145 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] |
| 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] |
| 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] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 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] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 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] |
| 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] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
| 7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
| 9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
| 15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 18153 | A number is a repeated operation [Wittgenstein] |
| 18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| 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] |
| 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] |
| 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] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 23466 | Objects are the substance of the world [Wittgenstein] |
| 23467 | Objects are simple [Wittgenstein] |
| 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] |
| 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] |
| 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] |
| 3568 | Surely ALL truths are externally justified, by the facts? [Cross,A] |
| 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] |
| 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] |
| 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] |