147 ideas
| 2937 | What we cannot speak about we must pass over in silence [Wittgenstein] |
| Full Idea: What we cannot speak about we must pass over in silence. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 7) | |
| A reaction: This is either a boring truism, or points towards some sort of verificationism (where we can speak meaninglessly). Compare Ideas 7973 and 6870. |
| 6870 | I say (contrary to Wittgenstein) that philosophy expresses what we thought we must be silent about [Ansell Pearson on Wittgenstein] |
| Full Idea: I recognise the incredible force of Wittgenstein's closing statement in the 'Tractatus', but I hold the opposite view: philosophy exists to give expression to that which we think we can only remain silent about. | |
| From: comment on Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 7) by Keith Ansell Pearson - Interview with Baggini and Stangroom p.267 | |
| A reaction: A wonderful remark, with which I totally agree. Compare Idea 1596. I think it is just a fact that philosophers are able to articulate a huge number of ideas which other intelligent people find very interesting but on which they are unable to speak. |
| 2944 | If a question can be framed at all, it is also possible to answer it [Wittgenstein] |
| Full Idea: If a question can be framed at all, it is also possible to answer it. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.5) | |
| A reaction: Just the sort of unsubstantiated metaphysical claim that philosophers are always making. |
| 9810 | The 'Tractatus' is a masterpiece of anti-philosophy [Badiou on Wittgenstein] |
| Full Idea: The 'Tractatus' is without doubt one of the masterpieces of anti-philosophy. | |
| From: comment on Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Alain Badiou - Mathematics and Philosophy: grand and little p.16 | |
| A reaction: French philosophers do love making wicked remarks like that. It seems that analysis is anti-philosophy, or 'little' philosophy in Badiou's parlance. |
| 23459 | This work solves all the main problems, but that has little value [Wittgenstein] |
| Full Idea: I believe myself to have found, on all essential points, the final solution of the problems. ….and this work shows how little is achieved when these problems are solved. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], Pref) | |
| A reaction: This is LW's deep pessimism about the value of philosophy, right from the start. You can only idolise LW if you agree with him on this. |
| 23512 | Once you understand my book you will see that it is nonsensical [Wittgenstein] |
| Full Idea: Anyone who understands me eventually recognises my propositions as nonsensical, when he has used them - as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.54) | |
| A reaction: A much discussed passage. It can't possibly say that his book is pointless, because you can't attain this recognition without climbing his ladder. He speaks like an eastern guru. Perhaps Hume should have ended 'so commit my book to the flames'? |
| 2938 | The limits of my language means the limits of my world [Wittgenstein] |
| Full Idea: The limits of my language means the limits of my world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.6) | |
| A reaction: This is dangerous rubbish. For a start, if you accept (as you should) the existence of propositions, our heads are full of unarticulated ones. And truth emerges by degrees from what cannot be articulated. |
| 6429 | All complex statements can be resolved into constituents and descriptions [Wittgenstein] |
| Full Idea: Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.0201) | |
| A reaction: Russell says this embodies Wittgenstein's belief in analysis. Obviously Wittgenstein is making this claim 'in principle', as life is very short, and people are rather dim. I don't know how to begin evaluating such a claim. |
| 23492 | Our language is an aspect of biology, and so its inner logic is opaque [Wittgenstein] |
| Full Idea: Everyday language is a part of the human organism and is no less complicated than it. It is not humanly possible to gather immediately from it what the logic of language is. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.002) | |
| A reaction: It is normally assumed that ordinary language philosophy was derived from the later Wittgenstein, but this para in the Tractatus seems to contain the germ of the idea. He is pessimistic about finding logical forms. |
| 23510 | Most philosophical questions arise from failing to understand the logic of language [Wittgenstein] |
| Full Idea: Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.003) | |
| A reaction: I'm not sure what the scope of 'logic' is here. I suppose it means everything about language which is expounded in the Tractatus. I assume this includes Plato and Aristotle? I don't think I agree. It's about concepts, not about logic. |
| 23499 | This book says we should either say it clearly, or shut up [Wittgenstein] |
| Full Idea: The whole sense of the book might be summed up in the following words: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], Pref) | |
| A reaction: This also provides the last sentence of his book. I think this is an axiom of modern analytic philosophy. The dream is to clarify everything, and belief that this is possible puts logic centre-stage, as the most precise language available. |
| 23508 | Science is all the true propositions [Wittgenstein] |
| Full Idea: The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences). | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.11) | |
| A reaction: So if it is true, it is science. What about truths about science? What about true speculations beyond science? What about bad science? What about trivial everyday truths? This is said to be a rare precursor of logical positivism in Tractatus. |
| 2939 | If a sign is useless it is meaningless; that is the point of Ockham's maxim [Wittgenstein] |
| Full Idea: If a sign is useless it is meaningless. That is the point of Occam's maxim. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.328) |
| 10910 | The best account of truth-making is isomorphism [Wittgenstein, by Mulligan/Simons/Smith] |
| Full Idea: The most sophisticated account of truth-making to have appeared to date is the 'isomorphism' theory of the Tractatus. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Mulligan/Simons/Smith - Truth-makers §5 | |
| A reaction: Wittgenstein's theory is clearly closely related to Russell's 'congruence' theory of correspondence of around 1912. |
| 23462 | He says the world is the facts because it is the facts which fix all the truths [Wittgenstein, by Morris,M] |
| Full Idea: Wittgenstein is thinking of the world as what makes truths true. …To get all the truths fixed we need more than the things: we need, as it were, the way things are - that is to say, the facts. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 1.12) by Michael Morris - Guidebook to Wittgenstein's Tractatus 1 | |
| A reaction: Morris says this is 'sometimes suggested'. It strikes me as plausible, and makes LW a key source for the modern truthmaker idea. Perhaps in David Lewis's version of it. The facts include the relations and processes of the things. |
| 18349 | All truths have truth-makers, but only atomic truths correspond to them [Wittgenstein, by Rami] |
| Full Idea: In 1922 Wittgenstein said that every truth has a truth-maker, but only atomic truths correspond to their truth-makers. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Adolph Rami - Introduction: Truth and Truth-Making note 04 | |
| A reaction: Presumably this is what logical atomism is meant to be (cf Russell). The atomic sentences plug into the world, and the rest are constructions from them, making the latter more remote from the truth-makers. |
| 10967 | Wittgenstein's picture theory is the best version of the correspondence theory of truth [Read on Wittgenstein] |
| Full Idea: Wittgenstein's picture theory is without doubt the best thought-out and developed of all the versions of the correspondence theory of truth. | |
| From: comment on Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Stephen Read - Thinking About Logic Ch.1 |
| 7087 | Language is [propositions-elementary propositions-names]; reality is [facts-states of affairs-objects] [Wittgenstein, by Grayling] |
| Full Idea: Language consists in propositions, which are made of 'elementary' propositions, which are based ultimately on names. This matches the world of facts, compounded out of 'states of affairs', which are compounded of objects. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by A.C. Grayling - Wittgenstein Ch.2 | |
| A reaction: This is Grayling's summary of the basic idea of the 'Tractatus'. The whole thing seems to be an elaborate version of Russell's 'congruence' account of the correspondence theory of truth. Later Wittgenstein is loss of faith in this theory. |
| 4702 | The account of truth in the 'Tractatus' seems a perfect example of the correspondence theory [Wittgenstein, by O'Grady] |
| Full Idea: Wittgenstein's account in the 'Tractatus' is often taken as a paradigm instance of a sophisticated correspondence theory of truth. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Paul O'Grady - Relativism Ch.2 | |
| A reaction: This might explain why I am so much more drawn to the 'Tractatus' than to the later relativistic anti-philosophical mind-eliminitavist, meaning-eliminativist Wittgenstein. |
| 7056 | Pictures reach out to or feel reality, touching at the edges, correlating in its parts [Wittgenstein] |
| Full Idea: A picture attaches to reality by reaching out to it; it is laid against reality like a measure; only the end-points actually touch the object; the pictorial relationship consists of correlations of picture's elements with things, the picture's feelers. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.1511-5) | |
| A reaction: (somewhat compressed). This is Wittgenstein's so-called 'picture theory' of meaning (replaced later by 'meaning is use'). It is perhaps better seen as an account of the correspondence theory of truth. Compare Russell's 'congruence' view (Idea 5427). |
| 23483 | Proposition elements correlate with objects, but the whole picture does not correspond to a fact [Wittgenstein, by Morris,M] |
| Full Idea: Correlation need only be between elements of the picture and things in reality; it is not also required that there be a correspondence between the picture as a whole and a fact in reality - so things can be depicted falsely. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.15121) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3C | |
| A reaction: To turn his picture theory into a correspondence theory of truth would need a further step, of saying the proposition is true when the two structures coincide. I don't think LW says that. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 23502 | Logic fills the world, to its limits [Wittgenstein] |
| Full Idea: Logic pervades the world: the limits of the world are also its limits. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.61) | |
| A reaction: This is a gospel belief for hardcore analytic philosophy. Hence Williamson writes a book on modal logic as metaphysics. |
| 23504 | Logic concerns everything that is subject to law; the rest is accident [Wittgenstein] |
| Full Idea: The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.3) | |
| A reaction: Why should laws be logical? Legislatures can pass whimsical laws. Does he mean that the laws of nature are logically necessary? He can't just mean logical laws. |
| 6428 | Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell] |
| Full Idea: I think Wittgenstein is right when he says (in the 'Tractatus') that logic consists wholly of tautologies. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Bertrand Russell - My Philosophical Development Ch.10 | |
| A reaction: Despite Russell's support, I find this hard to accept. While a 'pure' or 'Platonist' logic may be hard to demonstrate or believe, I have a strong gut feeling that logic is more of a natural phenomenon than a human convention. |
| 11062 | Logic is a priori because it is impossible to think illogically [Wittgenstein] |
| Full Idea: What makes logic a priori is the impossibility of illogical thought. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.4731) | |
| A reaction: That places the a priori aspect of it in us (in the epistemology), rather than in the necessity of the logic (the ontology), which is as Kripke says it should be. |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| Full Idea: If p follows from q, I can make an inference from q to p, deduce p from q. The nature of the inference can be gathered only from the two propositions. They are the only possible justification of the inference. 'Laws of Inference' would be superfluous. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.132) | |
| A reaction: That seems to imply that each inference is judged on its particulars. But logic aims to be general. There seem to be 'laws' at a more complex level in the logic. |
| 18162 | The propositions of logic are analytic tautologies [Wittgenstein] |
| Full Idea: The propositions of logic are tautologies. Therefore the propositions of logic say nothing. (They are the analytic propositions). | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1) |
| 7537 | Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk] |
| Full Idea: Russell took a Platonist view of logic, but reading the 'Tractatus' convinced him that logic was purely linguistic, so-called 'logical truths' being nothing more than tautologies. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.1 | |
| A reaction: If p-and-q and p-or-q are both tautologies, how do you explain the difference between them? The first is an indicative proposition about the actual world, but the second is modal. They are asserting very different things. |
| 23496 | Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein] |
| Full Idea: The simultaneous presence of two colours in the same place in the visual field is impossible, in fact logically impossible, since it is ruled out by the logical structure of colour. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.3751) | |
| A reaction: This sounds the wrong way around. We derive our concept of the logic of colour from experiencing the total incompatibility of two colours in the same location. What if each of our eyes saw a different colour? |
| 18154 | The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock] |
| Full Idea: The 'Tractatus' does not allow the introduction of a sign for identity. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 13429 | The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey] |
| Full Idea: Wittgenstein discovered that the sign of identity is not a necessary constituent of logical notation, but can be replaced by the convention that different signs must have different meanings. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Frank P. Ramsey - The Foundations of Mathematics p.139 | |
| A reaction: [Ramsey cites p.139 - need to track down the modern reference] Hence in modern logic it is usually necessary to say that we are using 'classical logic with identity', since the use of identity is very convenient, and reasonably harmless (I think). |
| 18268 | Apparent logical form may not be real logical form [Wittgenstein] |
| Full Idea: The apparent logical form of the proposition need not be its real logical form. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.0031), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 6 'The incom' | |
| A reaction: This is one of the key doctrines of modern analytic philosophy. |
| 10905 | My fundamental idea is that the 'logical constants' do not represent [Wittgenstein] |
| Full Idea: My fundamental idea is that the 'logical constants' do not represent; that the logic of facts does not allow of representation. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.0312) | |
| A reaction: This seems to a firm rebuttal of any sort of platonism about logic, and implies a purely formal account. |
| 23493 | 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein] |
| Full Idea: If there were an object called 'not', it would follow that 'not-not-p' would say something different from what 'p' said, just because the one proposition would then be about 'not', and the other would not. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.44) | |
| A reaction: That is, the first proposition would be about not-p, and the second would be about p. Assuming we can say what such things are 'about'. A rather good argument that the connectives are not entities. P and double-negated P should be indistinguishable. |
| 7784 | 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein] |
| Full Idea: The variable name ‘x’ is the proper sign of the pseudo-concept object. Wherever the word ‘object’ (‘thing’, ‘entity’, etc.) is rightly used, it is expressed in logical symbolism by the variable name. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.1272) | |
| A reaction: This seems to be the germ of Quine's famous dictum (Idea 1610). I am not persuaded that because logic must handle an object as a variable, that it follows that we are dealing with a pseudo-concept. Let logic limp behind life. |
| 23506 | Names are primitive, and cannot be analysed [Wittgenstein] |
| Full Idea: A name cannot be dissected any further by means of a definition: it is a primitive sign. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.26) | |
| A reaction: All logicians and analytic philosophers seem to agree on this. He means terms which pick out specific objects. |
| 7089 | A name is primitive, and its meaning is the object [Wittgenstein] |
| Full Idea: A name means an object; an object is its meaning. ...A name cannot be dissected further by means of a definition: it is a primitive sign. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.203/3.26) | |
| A reaction: This is the optimistic view of names, that they are the point at which language plugs into the world (Russell preferred demonstratives for that job). Kripke's baptismal view of names has the same aspiration. |
| 9467 | Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette] |
| Full Idea: Wittgenstein reduces the universal quantifier to conjunctions of singular predications, and the existential quantifier to disjunctions of singular predications. ..This is nowadays understood as a failed effort. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Dale Jacquette - Intro to III: Quantifiers p.143 | |
| A reaction: The problem this meets has something to do with infinite objects. In a domain of three objects it looks like a perfectly plausible strategy. 'All' is all three, and 'Some' is at least one of the three. |
| 15089 | Logical proof just explicates complicated tautologies [Wittgenstein] |
| Full Idea: Proof in logic is merely a mechanical expedient to facilitate recognition of tautologies in complicated cases. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1262) |
| 13830 | Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking] |
| Full Idea: Wittgenstein's by-product theory is that the meanings of the logical constants are conveyed by their introduction rules, and these rules have as a by-product the class of logical truths. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ian Hacking - What is Logic? §03 | |
| A reaction: I find this approach highly plausible. All the truths about chess openings are just a by-product of the original rules. |
| 19292 | Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein] |
| Full Idea: All the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived propositions. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.127) | |
| A reaction: So axioms are conventional. This specifically contradicts the claims of Frege and the earlier Russell. Their view is that logic has an explanatory essence, found in some core axioms or rules or concepts. I agree with them. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 18153 | A number is a repeated operation [Wittgenstein] |
| Full Idea: A number is the index of an operation. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.021) | |
| A reaction: Roughly, this means that a number indicates how many times some basic operation has been performed. Bostock 2009:286 expounds the idea. |
| 18160 | The concept of number is just what all numbers have in common [Wittgenstein] |
| Full Idea: The concept of number is simply what is common to all numbers, the general form of number. The concept of number is the variable number. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.022) |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| Full Idea: The theory of classes is completely superfluous in mathematics. This is connected with the fact that the generality required in mathematics is not accidental generality. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.031) | |
| A reaction: This fits Russell's no-class theory, which rests everything instead on propositional functions. |
| 6849 | Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk] |
| Full Idea: Wittgenstein didn't just have an arguments against logicism; he hated logicism, and described is as a cancerous growth. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ray Monk - Interview with Baggini and Stangroom p.12 | |
| A reaction: This appears to have been part of an inexplicable personal antipathy towards Russell. Wittgenstein appears to have developed a dislike of all reductionist ideas in philosophy. |
| 23509 | The logic of the world is shown by tautologies in logic, and by equations in mathematics [Wittgenstein] |
| Full Idea: The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.22) | |
| A reaction: White observes that this is Wittgenstein distinguishing logic from mathematics, and thus distancing himself from logicism. But see T 6.2. |
| 13133 | The world is facts, not things. Facts determine the world, and the world divides into facts [Wittgenstein] |
| Full Idea: The world is the totality of facts, not of things. The world is determined by the facts, and by their being all the facts. The totality of facts determines what is the case, and what is not the case. ..The world divides into facts. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 1 - 1.2) | |
| A reaction: This is said to be a radical new ontology, because the facts are held to be prior to the things and their properties, which are presumably abstractions from the primitive facts. The modern heir of this is Armstrong's 'states of affairs'. |
| 7090 | The 'Tractatus' is an extreme example of 'Logical Atomism' [Wittgenstein, by Grayling] |
| Full Idea: The 'Tractatus' is an uncompromising, indeed an extreme, example of 'Logical Atomism' | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by A.C. Grayling - Wittgenstein Ch.2 | |
| A reaction: Russell talked about his 'logical atomism' after 1918, but this reminds us that Wittgenstein was fulfilling a task set for him by Russell. Wittgenstein's atoms are names-plus-objects, Russell's are demonstratives-plus-sensedata. |
| 23464 | In atomic facts the objects hang together like chain links [Wittgenstein] |
| Full Idea: In an atomic fact [Sachverhalt] the objects hang one in another, like the links of a chain | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.03), quoted by Homer - The Iliad | |
| A reaction: So the world consists of facts, but the facts are composed of objects. The point seems to be that the truths of language refer to the facts, rather than to the objects. Objects 'don't hang' together in the fact of a chance encounter. |
| 23471 | The structure of an atomic fact is how its objects combine; this possibility is its form [Wittgenstein] |
| Full Idea: The way in which objects hang together in the atomic fact is the structure of the atomic fact. …The form is the possibility of the structure. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.032-3) | |
| A reaction: I very much like the way LW adds a modal dimension to his ontology. Why doesn't he talk of 'relations', rather than 'hanging together'? |
| 21682 | If a proposition is elementary, no other elementary proposition contradicts it [Wittgenstein] |
| Full Idea: It is a sign of a proposition's being elementary that there can be no elementary proposition contradicting it. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.211) | |
| A reaction: It is a hallmark of atomic atoms that they have no relations with other atoms, but are wholly independent. This obviously invites the question of how they are united. Are logical connectives intrinsically relational logical atoms? |
| 22319 | Analysis must end in elementary propositions, which are combinations of names [Wittgenstein] |
| Full Idea: It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.221), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 50 'Indep' | |
| A reaction: Not clear about 'combinations of names'. Does that include predicates? How do you combine two names? |
| 21683 | Nothing can be inferred from an elementary proposition [Wittgenstein] |
| Full Idea: From an elementary proposition no other can be inferred. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.134) | |
| A reaction: Russell was not so sure. This is the sort of remark that elicits from me the question that extravagent metaphysics also provokes - 'how on earth does he know what he claims to be true?'. |
| 23473 | Do his existent facts constitute the world, or determine the world? [Morris,M on Wittgenstein] |
| Full Idea: Wittgenstein's writing here is loose, and he seems to be conflating two claims: 1) The totality of existent facts is the world (everything that is the case), and 2) The totality of existent facts determines everything that is the case (the world). | |
| From: comment on Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.04) by Michael Morris - Guidebook to Wittgenstein's Tractatus 1E | |
| A reaction: [Also 2.06 and 2.063] Morris says he must actually mean the second version. |
| 22311 | The world is determined by the facts, and there are no further facts [Wittgenstein] |
| Full Idea: The world is determined by the facts, and by these being all the facts. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 1.11), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 47 'Mole' | |
| A reaction: He is denying negative facts (also written to Russell in 1919). Best approached through truthmakers, I suspect. There is no truthmaker for the supposed factual claim 'there are birds on Mars' - so it is a fact that there are no birds on Mars. |
| 22313 | The existence of atomic facts is a positive fact, their non-existence a negative fact [Wittgenstein] |
| Full Idea: The existence of atomic facts we also call a positive fact, their non-existence a negative fact. b...The existence and non-existence of atomic facts is the reality. ...[2.063] the total reality is the world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.06), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 47 'Mole' | |
| A reaction: Potter observes that he denies negative facts in a1919 letter to Russell, and at 1.11, but then affirms them at 2.06. |
| 22314 | On white paper a black spot is a positive fact and a white spot a negative fact [Wittgenstein] |
| Full Idea: On white paper, the fact that a point is black corresponds to a positive fact; to the fact that a point is white (not black), a negative fact. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.063), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 08 'Judg' | |
| A reaction: Elsewhere Wittgenstein is ambiguous as to whether he believes in negative facts [qv]. |
| 7969 | The order of numbers is an internal relation, not an external one [Wittgenstein] |
| Full Idea: The order of the number-series is not governed by an external relation but by an internal relation. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.1252) | |
| A reaction: He seems to mean something like a tautology (see Idea 7968). It is, I take it, part of the concept of any given integer that it has a place in the series. But do the concepts arise self-evidently, or from nature? |
| 7968 | A relation is internal if it is unthinkable that its object should not possess it [Wittgenstein] |
| Full Idea: A relation is internal if it is unthinkable that its object should not possess it. (This shade of blue and that one stand, eo ipso, in the internal relation of lighter to darker. It is unthinkable that these two objects should not stand in this relation). | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.123) | |
| A reaction: An epistemological definition. If only one shade of blue existed, would it still have this internal relation? Are things therefore full of potential internal relations with non-existent things? |
| 23466 | Objects are the substance of the world [Wittgenstein] |
| Full Idea: Objects make up the substance of the world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.021) | |
| A reaction: He doesn't say here that the objects are physical, and may be including Frege's abstract objects. His concept of substance seems more like Spinoza than Aristotle. |
| 23467 | Objects are simple [Wittgenstein] |
| Full Idea: Objects are simple | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.02) | |
| A reaction: Presumably all his objects are 'simples', and what we think of as normal objects are counted by LW as 'facts'. |
| 23468 | Apart from the facts, there is only substance [Wittgenstein] |
| Full Idea: Substance is what remains independently of what is the case. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.024) | |
| A reaction: He sees what is the case as comprised of objects, so substance is even more basic. It seems close to Spinoza's single-substance view. |
| 22321 | To know an object we must know the form and content of its internal properties [Wittgenstein, by Potter] |
| Full Idea: Wittgenstein explicitly said that to know an object I must know all its internal properties. ...Internal properties have form and content; form is 'possibility of occurrence in atomic facts' (2.0141), content is its being that specific object (2.0233). | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.01231) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 52 'Simp' | |
| A reaction: [check original quote] This seems to be an essentialist view of (formal) objects. See Potter 347-9 for discussion. The 'external properties' of an object are the atomic facts in which it occurs. |
| 6056 | Identity is not a relation between objects [Wittgenstein] |
| Full Idea: It is self-evident that identity is not a relation between objects. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5301) | |
| A reaction: Part of Wittgenstein's claim that identity statements are 'pseudo-propositions'. See, in reply, the ideas of McGinn on identity. This was part of the drive that led to the extremes of logical positivism, killing metaphysics for two generations. |
| 22322 | You can't define identity by same predicates, because two objects with same predicates is assertable [Wittgenstein] |
| Full Idea: Russell's definition of identity [x is y if any predicate of x is a predicate of y] won't do, because then one cannot say that two objects have all their properties in common | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5302), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 53 'Ident' | |
| A reaction: [The Russell is in Principia] Good. Even if Leibniz is right that no two obejcts have identical properties, it is at least meaningful to consider the possibility. Russell makes it an impossibility, rather than a contingent fact. |
| 6057 | Two things can't be identical, and self-identity is an empty concept [Wittgenstein] |
| Full Idea: Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5303) | |
| A reaction: Wittgenstein's attack on identity. It is best (following McGinn) to only speak of resemblance between two things (possibly to a very high degree, as in two electrons). Self-identity just is identity; you can drop the word 'identity', but not the concept. |
| 9442 | The only necessity is logical necessity [Wittgenstein] |
| Full Idea: The only necessity that exists is logical necessity. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.37) | |
| A reaction: For Wittgenstein that will mean conventional necessity. He is taking a standard Humean view of these things. |
| 23495 | The tautologies of logic show the logic of language and the world [Wittgenstein] |
| Full Idea: The fact that the propositions of logic are tautologies shows the formal - logical - properties of language and the world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.12) | |
| A reaction: This seems to me an extraordinarily hubristic remark (philosophically speaking), especially coming from a work which famously throws away its own ladder. He is very much pursuing Kant's project. |
| 23487 | What is thinkable is possible [Wittgenstein] |
| Full Idea: What is thinkable is possible too. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.02) | |
| A reaction: [Plucked from a context!] The modern tide has turned against this idea. The more clearly you understand the facts, the more restricted the possibilities become. If you think the impossible is possible, it is because you are bad at thinking. |
| 23470 | Each thing is in a space of possible facts [Wittgenstein] |
| Full Idea: Each thing is, as it were, in a space of possible states of affairs. This space I can imagine as empty, but not of the thing without the space. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.013) | |
| A reaction: A clear echo of Kant on natural space. LW calls it 'logical space' (1.13). I take this to be exactly the concept of the space of possibilities which contains the modern notion of possible worlds. |
| 23507 | Unlike the modern view of a set of worlds, Wittgenstein thinks of a structured manifold of them [Wittgenstein, by White,RM] |
| Full Idea: In 'Tractatus' Wittgenstein is not just thinking of a set of possible worlds (in the modern account), but of a structured manifold within which each 'possible world' is located. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Roger M. White - Wittgenstein's 'Tractatus Logico-Philosophicus' 3 'Positions' | |
| A reaction: So the modern view has the neutrality of a merely formal system, but LW is thinking of them as the modal structure of reality. |
| 23469 | An imagined world must have something in common with the real world [Wittgenstein] |
| Full Idea: It is obvious that an imagined world, however different it may be from the real one, must have something - a form - in common with it. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.022) | |
| A reaction: It is clear that Wittgenstein had a concept of possible worlds close to the modern view. |
| 11027 | To know an object you must know all its possible occurrences [Wittgenstein] |
| Full Idea: If I know an object I also know all its possible occurrences in states of affairs. (Every one of those possibilities must be part of the nature of the object.) A new possibility cannot be discovered later. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.0123) | |
| A reaction: The requirement that you know them 'all' seems absurd, especially if we need science to discover them. I take this idea to be extremely important, and essentially Aristotelian (connecting with the notion of 'potentiality'). We need to know the powers. |
| 23465 | The 'form' of an object is its possible roles in facts [Wittgenstein] |
| Full Idea: The possibility of its occurrence in atomic facts is the form of the object. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.0141) | |
| A reaction: Morris says this picks up the idea from Kant. We might now label the 'form' as the 'modal profile' of the object (a phrase I like). The modern issues over transworld identity seem to be a development of this thought. |
| 12869 | Two objects may only differ in being different [Wittgenstein] |
| Full Idea: If two objects have the same logical form, the only distinction between them, apart from their external properties, is that they are different. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.0233) | |
| A reaction: This isn't a commitment to haecceities, but it seems to be flirting with the idea. See Simons 1987:241. Kit Fine picks up the idea that objects, as well as sentences, might have 'logical form'. How can being 'different' be primitive? Spatial location? |
| 23503 | Strict solipsism is pure realism, with the self as a mere point in surrounding reality [Wittgenstein] |
| Full Idea: Solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.64) | |
| A reaction: Despite this, Michael Morris is more inclined to see him as an idealist. It is not clear whether the present account of solipsism is idealist or realist. Berkeley seemed to think his idealism was true realism. Can reality be co-ordinated with a point? |
| 16907 | If the truth doesn't follow from self-evidence, then self-evidence cannot justify a truth [Wittgenstein] |
| Full Idea: If the truth of a proposition does not follow from the fact that it is self-evident to us, then its self-evidence in no way justifies our belief in its truth. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.1363), quoted by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: Frege seems to have taken self-evidence as intrinsic justification, but Wittgenstein seems to demand a supporting inference. But what is it all based on? Stipulative definitions? |
| 23479 | The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths [Wittgenstein, by Morris,M] |
| Full Idea: We can see the 'Tractatus' as an attempt to make sense of what is necessarily true of the world - in general, and not just in the mathematical case - without appealing to synthetic a priori truths. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: Morris sees the Tractatus as firmly in the Kantian tradition, and exploring Kant's main project in the first Critique. |
| 23501 | There is no a priori order of things [Wittgenstein] |
| Full Idea: Whatever we can describe at all could be other than it is. There is no a priori order of things. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.634) | |
| A reaction: This is his rejection of Kant's dream, of inferring truths about the world by self-examination. However, compare Idea 23495. He clings to the faith that logic reveals 'something' about reality. |
| 7088 | Logic and maths can't say anything about the world, since, as tautologies, they are consistent with all realities [Wittgenstein, by Grayling] |
| Full Idea: Neither logical nor mathematical propositions say anything about the world, because in virtue of their always being true they are consistent with any way the world could happen to be. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by A.C. Grayling - Wittgenstein Ch.2 | |
| A reaction: This became the standard view for twentieth century empiricists, and appeared to rule out a priori synthetic knowledge forever. Kripke's proposal that there are a posteriori necessities, however, changes the picture. |
| 16909 | Logic is a priori because we cannot think illogically [Wittgenstein] |
| Full Idea: That logic is a priori consists in the fact that we cannot think illogically. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.4731), quoted by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: A rather startling claim. Presumably we have to say that when we draw a stupid inference, then we weren't really 'thinking'? |
| 23485 | No pictures are true a priori [Wittgenstein] |
| Full Idea: There are no pictures that are true a priori. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.225) | |
| A reaction: This is part of the growing modern doubts about the scope or possibility of a priori knowledge. A 'picture' here is the mental model which is the meaning of a proposition. |
| 6591 | Doubts can't exist if they are inexpressible or unanswerable [Wittgenstein] |
| Full Idea: Doubt can exist only where a question exists, a question only where an answer can exist, and an answer only where something can be said. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.51) | |
| A reaction: I don't agree with any of that. It is typical of the phase when philosophers were mesmerised by language. Cats look puzzled sometimes. A glimmering of doubt may be pre-linguistic, inexpressible and unanswerable, but still feels like a doubt. |
| 17665 | The 'Tractatus' is instrumentalist about laws of nature [Wittgenstein, by Armstrong] |
| Full Idea: Wittgenstein is an instrumentalist about laws of nature in 'Tractatus'. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by David M. Armstrong - What is a Law of Nature? 01.3 | |
| A reaction: [I record this, but don't know the reference] |
| 2941 | Induction accepts the simplest law that fits our experiences [Wittgenstein] |
| Full Idea: The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.363) |
| 17673 | The modern worldview is based on the illusion that laws explain nature [Wittgenstein] |
| Full Idea: The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.371) | |
| A reaction: Love it! Not only does it say that lawlike explanation is wrong, but it registers that this is a profound feature of the modern view of the world, and not just a slightly misguided philosophical theory. |
| 2940 | The subject stands outside our understanding of the world [Wittgenstein] |
| Full Idea: The subject does not belong to the world; rather, it is a limit of the world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.632) | |
| A reaction: Interesting. We must not confuse epistemology with ontology, but the perceived world exists between two limits - the farthest reaches of my perceptions, and the farthest reaches of myself. I wish I could clearly disentangle the nearer border. Dasein? |
| 23498 | The modern idea of the subjective soul is composite, and impossible [Wittgenstein] |
| Full Idea: Therre is no such thing as the soul - the subject, etc. - as it is conceived in the superficial psychology of the present day. Indeed a composite soul would no longer be a soul. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5421) | |
| A reaction: This seems to endorse Descartes' claim about the essential unity of the mind. I think Hume is in the background of LW's thought. Presumably the psychologist offered a 'composite' view. Prior discussion of belief leads into this remark. |
| 23475 | The form of a proposition must show why nonsense is unjudgeable [Wittgenstein] |
| Full Idea: The correct explanation of the form of the proposition 'A judges p' must show that it is impossible to judge a nonsense. (Russell's theory does not satisfy this condition). | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.5422) | |
| A reaction: In Notebooks p.96 LW gives the example 'this table penholders the book'. I take it Russell wanted judgement to impose unified meaning on sentences, but LW shows that assembling meaning must precede judgement. LW is right. |
| 7084 | What can be said is what can be thought, so language shows the limits of thought [Wittgenstein, by Grayling] |
| Full Idea: In Wittgenstein's view, what can be said is the same as what can be thought; so that once one has grasped the nature of language, one has shown the limit beyond which language and thought become nonsense. | |
| From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by A.C. Grayling - Wittgenstein Ch.2 | |
| A reaction: I just don't believe that what is thinkable is limited to what is expressible. A lot of philosophy is the struggle to find expression for thoughts which are just beyond the edge of current language. See Idea 6870. |
| 23482 | The 'form' of the picture is its possible combinations [Wittgenstein] |
| Full Idea: The form of depiction is the possibility that the things are combined with one another as are the elements of the picture. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.151) | |
| A reaction: This is why 'model' (or even 'simulation'?) is a better term than 'picture' for his proposal. Pictures are fixed, but models can be adjusted. |
| 8172 | To understand a proposition means to know what is the case if it is true [Wittgenstein] |
| Full Idea: To understand a proposition means to know what is the case if it is true. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.024) | |
| A reaction: This established the Frege truth-conditions theory of meaning, which was expanded by Davidson, and then possible worlds semantics. You can't assess truth without knowing meaning. Dummett says the two go together. |
| 7086 | Good philosophy asserts science, and demonstrates the meaninglessness of metaphysics [Wittgenstein] |
| Full Idea: The correct method in philosophy would be to say nothing except what can be said, i.e. propositions of natural science, and whenever someone wanted to say something metaphysical, to show that he had failed to give a meaning to signs in his propositions. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.53) | |
| A reaction: This seems to be the germ of logical positivism, picked up by the Vienna Circle, and passed on the Ayer and co. How, though, do you 'show' that a sign is meaningless? Very abstract ideas are too far away from experience to be analysed that way. |
| 23511 | Propositions use old expressions for a new sense [Wittgenstein] |
| Full Idea: A proposition must use old expressions to communicate a new sense. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.03) | |
| A reaction: A nicely expressed affirmation of the principle of compositionality. It entails that the propositions can be either true or false, according to LW. |
| 23488 | Propositions are understood via their constituents [Wittgenstein] |
| Full Idea: A proposition is understood by anyone who understands its constituents. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.024) | |
| A reaction: The 'constituents' had better include the grammatical relationships. Otherwise it's 'rearrange these words to make a well known saying'. That said, this strikes me as an important truth about language. We assemble sentence meanings. |
| 23486 | Pictures are possible situations in logical space [Wittgenstein] |
| Full Idea: A picture represents a possible situation in logical space. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.202) | |
| A reaction: This seems pretty close to the idea that propositions are sets of possible worlds (though that seems to add unnecessary extra baggage). If they just picture situations, why does he mention logical space? Within the limits of possible picturing? |
| 23497 | Solipsism is correct, but can only be shown, not said, by the limits of my personal language [Wittgenstein] |
| Full Idea: What the solipsist means is quite correct; only it cannot be said, but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language (of that language which I alone understand) mean the limits of my world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.62) | |
| A reaction: I take it that LW later showed that the remark in brackets is absurd, using his Private Language argument. Commentators seem unclear about how seriously to take this claim. |
| 23489 | We translate by means of proposition constituents, not by whole propositions [Wittgenstein] |
| Full Idea: When translating one language into another, we do not proceed by translating each proposition of the one into a proposition of the other, but merely by translating the constituents of propositions. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.025) | |
| A reaction: This seems opposed to Quine's later holistic view of translating whole languages. Is he objecting to Frege's context principle? |
| 2943 | Ethics cannot be put into words [Wittgenstein] |
| Full Idea: Ethics cannot be put into words. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.421) | |
| A reaction: Nonsense. There is lots of good writing about ethics. This is evasive mysticism. |
| 2942 | The sense of the world must lie outside the world [Wittgenstein] |
| Full Idea: The sense of the world must lie outside the world. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.41) | |
| A reaction: Since I don't believe that anything 'lies outside the world' I can't make sense of this. He implies that the Self lies outside of the world (to the point of solipsism), so I suppose that's it. |
| 21167 | Gravity is unusual, in that it always attracts and never repels [New Sci.] |
| Full Idea: Gravity is an odd sort of force, not least because it only ever works one way. Electromagnetism attracts and repels, but with gravity there are only positive masses always attract. | |
| From: New Scientist writers (Why the Universe Exists [2017], 05) | |
| A reaction: This leads to speculation about anti-gravity, but there is no current evidence for it. |
| 21176 | In the Big Bang general relativity fails, because gravity is too powerful [New Sci.] |
| Full Idea: At the origin of the universe gravity becomes so powerful that general relativity breaks down, giving infinity for every answer. | |
| From: New Scientist writers (Why the Universe Exists [2017], 09) |
| 21147 | Quantum electrodynamics incorporates special relativity and quantum mechanics [New Sci.] |
| Full Idea: The theory of electromagnetism that incorporates both special relativity and quantum mechanics is quantum electrodynamics (QED). It was developed by Dirac and others, and perfected in the 1940s. The field is a collection of quanta. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: This builds on Maxwell's earlier classical theory. QED is said to be the best theory in all of physics. |
| 21155 | Photons have zero rest mass, so virtual photons have infinite range [New Sci.] |
| Full Idea: Photons, the field quanta of the electromagnetic force, have zero rest mass, so virtual photons can exist indefinitely and travel any distance, meaning the electromagnetic force has an infinite range. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) |
| 21161 | In the standard model all the fundamental force fields merge at extremely high energies [New Sci.] |
| Full Idea: The standard model says that the fields of all fundamental forces should merge at extremely high energies, meaning there is also a unified, high-energy field out there. | |
| From: New Scientist writers (Why the Universe Exists [2017], 03) | |
| A reaction: Not quite sure what 'out there' means. This idea is linked to the quest for dark energy. Is this unified phenomenon only found near the Big Bang? |
| 21146 | Electrons move fast, so are subject to special relativity [New Sci.] |
| Full Idea: Electrons in atoms move at high speeds, so they are subject to the special theory of relativity. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: Presumably this implies a frame of reference, and defining velocities relative to other electrons. Plus time-dilation? |
| 21148 | The strong force is repulsive at short distances, strong at medium, and fades at long [New Sci.] |
| Full Idea: Experiments show that the nuclear binding force does not follow the inverse square law, but is repulsive at the shortest distances, then attractive, then fades away rapidly as distance increases further. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: So how does it know when to be strong? Magnetism doesn't vary according to distance, and light obeys the inverse square law, because everything is decided at the output. - See 21151 for an explanation. It interacts after departure. |
| 21151 | Gluons, the particles carrying the strong force, interact because of their colour charge [New Sci.] |
| Full Idea: In QCD the particles that carry the strong force are called gluons. ...Gluons carry their own colour charges, so they can interact with each other (unlike photons) via the strong nuclear force (which limits the range of the force). | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: So the force varies in strength with distance because the degree of separation among the spreading gluons varies? The force has one range, which is squashed when close, effective at medium, and loses touch with distance? |
| 21152 | The strong force binds quarks tight, and the nucleus more weakly [New Sci.] |
| Full Idea: The strong force holds quarks together within protons and neutrons, and residual effects of the strong force bind protons (whch repel one another) and neutrons together in nuclei. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: So the force is much stronger between quarks (which can't escape), and only 'residual' in the nucleus, which must be why smashing nuclei open is fairly easy, but smashin protons open needs higher energies. |
| 21143 | Quarks in threes can build hadrons with spin ˝ or with spin 3/2 [New Sci.] |
| Full Idea: Quarks in threes can build hadrons with spin ˝ (proton, duu; neutron, ddu; lambda, dus), or with spin 3/2 (omega-minus, sss). | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) |
| 21142 | Classifying hadrons revealed two symmetry patterns, produced by three basic elements [New Sci.] |
| Full Idea: Classifying hadrons according to charge, strangeness and spin revealed patterns of eight and ten particles (SU(3) symmetery). The mathematics then showed that these are built from a basic group of only three members. | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) |
| 21150 | Three different colours of quark (as in the proton) can cancel out to give no colour [New Sci.] |
| Full Idea: Just as mixing three colours of light gives white, so the three colour charges of quarks can add up to give no colour. This is what happens in the proton, which always contains one blue-charge quark, one red and one green. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) |
| 21145 | The four fundamental forces (gravity, electromagnetism, weak and strong) are the effects of particles [New Sci.] |
| Full Idea: There are four fundamental forces: gravity, electromagnetism, and the weak and strong nuclear forces. Particle physics has so far failed to encompass the force of gravity. The forces that shape our world are themselves the effect of particles. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: Philosophers must take note of the fact that forces are the effects of particles. Common sense pictures forces imposed on particles, like throwing a tennis ball, but the particles are actually the sources of force. The gravitino is speculative. |
| 21153 | The weak force explains beta decay, and the change of type by quarks and leptons [New Sci.] |
| Full Idea: The beta decay of the neutron (into a proton, an electron and an antineutrino) can be described in terms of the weak force, which is 10,000 times weaker than the strong force. It allows the quarks and leptons to change from one type to another. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: This seems to make it the key source of radioactivity. Perhaps it should be called the Force of Change? |
| 21154 | Three particles enable the weak force: W+ and W- are charged, and Z° is not [New Sci.] |
| Full Idea: The quantum field theory of the weak force needs three carrier particles. The W+ and W- are electrically charged, and enable the weak force to change the charge of a particle. The Z° is uncharged, and mediates weak interactions with no charge change. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) |
| 21156 | The weak force particles are heavy, so the force has a short range [New Sci.] |
| Full Idea: The W and Z particles are heavy, and so cannot travel far from their parents. The weak force therefore has a very short range. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) |
| 21164 | Why do the charges of the very different proton and electron perfectly match up? [New Sci.] |
| Full Idea: Why do the proton and electron charges mirror each other so perfectly when they are such different particles? | |
| From: New Scientist writers (Why the Universe Exists [2017], 04) | |
| A reaction: We seem to have reached a common stage in science, where we have a wonderful descriptive model (the Standard Model), but we cannot explain why what is modelled is the way it is. |
| 21170 | The Standard Model cannot explain dark energy, survival of matter, gravity, or force strength [New Sci.] |
| Full Idea: The standard model cannot explain dark matter, or dark energy (which is causing expansion to accelerate). It cannot explain how matter survived annihilation with anti-matter in the Big Bang, or explain gravity. The strength of each force is unexplained. | |
| From: New Scientist writers (Why the Universe Exists [2017], 06) | |
| A reaction: [compressed] P.141 adds that the model has to be manipulated to keep the Higgs mass low enough. |
| 21140 | Spin is a built-in ration of angular momentum [New Sci.] |
| Full Idea: Spin is a built-in ration of angular momentum. | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) | |
| A reaction: As an outsider all I can do is collect descriptions of such properties from the experts. The experts appear to be happy with the numbers inserted in the equations. |
| 21149 | Quarks have red, green or blue colour charge (akin to electric charge) [New Sci.] |
| Full Idea: Quarks have a property akin to electric charge, called their colour charge. It comes in three varieties, red, green and blue. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) |
| 21158 | Fermions, with spin ˝, are antisocial, and cannot share quantum states [New Sci.] |
| Full Idea: Particles with half-integer spin, such as electrons, protons or quarks (all spin ˝) have an asymmetry in their wavefunction that makes them antisocial. These particles (Fermions) cannot share a quantum state. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: This is said to explain the complexity of matter, with carbon an especially good example. |
| 21165 | Spin is akin to rotation, and is easily measured in a magnetic field [New Sci.] |
| Full Idea: Spin is a quantum-mechanical property of a particle akin to rotation about its own axis. Particles of different spins respond to magnetic fields in different ways, so it is a relatively easy thing to measure. | |
| From: New Scientist writers (Why the Universe Exists [2017], 04) | |
| A reaction: I wish I knew what 'akin to' meant. Maybe particles are not rigid bodies, so they cannot spin in the way a top can? It must be an electro-magnetic property. Idea 21166 says spin has two possible directions. |
| 21157 | Particles are spread out, with wave-like properties, and higher energy shortens the wavelength [New Sci.] |
| Full Idea: Particles obeying the laws of quantum mechanics have wave-like properties - moving as a quantum wave-function, spread out in space, with wavelengths that get shorter as their energy increases. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: Thus X-rays are dangerous, but long wave radio is not. De Broglie's equation. |
| 21163 | The mass of protons and neutrinos is mostly binding energy, not the quarks [New Sci.] |
| Full Idea: Most of a proton's or neutrino's mass is contained in the interaction energies of a 'sea' of quarks, antiquarks and gluons that bind them. ...You might feel solid, but in fact you're 99 per cent binding energy. | |
| From: New Scientist writers (Why the Universe Exists [2017], 04) | |
| A reaction: This is because energy is equivalent to mass (although gluons are said to have energy but no mass - puzzled by that). This is a fact which needs a bit of time to digest. Once you've grasped we are full of space, you still have understood it. |
| 21168 | Gravitional mass turns out to be the same as inertial mass [New Sci.] |
| Full Idea: There are two types of mass: gravitational mass quantifies how strongly an object feels gravity, while inertial mass quantifies an object's resistance to acceleration. There proven equality is at the heart of General Relativity. | |
| From: New Scientist writers (Why the Universe Exists [2017], 05) | |
| A reaction: It had never occurred to me that these two values might come apart. Doesn't their identical values demonstrate that they are in fact the same thing? Sounds like Hesperus/Phosphorus to me. The book calls it 'mysterious'. |
| 21138 | Neutrons are slightly heavier than protons, and decay into them by emitting an electron [New Sci.] |
| Full Idea: The proton (938.3 MeV) is lighter than the neutron (939.6 MeV) and does not decay, but the heavier neutron can change into a proton by emitting an electron. (If you gather a bucketful of neutrons, after ten minutes only half of them would be left). | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) | |
| A reaction: Protons are more or less eternal, but some theories have them decaying after billions of years. Smashing protons together is a popular pastime for physicists. |
| 21144 | Top, bottom, charm and strange quarks quickly decay into up and down [New Sci.] |
| Full Idea: Quarks can change from one variety to another, and the top, bottom, charm and strange quarks all rapidly decay to the up and down quarks of everyday life. | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) | |
| A reaction: Hence the universe is largely composed of up and down quarks and electrons. The other quarks seem to be more important in the early universe. |
| 21141 | Neutrinos were proposed as the missing energy in neutron beta decay [New Sci.] |
| Full Idea: When a neutron decays into a proton and an electron (one example of beta decay), the energy of the two particles adds up to less than the starting energy of the neutron. Pauli and Fermi concluded that a neutrino (an electron antineutrino) is emitted. | |
| From: New Scientist writers (Why the Universe Exists [2017], 01) | |
| A reaction: I'm wondering how much they could infer about the nature of the new particle (which was only confirmed 26 years later). |
| 21169 | Only neutrinos spin anticlockwise [New Sci.] |
| Full Idea: Neutrinos are the only particles that seem just to spin anticlockwise. | |
| From: New Scientist writers (Why the Universe Exists [2017], 06) | |
| A reaction: See 21166. Anti-neutrino spin is the opposite way. Which way up do you hold the neutrino when pronouncing that it is 'anticlockwise? |
| 21166 | Standard antineutrinos have opposite spin and opposite lepton number [New Sci.] |
| Full Idea: In the conventional standard model neutrinos have antiparticles - which spin in the opposite direction, and have the opposite lepton number. | |
| From: New Scientist writers (Why the Universe Exists [2017], 05) |
| 21171 | The symmetry of unified electromagnetic and weak forces was broken by the Higgs field [New Sci.] |
| Full Idea: In the very early hot universe the electromagnetic and weak nuclear forces were one. The early emergence of the Higgs field led to electroweak symmetry breaking. The W and Z bosons grew fat, and the photon raced away mass-free. | |
| From: New Scientist writers (Why the Universe Exists [2017], 07) |
| 21179 | Supersymmetric string theory can be expressed using loop quantum gravity [New Sci.] |
| Full Idea: String theory, together with its supersymmetric particles, has recently been rewritten in the space-time described by loop quantum gravity (which says that space-time ust be made from finite chunks). | |
| From: New Scientist writers (Why the Universe Exists [2017], 09) |
| 21178 | String theory is now part of 11-dimensional M-Theory, involving p-branes [New Sci.] |
| Full Idea: String theory has now been incorporated into Ed Witten's M-Theory, which is a mathematical framework that lives in 11-dimensional space-time, involving higher-dimensional objects called p-branes, of which strings are a special case. | |
| From: New Scientist writers (Why the Universe Exists [2017], 09) |
| 21175 | String theory might be tested by colliding strings to make bigger 'stringballs' [New Sci.] |
| Full Idea: A future accelerator might create 'stringballs', when two strings slam into one another and, rather than combining to form a stretched string, make a tangled ball. Finding them would prove string theory. | |
| From: New Scientist writers (Why the Universe Exists [2017], 08) | |
| A reaction: This is the only possible test for string theory which I have seen suggested. How do you 'slam strings together'? |
| 21177 | String theory offers a quantum theory of gravity, by describing the graviton [New Sci.] |
| Full Idea: String theory works as a quantum theory of gravity because string vibrations can describe gravitons, the hypothetical carriers of the gravitational force. | |
| From: New Scientist writers (Why the Universe Exists [2017], 09) | |
| A reaction: Presumably the main aim of a quantum theory of gravity is to include gravitons within particle theory. This idea has to be a main attraction of string theory. Compare Idea 21166. |
| 21162 | Only supersymmetry offers to incorporate gravity into the scheme [New Sci.] |
| Full Idea: Peter Higgs says he is a fan of supersymmetry, largely because it seems to be the only route by which gravity can be brought into the scheme. | |
| From: New Scientist writers (Why the Universe Exists [2017], 03) | |
| A reaction: Peter Higgs proposed the Higgs boson (now discovered). This seems a very good reason to favour supersymmetry. A grand unified theory that left out gravity doesn't seem to be unified quite grandly enough. |
| 21173 | Supersymmetry says particles and superpartners were unities, but then split [New Sci.] |
| Full Idea: The key to supersymmetry is that in the high-energy soup of the early universe, particles and their superpartners were indistinguishable. Each pair existed as single massless entities. With expansion and cooling this supersymmetry broke down. | |
| From: New Scientist writers (Why the Universe Exists [2017], 08) |
| 21172 | The evidence for supersymmetry keeps failing to appear [New Sci.] |
| Full Idea: The old front-runner theory, supersymmetry, has fallen from grace as the Large Hadron Collider keeps failing to find it. | |
| From: New Scientist writers (Why the Universe Exists [2017], 07) |
| 21159 | Supersymmetry has extra heavy bosons and heavy fermions [New Sci.] |
| Full Idea: Supersymmetry posits heavy boson partners for all fermions, and heavy fermions for all bosons. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: The main Fermions are electron, proton and quark. Do extra bosons imply extra forces? Peter Higgs favours supersymmetry. |
| 21160 | The Higgs field means even low energy space is not empty [New Sci.] |
| Full Idea: The point about the Higgs field is that even the lowest-energy state of space is not empty. | |
| From: New Scientist writers (Why the Universe Exists [2017], 02) | |
| A reaction: So where is the Higgs field located? Even if there is no utterly empty space, the concept of location implies a concept of space more basic than the fields (about 16, I gather) which occupy it. You can't describe movement without a concept of location. |
| 21174 | Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [New Sci.] |
| Full Idea: Whatever dark matter is made of, it must have mass to feel and generate gravity; but no electric charge, so it does not interact with light. The leading candidate has been the weakly interacting massive particle (WIMP), much heavier than a proton. | |
| From: New Scientist writers (Why the Universe Exists [2017], 08) | |
| A reaction: Note that it must 'generate' gravity. The idea of a law of gravity which is externally imposed on matter is long dead. Heavy WIMPs have not yet been detected. |