magidor] |
| 18027 | Metaphors as substitutes for the literal misses one predicate varying with context [Magidor] |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| 19950 | Entropy is the only time-asymmetric law, so time may be linked to entropy [New Sci.] |
| 19478 | Light moves at a constant space-time speed, but its direction is in neither space nor time [New Sci.] |
| 19474 | Quantum states are measured by external time, of unknown origin [New Sci.] |
| 19473 | The Schrödinger equation describes the evolution of an object's wave function in Hilbert space [New Sci.] |
| 19953 | In string theory space-time has a grainy indivisible substructure [New Sci.] |
| 19476 | String theory needs at least 10 space-time dimensions [New Sci.] |
| 19954 | It is impossible for find a model of actuality among the innumerable models in string theory [New Sci.] |
| 19947 | Hilbert Space is an abstraction representing all possible states of a quantum system [New Sci.] |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| 19955 | Space-time may be a geometrical manifestation of quantum entanglement [New Sci.] |
| 19475 | Relativity makes time and space jointly basic; quantum theory splits them, and prioritises time [New Sci.] |
| 19948 | Einstein's merging of time with space has left us confused about the nature of time [New Sci.] |
| 19949 | Quantum theory relies on a clock outside the system - but where is it located? [New Sci.] |
| 19951 | Entropy is puzzling, so we may need to build new laws which include time directionality [New Sci.] |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| 19952 | Black holes have entropy, but general relativity says they are unstructured, and lack entropy [New Sci.] |
| 19477 | General relativity predicts black holes, as former massive stars, and as galaxy centres [New Sci.] |
| 16420 | 84.5 percent of the universe is made of dark matter [New Sci.] |
| 17604 | We are halfway to synthesising any molecule we want [New Sci.] |
| 17603 | Chemistry just needs the periodic table, and protons, electrons and neutrinos [New Sci.] |