362 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] |
| 2512 | Philosophy is a battle against the bewitchment of our intelligence by means of language [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] |
| 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] |
| 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] |
| 4148 | What is your aim in philosophy? - To show the fly the way out of the fly-bottle [Wittgenstein] |
| 2938 | The limits of my language means the limits of my world [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] |
| 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] |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| 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] |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| 18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
| 18735 | Talking nonsense is not following the rules [Wittgenstein] |
| 18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
| 18731 | There is no theory of truth, because it isn't a concept [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] |
| 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] |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| 11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
| 13643 | Aristotelian logic is complete [Shapiro] |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| 10207 | Anti-realists reject set theory [Shapiro] |
| 23502 | Logic fills the world, to its limits [Wittgenstein] |
| 18724 | In logic nothing is hidden [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] |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| 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] |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| 10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
| 10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
| 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] |
| 10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 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] |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| 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] |
| 10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| 18723 | We may correctly use 'not' without making the rule explicit [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] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 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] |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
| 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] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| 10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
| 10240 | Model theory deals with relations, reference and extensions [Shapiro] |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| 19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| 13628 | We can live well without completeness in logic [Shapiro] |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| 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] |
| 10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| 18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
| 10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
| 18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
| 18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| 10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| 10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 18153 | A number is a repeated operation [Wittgenstein] |
| 18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| 10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
| 10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
| 10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
| 10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
| 10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
| 10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
| 10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| 10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
| 10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
| 8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
| 10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
| 10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
| 10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
| 10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
| 10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| 10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
| 11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 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] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
| 10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
| 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] |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 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] |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 23466 | Objects are the substance of the world [Wittgenstein] |
| 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] |
| 10275 | A blurry border is still a border [Shapiro] |
| 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] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 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] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 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] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 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] |
| 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] |
| 4158 | An 'inner process' stands in need of outward criteria [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] |
| 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] |
| 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] |
| 10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
| 9626 | A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro] |
| 10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
| 9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
| 10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
| 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] |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| 18283 | Language pictures the essence of the world [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] |
| 23497 | Solipsism is correct, but can only be shown, not said, by the limits of my personal language [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] |
| 4136 | To imagine a language means to imagine a form of life [Wittgenstein] |
| 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] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 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] |