266 ideas
7536 | If you hope to improve the world, all you can do is improve yourself [Wittgenstein] |
16010 | While faith is a passion (as Kierkegaard says), wisdom is passionless [Wittgenstein] |
18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
2937 | What we cannot speak about we must pass over in silence [Wittgenstein] |
2626 | A philosopher is outside any community of ideas [Wittgenstein] |
7085 | The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling] |
6870 | I say (contrary to Wittgenstein) that philosophy expresses what we thought we must be silent about [Ansell Pearson on Wittgenstein] |
2512 | Philosophy is a battle against the bewitchment of our intelligence by means of language [Wittgenstein] |
18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [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] |
4148 | What is your aim in philosophy? - To show the fly the way out of the fly-bottle [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] |
18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [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] |
18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
22490 | Bring words back from metaphysics to everyday use [Wittgenstein] |
18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
23499 | This book says we should either say it clearly, or shut up [Wittgenstein] |
23508 | Science is all the true propositions [Wittgenstein] |
6566 | The problem is to explain the role of contradiction in social life [Wittgenstein] |
2939 | If a sign is useless it is meaningless; that is the point of Ockham's maxim [Wittgenstein] |
8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
18735 | Talking nonsense is not following the rules [Wittgenstein] |
18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
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] |
18707 | All thought has the logical form of reality [Wittgenstein] |
23483 | Proposition elements correlate with objects, but the whole picture does not correspond to a fact [Wittgenstein, by Morris,M] |
11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
8694 | Free logic was developed for fictional or non-existent objects [Friend] |
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
8672 | A 'powerset' is all the subsets of a set [Friend] |
8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
8666 | Infinite sets correspond one-to-one with a subset [Friend] |
8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
23502 | Logic fills the world, to its limits [Wittgenstein] |
16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
23504 | Logic concerns everything that is subject to law; the rest is accident [Wittgenstein] |
18724 | In logic nothing is hidden [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] |
18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
7537 | Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk] |
18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
23496 | Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein] |
18736 | Contradiction is between two rules, not between rule and reality [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] |
18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
18743 | Wittgenstein says we want the grammar of problems, not their first-order logical structure [Wittgenstein, by Horsten/Pettigrew] |
18268 | Apparent logical form may not be real logical form [Wittgenstein] |
10905 | My fundamental idea is that the 'logical constants' do not represent [Wittgenstein] |
6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
18718 | Saying 'and' has meaning is just saying it works in a sentence [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] |
18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
4139 | Naming is a preparation for description [Wittgenstein] |
4946 | A name is not determined by a description, but by a cluster or family [Wittgenstein, by Kripke] |
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] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
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] |
8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
6569 | 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin] |
18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
8668 | The 'rational' numbers are those representable as fractions [Friend] |
8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
18153 | A number is a repeated operation [Wittgenstein] |
8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
11073 | Two and one making three has the necessity of logical inference [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] |
8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
8706 | Constructivism rejects too much mathematics [Friend] |
8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
23463 | Atomic facts correspond to true elementary propositions [Wittgenstein] |
23472 | The sense of propositions relies on the world's basic logical structure [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] |
18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
22312 | Facts can be both positive and negative [Wittgenstein, by Potter] |
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] |
18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
23466 | Objects are the substance of the world [Wittgenstein] |
8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
22320 | An 'object' is just what can be referred to without possible non-existence [Wittgenstein] |
23467 | Objects are simple [Wittgenstein] |
23468 | Apart from the facts, there is only substance [Wittgenstein] |
10710 | We accept substance, to avoid infinite backwards chains of meaning [Wittgenstein, by Potter] |
15106 | Essence is expressed by grammar [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] |
18726 | For each necessity in the world there is an arbitrary rule of language [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] |
18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
6600 | The belief that fire burns is like the fear that it burns [Wittgenstein] |
4153 | Are sense-data the material of which the universe is made? [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] |
23500 | My main problem is the order of the world, and whether it is knowable a priori [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] |
18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
6501 | As sense-data are necessarily private, they are attacked by Wittgenstein's objections [Wittgenstein, by Robinson,H] |
11079 | How do I decide when to accept or obey an intuition? [Wittgenstein] |
18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
3597 | Foundations need not precede other beliefs [Wittgenstein] |
3790 | Causes of beliefs are irrelevant to their contents [Wittgenstein] |
6591 | Doubts can't exist if they are inexpressible or unanswerable [Wittgenstein] |
3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
4160 | One can mistrust one's own senses, but not one's own beliefs [Wittgenstein] |
17665 | The 'Tractatus' is instrumentalist about laws of nature [Wittgenstein, by Armstrong] |
2941 | Induction accepts the simplest law that fits our experiences [Wittgenstein] |
18721 | Explanation and understanding are the same [Wittgenstein] |
18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
17673 | The modern worldview is based on the illusion that laws explain nature [Wittgenstein] |
18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
19273 | I don't have the opinion that people have minds; I just treat them as such [Wittgenstein] |
5663 | It is irresponsible to generalise from my own case of pain to other people's [Wittgenstein] |
19272 | To imagine another's pain by my own, I must imagine a pain I don't feel, by one I do feel [Wittgenstein] |
4161 | If a lion could talk, we could not understand him [Wittgenstein] |
7392 | If a lion could talk, it would be nothing like other lions [Dennett on Wittgenstein] |
22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
2940 | The subject stands outside our understanding of the world [Wittgenstein] |
5676 | To say that I 'know' I am in pain means nothing more than that I AM in pain [Wittgenstein] |
22419 | 'I' is a subject in 'I am in pain' and an object in 'I am bleeding' [Wittgenstein, by McGinn] |
23498 | The modern idea of the subjective soul is composite, and impossible [Wittgenstein] |
4154 | Why are we not aware of the huge gap between mind and brain in ordinary life? [Wittgenstein] |
8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
23475 | The form of a proposition must show why nonsense is unjudgeable [Wittgenstein] |
6165 | Every course of action can either accord or conflict with a rule, so there is no accord or conflict [Wittgenstein] |
4143 | One cannot obey a rule 'privately', because that is a practice, not the same as thinking one is obeying [Wittgenstein] |
7092 | If individuals can't tell if they are following a rule, how does a community do it? [Grayling on Wittgenstein] |
4158 | An 'inner process' stands in need of outward criteria [Wittgenstein] |
4138 | Is white simple, or does it consist of the colours of the rainbow? [Wittgenstein] |
7055 | Externalist accounts of mental content begin in Wittgenstein [Wittgenstein, by Heil] |
8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
12576 | Possessing a concept is knowing how to go on [Wittgenstein, by Peacocke] |
4157 | Concepts direct our interests and investigations, and express those interests [Wittgenstein] |
12606 | Man learns the concept of the past by remembering [Wittgenstein] |
4141 | Various games have a 'family resemblance', as their similarities overlap and criss-cross [Wittgenstein] |
7084 | What can be said is what can be thought, so language shows the limits of thought [Wittgenstein, by Grayling] |
23450 | Wittgenstein rejected his earlier view that the form of language is the form of the world [Wittgenstein, by Morris,M] |
23482 | The 'form' of the picture is its possible combinations [Wittgenstein] |
18283 | Language pictures the essence of the world [Wittgenstein] |
23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
8172 | To understand a proposition means to know what is the case if it is true [Wittgenstein] |
18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
18282 | You can't believe it if you can't imagine a verification for it [Wittgenstein] |
18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
7086 | Good philosophy asserts science, and demonstrates the meaninglessness of metaphysics [Wittgenstein] |
4150 | Asking about verification is only one way of asking about the meaning of a proposition [Wittgenstein] |
6567 | For Wittgenstein, words are defined by their use, just as chess pieces are [Wittgenstein, by Fogelin] |
6169 | We do not achieve meaning and understanding in our heads, but in the world [Wittgenstein, by Rowlands] |
4155 | We all seem able to see quite clearly how sentences represent things when we use them [Wittgenstein] |
4137 | In the majority of cases the meaning of a word is its use in the language [Wittgenstein] |
18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
4142 | To understand a sentence means to understand a language [Wittgenstein] |
4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |
4149 | We don't have 'meanings' in our minds in addition to verbal expressions [Wittgenstein] |
4156 | Make the following experiment: say "It's cold here" and mean "It's warm here" [Wittgenstein] |
4145 | How do words refer to sensations? [Wittgenstein] |
4140 | The standard metre in Paris is neither one metre long nor not one metre long [Wittgenstein] |
23511 | Propositions use old expressions for a new sense [Wittgenstein] |
23488 | Propositions are understood via their constituents [Wittgenstein] |
18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
23486 | Pictures are possible situations in logical space [Wittgenstein] |
23490 | A thought is mental constituents that relate to reality as words do [Wittgenstein] |
4136 | To imagine a language means to imagine a form of life [Wittgenstein] |
6166 | Was Wittgenstein's problem between individual and community, or between occasions for an individual? [Rowlands on Wittgenstein] |
7875 | If a brilliant child invented a name for a private sensation, it couldn't communicate it [Wittgenstein] |
4146 | We cannot doublecheck mental images for correctness (or confirm news with many copies of the paper) [Wittgenstein] |
4147 | If we only named pain by our own case, it would be like naming beetles by looking in a private box [Wittgenstein] |
5659 | If the reference is private, that is incompatible with the sense being public [Wittgenstein, by Scruton] |
4152 | Getting from perceptions to words cannot be a private matter; the rules need an institution of use [Wittgenstein] |
23497 | Solipsism is correct, but can only be shown, not said, by the limits of my personal language [Wittgenstein] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
23489 | We translate by means of proposition constituents, not by whole propositions [Wittgenstein] |
6318 | The doctrine of indeterminacy of translation seems implied by the later Wittgenstein [Wittgenstein, by Quine] |
4144 | Common human behaviour enables us to interpret an unknown language [Wittgenstein] |
11049 | To communicate, language needs agreement in judgment as well as definition [Wittgenstein] |
6658 | What is left over if I subtract my arm going up from my raising my arm? [Wittgenstein] |
6606 | Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein] |
2943 | Ethics cannot be put into words [Wittgenstein] |
2942 | The sense of the world must lie outside the world [Wittgenstein] |
4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |
4151 | Grammar tells what kind of object anything is - and theology is a kind of grammar [Wittgenstein] |
4159 | The human body is the best picture of the human soul [Wittgenstein] |