165 ideas
3600 | Slow and accurate thought makes the greatest progress [Descartes] |
3601 | Most things in human life seem vain and useless [Descartes] |
3602 | Almost every daft idea has been expressed by some philosopher [Descartes] |
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] |
3603 | Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG] |
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] |
3612 | Clear and distinct conceptions are true because a perfect God exists [Descartes] |
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] |
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] |
18011 | Category mistakes seem to be universal across languages [Magidor] |
18016 | Two good sentences should combine to make a good sentence, but that might be absurd [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] |
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] |
18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
18058 | Maybe the presuppositions of category mistakes are the abilities of things? [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] |
3610 | Truth is clear and distinct conception - of which it is hard to be sure [Descartes] |
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] |
14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
14106 | Implication cannot be defined [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] |
14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
14154 | Geometry throws no light on the nature of actual space [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] |
14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
14141 | Ordinals are defined through mathematical induction [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] |
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] |
3605 | We can believe a thing without knowing we believe it [Descartes] |
1583 | In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes] |
3607 | In thinking everything else false, my own existence remains totally certain [Descartes] |
3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
3611 | Understanding, rather than imagination or senses, gives knowledge [Descartes] |
3606 | I was searching for reliable rock under the shifting sand [Descartes] |
3604 | When rebuilding a house, one needs alternative lodgings [Descartes] |
3618 | Only experiments can settle disagreements between rival explanations [Descartes] |
3615 | Little reason is needed to speak, so animals have no reason at all [Descartes] |
3609 | I am a thinking substance, which doesn't need a place or material support [Descartes] |
3608 | I can deny my body and the world, but not my own existence [Descartes] |
3613 | Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes] |
3616 | The soul must unite with the body to have appetites and sensations [Descartes] |
18020 | Propositional attitudes relate agents to either propositions, or meanings, or sentence/utterances [Magidor] |
3614 | A machine could speak in response to physical stimulus, but not hold a conversation [Descartes] |
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] |
17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [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] |
18050 | If both s and not-s entail a sentence p, then p is a presupposition [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] |
18054 | Why do certain words trigger presuppositions? [Magidor] |
18022 | Metaphors tend to involve category mistakes, by joining disjoint domains [Magidor] |
18023 | Theories of metaphor divide over whether they must have literal meanings [Magidor] |
18024 | One theory says metaphors mean the same as the corresponding simile [Magidor] |
18027 | Metaphors as substitutes for the literal misses one predicate varying with context [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] |
1581 | Greeks elevate virtues enormously, but never explain them [Descartes] |
14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
14175 | We can drop 'cause', and just make inferences between facts [Russell] |
16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |
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] |
14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
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] |