148 ideas
2937 | What we cannot speak about we must pass over in silence [Wittgenstein] |
21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
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] |
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] |
2938 | The limits of my language means the limits of my world [Wittgenstein] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
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] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16324 | Any definition of truth requires a metalanguage [Halbach] |
16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
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] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
16309 | Every attempt at formal rigour uses some set theory [Halbach] |
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] |
16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
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] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
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] |
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] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
18153 | A number is a repeated operation [Wittgenstein] |
16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
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] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
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] |
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] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
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] |
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] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
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] |