178 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. |
| 11283 | There is pure deductive reasoning, and explanatory demonstration reasoning [Aristotle, by Politis] |
| Full Idea: Aristotle distinguishes between deductive reasoning (sullogismos) and demonstration (apodeixis). All demonstration is deductive reasoning, but not all deductive reasoning is demonstration. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], Bk I.2) by Vassilis Politis - Aristotle and the Metaphysics 5.3 | |
| A reaction: This sounds not far off the distinction between single-turnstile (formal proof) and double-turnstile (semantic consequence). Politis says, though, that the key point is the demonstration is explanatory. |
| 1672 | Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle] |
| Full Idea: Some optimists think understanding arises only through demonstration, but say there could be demonstration of everything, for it is possible to demonstrate in a circle or reciprocally. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b16) | |
| A reaction: I'm an optimist in this sense, though what is being described would probably best be called 'large-scale coherence'. Two reciprocal arguments look bad, but a hundred look good. |
| 1684 | Two falsehoods can be contrary to one another [Aristotle] |
| Full Idea: There are falsehoods which are contrary to one another and cannot be the case together e.g. that a man is a horse or a cow. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a29) |
| 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) |
| 12145 | Definitions are of what something is, and that is universal [Aristotle] |
| Full Idea: Definitions are thought to be of what something is, and what something is is in every case universal and positive. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b05) | |
| A reaction: This is exhibit A for those who think that Aristotelian essences concern the genus, rather than the particular. I suspect that this idea is best expressed as 'all we can say by way of definition of a particular thing involves the use of universals'. |
| 12075 | An Aristotelian definition is causal [Aristotle, by Witt] |
| Full Idea: An Aristotelian definition is causal. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], Bk II.2) by Charlotte Witt - Substance and Essence in Aristotle 1.5 | |
| A reaction: [She refers us to Posterior Analytics II.2] This is important if we are tempted to follow a modern line of saying that we want Aristotelian essences, and that these are definitions. We ain't thinking of dictionaries. |
| 12384 | Definition by division needs predicates, which are well ordered and thorough [Aristotle] |
| Full Idea: To establish a definition through division, you must aim for three things: you must take what is predicated in what the thing is; you must order these items as first or second; and you must ensure that these are all there are. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97a23) | |
| A reaction: This gives an indication of the thoroughness that Aristotle expects from a definition. They aren't like dictionary definitions of words. He expects definitions to often be very lengthy (see Idea 12292). |
| 9066 | You can define objects by progressively identifying what is the same and what is different [Aristotle] |
| Full Idea: Find what is in common among items similar and undifferentiated, then do the same for items of the same kind as the first group but a different form, and so on, till you come to a single account: this will be the definition of the object. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97b07-14) | |
| A reaction: [His example is distinguishing 'magnanimity' from 'indifference to fortune' among people] Presumably this process works for the formation of new concepts (e.g. in biology), as well as for the definition of familiars in terms of other familiars. |
| 12382 | What it is and why it is are the same; screening defines and explains an eclipse [Aristotle] |
| Full Idea: What it is and why it is are the same. What is an eclipse? Privation of light from the moon by screening of the earth. Why is there an eclipse? ...What is a harmony? A numerical ratio between high and low. Why do the high and low harmonize? The ratio. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90a15) | |
| A reaction: This is right at the heart of Aristotelian essentialism, and (I take it) modern scientific essentialism. If you fully know what cigarette tars are, and what human cell structure is, you understand immediately why cigarettes cause cancer. |
| 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. |
| 1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
| Full Idea: An axiom is a principle which must be grasped if anyone is going to learn anything whatever. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a17) |
| 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. |
| 12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
| Full Idea: Demonstrations by reduction to the impossible assume that everything is asserted or denied. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 77a23) | |
| A reaction: This sounds like the lynchpin of classical logic. |
| 12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
| Full Idea: Something holds universally when it is proved of an arbitrary and primitive case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73b33) | |
| A reaction: A key idea in mathematical logic, but it always puzzles me. If you snatch a random person in London, and they are extremely tall, does that prove that people of London are extremely tall? How do we know the arbitrary is representative? |
| 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. |
| 12363 | Everything is either asserted or denied truly [Aristotle] |
| Full Idea: Of the fact that everything is either asserted or denied truly, we must believe that it is the case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71a14) | |
| A reaction: Presumably this means that every assertion which could possibly be asserted must come out as either true or false. This will have to include any assertions with vague objects or predicates, and any universal assertions, and negative assertions. |
| 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. |
| 13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
| Full Idea: Aristotle's way with axioms, rather than Euclid's, is as assumptions which we are willing to agree on while awaiting an opportunity to prove them | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], 76b23-) by Gottfried Leibniz - New Essays on Human Understanding 4.07 | |
| A reaction: Euclid's are understood as basic self-evident truths which will be accepted by everyone, though the famous parallel line postulate undermined that. The modern view of axioms is a set of minimum theorems that imply the others. I like Aristotle. |
| 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) |
| 12377 | Mathematics is concerned with forms, not with superficial properties [Aristotle] |
| Full Idea: Mathematics is concerned with forms [eide]: its objects are not said of any underlying subject - for even if geometrical objects are said of some underlying subject, still it is not as being said of an underlying subject that they are studied. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 79a08) | |
| A reaction: Since forms turn out to be essences, in 'Metaphysics', this indicates an essentialist view of mathematics. |
| 12372 | The essence of a triangle comes from the line, mentioned in any account of triangles [Aristotle] |
| Full Idea: Something holds of an item in itself if it holds of it in what it is - e.g., line of triangles and point of lines (their essence comes from these items, which inhere in the account which says what they are). | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73a35) | |
| A reaction: A helpful illustration of how a definition gives us the essence of something. You could not define triangles without mentioning straight lines. The lines are necessary features, but they are essential for any explanation, and for proper understanding. |
| 12369 | A unit is what is quantitatively indivisible [Aristotle] |
| Full Idea: Arithmeticians posit that a unit is what is quantitatively indivisible. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a22) | |
| A reaction: Presumably indeterminate stuff like water is non-quantitatively divisible (e.g. Moses divides the Red Sea), as are general abstracta (curved shapes from rectilinear ones). Does 'quantitative' presupposes units, making the idea circular? |
| 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? |
| 18910 | To seek truth, study the real connections between subjects and attributes [Aristotle] |
| Full Idea: If, however, one is aiming at truth, one must be guided by the real connexions of subjects and attributes. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 81b22), quoted by George Engelbretsen - Trees, Terms and Truth 3 | |
| A reaction: I take this to be a warning that predicates that indicate mere 'Cambridge properties' (such as relations, locations, coincidences etc) have nothing to do with ontology. See Shoemaker on properties. |
| 1675 | Separate Forms aren't needed for logic, but universals (one holding of many) are essential [Aristotle] |
| Full Idea: There need be no forms (one item apart from the many) for demonstrations. But there must be universals, where one thing holds of the many. Without universals there are no middle terms, and so no demonstrations. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 77a05) |
| 1677 | We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations [Aristotle] |
| Full Idea: We can say goodbye to the forms. They are nonny-noes; and if there are any they are irrelevant - for demonstrations are not concerned with them. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 83a34) |
| 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'. |
| 1687 | Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't? [Aristotle] |
| Full Idea: Why will a man be a two-footed terrestrial animal and not an animal and terrestrial? Assumptions do not make it necessary that what is predicated form a unity - rather, it is as if the same man were musical and literate. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 92a30) |
| 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. |
| 1681 | Units are positionless substances, and points are substances with position [Aristotle] |
| Full Idea: A unit is a positionless substance, and a point a substance having position. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 87a36) |
| 12146 | Definitions recognise essences, so are not themselves essences [Aristotle] |
| Full Idea: If a definition is the recognition of some essence, it is clear that such items are not essences. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b17) | |
| A reaction: So definitions are not themselves essences (as some modern thinkers claim). The idea seems obvious to me, but it is a warning against a simplistic view of Aristotelian essences, and a reminder that such things are real, not verbal. |
| 17039 | The predicates of a thing's nature are necessary to it [Aristotle] |
| Full Idea: Whatever is predicated in what something is is necessary. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 96b03) | |
| A reaction: This does NOT say that the essence is just the necessities. He goes on to say to say separately that certain properties of a triplet are part of the essence, as well as being necessary. This shows the nature of a thing is also necessary. |
| 11994 | Aristotelian essences are properties mentioned at the starting point of a science [Aristotle, by Kung] |
| Full Idea: As Aristotle uses the term 'essence', only those properties which are mentioned in or relatively close to the starting points of the science will be essential. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Joan Kung - Aristotle on Essence and Explanation II | |
| A reaction: I take this to be the correct way to understand Aristotelian essence - as something understood by its role in scientific explanations. We may, of course, work back to the starting point of a science, by disentangling the mess in the middle. |
| 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. |
| 12381 | What is necessary cannot be otherwise [Aristotle] |
| Full Idea: What is necessary cannot be otherwise. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88b32) | |
| A reaction: If the next interesting question is the source of necessity, then the question seems to be 'what prevents it from being otherwise?'. |
| 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. |
| 1690 | A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle] |
| Full Idea: There are two types of necessity, one according to nature and impulse, the other by force and contrary to impulse. A stone travels upwards and downwards from different necessities. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 94b38) |
| 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? |
| 12072 | For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Aristotle, by Witt] |
| Full Idea: For Aristotle, knowledge is explanatory, for to know something is to understand it, and to understand something is to grasp its principles or causes. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Charlotte Witt - Substance and Essence in Aristotle 1.2 | |
| A reaction: Thus the kind of 'knowledge' displayed in quiz shows would not count as knowledge at all, if it was mere recall of facts. To know is to be able to explain, which is to be able to teach. See Idea 11241. |
| 12073 | 'Episteme' means grasping causes, universal judgments, explanation, and teaching [Aristotle, by Witt] |
| Full Idea: For Aristotle, a person who has 'episteme' grasps the cause of a given phenomenon, can make a universal judgment about it, can explain it, and can teach others about it. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Charlotte Witt - Substance and Essence in Aristotle 1.2 | |
| A reaction: This I take to be the context in which we should understand what Aristotle means by an 'essence' - it is the source of all of the above, so it both makes a thing what it is, and explains why it shares features with other such things. |
| 12378 | The reason why is the key to knowledge [Aristotle] |
| Full Idea: Study of the reason why has the most importance for knowledge. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 79a24) | |
| A reaction: I take the study of reasons for belief to be much more central to epistemology than finding ways to answer radical sceptics about the basic possibility of knowledge. |
| 12364 | We understand a thing when we know its explanation and its necessity [Aristotle] |
| Full Idea: We understand something simpliciter when we think we know of the explanation because of which the object holds that it is its explanation, and also that it is not possible for it to be otherwise. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b10) | |
| A reaction: The second half sounds odd, since we ought to understand that something could have been otherwise, and knowing whether or not it could have been otherwise is part of the understanding. It sounds like Spinozan determinism. |
| 12366 | We only understand something when we know its explanation [Aristotle] |
| Full Idea: We only understand something when we know its explanation. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b30) | |
| A reaction: If we believe that the whole aim of philosophy is 'understanding' (Idea 543) - and if it isn't then I am not sure what the aim is, and alternative aims seem a lot less interesting - then we should care very much about explanations, as well as reasons. |
| 12370 | Some understanding, of immediate items, is indemonstrable [Aristotle] |
| Full Idea: Not all understanding is demonstrative: rather, in the case of immediate items understanding is indemonstrable. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b19) | |
| A reaction: These are the foundations of Aristotle's epistemology, and I take it that they can be both empiricist and rationalist - sense experiences, and a priori intuitions. |
| 1685 | No one has mere belief about something if they think it HAS to be true [Aristotle] |
| Full Idea: No one holds something as an opinion when he thinks that it is impossible for it to be otherwise - for then he thinks he understands it. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 89a07) |
| 1673 | Knowledge proceeds from principles, so it is hard to know if we know [Aristotle] |
| Full Idea: It is difficult to know whether you know something or not. For it is difficult to know whether or not our knowledge of something proceeds from its principles - and this is what it is to know something. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 76a25) |
| 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. |
| 12379 | You cannot understand anything through perception [Aristotle] |
| Full Idea: You cannot understand anything through perception. Demonstrations are universal, and universals cannot be perceived. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 87b28) |
| 16725 | Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced [Aristotle] |
| Full Idea: The loss of any one of the senses entails the loss of a corresponding portion of knowledge, and since we learn either by induction or by demonstration, this knowledge cannot be acquired. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 81a37) | |
| A reaction: This suggests Jackson's 'knowledge argument', that raw experience contains some genuine knowledge, for which there is no mechanistic substitute. Not that I accept…. |
| 23309 | Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M] |
| Full Idea: It is a certain notion of understanding and, correspondingly, explanation which makes Aristotle think that knowledge, properly speaking, could not be a matter of mere experience. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Michael Frede - Aristotle's Rationalism p.160 | |
| A reaction: Frede says this means that Aristotle is a rationalist, though few empiricists think understanding is 'merely' a matter of experience. My own epistemology is Explanatory Empiricism, which I see as more empiricist than rationalist. |
| 1693 | Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle] |
| Full Idea: In some animals the perception is retained, and in some not. Without retention knowledge is impossible. Some animals go further and form an account based on the perception. This leads to memory and experience, and so to either skill or understanding. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 99b35-) |
| 9067 | Many memories of the same item form a single experience [Aristotle] |
| Full Idea: When it occurs often in connection with the same item, ..memories which are many in number form a single experience. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a05) | |
| A reaction: This is Aristotle at his most empirical. He is not describing an operation of the understanding, but a process of association. The process he alludes to is at the heart of the abstractionist view of concept-formation. |
| 1671 | Sceptics say justification is an infinite regress, or it stops at the unknowable [Aristotle] |
| Full Idea: Sceptics say that there is either an infinite regress of ideas based on one another, or things come to a stop at primitives which are unknowable (because they can't be demonstrated). | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b09) | |
| A reaction: This is one strand of what eventually becomes the classic Agrippa's Trilemma (Idea 8850). For Aristotle's view on this one, see Idea 562. |
| 1670 | When you understand basics, you can't be persuaded to change your mind [Aristotle] |
| Full Idea: Anyone who understands anything simpliciter (as basic) must be incapable of being persuaded to change his mind. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b04) | |
| A reaction: A typical Aristotle test which seems rather odd to us. Surely I can change my mind, and decide that something is not basic after all? But, says Aristotle, then you didn't really think it was basic. |
| 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. |
| 12383 | There must be definitions before demonstration is possible [Aristotle] |
| Full Idea: There is no demonstration of anything of which there is no definition. Definitions are of what something is, i.e. of its essence, but all demonstrations clearly suppose and assume what a thing is. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b30) | |
| A reaction: Note that while essentialism rests on definitions, the job is not yet complete once the definitions are done. With good definitions, it should be easy to show how the pieces of the jigsaw fit together. |
| 1674 | All demonstration is concerned with existence, axioms and properties [Aristotle] |
| Full Idea: All demonstrative science [apodeiktike episteme] is concerned with three things: what it posits to exist (the kind), the axioms (primitives basic to demonstration), and the attributes. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 76b12) |
| 24068 | Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki] |
| Full Idea: Aristotle's demonstration encompasses more than deductive entailment, in that the explanatory order of priority represented in a successful demonstration must mirror precisely the causal order of priority in the phenomena in question. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Kathrin Koslicki - Form, Matter and Substance 4.5 | |
| A reaction: Interesting. I presume this is correct, but is not an aspect I had registered. In Metaphysics his essentialist explanations are causal, so it all hangs together. |
| 17310 | Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki] |
| Full Idea: In Aristotle's system, the relevant notion of asymmetric consequence that is operative in his model of scientific explanation is that of demonstration. ...It is a theoretical/linguistic reflection of an asymmetric real-world relation of causal priority. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Kathrin Koslicki - Varieties of Ontological Dependence 7.3 n7 | |
| A reaction: The asymmetry is required for explanation, and for grounding. |
| 21359 | Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle] |
| Full Idea: There is a conflict between the syllogistic theory of demonstration of the Posterior Analytics, with its austere programme of certainties, and how Aristotle actually does science. | |
| From: comment on Aristotle (Posterior Analytics [c.327 BCE]) by Armand Marie LeRoi - The Lagoon: how Aristotle invented science 104 | |
| A reaction: Leroi observes that there are no demonstrations anywhere in the biological writings. Biology probably lends itself least to such an approach. |
| 1667 | Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle] |
| Full Idea: Demonstrative understanding must proceed from items which are true and primitive and immediate and more familiar and prior to and explanatory of the conclusions. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b22) |
| 12365 | We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle] |
| Full Idea: We know things through demonstration, by which I mean a scientific deduction, and by 'scientific' I mean a deduction by possessing which we understand something. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b17) | |
| A reaction: This is a distinctively Aristotelian account of what science aims at, and which seems to have dropped out of modern accounts of science, which are still under the influence of logical positivism. Time to revive it. |
| 10918 | Demonstrative understanding rests on necessary features of the thing in itself [Aristotle] |
| Full Idea: If demonstrative understanding proceeds from necessary principles, and whatever holds of an object in itself is necessary, then it is clear that demonstrative deductions will proceed from certain items of this sort. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 74b05-) | |
| A reaction: This is the characterization of the essence of something in terms of what counts as a good explanation of that thing. Although explanation is a bit subjective, I like this approach, because you will dig down to the source of the powers of the thing. |
| 12374 | Demonstrations must be necessary, and that depends on the middle term [Aristotle] |
| Full Idea: If you understand something demonstratively, it must hold from necessity, so it is plain that your demonstration must proceed through a middle term which is necessary. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 75a13) | |
| A reaction: How can a middle 'term' be necessary, if it is not a proposition? Presumably Socrates is necessarily a man, and men are necessarily mortal, so it is the predication which is necessary. |
| 12148 | Demonstrations are syllogisms which give explanations [Aristotle] |
| Full Idea: Demonstrations are probative deductions [sullogismos] which give the explanation [aitias] and the reason why. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 85b24) | |
| A reaction: This notion seems to have slipped out of modern philosophy of science, because (while scientists have just pressed on) philosophers of science have raised so many sceptical questions that they have, I would say, lost the plot. |
| 1679 | Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle] |
| Full Idea: Universal demonstrations are objects of thought, particular demonstrations terminate in perception. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 86a30) |
| 1680 | Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle] |
| Full Idea: A demonstration is superior if it depends on fewer suppositions or propositions - for if these are familiar, knowledge will come more quickly, and this is preferable. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 86a35) |
| 1691 | Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle] |
| Full Idea: Divide a whole into its primitives, then try to get definitions of these. Thus you establish the kind, and then study the attributes through the primitive common items. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 96b16) |
| 12147 | The principles of demonstrations are definitions [Aristotle] |
| Full Idea: The principles of demonstrations are definitions. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b25) | |
| A reaction: This I take to be a key idea linking Aristotle's desire to understand the world, by using demonstrations to reach good explanations. Definitions turn out to rest on essences, so our understanding of the world rests on essences. |
| 12371 | A demonstration is a deduction which proceeds from necessities [Aristotle] |
| Full Idea: A demonstration is a deduction which proceeds from necessities. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73a24) | |
| A reaction: Elsewhere he tells us that demonstration that brings understanding (Idea 12365), so this is an interesting gloss. He says that the middle term of the syllogism gives the understanding, but necessities reside in the whole propositions of the premisses. |
| 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) |
| 1683 | We learn universals from many particulars [Aristotle] |
| Full Idea: It is from many particulars that the universal becomes plain. Universals are valuable because they make the explanation plain. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a05) |
| 12367 | What is most universal is furthest away, and the particulars are nearest [Aristotle] |
| Full Idea: What is most universal is furthest away, and the particulars are nearest. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a05) | |
| A reaction: This is the puzzle that bother Aristotle about explanation, that we can only grasp the universals, when we want to explain the particulars. |
| 12380 | Universals are valuable because they make the explanations plain [Aristotle] |
| Full Idea: Universals are valuable because they make the explanations plain. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a06) | |
| A reaction: Everything in Aristotle comes back to human capacity to understand. There seems to be an ideal explanation consisting entirely of particulars, but humans are not equipped to grasp it. We think in a broad brush way. |
| 12385 | Are particulars explained more by universals, or by other particulars? [Aristotle] |
| Full Idea: Which of the middle terms is explanatory for the particulars - the one which is primitive in the direction of the universal, or the one which is primitive in the direction of the particular? | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 99b09) | |
| A reaction: I'm not clear about this, but it shows Aristotle wrestling with the issue of whether explanations are of particulars or universals, and whether they employ particulars as well as employing universals. The particular must be defined! |
| 1689 | Explanation is of the status of a thing, inferences to it, initiation of change, and purpose [Aristotle] |
| Full Idea: There are four sorts of explanation: what it is to be something, that if certain items hold it is necessary for this to hold, what initiated the change, and the purpose. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 94a21) | |
| A reaction: This might be summed up as: 'we want to know the essence, the necessary conditions, the cause, and the purpose'. Can anyone improve on that as the aims of explanation? The second explanation (necessary preconditions) isn't in 'Physics' - Idea 8332. |
| 1686 | What we seek and understand are facts, reasons, existence, and identity [Aristotle] |
| Full Idea: The things we seek are equal in number to those we understand: the fact, the reason why, if something is, and what something is. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 89b24) |
| 12357 | Explanation and generality are inseparable [Aristotle, by Wedin] |
| Full Idea: For Aristotle, explanation and generality are fellow-travellers. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance X.11 | |
| A reaction: This isn't 'lawlike' explanation, but it is interestingly close to it. It seems to be based on the fact that predicates are universals, so we can only state truths in general terms. |
| 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. |
| 1669 | The foundation or source is stronger than the thing it causes [Aristotle] |
| Full Idea: Something always holds better because of that because of which it holds - e.g. that because of which we love something is better loved. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a30) |
| 1678 | Universals give better explanations, because they are self-explanatory and primitive [Aristotle] |
| Full Idea: Universals are more explanatory (for something which holds in itself is itself explanatory of itself; and universals are primitive; hence universals are explanatory) - so universal demonstrations are better. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 85b25) |
| 9068 | Perception creates primitive immediate principles by building a series of firm concepts [Aristotle] |
| Full Idea: Primitive immediate principles ...come about from perception - as in a battle, when a rout has occurred, first one man makes a stand, then another, and then another, until a position of strength is reached. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a12) | |
| A reaction: Philosophers don't create imagery like that any more. This empiricist account of how concepts and universals are created is part of a campaign against Plato's theory of forms. [Idea 9069 continues his idea] |
| 9069 | A perception lodging in the soul creates a primitive universal, which becomes generalised [Aristotle] |
| Full Idea: When one undifferentiated item in perception makes a stand, there is a primitive universal in the soul; for although you perceive particulars, perception is of universals - e.g. of man, not of Callias the man. One animal makes a stand, until animal does. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a15-) | |
| A reaction: This is the quintessential account of abstractionism, with the claim that primitive universals arise directly in perception, but only in repeated perception. How the soul does it is a mystery to Aristotle, just as associations are a mystery to Hume. |
| 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. |
| 9070 | We learn primitives and universals by induction from perceptions [Aristotle] |
| Full Idea: We must get to know the primitives by induction; for this is the way in which perception instils universals. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100b04) | |
| A reaction: This statement is so strongly empirical it could have come from John Stuart Mill. The modern post-Fregean view of universals is essentially platonist - that they have a life and logic of their own, and their method of acquisition is irrelevant. |
| 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? |
| 12368 | Negation takes something away from something [Aristotle] |
| Full Idea: The part of a contradictory pair which says something of something is an affirmation; the part which takes something from something is a negation. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a14) | |
| A reaction: So affirmation is predication about an object ['Fa'], and negation is denial of predication. We have a scope problem: there is nothing which is F [¬∃x(Fx)], or there is a thing which is not-F [∃x(¬Fx)]. Aristotle seems to mean the latter. |
| 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? |
| 1692 | If you shouldn't argue in metaphors, then you shouldn't try to define them either [Aristotle] |
| Full Idea: If you should not argue in metaphors, it is plain too that you should neither define by metaphors nor define what is said in metaphors; for then you will necessarily argue in metaphors. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97b37) | |
| A reaction: Impeccable logic, but seeing a similarity can be a wonderful shortcut to seeing a great truth. |
| 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. |
| 12375 | Whatever holds of a kind intrinsically holds of it necessarily [Aristotle] |
| Full Idea: In each kind, whatever holds of something in itself and as such holds of it from necessity. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 75a30) | |
| A reaction: This seems to confirm the view that essential properties are necessary, but it does not, of course, follow that all necessary properties are essential properties (e.g. trivial necessities are not essential). |
| 1688 | Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence [Aristotle] |
| Full Idea: Everything which a thing is must be proved through a demonstration - except its essence. But existence is not the essence of anything; for the things that exist do not constitute a kind. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 92b14) |