160 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] |
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [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] |
| 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] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
| 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] |
| 14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| 14443 | The British parliament has one representative selected from each constituency [Russell] |
| 14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
| 14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
| 14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| 14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| 8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [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] |
| 14452 | All the propositions of logic are completely general [Russell] |
| 11062 | Logic is a priori because it is impossible to think illogically [Wittgenstein] |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| 18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| 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] |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| 7784 | 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein] |
| 23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
| 7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
| 7311 | The only genuine proper names are 'this' and 'that' [Russell] |
| 14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [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] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
| 14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
| 13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
| 14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
| 14439 | A complex number is simply an ordered couple of real numbers [Russell] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |
| 14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
| 14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
| 14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 18153 | A number is a repeated operation [Wittgenstein] |
| 18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
| 14425 | A number is something which characterises collections of the same size [Russell] |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| 14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| 13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
| 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] |
| 14449 | There is always something psychological about inference [Russell] |
| 14463 | Existence can only be asserted of something described, not of something named [Russell] |
| 13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
| 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] |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| 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] |
| 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] |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| 23466 | Objects are the substance of the world [Wittgenstein] |
| 23467 | Objects are simple [Wittgenstein] |
| 23468 | Apart from the facts, there is only substance [Wittgenstein] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 22321 | To know an object we must know the form and content of its internal properties [Wittgenstein, by Potter] |
| 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] |
| 9442 | The only necessity is logical necessity [Wittgenstein] |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| 14450 | All forms of implication are expressible as truth-functions [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] |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| 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] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 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] |
| 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] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 23486 | Pictures are possible situations in logical space [Wittgenstein] |
| 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] |
| 2942 | The sense of the world must lie outside the world [Wittgenstein] |