151 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] |
13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
13714 | We can treat modal worlds as different times [Sider] |
13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
13723 | System B is needed to prove the Barcan Formula [Sider] |
13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
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] |
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] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
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] |
13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
13700 | A 'total' function must always produce an output for a given domain [Sider] |
23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
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] |
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] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
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] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
9442 | The only necessity is logical necessity [Wittgenstein] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
13709 | Logical truths must be necessary if anything is [Sider] |
13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
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] |
13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
12869 | Two objects may only differ in being different [Wittgenstein] |
13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
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] |
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] |