Tractatus Blogico-Philosophicus

Hey, free book!

2009-05-15T05:50:00.000-07:00

Here's a draft of a book based on this blog: Wittgenstein's Tractatus: A Student's Guide. It should appear in book format if you print two pages per sheet.

2007-12-05T11:02:00.000-08:00

7 Whereof one cannot speak, thereof one must be silent.

And this tautology is what is so hard for the philosopher to accept. The goal of the book, it seems, is to lead one to acceptance, to peace. Cf. PI 133. The TLP offers one method, the PI perhaps another. Or more than one. Cf. Schopenhauer: Kant “had circumnavigated the world and shown that because it is round, one cannot get out of it by horizontal movement.” (The World as Will and Idea trans. R. B. Haldane and J. Kemp (3 volumes, Routledge and Kegan Paul, London, 1883), vol. II, p. 10).

Ostrow (p. 133) sees an ethical obligation here, since failure to remain silent would indicate a refusal to accept reality or the course of one’s own experience. Yet see what Wittgenstein says about talking nonsense in the Lecture on Ethics.

Friedlander (p. 148) notes that Wittgenstein talks about speaking (sprechen) not saying (sagen). “What is at stake here is, then, an actual intervention with speech rather than the abstract opposition of the sayable and the unsayable.” He continues, in the next paragraph: “Moreover, the opposite of silence is not necessarily speaking with sense but, rather, making noise. Speaking without sense is one way of being noisy. The ending of the Tractatus should therefore be read in conjunction with the epigraph of the book, which places the act of expression against a background of noise: “…and whatever a man knows, whatever is not mere rumbling and roaring that he has heard, can be said in three words.” The implication is that the noise of empty talk, whether it be nonsense or mere mindlessness, conceals something. To be silent means primarily not to fall prey to the rumbling and roaring of rumor. Silence is what we need in order to be attentive to what there is, to the showing of truth.”

This seems to go perhaps farther than the text warrants, but Wittgenstein’s remarks about Moore (in his comment on Heidegger) bear some of it out. As does Kierkegaard’s valuing of silence. There is still some dubious residue though, I think.

Friedlander (pp. 149-150) goes on to show how Wittgenstein’s views on silence were not simple, at least later in his life. We must not, he seems to say there, be silent about important matters (e.g. God) just because chatterboxes talk a lot of nonsense about such things. But it still seems important to him not to be one of these chatterboxes. He gave his word to a friend of his (Drury) that he would not refuse to talk to him about God or religion. It does not follow that he would have no objection to a philosopher publishing works for a general (i.e. wide, impersonal) audience on such subjects.

Then again, Nordmann (p. 156) says that “one remains silent when speaking nonsense knowingly.” As long as we do not actually say anything, we can speak as much as we like (which perhaps will not be very much, of course), so long as we know what we are doing and do not lay any “claim on what is inexpressible in speech.”

Schopenhauer Fourfold Root p. 154: “Indeed, there are some [ideas] which never find words, and alas these are the best.”

Black (p. 378) quotes Silesius: “Schweig, Allerliebster, schweig: kannst du nur gänzlich schweigen,/ So wird dir Gott mehr Gut’s, als du begehrst, erzeigen." This is translated by Maria Shrady in Angelus Silesius The Cherubinic Wanderer (Paulist Press, 1986) thus: "Silence, Beloved, be still; if you be wholly quiet, God will show you more good than you know how to desire." (p. xi) This disguises the repetition of schweigen, though, so perhaps "Silence, beloved, silence: if you can only be completely silent, then God will show you more good than you know how to desire" might be preferable.

2007-12-05T10:53:00.000-08:00

6.54 My propositions elucidate by whoever understands me perceiving them in the end as nonsensical, when through them – upon them – over them, he has climbed out. (He must, so to speak, throw away the ladder after he has climbed out upon it.)

He must overcome these propositions, then he sees the world rightly.

More images of inversion, like a kitten escaping from a sweater by, trying to run or climb, turning the sweater inside out. What does the enlightened reader climb out of after all? Surely the very propositions that he climbs through, on, and over. And how can Wittgenstein be so sure that he will then see the world rightly? Because, whatever else might be the case, he will no longer be in the grip of philosophical/metaphysical illusion. “Overcome” is more literal and everyday than “transcend,” and gets across the idea of struggle. It is preferred therefore by Cora Diamond. See footnote 33, p. 121 of Diarmuid Costello “’Making Sense’ of Nonsense” in Barry Stocker, ed. Post-Analytic Tractatus, Ashgate, 2004.

The ladder image occurs in Fritz Mauthner’s Beiträge zu einer Kritik der Sprache (Stuttgart: Cotta, 1901-3), vol. I, p. 2, and in Schop WWR vol. 2, p. 80.

On p. 78 Anscombe says that “Wittgenstein used to say that the Tractatus was not all wrong: it was not like a bag of junk professing to be a clock, but like a clock that did not tell you the right time.”

Friedlander (p. 13) says: “Logically speaking, the Tractatus does not exist.”

Cf. CV p. 7: "I might say: if the place I want to get to could only be reached by way of a ladder, I would give up trying to get there. For the place I really have to get to is a place I must already be at now.

"Anything that I might reach by climbing a ladder does not interest me."

Nordmann (p. 23) quotes Lichtenberg: “we always teach true philosophy with the language of the false one.” From Georg Christoph Lichtenberg Aphorisms and Letters ed. Franz Mautner and Henry Hatfield, London: Jonathan Cape, 1969, p. 53. According to Nordmann (p. 199, note 86): “TLP 6.54 (“my sentences are nonsensical”) is nonsense par excellence and therefore self-exemplifying.”

Cf. also Plato’s divided line in the Republic (Book VI, especially 511b-e). Here Plato contrasts the activity of geometers with that of philosophers, philosophers being distinguished by their going back to the beginning and not basing their reasoning on any assumptions. In philosophy, in Waterfield’s translation (p. 239), “When [reason] takes things for granted, it doesn’t treat them as starting-points, but as basic in the strict sense—as platforms and rungs, for example. These serve it until it reaches a point where nothing needs to be taken for granted, and which is the starting-point for everything. Once it has grasped this starting-point, it turns around and by a process of depending on the things which depend from the starting-point, it descends to an end-point. It makes absolutely no use of anything perceptible by the senses: it aims for types by means of types alone, in and of themselves, and it ends its journey with types.” It is worth noting that Russell’s The Problems of Philosophy, which was published in 1912, specially recommends Plato’s Republic for the “student who wishes to acquire an elementary knowledge of philosophy” (along with six classics of early modern philosophy) and especially picks out Books VI and VII from the Republic. It seems likely, then, that Wittgenstein, who was first formally taught philosophy by Russell in late 1911, would have read this part of the Republic.

Also possibly relevant, from Book VII of the Republic 533c: “For if your starting-point is unknown, and your end-point and intermediate stages are woven together out of unknown material, there may be coherence, but knowledge is completely out of the question.”

And compare Schopenhauer Fourfold Root p. 120: “But it would be downright chicanery and nothing else, if the attempt were made to compare or even identify the honest and thorough analysis here given of empirical intuitive perception into its elements, such elements proving to be subjective, with Fichte’s algebraical equations between the ego and non-ego; with that sophist’s pseudo-demonstrations, requiring the cloak of incomprehensibility and even nonsense to deceive the reader; with explanations such as the ego spinning the non-ego out of itself; in short, with all the tomfoolery of scientific emptiness.” Is the TLP comparable to Fichte’s work in some such way?

White (pp. 115-117) sets out various ways in which Wittgenstein has ‘said’ things that, he says, cannot be said, e.g. in his remarks on formal concepts and the logical form of propositions that is shared with reality.

Schopenhauer WWR Vol. II, p. 80: “However, for the man who studies to gain insight, books and studies are merely rungs of the ladder on which he climbs to the summit of knowledge. As soon as a rung has raised him one step, he leaves it behind. On the other hand, the many who study in order to fill their memory do not use the rungs of the ladder for climbing, but take them off and load themselves with them to take away, rejoicing at the increasing weight of the burden. They remain below forever, because they bear what should have borne them.” See David Avraham Weiner Genius and Talent: Schopenhauer’s Influence on Wittgenstein’s Early Philosophy (Associated University Presses, London, 1992), pp. 42-43 for more on this.

Black (p. 377) also quotes Sextus Empiricus comparing a skeptic who proves the non-existence of proof to a man who kicks over a ladder after he has used it to climb to a high place.

2007-12-05T08:31:00.000-08:00

6.53 The right method for philosophy would properly be this: To say nothing other than what can be said, thus propositions of natural science – thus something that has nothing to do with philosophy –, and then always, if another wanted to say something metaphysical, to point out to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying for the other person – he would not have the feeling that we were teaching him philosophy – but it would be the only strictly correct one.

Not the method used in the Tractatus, apparently (it does not seem to consist solely of propositions of natural science, after all), but perhaps the one used (in attempt, at least) by certain Wittgensteinians. Why does he not use it here? It is an ad hominem method, and here he wants a general approach. He, as it were, demonstrates a method, by examples. But it also is somewhat ad hominem, with Frege and Russell being the most obvious targets.

How would the strictly correct method be justified? The demonstration of a method (or methods) works, if at all, by being shown or found to be successful. If the aim is clarity, then the method would be justified by being shown to lead to clarity.

Consider the method advocated here in possible application to Frege. Frege never defines “course-of-values.” See Basic Laws vol. 2 §146. He says it cannot be defined, even though he uses the concept a lot and introduces it as early as §3. All that he can do, he says, is to give hints as to the meanings of such terms, and hope that the reader gets the idea. But in such cases, Weiner points out (see pp. 159-160 of Reck), it is possible that the author himself has failed to give a meaning to his term.

Anscombe (p. 151): “The criticism of sentences as expressing no real thought, according to the principles of the Tractatus, could never be of any very simple general form; each criticism would be ad hoc, and fall within the subject-matter with which the sentence professed to deal.” Wittgenstein is not, for instance, putting forward a verificationist criterion of meaning.

Black (p. 377): “It will be noticed, of course, that the method pursued in the Tractatus is not the ‘correct’ one.”

2007-12-05T08:28:00.000-08:00

6.522 There is to be sure the unspeakable [unutterable, ineffable]. This shows itself, it is the mystical.

Black (p. 376) offers “the inexpressible” as a literal translation of Unaussprechliches. Does Wittgenstein mean that philosophers want to do something that cannot be done, and that this something is the mystical? Is it mystical that there should be such a problem? Or does he mean that we can call “the ineffable” or “the mystical” whatever it is (although, in fact, he has shown it to be illusory) that philosophers want to try to express? Otherwise 6.522 seems to contradict 6.5, on which it is a comment! In Letters to Ogden, p. 37, he says that das Mystiche here is the same as in the case of 6.44 but not the same as 6.45. So is it not a feeling?

Anscombe (p. 19): “There is indeed much that is inexpressible—which we must not try to state, but must contemplate without words.” See comment on 1.1.

Friedlander (p. 143 note 19) argues that Ogden’s translation of “Es gibt” as “There is” is preferable to P&McG’s reference to things that make themselves manifest, since that “makes the ending most problematic.”

Nordmann (pp. 50-51) argues that unaussprechlich should be translated ‘inexpressible in speech.’ It is not the same as ‘unsayable’, since a proposition can say (as in 5.542’s “’p’ says p”), but refers rather to the ability (or inability) of a human subject to get something out in language. 4.115 is the only place in the TLP where Wittgenstein mentions the sayable and the unsayable. Nordmann contrasts the expressible in speech with what is expressible in music, gesture, or conduct. He sees this remark as following from the denial of what needs to be denied (its contrary) in order to avoid the contradiction in 6.41 (see p. 194). Yet he also sees this remark itself as nonsensical because it fails to establish a subject-predicate relation, and is therefore ungrammatical. See p. 198. Nevertheless, he persists. On pp. 198-199 he writes: “That the words “there is indeed the inexpressible in speech” are nonsensical and have no sense makes the point that there is, indeed, the inexpressible in speech.”

2007-12-05T08:27:00.001-08:00

6.521 The solution of the problem of life is perceived in the vanishing of this problem.

(Is not this the reason why people to whom the meaning [Sinn] of life has become clear after long doubt could not then say in what this meaning consists?)

Anscombe says (p. 170) that this shows that Wittgenstein does not think all thoughts of the meaning of life are nonsense. After all, how could it become clear unless it could at least be shown?

2007-12-05T08:25:00.000-08:00

6.52 We feel that even if all possible questions of natural science were to be answered, our life problems [existential problems?] would still not have been touched at all. Of course there would then be no more questions remaining; and just this is the answer.

It is? One possible interpretation: These questions, the life ones, are illusory. They are not questions, but feelings of a certain kind. Feelings that feel as though they will go away when an answer is found, but that can be shown to be unanswerable by any possible answer. And so we see that the feelings are misleading. Will they then go away? Maybe, maybe not. But we can at least deal with them honestly, knowing them for what they are (not).

2007-12-05T08:24:00.000-08:00

6.51 Skepticism is not irrefutable, but rather manifestly nonsensical [offenbar unsinnig], if it would doubt where nothing can be asked.

Since doubt can only exist where a question exists; a question only where an answer exists, and this only where something can be said.

The ‘if’ might be worth noting here. Wondering about the meaning of life would then be manifestly nonsensical too. Cf. Kant’s Critique of Pure Reason: “To know what questions may reasonably be asked is already a great and necessary proof of sagacity and insight. For if a question is absurd in itself and calls for an answer where none is required, it not only brings shame on the propounder of the question, but may betray an incautious listener into absurd answers, thus presenting, as the ancients said, the ludicrous spectacle of one man milking a he-goat and the other holding a sieve underneath.” (A 58/B 82-83)

2007-12-05T08:23:00.000-08:00

6.5 If it requires an answer that one cannot articulate, then one also cannot articulate the question.

The riddle does not exist.

If a question can be put at all, then it can also be answered.

The second sentence refers back to 6.4312. 6.5 supports my interpretation of 6.4312. But is even 6.5 meant to be nonsense? What are we told here, after all? In Letters to Ogden, Wittgenstein says (p. 37) that his reference here to “the riddle” “means as much as “the riddle ‘par excellence’”.” Joachim Schulte on p. 132 of his essay in Stern and Szabados eds. Wittgenstein Reads Weininger suggests that the reference here and in 6.4312 might be allusions to Weininger. On pp. 128-129 Schulte quotes Weininger to the effect that “the deepest problem in the universe” is constituted by the riddle of life together with the riddle of the world. The riddle of the world is said to be the riddle of dualism, while the riddle of life is the riddle of time. Weininger links the fact that life is not reversible with the meaning of life, and claims that, “The unidirectionality of time is … identical with the fact that the human being is at bottom a being that wills.”[1] Of course, as Schulte notes, there is a lot of irony and paradox in Weininger. Wittgenstein discusses the unidirectionality of time in Notebooks 12 October 1916.

[1] Weininger On Last Things, p. 89.

2007-12-05T08:21:00.000-08:00

6.45 The contemplation of the world sub specie aeterni is its contemplation as a – limited – whole.

The feeling of the world as a limited whole is the mystical.

But this too is impossible, nonsense. Isn’t it? Wittgenstein says ““das mystiche” is an adjective belonging to “Gefühl” here, and considers the translation “the mystical feeling,” although he prefers simply “the mystical,” see Letters to Ogden, pp. 36-37. See notes on 1 for Spinoza and Schopenhauer on this kind of contemplation.

2007-12-04T06:09:00.000-08:00

6.44 The mystical is not how the world is, but rather that it is.

And this is beyond language, haven’t we seen above? Indeed, isn’t “There is a world” nonsense? Frege distinguishes between mere existence and actuality, between existence and existence in a spatio-temporal field, causal chains, etc. (See Sluga’s book on Frege, pp. 88-90.) In Frege’s terms, ‘is’ in ‘There is a world’ could only be used in the very thin sense, and it isn’t clear what this sense is. “Affirmation of existence is indeed nothing other than denial of the number zero. Since existence is a property of concepts, the ontological proof of the existence of God fails in its aim.” (Foundations of Arithmetic, §53.) Saying ‘A world exists’ is saying something about the concept world, namely that it is instantiated, while saying ‘The world exists’, if “the world” is meant to be the name of something specific, makes no sense. “With a concept the question is always whether anything, and if so what, falls under it. With a proper name such questions make no sense. We should not be deceived by the fact that language makes use of proper names, for instance Moon, as concept words, and vice versa; this does not affect the distinction between the two. As soon as a word is used with the indefinite article or in the plural without any article, it is a concept word.” (Foundations of Arithmetic, §51).

2007-12-04T06:08:00.000-08:00

6.4321 The facts all belong only to the assignment, not to the correct response to it.

If we see life in these terms, that is. “Correct response” instead of “solution” because in Letters to Ogden, p. 36, Wittgenstein says the word should be appropriate for, e.g. the digging of a hole when someone tells someone to dig a hole.

2007-12-04T06:07:00.000-08:00

6.432 How the world is, is completely indifferent for what is Higher. God does not disclose [or: manifest, reveal] himself in the world.

What believer could accept this? God is not manifest in the world, and couldn’t care less what happens in it? Is this pure atheism, or a kind of philosophical theism taken to its limit?

2007-12-04T06:06:00.000-08:00

6.4312 The temporal immortality of the soul of man, meaning therefore its eternal survival even after death, is not only in no way guaranteed, but in the first place this assumption does not at all do what people have always wanted to achieve with it. Is a riddle thereby solved, because I survive eternally? Is eternal life, on this account, then not just as mysterious as the present one? The solving of the riddle of life in space and time lies outside of space and time.

(It is indeed not problems of natural science that are to be solved.)

Ah, but is the solution to this riddle found in the disappearance of the riddle? See CV, p. 27 (1937), and p. 74 and p. 75. Is there a riddle really? Or is the experience of life as a riddle more like an unpleasant feeling in response to awareness of the mystery of life. And that awareness itself might not seem to be anything (awareness of anything) if we think it through. “Mystery” might perhaps be better than “riddle” here. Wittgenstein, in Letters to Ogden, p. 36, says: “I don’t wish that there should be anything ridiculous or profane or frivolous in the word when used in the connection “riddle of life” etc.”

2007-12-04T06:05:00.000-08:00

6.4311 Death is not an event in life. One does not live through death.

If one understands eternity not as an endless period of time but as timelessness, then he who lives in the present lives eternally.

Our life is just as endless as our field of vision is limitless.

I.e., not really, but in some, not very comforting, sense. I think nonsensical ideas are being deflated here, but quite possibly ones to which Wittgenstein felt very drawn. Hence the ethical, practical nature of the ironic debunking of treasured idols. The irony here is not sarcasm but a pretty much essential means to the kind of goal Wittgenstein is aiming at. He must say nothing false, but speak only truth and nonsense. The nonsense is revealed as nonsense by being pushed through to its painful conclusion. This involves a kind of inversion, as does irony. Wittgenstein suggested “without limit” instead of “limitless,” but only on the grounds that “limitless” is not normal English. I think it is though, so I have left it in. It is a more literal translation of the German grenzenlos.

2007-12-04T06:04:00.000-08:00

6.431 As too at death the world does not change, but rather stops.

Why say “the world” here instead of “my world”?

2007-12-04T06:01:00.000-08:00

6.43 If good or evil willing alters the world, then it can only alter the limits of the world, not the facts; not that which can be expressed through language.

In short, the world must then thereby become an altogether different one. It must, so to speak, wane or wax as a whole.

The world of the happy is a different one than that of the unhappy.

But how can it be? Is this a kind of reductio? It shows that good or evil willing cannot alter the world. This is also shown by the fact that, if it were otherwise, such willing would change something that cannot be expressed through language. But there is no such thing, we cannot possibly make sense of this idea. And what cannot be said cannot be thought, or believed, or etc. Pears and McGuinness have “happy man” even though Wittgenstein explicitly asked Ogden to remove the word “man” from the translation (see Letters to Ogden p. 35).

Cf. Notebooks p. 73.

Schopenhauer contrasts altruism with egoism in a way that comes readily to mind when reading TLP 6.43. Egoism concentrates, while altruism expands. See WWR I: 373-4, and Young Schopenhauer pp. 229-231. “That Wittgenstein’s waxing/waning metaphor so strongly recalls Schopenhauer’s expansion/contraction metaphor makes it look as though Wittgenstein’s person of ‘good will’ is the Schopenhauerian altruist and the person of ‘bad will’ is the Schopenhauerian egoist. In fact, though, I think, only the second half of this equation holds. What Wittgenstein really means by the ‘good exercise of the will’ is a version of asceticism, of Schopenhauer’s ‘denial of the will.’”[1] So it is not about altruistic willing, but rather giving up willing altogether, as far as that can be done.

According to Schopenhauer, we need not only detachment from desire (Stoicism) but the abandonment of desire (Cynicism). Wittgenstein seems to have lived like a Cynic, choosing poverty and asceticism.[2]

Mounce (p. 96): “Wittgenstein does not mean that the ethical attitude is itself a matter of temperament. On the contrary, one’s temperament is just another of the facts towards which one has to adopt an ethical attitude.” [But, Friedlander asks, “what is an attitude toward the world, and in what sense is it not part of psychology?” (pp. 197-198)] The stuff about the world of the happy is only an analogy, Mounce insists.

Anscombe calls the will that alters the limits of the world but effects nothing in it “chimerical” (p. 172). Will, like intention, she suggests, resides in what we do. See PI 644. In a footnote on p. 172, she says that Schopenhauer identifies the world with my will, and regards them both as bad. Wittgenstein sees the world as good and independent of my will. Schopenhauer’s idea of a good will is one that denies itself. Similarly, Wittgenstein’s good will is not concerned with how things are, it accepts the world as it is, however it is, “and in that sense is like Schopenhauer’s good will.”

[1] Young Schopenhauer p. 230.

[2] See Young p. 232. Young cites Schopenhauer WWR II: 155-6.

2007-12-04T05:58:00.000-08:00

6.423 Of the will as the bearer of the ethical, nothing can be said.

And the will as a phenomenon is interesting only to psychology.

Very Schopenhaurian/Kantian. But then so is the kind of ethics he is talking about, and perhaps criticizing. See Wiggins (2004, in Philosophy) on this passage. Some of Schopenhauer’s thoughts on ethics: The aim of all art is to communicate platonic Ideas, not concepts. Allegorical paintings are mere hieroglyphics. These Ideas are the various grades of the will’s objectification. “[T]he Idea can be known only by perception; but knowledge of the Idea is the aim of all art.”[1] Poetry uses abstract concepts, but skillful poets combine them in such a way that, given imagination in the reader, the desired idea is communicated.

“The poet comprehends the Idea, man’s inner nature apart from all relations, outside all time, the adequate objectivity of the thing-in-itself at its highest grade. Although even in the historian’s perspective, the inner nature, the significance of the phenomena, the germ within all those husks, can never be utterly lost (and he, at least, who seeks it, may still find it and recognise it), what is significant in itself and not in its relations, the real unfolding of the Idea, will be found far more accurately and distinctly in poetry than in history; and therefore, however paradoxical it may sound, far more actual genuine inner truth is to be imputed to poetry than to history.”[2]

“The poet is … the universal man; … And no one has the right to prescribe to the poet what he ought to be – noble and sublime, moral, pious, Christian, one thing or another – still less to reproach him because he is one thing and not another. He is the mirror of mankind, and brings to its consciousness what it feels and does.”[3]

“For both in poetry and in painting we demand the faithful mirror of life, of man, of the world – only made more clear by the presentation and more meaningful by the arrangement.”[4] Cf. 6.43 and Bearn (Waking to Wonder) on how the world of the happy differs by being more meaningful.

Perhaps here also see Schopenhauer Fourfold Root p. 211: “Now the identity of the subject of willing with that of knowing by virtue whereof (and indeed necessarily) the word “I” includes and indicates both, is the knot of the world, and hence inexplicable.” Again, pp. 211-212: “But whoever really grasps the inexplicable nature of this identity, will with me call it the miracle “par excellence.””

[1] Everyman edition of Schopenhauer’s WWR, p. 153.

[2] Ibid., p. 155.

[3] Ibid., p. 157.

[4] Ibid., p. 158.

2007-12-03T11:14:00.000-08:00

6.422 The first thought at the setting up of an ethical law of the form “thou shalt….” is: And what then, if I don’t do it? It is clear, however, that ethics has nothing to do with punishment and reward in the ordinary sense. Therefore this question as to the consequences of an act must be irrelevant. – At least these consequences should not be events. Since something must be right in the putting of this question. There must certainly be a kind of ethical reward and ethical punishment, but these must lie in the action itself.

(And this too is clear, that the reward must be something agreeable, the punishment something disagreeable.)

“Ethics” here means ethics in the relevant sense. If anyone wants to talk of ethics in some other sense, that is not contradicted here but ignored. Why must there be something right in the question? Perhaps because its form matches the form in which the Thou shalt is expressed, so it is, as it were, called for. It must somehow, in some sense, be appropriate.

2007-12-03T11:04:00.000-08:00

6.421 It is clear that ethics cannot be articulated.

Ethics is transcendental.

(Ethics and aesthetics are one.)

Is “It is clear” always a mark of irony in the Tractatus? Ethical and aesthetic value are beyond words, since no words we have will do, since what will satisfy is nothing in the world, i.e. nothing at all. But is this really true? Or is it only that no theory will satisfy us, just as physics is OK but the meta-theoretical “There are laws of nature” cannot work?

Some notes and quotes on Schopenhauer’s ethics: According to Schopenhauer, every living being is essentially egoistic, and yet in truth there is only one will, since the principle of individuation applies only to the phenomenal. Wrong is what we call one will’s encroaching on another, seen at its extreme in cannibalism. Right is a negative term, meaning only the opposite of this. What is on the side of our will we call ‘good’, and what is opposed to it we call ‘bad’ or, rarely, ‘evil’. “[T]hus every good is essentially relative, for it has its essential nature only in its relation to a desiring will. Absolute good is, therefore, a contradiction in terms …”[1] The highest or ultimate good would be something that so satisfies the will that it never wanted again, but it is the nature of the will always to desire more, never to be satisfied. So there can be no such thing: the concept is self-contradictory.

“A theory of morals which is not properly argued – in other words, mere moralizing – can effect nothing, because it does not motivate. A theory of morals which does motivate can do so only by working on self-love. But what springs from this latter has no moral worth. It follows that no genuine virtue can be produced through moral theory or abstract knowledge of any kind, but that such virtue must spring from that intuitive knowledge which recognises in the individuality of others the same essence as in our own.”[2] (This seems to have been Wittgenstein's view of moral philosophy. At least his remarks to O. K. Bouwsma later in his life about what possible value teaching moral philosophy could have strike me as compatible with what Schopenhauer says here.)

“Truly, it would be very bad if the chief business in human life, its ethical value, that value which counts for eternity, were dependent upon anything of which the attainment is so much a matter of chance as is the case with dogmas, religious doctrines, and philosophical theories.”[3]

“[I]n themselves all deeds (opera operata) are merely empty figures, and only the disposition which leads to them gives them moral significance.”[4]

Goodness does come from knowledge, but not a knowledge that can be communicated. Only the concept of this knowledge can be conveyed.

The negation of wickedness is justice. “When we examine the kernel of this justice, we find in it the intention not to go so far in the affirmation of one’s own will as to deny the manifestations of will in others by compelling them to serve one’s own. One will therefore wish to do as much for the benefit of others as one enjoys at their hands. The highest degree of this disposition to justice (which, however, is always allied with real goodness whose character is now not merely negative) leads a man to doubt his right to inherited property; to want to maintain his body solely by his own energy, mental and physical; to feel every service rendered by others, every luxury, as a reproach; and ultimately, of his own free will, to embrace poverty.”[5] (Again very reminiscent of Wittgenstein's chosen way of life after World War I.)

“I by no means wish to conceal a criticism that relates to this last part of my exposition, but rather to point out that it inheres in the nature of the material, and that it cannot be helped. [cf. Frege--DR] It is this, that after our study has finally reached the point at which in perfect holiness we see the denial and surrender of all volition – and thereby the redemption from a world whose whole existence presented itself to us as suffering – this appears to us as a transition into empty nothingness.”[6]

“Every nothing is such only when thought of in relation to something else, and presupposes this relation [i.e. negation], and thus also this something else. Even a logical contradiction is only a relative nothing. It is not a thought of reason, but it is not on that account an absolute nothing; for it is a combination of words; it is an example of the unthinkable, which is necessary in logic in order to prove the laws of thought. So, if for this purpose we seek such an example, we will hold fast to the nonsense as being the positive which we are in search of, and pass over the sense as the negative.”[7]

“What is generally accepted as positive, which we call being, and the negation of which is expressed by the concept nothing in its most general sense, is precisely the world as idea, which I have shown to be the objectivity and mirror of the will. … Denial, suspension, conversion of the will are also the suspension and the disappearance of the world, its mirror. If we no longer glimpse the will in this mirror, we ask in vain where it has gone, and then, because it has no longer any where and when, we lament that it has strayed into nothingness, and is lost.”[8]

Cf. Heidegger and Wittgenstein’s comments about him and the Nothing, etc. Also, perhaps, Russell (in The Principles of Mathematics) on nothing: “Great difficulties are associated with the null-class, and generally with the idea of nothing. It is plain that there is such a concept as nothing, and that in some sense nothing is something.” (p. 73)

“It is necessary to realize, in the first place, that a concept may denote although it does not denote anything.” (p. 73)

“The proposition which looks so paradoxical means no more than this: Nothing, the denoting concept, is not nothing, i.e. is not what itself denotes.” (p. 75)

(So, according to Schopenhauer, the unthinkable is exemplified in logical contradiction, which is necessary to prove the laws of thought. Why? And the concept of nothing is always relative to some positive concept of being, yet which is positive and which is negative depends on how you see it, on what your purpose is, on the will. You might, after all, be looking for an example of something negative in order to make a point about negation, about logic. Perfect holiness = denial of the will = suspension of the world = having a sense of a nothingness in which being can be lost. Philosophy can express this only negatively. We might talk about ecstasy, union with God, etc., but such states cannot be counted as knowledge really, and cannot be communicated – they must be experienced first-hand.)

Schopenhauer’s ethics do not present a view from nowhere, as he seems to think. Instead they reflect his own pessimistic outlook. So argues Konstantin Kolenda in “Schopenhauer’s Ethics: A View from Nowhere,” in von der Luft pp. 247-256. If everyone’s direct experiences were consulted, neither pessimism nor optimism would win the day. (But does Schopenhauer really claim to be able to identify values objectively?)

Cf. Nietzsche Beyond Good and Evil §§55-56 on the nothing as a replacement for God in Schopenhauer.

Glock notes three problems with Schop’s ethics (see pp. 442-43): 1) they seem to require both denial of the will and altruistic willing in the form of compassion (see WWR vol. 2, chapters 47-49), 2) the denial of the will is itself an act of will, “will turning against itself” (WWR vol. I, p. 412), 3) the cosmic will, the blind force, the thing in itself, “is so quintessentially undesirable, it is difficult to see how the mystical experience of feeling at one with this will should provide a kind of moral salvation.”[9]

LW avoids all these problems by distinguishing, Glock says, between good and bad willing (see Notebooks 21, 24, and 29/7/16, and TLP 6.43).]

[1] Everyman edition of Schopenhauer’s WWR, §65, p. 224.

[2] Ibid., §66, p. 230.

[3] Ibid., pp. 230-31.

[4] Ibid., p. 232.

[5] Ibid., p. 233.

[6] Ibid., §71, p. 259.

[7] Ibid., pp. 259-60.

[8] Ibid., p. 260.

[9] Hans-Johann Glock “Schopenhauer and Wittgenstein: Language as Representation and Will,” in Christopher Janaway (ed.) The Cambridge Companion to Schopenhauer Cambridge: Cambridge University Press, 1999, pp. 422-458, pp. 442-43.

2007-12-03T11:02:00.000-08:00

6.42 Hence there can also be no propositions of ethics. Propositions can express nothing Higher.

Mustn't "Higher" here be taken as nonsense? There is at least an air of self-contradiction here.

2007-12-03T10:59:00.000-08:00

6.41 The sense of the world must lie outside of it. In the world everything is as it is and happens as it happens; there is no value in it – and if there were, then it [this value, that is] would be of no value.

If there is a value, which is of value, then it must lie outside all happening and being-so. Since all happening and being-so is accidental.

What makes it non-accidental cannot lie in the world, since otherwise this would again be accidental.

It must lie outside the world.

I’m very close to Ogden here, including the word ‘being-so’. This seems like intentional nonsense to me. Just the kind of Platonism, this time about value, that we see rejected a) throughout the Tractatus, and b) in recent dealings with such things as the law of causality. Contingent value is not what is wanted, so only a transcendent value will do. That is, only a nonsense will do. So nothing will do, in fact. Our desire is for something incoherent.

Stokhof (p. 239): “Neither the Tractatus nor the Notebooks contains any argument or reasoning to establish the existence of values or their absolute character. (Analogously, there is no argument for the absolute status of logic either.) In other words, the entire construction is based on a certain kind of experience.”

Wittgenstein might be thinking of Kant here. Cf. Groundwork of the Metaphysic of Morals in the chapter on the dignity of virtue (pp. 77-78 in the second edition, p. 102 in H. J. Paton’s translation, Harper Torchbooks, 1964): “Skill and diligence in work have a market price; wit, lively imagination, and humour have a fancy price; but fidelity to promises and kindness based on principle (not on instinct) have an intrinsic worth. In default of these, nature and art alike contain nothing to put in their place; for their worth consists, not in the advantage or profit they produce, but in the attitudes of mind—that is, in the maxims of the will—which are ready in this way to manifest themselves in action even if they are not favoured by success.” Attitudes of mind alone can have dignity, and these might show themselves in behavior, but they are certainly not identical with any particular kinds of behavior. Nor brain-states, etc.

2007-12-03T10:58:00.000-08:00

6.4 All propositions are of equal value.

Literally: All propositions are equivalent. But presumably he doesn’t mean that.

Black (p. 370) says that the value in every case is zero, since “nothing of value is expressed by any significant proposition (6.41c).”

2007-12-03T10:57:00.002-08:00

6.3751 It is impossible, that is, logically impossible, for, e.g., two colors to be at the same point in the field of vision, since this is excluded by the logical structure of color.

Let us consider how this contradiction presents itself in physics. Approximately thus: That a particle cannot have two velocities at the same time; meaning that it cannot be in two places at the same time; meaning that particles in different places at one time cannot be identical.

(It is clear that the logical product of two elementary propositions can be neither a tautology nor a contradiction. The expression that a point in the field of vision has two different colors at the same time is a contradiction.)

These are rules, then, of the ‘logics’ of physics and of color. These language-games have their own grammars, the later Wittgenstein would say.

2007-12-03T10:57:00.001-08:00

6.375 As there is only a logical necessity, so there is also only a logical impossibility.

Fair enough.

2007-12-03T10:56:00.000-08:00

6.374 Even if all that we wished happened, then this would still only, so to speak, be a gift of fate, since there is no logical connection between will and world that would guarantee this, and the assumed physical connection itself we could surely not in turn will.

I.e. we might want it, but we couldn’t bring about by willing the power of our will to bring things about. So it must be a kind of accident if things in the world turn out how I want them to be, even in cases such as my leg getting scratched when I want to (and therefore do) scratch it. Something wrong here? See Anscombe, e.g., on causation in her essay on the reality of the past. If something is wrong, did Wittgenstein know it?

2007-12-03T10:53:00.000-08:00

6.373 The world is independent of my will.

Schopenhauer on the will: “My philosophy … is the only one that grants to morality its complete and entire rights; for only if the true nature of man is his will, consequently only if he is, in the strictest sense, his own work, are his deeds actually entirely his and attributable to him. On the other hand, as soon as he has another origin, or is the work of a being different from himself, all his guilt falls back on to this origin or originator”[1]

The being of matter is its acting. For it, reality is actuality or having effects.

The will is not a phenomenon, so it can never be a cause. The will does not cause actions. The will (noumenon) is the body (phenomenon), so acts of the body are acts of the will. The relation is one of identity, not cause and effect. Cf. TLP 5.631.

Will is a very tricky notion for Schopenhauer. All idea, all object, is phenomenon, “but the will alone is thing-in-itself.”[2]

“Now, if we are to think as an object this thing-in-itself (we will keep the Kantian term as a standing phrase) – which, as such will never be object, because all object has in its turn already become its mere manifestation, and is no longer itself – we must borrow for it the name and concept of an object …”[3] (This looks like a bad idea, similar also to Frege’s talk of concepts. Magee says, on p. 140, that Schopenhauer was aware of a difficulty here, discusses it at length, and decides only “with some misgiving” to give it a name: will. See Magee pp. 140-144. But note, Magee thinks the problem would be solved if only Schopenhauer gave the noumenon a less misleading name, such as force or energy.)

“The will as a thing in itself is totally different from its phenomenon, and entirely free from all the forms of the phenomenal.”[4] Hence it is independent of time, space, and causality. Plurality cannot apply to it, since this concept belongs to the phenomenal, to the realm of time and space. (But surely unity cannot apply to it either, and it is not even an object in the first place.)

“I wish that by a clear exposition it had been possible for me to dispel the obscurity which clings to the subject of these thoughts; but I see very well that the reader’s own reflection on the matter must come to my aid if I am ever to be fully and correctly understood.”[5]

Anscombe sees the independence of the will and the world here and in 6.374 as undesirable consequences of the picture theory and the theses about modality that it implies. See Anscombe pp. 80-81.

[1] WWR v. 2, pp. 589-590.

[2] Everyman edition of WWR, p. 42.

[3] Ibid., p. 42, §22.

[4] Ibid., p. 44, §23.

[5] Ibid., p. 72, §27.

2007-12-03T10:51:00.000-08:00

6.372 Thus they stop at laws of nature as at something sacrosanct, as the ancients stopped at God or fate.

And indeed they are both right, and wrong. The ancients are certainly clearer in so far as they recognize a clear conclusion, whereas in the new system it is supposed to seem as if everything were explained.

Are the moderns being said to be right within their system? Wrong to think it the only possible one? I'm not quite sure about this. Is it perhaps this: the moderns are right that it is not God or fate that explains everything, but wrong to think that everything can be explained?

2007-12-03T10:50:00.000-08:00

6.371 At the root of the whole modern worldview [Weltanschauung] lies the mistaken view [or: illusion] that the so-called laws of nature are the explanation of natural phenomena.

Are they then no explanation, or simply not the explanation? Worthless, or merely not absolute? What is wrong with “It always does that” as an explanation, if it satisfies the inquirer and is true? Is this an attack on science, or on scientism?

2007-12-03T10:49:00.000-08:00

6.37 There is no force such as to necessitate one thing’s happening on the strength of another thing’s having happened. There is only a logical necessity.

A somewhat loose translation. Cf. the others. The point is that the only necessity is logical necessity. But what then does ‘necessity’ mean? Is this a denial of physical laws of the form ‘If x then y [must happen]’?

Anscombe (see p. 80) says that this view about necessity is a direct consequence of the picture theory, and seems to think that it has nothing else to be said for it.

2007-12-03T10:48:00.000-08:00

6.36311 That the sun will rise tomorrow is an hypothesis; and that means: we do not know whether it will rise.

Cf. Wittgenstein’s later remark (in CV?) about how we might see the earth and sun from space and see that the sun will rise tomorrow. Since we don’t occupy such a vantage point, we don’t know if it will rise. But this is as much a fact about us as it is about the workings of the universe. The regularity of the laws of nature is not an hypothesis, is it?

2007-12-03T10:47:00.002-08:00

6.3631 This process though has no logical, but only a psychological grounding.

It is clear that there exists no ground for believing that the simplest case will also be the actual one that comes to be.

But then why prefer one physics to another? Psychology again, presumably.

2007-12-03T10:47:00.001-08:00

6.363 The process of induction consists in our assuming the simplest law that can be brought into unison with our experiences.

OK. Black (p. 365) says that this resumes the argument of 6.31, but is not consistent with it.

2007-12-03T10:46:00.001-08:00

6.362 What can be described can also take place, and what is supposed to be excluded by the law of causality cannot even be described.

Can take place in what sense? A logical one? The law of causality gives the form of physics, but is not meant merely to describe one possible kind of physics. It is meant, after all, to be a law. So there can be laws of this kind, there can be physics as we know it, but such a general law cannot be part of physics.

2007-12-03T10:42:00.000-08:00

6.36111 The Kantian problem of the right and left hand, that one cannot make cover each other, exists already in a plane, indeed in one-dimensional space, where the two congruent figures a and b also cannot be made to cover each other without moving them outside this space:

-----o——x-----x——o

a b

Right and left hand are actually completely congruent. And the fact that one cannot make one cover the other has nothing to do with it.

A right-hand glove could be put on the left hand if one could turn it around in four-dimensional space.

This problem is discussed by Kant in the Prolegomena. Schopenhauer refers to it twice in the Fourfold Root, once on p. 40 and on p. 194. His claim is that the difference between a left glove and a right glove can only be seen, not explained from concepts alone. That is, it cannot “be made intelligible except by means of intuition” (p. 194). The idea is that space is thereby shown to be an a priori form of intuition, since such differences in space must be intuited.

Is Wittgenstein’s last sentence a joke, or a real solution? My version of the figure is based on Letters to Ogden p. 61, and is different from the one in the other translations.

Henk Visser in “Wittgenstein’s Debt to Mach’s Popular Scientific Lectures” Mind (1982) Vol. VCI, pp. 102-105, says that what Wittgenstein says about Kant is conspicuously similar to what Mach says on the same issue, and Mach in turn credited Möbius as the source of the idea.

Black (p. 363) says that according to Kant things such as left and right hands or gloves can be “exactly alike in all spatial respects” and yet do not fit the same space, i.e. they are different. In intuition we get the difference, but the Understanding cannot (according to Kant) grasp it. Black (pp. 363-4):

"Kant used the argument several times—and to prove opposite conclusions. It was omitted from the second edition of the Critique—because, according to Kemp Smith, Kant had realized it was based ‘upon a false view of the understanding’ (op. cit. p. 165).

"W. says that the impossibility of making counterparts fill the same space (at least without entry into a higher dimension) leaves their congruence unchallenged. But Kant would readily have agreed: W. does nothing to explain how the congruent counterparts can be numerically distinct, which was Kant’s puzzle. On the face of it, the possibility of non-identical counterparts does not square with 6.3611 (3)—unless we take W. to be suggesting that the counterparts must have different causal antecedents by which alone they can be distinguished? (And this is now close to Kant’s conclusion.)"

2007-12-03T10:41:00.000-08:00

6.3611 We cannot compare any process with the “passage of time” – there is no such thing – but rather only with another process (perhaps with the working of the chronometer).

Hence the description of a temporal process is only possible if we rely on another process.

Exactly the same kind of thing goes for space. Where one, e.g., says that neither of two events (that are mutually exclusive) can occur, because no reason exists why the one rather than the other should occur, there it is really a matter of one not being at all able to describe one of the two events without some asymmetry existing. And if there is such an asymmetry, then we can understand this as the reason for the occurrence of the one and the non-occurrence of the other.

There is no such thing as the passage of time? Or there is no such thing as comparing a process with the passage of time? The latter sounds [even] more plausible. This all sounds like a kind of idealism. A pragmatic kind. Nordmann criticizes Wittgenstein for being “caught in the present” in the Tractatus on pp. 128-133. But, of course, it is at least possible that the idea that the world is all that is (present tense) the case is meant to be overcome and discarded. Indeed, Nordmann regards the book as being written in the subjunctive mood. It is, he thinks, a kind of reductio.

2007-12-03T10:28:00.000-08:00

6.361 In Hertz’s way of speaking, one could say: Only regular [law-like, lawful] combinations [connections] are thinkable.

This net rules out lawlessness or chance in nature. Pears & McGuinness have “subject to law” instead of “regular.” Ogden has “uniform” even though Wittgenstein said this was wrong and told him to look up the English translation of Hertz (Letters to Ogden p. 35). I have not found the relevant passage in Hertz yet.

Black (p. 362) says the allusion to “Hertz’s terminology” is obscure. He suggests (pp. 362-3) that Wittgenstein might have had in mind something like this passage from Hertz’s Principles § 109: “There exists a connexion between a series of material points when from a knowledge of some of the components of the displacements of these points we are able to state something as to the remaining components.”

2007-11-30T11:23:00.001-08:00

6.36 If there were a law of causality, then it could read: “There are laws of nature.”

But of course one cannot say that: it shows itself.

So is there no such law? What about 6.321? Physics unapplied is quite formal, and empty. Perhaps that is the point. For “There are laws of nature” to be a law of physics would be utterly pointless (a pointless utterance). Instead, physics tells us various laws of nature. Without such action/application the “law” would be quite empty, lacking content (what laws of nature?). With it, it loses any point it might have.

Black (p. 362): “W. should probably be read here as denying the significance of any notion of ‘causality’ (cf. his denial of the ‘causal nexus’ at 5.136). He might have agreed with other writers on the philosophy of science that the laymen’s notion of ‘cause’ comes to be superseded by a notion of ‘law’, adding a caveat about the latter being a formal notion.”

2007-11-30T11:22:00.000-08:00

6.35 Although the spots in our picture are geometrical figures, geometry can still obviously say absolutely nothing about their actual form and position. But the net is purely geometrical, all its properties can be given a priori.

Laws, like the principle of sufficient reason, etc., deal with the net, not with what the net describes.

So geometry can be used to describe the spots, but there is no a priori knowing their shape or position. The net can be described a priori, though, so it belongs to logic. So what is the relation between a particular net and all possible nets?

Black (p. 361) says that “purely geometrical” is a reference to pure, as opposed to applied, geometry.

2007-11-30T11:21:00.000-08:00

6.3432 We must not forget that the description of the world with mechanics is always completely general. In it there is never, e.g., talk of particular material points, but rather always only about any such points.

Pears & McGuinness have “point-masses” for “material points.” I should check this.

Black (p. 361) says that this should be read in connection with 6.35.

2007-11-30T11:17:00.002-08:00

6.3431 Through the whole logical apparatus, throughout the physical laws still speak of the objects of the world.

Huh? Maybe I should leave “throughout” out, or else move it to the very end. Wittgenstein (Letters to Ogden p. 35) says the first “through” means the same as in “I speak through a tube.” So Pears and McGuinness seem quite wrong this time. (They have "The laws of physics, with all their logical apparatus, still speak, however indirectly, about the objects of the world.") How about: "Via the whole logical apparatus, the physical laws still speak throughout of the objects of the world."?

Black (p. 361) suggests that this comment “Can be read as a summary comment on 6.342 (2).”

2007-11-30T11:17:00.001-08:00

6.343 Mechanics is an attempt to construct according to one plan all true propositions that we need for a description of the world.

OK, but what is logic?

2007-11-30T11:16:00.000-08:00

6.342 And now we see the relative position of logic and mechanics. (One could also have a net consisting of different kinds of shapes, such as triangles and hexagons.) It says nothing about a picture, such as the one mentioned above, that it can be described by a net of a given form. (Since this goes for every picture of this kind.) However it does characterize the picture that it can be completely described with a specific net of a specific fineness.

Thus too it says nothing about the world that it can be described with Newtonian mechanics; but [it does say something] that it can be described in that particular way in which indeed it is described. It also says something about the world that it can be described more simply with one mechanics than with another.

So there is no absolutely right kind of mechanics, but some are more useful than others, given the way the world is. And given, presumably, what kind of thing we find easy. But what then is the relative position of logic to mechanics? Logic seems unable to choose our mechanics for us. Here I follow Wittgenstein’s comments on the translation of the penultimate sentence on p. 50 of Letters to Ogden.

2007-11-30T11:14:00.002-08:00

6.341 Newtonian mechanics, e.g., brings the description of the world to a unified form. Let us think of a white surface with irregular black spots on it. Now we say: Whatever kind of picture these spots produce, I can always describe it as closely as you like by covering the spots with a suitably fine square netting and now say of every square that it is white or black. In this way, I will have brought the description of the spots to a unified form. This form is arbitrary, since I could have used with the same success a net with triangular or hexagonal holes. It is possible that the description would have been simpler with the help of a triangular net; meaning that we could have described the spots more closely with a bigger triangular net than with a finer square one (or vice versa), and so on. Different systems of world description correspond to different nets. Mechanics defines a form of world description by saying: All propositions of the description of the world must be obtained from a number of given propositions – the axioms of mechanics – in a given way. In this way it supplies the building stones for the construction of the scientific edifice and says: Whatever edifice you want to build, you must somehow put together with these and only these building stones.

(With the system of mechanics, one must be able to write down any arbitrary proposition of physics, as one can [write down] any arbitrary number with the number system.)

A priori axioms are normative, then, and might make our lives easier or harder, but they cannot make them possible or impossible. Nor can they tell us anything synthetic.

2007-11-30T11:14:00.001-08:00

6.34 All these propositions, like the principle of sufficient reason, of continuity in nature, of least expenditure in nature, etc. etc., all these are a priori insights concerning the possible fashioning of propositions of science.

So a feeling that there must be a certain kind of law is the recognition that there is room in the system for such a law, a law of that (so far fairly vague) type?

Black (p. 346) says that in a letter to Russell (129, 2) Wittgenstein treats “principle of sufficient reason” and “law of causation” as synonymous.

2007-11-30T11:13:00.000-08:00

6.33 We do not believe a priori in a law of conservation, but rather we know a priori the possibility of a logical form.

Black (p. 346) points out that “if form is itself a possibility, the phrase [i.e. “the possibility of a logical form”] shows redundancy.”

2007-11-30T11:12:00.000-08:00

6.3211 One indeed also had a presentiment that there must be a “law of least action”, before one knew precisely how it went. (Here, as ever, the a priori certain proves to be something purely logical.)

So what was a priori certain here? The presentiment? Why must there be such a law?

2007-11-30T11:11:00.000-08:00

6.321 “Law of causality” – that is a generic name. And as we say there are minimum laws in mechanics, – such as that of the least action – so there are in physics laws of causality, laws of the causality form.

Laws like the one discussed in 6.32, presumably.

Black (p. 346) quotes Mach (Mechanics, p. 460) saying that: “Maupertuis really had no principle, properly speaking, but only a vague formula, which was forced to do duty as the expression of different familiar phenomena not really brought under one conception.” On p. 551 Mach adds that Euler changed the principle (i.e. the law of least action) “into something new and really serviceable.”

2007-11-30T11:10:00.000-08:00

6.32 The law of causality is not a law, but rather the form of a law.

Mounce (see pp. 75-76) says that the law of causality is the law of sufficient reason, i.e. the idea that everything has a cause. This, as he reads Wittgenstein, is not a law because it tells us nothing about the world. So far as two events can be distinguished, they must have some difference, and this difference can always be regarded as causally relevant. Saying “everything has a cause” then is not really reporting on a contingent generality but insisting a priori that every event will be interpreted as caused, as it can be.

Black (p. 345) points out that at 2.033 and 2.151 Wittgenstein links form with possibility. If he is talking about the possibility of a certain kind of empirical generalization then, Black thinks, this fits with 6.321-6.34, but not with 6.36.

My original comment: What is the law of causality? No event without a cause? But then what is an event? How are we to divide time up into events? Perhaps this is why this is not really a law. It says, in effect, no x without a y. And that is the form of a law, i.e., as Russell says in his footnote to the Ogden translation, “not the form of one particular law, but of any law of a certain sort.” I take it that “B. R.” here refers to Russell.

Black (p. 345) says that by 6.36 “the ‘law of causality’ has been emptied of any determinate meaning.”

2007-11-30T11:09:00.000-08:00

6.31 The so-called law of induction cannot in any event be a logical law, since it is clearly a meaningful [sinnvoller] proposition. – And therefore it also cannot be an a priori law.

So it’s really no law at all. But, as Black (p. 345) says, “Which ‘law of induction’ did W. have in mind? Perhaps, with echoes of Aristotle, one allegedly permitting an inference from ‘Some A’s are B’ to ‘All A’s are B’?”

2007-11-30T11:08:00.000-08:00

6.3 The exploration of logic means the exploration of all regularity [lawfulness]. And outside logic everything is accidental.

Logic deals with the necessary, the a priori. Outside logic everything else is a posteriori and contingent. So have we had somewhere already proof that Kant was wrong? The synthetic a priori seems to be being rejected here. On what grounds?

2007-11-30T11:04:00.000-08:00

6.241 So the proof of the proposition 2 x 2 = 4 runs thus:

(^v)^µ'x=^v×µ'x Def.
^2×2'x = (²)²'x = (²)¹⁺¹'x = ²'²'x = ¹⁺¹'¹⁺¹'x
= (')'(')'x = ''''x = ^1+1+1+1'x = ⁴'x.

What’s going on here? I thought there was no proof in mathematics? See 6.2321.

Black (p. 343): “W.’s proposed ‘proof’ is eccentric and would not satisfy contemporary standards of mathematical rigour. It may be pointed out, for instance, that he has provided no rules for the use of variable superscripts with the lamda symbol.”

2007-11-29T09:00:00.001-08:00

6.24 The method of mathematics, to get to its equations, is the method of substitution.

Since equations express the substitutability of two expressions and we proceed from a number of equations to new equations by substituting other expressions in accordance with the equations.

2007-11-29T08:58:00.002-08:00

6.2341 The essence of the mathematical method is to work with equations. On this method depends precisely the fact that every proposition of mathematics must go without saying.

OK. The first sentence here would be controversial, I imagine, but it isn't really a new idea at this point in the Tractatus.

2007-11-29T08:58:00.001-08:00

6.234 Mathematics is a method of logic.

Cf. 6.2

2007-11-29T08:56:00.000-08:00

6.2331 The process of calculation brings about precisely this intuition.

Calculation is not an experiment.

The result cannot be a surprise (even if it isn't what you expected).

2007-11-28T13:36:00.001-08:00

6.233 The question whether one needs intuition to solve mathematical problems must be answered by the fact that language itself here supplies the necessary intuition.

No, in other words.

2007-11-28T13:35:00.000-08:00

6.2323 An equation marks only the standpoint from which I regard the two expressions, namely the standpoint of their equality of meaning.

Black (p. 342) says “identity” would be better than “equation” here.

2007-11-28T13:34:00.000-08:00

6.2322 The identity of the meaning [Bedeutung] of two expressions cannot be asserted [maintained, contended]. Because in order to be able to assert something about their meaning, I must be acquainted with their meaning: and in being acquainted with their meaning, I know whether the meaning is the same or different.

So in some sense I cannot say [“maintain” is another possible translation of behaupten] “The Morning Star” refers to the same thing [has the same Bedeutung] as “the Evening Star.” That is, I cannot hold or prove that this is a fact. “Facts” about expressions are tautologies, matters of definition, not contentions.

2007-11-28T13:33:00.000-08:00

6.2321 And, that the propositions of mathematics can be proved, means indeed nothing other than that their correctness can be seen without it being necessary to compare what they express with the objects in order to determine its correctness.

Pears & McGuinness are good here. So mathematical proof is a priori, like “proof” in logic.

2007-11-28T13:29:00.002-08:00

6.232 Frege says the two expressions have the same meaning [Bedeutung] but different senses [Sinn].

But the essence of an equation is that it is not necessary in order to show that the two expressions that the equals sign combines have the same meaning [Bedeutung], since this can be seen from the two expressions themselves.

The distinction between meaning and sense (and hence between senselessness and nonsense?) breaks down, because, roughly speaking at least, meaning is use. The notion of sense is seemingly treated here as unnecessary or irrelevant. If 1+1 = (1+1) then this should be manifest in all sorts of ways within mathematics. We do not need to be told it, as if it were an axiom or first principle. To know what (1+1) means is to know, among other things perhaps, that it means (is substitutable for) 1+1. The substitutability of these expressions for each other is not an additional fact, additional to the meaning of each.

2007-11-28T13:29:00.001-08:00

6.231 It is a property of assertion that one can understand it as double negation.

It is a property of “1+1+1+1” that one can understand it as “(1+1) = (1+1)”.

Assertion is hardly what I would call an expression, although “1+1+1+1” is. He means something like signs/symbols in use, it seems.

2007-11-28T13:28:00.000-08:00

6.23 If two expressions are combined with the identity sign, this means that they are substitutable for one another. But whether this is the case must be evident in the two expressions themselves.

It is a characteristic of the logical form of two expressions that they are substitutable for one another.

What is meant by an expression here? Is it evident in the expression “4” that it is identical with the expression “2 = 2”? Perhaps “expression” means “expression rightly and fully understood”.

2007-11-28T13:26:00.000-08:00

6.22 The logic of the world, which the propositions of logic show in tautologies, mathematics shows in equations.

So equations are at least like tautologies. And the logic of the world is the logic of language, since their limits are the same, making them co-extensive. Looks like linguistic idealism, doesn’t it?

White (pp. 109-110): "To understand what Wittgenstein means by ‘equations’, we need to refer back to 4.241-4.242. There they are described as only ‘representational devices’ and that is what we need to understand if we are to interpret the claim that they are ‘pseudo-propositions’.”

Black (p. 341): “It is hard to see how what is shown in equations can be assimilated in this way to what is shown in tautologies.”

2007-11-28T13:25:00.000-08:00

6.211 In life it is indeed never the mathematical proposition that we need, but rather we use mathematical propositions only in order to infer from propositions that do not belong to mathematics to others that likewise do not belong to mathematics.

(In philosophy the question “To what end do we really use this word, that proposition” leads time and again to valuable insights.)

So, for instance, “I have to give Jo this five-dollar bill” is not part of mathematics, but we might use mathematics to reach this practical conclusion from “Jo gave me a ten-dollar bill for this five-dollar soup and focaccia.” “Meaning is use” here as a guiding principle.

2007-11-28T13:23:00.000-08:00

6.21 A proposition of mathematics expresses no thoughts.

Because it is not a science, but something of logic. An equation is a kind of tautology after all. He appears to be saying that mathematics belongs to logic, but not that it is based on or derived from logic. There is no rank in logic.

2007-11-28T09:43:00.002-08:00

6.2 Mathematics is a logical method.

The propositions of mathematics are equations, hence pseudo-propositions.

Black (p. 341): “In discussing the proposed view of mathematics, Ramsey says: ‘this is obviously a ridiculously narrow view of mathematics, and confines it to simple arithmetic’ (Foundations, p. 17). One difficulty raised by him is the presence in mathematics of inequalities (op. cit. p. 282). But the more serious difficulty, he holds, is that of accounting, on W.’s view, for the applicability of arithmetic (op. cit. p. 19).”

2007-11-28T09:43:00.001-08:00

6.13 Logic is not a theory [doctrine, science], but rather a mirror-image of the world.

Logic is transcendental.

Does this mean: It is not hypothetical in any way, but a direct reflection of how the world is? And transcendental in what sense?

Black (p. 340) says it means beyond experience or a priori.

2007-11-28T09:41:00.002-08:00

6.1271 It is clear that the number of “logical basic laws” is arbitrary, since one could indeed derive logic from a single basic law, by simply, e.g., forming the logical product of Frege’s basic laws [Grundgesetzen]. (Frege would perhaps say that this basic law is now no longer immediately self-evident. But it is remarkable that so exact a thinker as Frege appealed to the degree of self-evidence as the criterion of a logical proposition.)

Yes, what is self-evident in this sense, or degree of self-evidence at any rate, is a psychological matter, not a logical one. The anti-psychologism Frege, of all people, should have seen that.

2007-11-28T09:41:00.001-08:00

6.127 All propositions of logic have equal rights [i.e. (legal) status], there are among them no essential basic laws or derived propositions.

Every tautology shows by itself that it is a tautology.

I like the more literal translation of “equal rights”. It is all flat, all tautology.

2007-11-28T09:40:00.000-08:00

6.1265 One can always conceive of logic in such a way that every proposition is its own proof.

Propositions of logic are rules that say that propositions of that form, i.e. their own form, are legitimate or correct. So they are self-validating. Or so we can understand them.

White (p. 108): “We may consider 6.1265 to be half truth. If it only means that a truth of logic contains within itself all the information necessary to settle its truth value, without using an idea of its derivability from other propositions as a criterion of its being a truth of logic, that can be allowed to stand. If, however, as is natural, we take ‘proof’ to be an epistemological concept, implying that we can always tell whether or not a proposition is logically true by ‘calculating the logical properties of the symbol’ (6.126), we now know that to be false.”

2007-11-28T09:39:00.000-08:00

6.1264 A meaningful proposition states something, and its proof shows that it is so; in logic every proposition is the form of a proof.

Every proposition of logic is a modus ponens presented in signs. (And one cannot express the modus ponens with a proposition.)

Modus ponens is argument of the form: If p then q, p, therefore q. Why is all logic just this in different forms? Why can’t this be expressed in a proposition? Perhaps because it is the general form that matters. What is p, after all, but a variable? Replace it with something specific and the general form goes away. But without such replacement, we don’t have a sinnvollen proposition.

2007-11-28T09:38:00.000-08:00

6.1263 It would indeed be all too remarkable if one could prove a meaningful [sinnvollen] proposition logically from another, and a logical proposition too. It is clear in advance that the logical proof of a meaningful proposition and proof in logic must be two completely different things.

Logical propositions are not sinnvollen, of course. Proof in logic must not be proof of sinnvollen propositions. But can there be logical proof of such propositions? He doesn’t say. If there is, though, it must something other than “proof” in logic.

2007-11-28T09:37:00.000-08:00

6.1262 Proof in logic is only a mechanical means to make perception of a tautology easier in cases where it is complicated.

Hence the quotation marks earlier (6.126) around “proof”. Proof is relative to a system. Proof of guilt in law is proof of guilt beyond a reasonable doubt. Proof in mathematics depends on the laws/rules in play. For Frege, proof means logical proof, i.e. demonstration that a sentence/formula is equivalent to an axiom or derivable from some other part of the system. Derivable, presumably, according to the rules of derivation in the system. But presumably something, whether axioms or processes of derivation, must be simply given or accepted as intuitively obvious. Experiments are particular. Manipulation of actual rods might be an experiment in physics, but there are no experiments in mathematics. If one rod breaks, this can prove nothing mathematical. Similarly if the paper tears when drawing a diagram. A diagram might prove something in geometry, but only if taken a certain way, so that physical features of the diagram are ignored, for instance.

McManus p. 85: “ontological distinctions are now [with the right mechanical means, i.e. Begriffsschrift] shown simply in that ‘they’ are shown up for what they are: namely, the confused product of word-play.”

2007-11-28T09:36:00.001-08:00

6.1261 In logic progress and result are equivalent. (Hence no surprises.)

It just is a calculus, not a machine or mechanism. Nothing is produced. There is no cause and effect. Only the application of rules (in accordance, can I say?, with themselves).

2007-11-28T09:32:00.000-08:00

6.126 One can figure out whether a proposition belongs to logic by figuring out the logical properties of symbols.

And this is what we do when we “prove” a logical proposition. Because without concerning ourselves with a sense [Sinn] and a meaning [Bedeutung] we construct the logical proposition from others according to mere rules for signs.

The proof of a logical proposition consists in our being able to establish it from other logical propositions with successive applications of certain operations, which produce ever more tautologies from the first one. (In fact from a tautology only tautologies follow.)

Of course this way of showing that its propositions are tautologies is thoroughly inessential to logic. Because the propositions, from which the proof starts out, must show, indeed without proof, that they are tautologies.

Logic is, or belongs to, a system that cannot justify itself.

Frascolla (p. 141): “If we take the expression ‘logical proof’ in its more general meaning, and if we call ‘mechanical’ any procedure of calculation, understood as a set of effective instructions for manipulating symbols, then in the light of Church’s Theorem of Undecidability of the first-order predicative calculus, Wittgenstein’s thesis is simply false, since no mechanical procedure can exist which enables us to decide, given any arbitrary formula of the first-order predicative calculus (which is included in the calculus of Principia Mathematica), whether it is a tautology or not.”

2007-11-28T09:31:00.000-08:00

6.1251 Hence there can also never be surprises in logic.

OK. Nothing contingent, that is. We cannot guarantee that someone won't feel surprised at something in logic.

2007-11-28T09:29:00.000-08:00

6.125 It is possible, in fact also according to the old conception of logic, to give in advance a description of all “true” logical propositions.

It’s all a priori, in other words.

2007-11-27T10:05:00.000-08:00

6.124 Logical propositions describe the frame of the world, or rather they present it. They “deal” with nothing. They presuppose that names have meaning and elementary propositions sense: And this is their connection with the world. It is clear that it must show [anzeigen] something about the world that certain combinations of symbols – which essentially have a specific character – are tautologies. Herein lies the decisive thing. We said that much in the symbols that we use is arbitrary, much not. In logic only this latter expresses anything: That means however that in logic we do not express what we want with the aid of signs, but rather in logic the nature of the constitutionally necessary signs exhausts itself: If we are acquainted with the logical syntax of some sign language, then all the propositions of logic are already given.

I originally had “physically necessary” for naturnotwendigen because that is the only meaning given by my dictionary for this word, but I think "constitutionally necessary" might be a better translation. Ogden has “essentially necessary” and P&McG have “absolutely necessary.” Black (p. 336) says that the sense of the expression “is that the signs needed are of a nature that is necessitated.” I think Ogden’s translation might be best, but when in doubt I prefer to be literal.

The rest I think makes sense and sounds right, apart from the slightly worrying (because it still is not wholly clear what these are) talk of names and elementary propositions, but I assume these now mean basically just “words” and “propositions” or “sentences” (like p and ~p) that are combined in logic in various ways. The really worrying thing is the claim that the existence of tautologies must show something about the world. What does it, could it, show except itself? Well, Wittgenstein does not claim that it shows anything more than this.

Black (p. 331) points out that the image of scaffolding (Gerüst) occurs also at 3.42 and 4.023.

2007-11-27T10:04:00.000-08:00

6.1233 A world can be conceived in which the axiom of reducibility does not hold. But it is clear that logic has nothing to do with the question whether our world really is thus or not.

What grounds did Russell have for calling the Axiom of Reducibility a principle of logic? The axiom in question says that any higher-order property or proposition can be reduced to an equivalent first-order one. It means that the same class is determined by two propositional functions that are equivalent.[1] Every propositional function is thus logically equivalent to a predicative function. The axiom is introduced because without it the ramified theory of types makes certain mathematical proofs impossible. This kind of thing belongs to logic, in Russell’s view, because it is necessary in order to overcome logical, not just mathematical, paradoxes, e.g. about the class of classes not members of themselves as well as paradoxes about infinity. Ramsey and Wittgenstein showed that the axiom was not necessary.

[1] See p. 299 of the Cambridge Companion to Russell.

2007-11-27T10:03:00.000-08:00

6.1232 One could call logical general validity essential, in contrast to accidental general validity, for instance of the proposition “All men are mortal.” Propositions like Russell’s “axiom of reducibility” are not logical propositions, and this explains our feeling that, if true, they could be true only by a propitious accident.

So Russell imports alleged facts into logic. Tut tut.

2007-11-27T10:02:00.000-08:00

6.1231 The mark of a logical proposition is not its general validity.

To be general indeed means only: to happen to be valid for all things. An ungeneralized proposition can indeed be just as tautologous as a generalized one.

Cf. 6.031 on kinds of generality. Is there a contradiction here? Or in 6.1231 is "general" being used in a particular sense, distinct from, say, necessary or a priori?

2007-11-27T08:22:00.000-08:00

6.123 It is clear: The logical laws must not themselves be subject to further logical laws.

(There is not, as Russell thought, a unique law of contradiction for each “type”, rather one is enough, since it is not to be applied to itself.)

Black (p. 326) quotes Russell’s Principia vol. 1, p. 127 “Negation and disjunction and their derivatives must have a different meaning when applied to elementary propositions from that which they have when applied to such propositions as (x).φx or (Ex).φx” and Logic and Knowledge p. 63 “The first difficulty that confronts us [after adopting the “vicious circle principle”] is as to the fundamental principles of logic known under the quaint name of “laws of thought”. “All propositions are either true or false”, for example, has become meaningless. If it were significant, it would be a proposition, and would come under its own scope.”

On Wittgenstein’s view, apparently, there is only logic, rules for the combination of propositions into tautologies, contradictions, and other propositions. There is no logic of logic, rules for the application of the rules.

2007-11-27T08:21:00.000-08:00

6.1224 It becomes clear now also why logic has been called the theory of forms and of inference.

Who calls logic the theory of forms and inference?

2007-11-27T08:20:00.000-08:00

6.1223 Now it becomes clear why it has often been felt as if “logical truths” were “postulated” by us: We can indeed [nämlich] postulate them in so far as we can postulate an adequate notation.

Why “postulated by” instead of “exacted from”? Black (p. 325) suggests ‘require’ or ‘demand.’ Anyway, the sense is clear enough. The form of logical propositions depends solely on the notation we use, which is invented by us. Which is why logic can seem to be invented, although of course it has a kind of (non-metaphysical) independence.

2007-11-27T08:19:00.000-08:00

6.1222 This throws light on the question why logical propositions cannot be confirmed by experience, any more than [just as little as] they can be confuted by experience. Not only must a proposition of logic be capable of confutation by no possible experience, but it must also not be confirmable by any such thing.

Because a proposition of logic is, as such, a mere combination of signs.

2007-11-27T08:17:00.000-08:00

6.1221 If, e.g., two propositions “p” and “q” in the combination “p → q” give a tautology, then it is clear that q follows from p.

That, e.g., “q” follows from “p → q . p”, we see from these two propositions themselves, but we can also see it by combining them into “p → q . p:→ : q” and now showing that this is a tautology.

2007-11-20T09:40:00.000-08:00

6.122 From which it follows that we can go on without logical propositions, since we can perceive in an appropriate notation the formal properties of propositions with a simple look at these propositions.

What would such a notation be?

Black (p. 324) suggests ‘corresponding’ for entsprechend where P&McG have ‘suitable’ and I have ‘appropriate.’ He adds that “In a sense, every notation is suitable.” On p. 325 he says that “in a sense, every notation is ‘adequate’ to express whatever meaning it expresses.”

White (p. 105): “Wittgenstein goes badly astray in his development of this train of thought [i.e. that found in the 6.1s], and subsequent developments in logic [Alonzo Church, 1936] have shown that what he says at 6.122 is demonstrably false.” On p. 107 he writes: “What Wittgenstein overlooks is that once he allows the possibility of there being infinitely many elementary propositions, he has to allow the possibility of quantification over infinite domains. If we then have propositions involving multiple quantifiers ranging over infinite domains, then even the most perspicuous notation may not be able to display the information that a given proposition is a tautology in a form that is surveyable by us. So that even if we continue to say that a tautology shows that it is such, it may not do so in a form that is recognizable by us: we may simply lack any method for extracting the fact that it is a tautology. This means that in this use of the concept of ‘showing’ at least, ‘showing’ cannot be treated as a straightforward epistemological concept.”

2007-11-20T09:38:00.000-08:00

6.121 The propositions of logic demonstrate the logical properties of propositions, by combining them into propositions that say nothing [nichtssagenden Sätzen].

One could also call this method a null method. In a logical proposition, propositions are brought into equilibrium with one another and the state of equilibrium then shows how these propositions must be logically constituted.

By combining propositions into tautologies and contradictions, we show how tautologies and contradictions are made, and that such combinations do indeed produce nothing but tautologies and contradictions. Such is philosophy. Dictionary.com defines a null method thus: Zero method (Physics), a method of comparing, or measuring, forces, electric currents, etc., by so opposing them that the pointer of an indicating apparatus, or the needle of a galvanometer, remains at, or is brought to, zero, as contrasted with methods in which the deflection is observed directly; -- called also null method. The Letters to Ogden, p. 34, confirm that this is the sense Wittgenstein has in mind here.

2007-11-20T09:22:00.002-08:00

6.1203 In order to perceive a tautology as such, one can, in cases in which no sign of generality occurs in the tautology, avail oneself of the following method: I write “TpF”, “TqF”, “TrF”, etc. in stead of “p”, “q”, “r”, etc. I express the truth-combinations with brackets, e.g.:

The coordination of the truth or falsity of the whole proposition and the truth-combinations of the truth-arguments with lines in the following way:

T (T/F)->F" shapes="_x0000_i1026" height="96" width="128">

This sign, e.g., would therefore present the proposition p → q. Now I will investigate on the strength of that whether, e.g., the proposition ~(p. ~p) (the Law of Contradiction) is a tautology. The form “~ξ” gets written in our notation as;

T, (T)->F" shapes="_x0000_i1029" height="64" width="64">T, (T)->F" shapes="_x0000_i1029" height="64" width="64">T, (T)->F" shapes="_x0000_i1029" height="64" width="64">

the form “ξ . η” thus:

F (T/T)->T" shapes="_x0000_i1032">

So the proposition ~(p. ~q) goes thus:

T, T/F->F" shapes="_x0000_i1033">T, T/F->F" shapes="_x0000_i1033">T, T/F->F" shapes="_x0000_i1033">

If we put here “p” instead of “q” and investigate the combination of the outermost T and F with the innermost, then we get the result that the truth of the whole proposition is coordinated with all the truth-combinations of its arguments, its falsity with none of the truth-combinations.

A somewhat complicated way of demonstrating an obvious truth, but I suppose it’s the demonstration that matters here. Or maybe the point is that this is all that logic can be/do.

2007-11-20T09:22:00.001-08:00

6.1202 It is clear that one could use contradictions instead of tautologies to the same end.

Yes it is.

2007-11-20T09:13:00.000-08:00

6.1201 That, e.g., the propositions “p” and “~p” in the combination “~(p. ~p)” give a tautology, shows that they contradict one another. That the propositions “p → q”, “p” and “q” combined with one another in the form “(p → q) . (p) :→: (q)” give a tautology, shows that q follows from p and p → q. That “(x) . fx :→: fa” is a tautology, shows that fa follows from (x) . fx, etc. etc.

I'm using the arrow for "if ... then."

2007-11-20T09:11:00.000-08:00

6.12 That the propositions of logic are tautologies shows the formal – logical – properties of language, of the world.

The fact that its parts connecting together just so gives a tautology characterizes the logic of its parts.

For propositions, connected in a specific way, to make a tautology, they must have specific structural properties. That they [do] make a tautology when so connected shows therefore that they [do] have these structural properties.

I translate bestimmte as ‘specific,’ where P&McG have ‘certain’ and Black (p. 321) suggests ‘determinate.’ ‘Definite’ might be good too.

What properties? It’s all grammar isn’t it, arbitrary? So are the formal properties of the world arbitrary too? Maybe. They are (only) formal, after all.

2007-11-20T09:08:00.000-08:00

6.113 It is the peculiar characteristic of logical propositions that one can perceive from the symbol alone that they are true, and this fact contains in itself the whole philosophy of logic. And thus it is also one of the most important facts, that the truth or falsehood of non-logical propositions cannot be perceived from the proposition alone.

Logic says nothing about the world, it is all (?) a matter of arbitrary conventions. Other propositions are of a wholly different kind and cannot be known a priori. Is this what he is saying? Is this the whole of the philosophy of logic, the whole message of the Tractatus?

Now, how can a tautology be true, given 4.06? Proops argues that he means ‘true’ “only in an honorary sense.” (p. 4, note 38). After all, at 6.125 he puts ‘true’ in scare quotes, and in his Notes to G. E. Moore he says that “logical propositions are neither true nor false” and refers to “what is called the truth of a logical proposition.” (Notebooks p. 109 and p. 108, quoted in Proops.)

2007-11-20T09:07:00.000-08:00

6.112 The right explanation of a logical proposition must give it a unique position among all propositions.

Because logical propositions are not the same kind of thing as other propositions.

2007-11-19T10:38:00.000-08:00

6.111 Theories that allow a proposition of logic to seem have content are always false. One could e.g. believe that the words “true” and “false” signify two properties among other properties, and then it would seem a remarkable fact that every proposition possesses one of these properties. This now seems [would then seem] to be anything but self-evident, just as little self-evident as the proposition “All roses are either yellow or red” would sound, even if it were true. Indeed, every proposition now takes on completely the character of a natural scientific proposition and this is a sure sign that it has been falsely understood.

Here again we have logic versus metaphysics, clearly stated for once.

Proops (p. 1) notes that here and in 6.112, 6.1231, and 6.13, Wittgenstein rejects the universalist conception of logic, according to which “logic is a theory of the most general features of reality,” (Proops, p. 1) which he found in Frege and Russell.

2007-11-19T10:37:00.002-08:00

6.11 The propositions of logic therefore say nothing. (They are analytical propositions.)

Black (pp. 319-320) notes that this is the only occurrence of the word analytischen in the Tractatus, and suggests that it probably does not mean “true by definition” or “true in virtue of the meanings of its component words” here, nor have its original, Kantian sense, but rather is here simply a synonym for “propositions that say nothing.”

2007-11-19T10:37:00.001-08:00

6.1 The propositions of logic are tautologies.

This implies, at least as Russell, e.g., uses the word ‘tautology’, that they are empty or insignificant. And that was the point of using that word, according to Burton Dreben and Juliet Floyd in “Tautology: How not to use a word,” Synthese 87 (1991), pp. 23-49.

2007-11-19T10:35:00.000-08:00

6.031 The theory of classes is completely superfluous in mathematics.

That the generality that we need in mathematics is not the accidental [contingent] kind hangs together with this.

Russell says, “the class of all couples will be the number 2, according to our definition. At the expense of a little oddity, this definition secures definiteness and indubitableness.” (Introduction to Mathematical Philosophy, p. 18) But then the number 2 depends on the existence of a class of couples, i.e. on the existence of couples. And the number 1000 depends on the existence of 1000 things. And so on. But Russell admits that “Logical propositions are such as can be known a priori, without study of the actual world,” and it is not logically necessary that even one thing exists, he says, let alone 1000, or, even worse, infinity. (ibid., p. 204)

2007-11-19T10:34:00.000-08:00

6.03 The general form of integers is: [0, ξ, ξ + 1].

OK, so that’s what a general form is/looks like.