193 ideas
| 2937 | What we cannot speak about we must pass over in silence [Wittgenstein] |
| 6870 | I say (contrary to Wittgenstein) that philosophy expresses what we thought we must be silent about [Ansell Pearson on Wittgenstein] |
| 2944 | If a question can be framed at all, it is also possible to answer it [Wittgenstein] |
| 9810 | The 'Tractatus' is a masterpiece of anti-philosophy [Badiou on Wittgenstein] |
| 23459 | This work solves all the main problems, but that has little value [Wittgenstein] |
| 23512 | Once you understand my book you will see that it is nonsensical [Wittgenstein] |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 2938 | The limits of my language means the limits of my world [Wittgenstein] |
| 6429 | All complex statements can be resolved into constituents and descriptions [Wittgenstein] |
| 23492 | Our language is an aspect of biology, and so its inner logic is opaque [Wittgenstein] |
| 23510 | Most philosophical questions arise from failing to understand the logic of language [Wittgenstein] |
| 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] |
| 23499 | This book says we should either say it clearly, or shut up [Wittgenstein] |
| 23508 | Science is all the true propositions [Wittgenstein] |
| 2939 | If a sign is useless it is meaningless; that is the point of Ockham's maxim [Wittgenstein] |
| 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] |
| 10910 | The best account of truth-making is isomorphism [Wittgenstein, by Mulligan/Simons/Smith] |
| 23462 | He says the world is the facts because it is the facts which fix all the truths [Wittgenstein, by Morris,M] |
| 18349 | All truths have truth-makers, but only atomic truths correspond to them [Wittgenstein, by Rami] |
| 10967 | Wittgenstein's picture theory is the best version of the correspondence theory of truth [Read on Wittgenstein] |
| 7087 | Language is [propositions-elementary propositions-names]; reality is [facts-states of affairs-objects] [Wittgenstein, by Grayling] |
| 4702 | The account of truth in the 'Tractatus' seems a perfect example of the correspondence theory [Wittgenstein, by O'Grady] |
| 7056 | Pictures reach out to or feel reality, touching at the edges, correlating in its parts [Wittgenstein] |
| 23483 | Proposition elements correlate with objects, but the whole picture does not correspond to a fact [Wittgenstein, by Morris,M] |
| 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] |
| 23502 | Logic fills the world, to its limits [Wittgenstein] |
| 23504 | Logic concerns everything that is subject to law; the rest is accident [Wittgenstein] |
| 6428 | Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell] |
| 11062 | Logic is a priori because it is impossible to think illogically [Wittgenstein] |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| 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] |
| 18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
| 7537 | Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk] |
| 23496 | Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein] |
| 18154 | The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock] |
| 13429 | The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey] |
| 18268 | Apparent logical form may not be real logical form [Wittgenstein] |
| 10905 | My fundamental idea is that the 'logical constants' do not represent [Wittgenstein] |
| 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] |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| 7784 | 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein] |
| 23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
| 7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
| 15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
| 13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
| 19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
| 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] |
| 18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
| 18153 | A number is a repeated operation [Wittgenstein] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 14117 | Numbers are properties of classes [Russell] |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| 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] |
| 6849 | Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk] |
| 23509 | The logic of the world is shown by tautologies in logic, and by equations in mathematics [Wittgenstein] |
| 13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
| 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] |
| 7090 | The 'Tractatus' is an extreme example of 'Logical Atomism' [Wittgenstein, by Grayling] |
| 23464 | In atomic facts the objects hang together like chain links [Wittgenstein] |
| 23471 | The structure of an atomic fact is how its objects combine; this possibility is its form [Wittgenstein] |
| 21682 | If a proposition is elementary, no other elementary proposition contradicts it [Wittgenstein] |
| 22319 | Analysis must end in elementary propositions, which are combinations of names [Wittgenstein] |
| 21683 | Nothing can be inferred from an elementary proposition [Wittgenstein] |
| 23473 | Do his existent facts constitute the world, or determine the world? [Morris,M on Wittgenstein] |
| 22311 | The world is determined by the facts, and there are no further facts [Wittgenstein] |
| 22313 | The existence of atomic facts is a positive fact, their non-existence a negative fact [Wittgenstein] |
| 22314 | On white paper a black spot is a positive fact and a white spot a negative fact [Wittgenstein] |
| 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] |
| 7969 | The order of numbers is an internal relation, not an external one [Wittgenstein] |
| 7968 | A relation is internal if it is unthinkable that its object should not possess it [Wittgenstein] |
| 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] |
| 23466 | Objects are the substance of the world [Wittgenstein] |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| 23467 | Objects are simple [Wittgenstein] |
| 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] |
| 23468 | Apart from the facts, there is only substance [Wittgenstein] |
| 22321 | To know an object we must know the form and content of its internal properties [Wittgenstein, by Potter] |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| 6056 | Identity is not a relation between objects [Wittgenstein] |
| 22322 | You can't define identity by same predicates, because two objects with same predicates is assertable [Wittgenstein] |
| 6057 | Two things can't be identical, and self-identity is an empty concept [Wittgenstein] |
| 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] |
| 9442 | The only necessity is logical necessity [Wittgenstein] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 23495 | The tautologies of logic show the logic of language and the world [Wittgenstein] |
| 23487 | What is thinkable is possible [Wittgenstein] |
| 23470 | Each thing is in a space of possible facts [Wittgenstein] |
| 23507 | Unlike the modern view of a set of worlds, Wittgenstein thinks of a structured manifold of them [Wittgenstein, by White,RM] |
| 23469 | An imagined world must have something in common with the real world [Wittgenstein] |
| 11027 | To know an object you must know all its possible occurrences [Wittgenstein] |
| 23465 | The 'form' of an object is its possible roles in facts [Wittgenstein] |
| 12869 | Two objects may only differ in being different [Wittgenstein] |
| 23503 | Strict solipsism is pure realism, with the self as a mere point in surrounding reality [Wittgenstein] |
| 16907 | If the truth doesn't follow from self-evidence, then self-evidence cannot justify a truth [Wittgenstein] |
| 23479 | The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths [Wittgenstein, by Morris,M] |
| 23501 | There is no a priori order of things [Wittgenstein] |
| 7088 | Logic and maths can't say anything about the world, since, as tautologies, they are consistent with all realities [Wittgenstein, by Grayling] |
| 16909 | Logic is a priori because we cannot think illogically [Wittgenstein] |
| 23485 | No pictures are true a priori [Wittgenstein] |
| 6591 | Doubts can't exist if they are inexpressible or unanswerable [Wittgenstein] |
| 17665 | The 'Tractatus' is instrumentalist about laws of nature [Wittgenstein, by Armstrong] |
| 2941 | Induction accepts the simplest law that fits our experiences [Wittgenstein] |
| 17673 | The modern worldview is based on the illusion that laws explain nature [Wittgenstein] |
| 2940 | The subject stands outside our understanding of the world [Wittgenstein] |
| 23498 | The modern idea of the subjective soul is composite, and impossible [Wittgenstein] |
| 23475 | The form of a proposition must show why nonsense is unjudgeable [Wittgenstein] |
| 7084 | What can be said is what can be thought, so language shows the limits of thought [Wittgenstein, by Grayling] |
| 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] |
| 23482 | The 'form' of the picture is its possible combinations [Wittgenstein] |
| 8172 | To understand a proposition means to know what is the case if it is true [Wittgenstein] |
| 7086 | Good philosophy asserts science, and demonstrates the meaninglessness of metaphysics [Wittgenstein] |
| 23511 | Propositions use old expressions for a new sense [Wittgenstein] |
| 23488 | Propositions are understood via their constituents [Wittgenstein] |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| 23486 | Pictures are possible situations in logical space [Wittgenstein] |
| 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] |
| 23497 | Solipsism is correct, but can only be shown, not said, by the limits of my personal language [Wittgenstein] |
| 23489 | We translate by means of proposition constituents, not by whole propositions [Wittgenstein] |
| 2943 | Ethics cannot be put into words [Wittgenstein] |
| 6017 | Nomos is king [Pindar] |
| 2942 | The sense of the world must lie outside the world [Wittgenstein] |
| 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] |