156 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] |
| 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] |
| 3137 | Varieties of singular terms are used to designate token particulars [Rey] |
| 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] |
| 3143 | Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey] |
| 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] |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| 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] |
| 3145 | The Indiscernibility of Identicals is a truism; but the Identity of Indiscernibles depends on possible identical worlds [Rey] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 3172 | Empiricism says experience is both origin and justification of all knowledge [Rey] |
| 3166 | Animal learning is separate from their behaviour [Rey] |
| 3232 | Abduction could have true data and a false conclusion, and may include data not originally mentioned [Rey] |
| 3128 | It's not at all clear that explanation needs to stop anywhere [Rey] |
| 3136 | The three theories are reduction, dualism, eliminativism [Rey] |
| 3141 | Is consciousness 40Hz oscillations in layers 5 and 6 of the visual cortex? [Rey] |
| 3148 | Dualist privacy is seen as too deep for even telepathy to reach [Rey] |
| 3164 | Intentional explanations are always circular [Rey] |
| 3138 | Arithmetic and unconscious attitudes have no qualia [Rey] |
| 3142 | Why qualia, and why this particular quale? [Rey] |
| 3224 | If qualia have no function, their attachment to thoughts is accidental [Rey] |
| 3227 | Are qualia a type of propositional attitude? [Rey] |
| 3226 | Are qualia irrelevant to explaining the mind? [Rey] |
| 3229 | If colour fits a cone mapping hue, brightness and saturation, rotating the cone could give spectrum inversion [Rey] |
| 3223 | Self-consciousness may just be nested intentionality [Rey] |
| 3162 | Experiments prove that people are often unaware of their motives [Rey] |
| 3163 | Brain damage makes the unreliability of introspection obvious [Rey] |
| 3195 | If reason could be explained in computational terms, there would be no need for the concept of 'free will' [Rey] |
| 3196 | Free will isn't evidence against a theory of thought if there is no evidence for free will [Rey] |
| 3180 | Maybe behaviourists should define mental states as a group [Rey] |
| 3165 | Behaviourism is eliminative, or reductionist, or methodological [Rey] |
| 3167 | Animals don't just respond to stimuli, they experiment [Rey] |
| 3173 | How are stimuli and responses 'similar'? [Rey] |
| 3179 | Behaviour is too contingent and irrelevant to be the mind [Rey] |
| 3186 | If a normal person lacked a brain, would you say they had no mind? [Rey] |
| 3127 | Dualism and physicalism explain nothing, and don't suggest any research [Rey] |
| 3188 | Homuncular functionalism (e.g. Freud) could be based on simpler mechanical processes [Rey] |
| 3216 | Is the room functionally the same as a Chinese speaker? [Rey] |
| 3220 | Searle is guilty of the fallacy of division - attributing a property of the whole to a part [Rey] |
| 3206 | One computer program could either play chess or fight a war [Rey] |
| 3140 | If you explain water as H2O, you have reduced water, but not eliminated it [Rey] |
| 3134 | Human behaviour can show law-like regularity, which eliminativism can't explain [Rey] |
| 3200 | Pattern recognition is puzzling for computation, but makes sense for connectionism [Rey] |
| 3201 | Connectionism explains well speed of perception and 'graceful degradation' [Rey] |
| 3202 | Connectionism explains irrationality (such as the Gamblers' Fallacy) quite well [Rey] |
| 3199 | Connectionism assigns numbers to nodes and branches, and plots the outcomes [Rey] |
| 3150 | Can identity explain reason, free will, non-extension, intentionality, subjectivity, experience? [Rey] |
| 3129 | Physicalism offers something called "complexity" instead of mental substance [Rey] |
| 3139 | Some attitudes are information (belief), others motivate (hatred) [Rey] |
| 3174 | Good grammar can't come simply from stimuli [Rey] |
| 3171 | Children speak 90% good grammar [Rey] |
| 3213 | Animals may also use a language of thought [Rey] |
| 3170 | We train children in truth, not in grammar [Rey] |
| 3215 | Images can't replace computation, as they need it [Rey] |
| 3194 | CRTT is good on deduction, but not so hot on induction, abduction and practical reason [Rey] |
| 3147 | Problem-solving clearly involves manipulating images [Rey] |
| 3175 | Animals map things over time as well as over space [Rey] |
| 3207 | Simple externalism is that the meaning just is the object [Rey] |
| 3176 | Anything bears a family resemblance to a game, but obviously not anything counts as one [Rey] |
| 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] |
| 3181 | A one hour gap in time might be indirectly verified, but then almost anything could be [Rey] |
| 3204 | The meaning of "and" may be its use, but not of "animal" [Rey] |
| 3205 | Semantic holism means new evidence for a belief changes the belief, and we can't agree on concepts [Rey] |
| 3209 | Causal theories of reference (by 'dubbing') don't eliminate meanings in the heads of dubbers [Rey] |
| 3210 | If meaning and reference are based on causation, then virtually everything has meaning [Rey] |
| 3149 | Referential Opacity says truth is lost when you substitute one referring term ('mother') for another ('Jocasta') [Rey] |
| 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] |
| 3169 | A simple chaining device can't build sentences containing 'either..or', or 'if..then' [Rey] |
| 3221 | Our desires become important when we have desires about desires [Rey] |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| 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] |
| 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] |