136 ideas
14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
5486 | Essentialism says metaphysics can't be done by analysing unreliable language [Ellis] |
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] |
18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
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] |
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] |
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] |
5468 | Properties are 'dispositional', or 'categorical' (the latter as 'block' or 'intrinsic' structures) [Ellis, by PG] |
5469 | The passive view of nature says categorical properties are basic, but others say dispositions [Ellis] |
5456 | Redness is not a property as it is not mind-independent [Ellis] |
5481 | Properties have powers; they aren't just ways for logicians to classify objects [Ellis] |
5458 | Nearly all fundamental properties of physics are dispositional [Ellis] |
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] |
5443 | Kripke and others have made essentialism once again respectable [Ellis] |
5444 | 'Individual essences' fix a particular individual, and 'kind essences' fix the kind it belongs to [Ellis] |
5462 | Essential properties are usually quantitatively determinate [Ellis] |
5448 | 'Real essence' makes it what it is; 'nominal essence' makes us categorise it a certain way [Ellis] |
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] |
5477 | One thing can look like something else, without being the something else [Ellis] |
5479 | Scientific essentialists say science should define the limits of the possible [Ellis] |
22303 | It makes no sense to say that a true proposition could have been false [Russell] |
5483 | Essentialists deny possible worlds, and say possibilities are what is compatible with the actual world [Ellis] |
5447 | Metaphysical necessities are true in virtue of the essences of things [Ellis] |
5476 | Essentialists say natural laws are in a new category: necessary a posteriori [Ellis] |
5478 | Imagination tests what is possible for all we know, not true possibility [Ellis] |
5482 | Possible worlds realism is only needed to give truth conditions for modals and conditionals [Ellis] |
5453 | Essentialists mostly accept the primary/secondary qualities distinction [Ellis] |
5466 | Primary qualities are number, figure, size, texture, motion, configuration, impenetrability and (?) mass [Ellis] |
5485 | Emeralds are naturally green, and only an external force could turn them blue [Ellis] |
5484 | Essentialists don't infer from some to all, but from essences to necessary behaviour [Ellis] |
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] |
5457 | Predicates assert properties, values, denials, relations, conventions, existence and fabrications [Ellis, by PG] |
14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
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] |
5488 | Regularity theories of causation cannot give an account of human agency [Ellis] |
5489 | Humans have variable dispositions, and also power to change their dispositions [Ellis] |
5490 | Essentialism fits in with Darwinism, but not with extreme politics of left or right [Ellis] |
5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
5472 | Natural kinds are of objects/substances, or events/processes, or intrinsic natures [Ellis] |
5471 | Essentialism says natural kinds are fundamental to nature, and determine the laws [Ellis] |
5446 | For essentialists two members of a natural kind must be identical [Ellis] |
5480 | The whole of our world is a natural kind, so all worlds like it necessarily have the same laws [Ellis] |
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] |
5445 | Essentialists regard inanimate objects as genuine causal agents [Ellis] |
5463 | Essentialists believe causation is necessary, resulting from dispositions and circumstances [Ellis] |
5491 | A general theory of causation is only possible in an area if natural kinds are involved [Ellis] |
5442 | For 'passivists' behaviour is imposed on things from outside [Ellis] |
5473 | The laws of nature imitate the hierarchy of natural kinds [Ellis] |
5474 | Laws of nature tend to describe ideal things, or ideal circumstances [Ellis] |
5475 | We must explain the necessity, idealisation, ontology and structure of natural laws [Ellis] |
5460 | Causal relations cannot be reduced to regularities, as they could occur just once [Ellis] |
5459 | Essentialists say dispositions are basic, rather than supervenient on matter and natural laws [Ellis] |
5461 | The essence of uranium is its atomic number and its electron shell [Ellis] |
5464 | For essentialists, laws of nature are metaphysically necessary, being based on essences of natural kinds [Ellis] |
5487 | Essentialism requires a clear separation of semantics, epistemology and ontology [Ellis] |
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] |
5048 | Perfection is simply quantity of reality [Leibniz] |
5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |