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MR. WITTGENSTEIN'S Tractatus Logico-Phil- osophicus, whether or not it prove to give the ultimate truth on the matters with which it deals. Ludwig Wittgenstein, Tractatus Logico-Philosophicus, translated C. K. Ogden, London: Kegan Paul, Trench, Trubner & CO., New York: Harcourt. Wittgenstein's Tractatus: A Student's Edition Introduction This book aims to do two things: to provide a new and im- proved translation of Ludwig Wittgenstein's.


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In the PDF file, the proposition numbers are linked back and In rendering Mr Wittgenstein's Tractatus Logico-Philosophicus avail- able for. 5. Febr. MR. WITTGENSTEIN'S Tractatus Logico-Philosophicus, whether or not it prove to give the ultimate truth on the matters with which it deals. Mr Wittgenstein's Tractatus Logico-Philosophicus, whether or not it prove to give the ultimate truth on the matters with which it deals, certainly deserves, by its.

So it is not always obvious what is a name and what is a description. Logic is prior to every experience-- that something is so. In the Investigations, he thinks of logical form as being a kind of formalization of the rules of language and these arise out of its use; they do not underlie and guarantee its intelligibility. The emphasis is on logic, not epistemology. And here it is not a question of a coordination of a fact and an object, but rather of the coordination of facts by way of the coordination of their objects. Logical signs, as Wittgenstein in- dicates elsewhere, are not primitive signs.

William H. Brenner and John F. Other works are pointed to in the text that follows. But we should probably not read too much into the title, since it was not his idea originally and he seems to have accepted it slightly reluctantly, in the absence of any better ideas. See Monk p.

Indeed, I did not un- derstand it until I had myself independently discovered most of what it contained. One could put the whole sense of the book perhaps in these words: What can be said at all, can be said clearly; and whereof one cannot speak, thereof one must be silent. Be- cause in order to draw a limit to thinking, we would have to be able to think both sides of this limit we would thus have to be able to think what cannot be thought.

So the limit can only be drawn in language and what lies on the other side of the limit will simply be nonsense. There has been some disa- greement about this, but it is cleared up in Nordmann, p. Morris and Dodd p. What we have here is the careful replacement of a form of words that seems to try to do something that cannot be done. But there is a double paradox in this replacement. First, the inappropriate form of words is left on the page: And, secondly, the sup- posed improvement seems to be subject to the very fault that has been so carefully explained in connection with the first formula- tion.

We think for a moment that we have avoided paradox, but on reflection we realize that we are no better off. The point of this delay of self-refutation, we suggest, is to give us time to achieve acquaintance with the world as a limited whole; and the sustaining of this acquaintance is the mystical outlook.

Indeed what I have written here makes no particular claim to novelty; and therefore I give no sources, because it is all the same to me if what I have thought has already been thought by another before me. I will mention only that I owe a large part of the stimulus to my thoughts to the great works of Frege and to the work of my friend Mr.

Bertrand Russell. Perhaps Wittgens- tein was simply trying to encourage more people to read Frege. Like G. This, Proops thinks, is significant, because it was only in the next year that Wittgenstein wrote his Notes on Logic, much of which was copied directly into the Tractatus.

He referred to that work as a summary of what he had done at Cambridge up to that point. In Letters p. And the Prototractatus is quite close to the Tractatus proper. First in that thoughts are expressed in it, and this value will be the greater the better the thoughts are expressed.

The more the nail has been hit on the head. Simply because my ability to ac- complish the task is too slight. On the other hand the truth of the thoughts communicated here seems to me unassailable and definitive. I am therefore of the opinion that the problems have in essentials been finally solved.

And if I am not wrong in this, then the value of this work now consists secondly in that it shows how little has been achieved by the of solving these problems. Vienna, Bearn says, in Waking to Wonder: In the Tractatus these are states of affairs, combinations of objects. The universe is implicitly not a thing, not some- thing that can be referred to by a name.

See Black pp. Frege has a notion of fact that is worth bearing in mind here. Thoughts are imperceptible. We may see the sun rise, but we do not in the same sense see that the sun rises. That the sun is 11 The decimal numerals given as numbers of the individual proposi- tions indicate the logical importance of the propositions, the emphasis placed on them in my presentation.

The propositions n. Thoughts are not external, perceptible objects, but neither are they private, subjective, individual, psychological ideas. Wittgenstein, Amsterdam: Rodopi, , pp. Nordmann comments that: For Frege, Vorstellungen conceptions or ideas are purely, indeed necessarily, individual or private, while sense can be common property. See p. Nordmann suggests on p. His view is that these two sentences i. Russell had not seen or heard from Wittgenstein since August Ostrow pp.

Yet 5. And, as Ostrow notes p. Frascolla says p. As Sullivan notes, Whitehead and Russell on p. However, Black notes, Witt- genstein uses Sachverhalt in seemingly inconsistent ways.

Most of the time he uses it to mean an actual combination of objects, but he also sometimes uses it to mean a combination that does not exist e. Stenius p. Black argues pp. Frascolla p. Items, things. In The Principles of Mathematics, Russell writes: This, then, is the widest word in the philosophical vocabulary. I shall use as synonymous with it the words unit, individual, and entity. White p.

Objects etc. McGinn p. Commentators usually ask whether he took them to be material points point-masses or sense-data. The Note- books, which record exploratory work, canvas both possibili- ties, and in the Tractatus, where he might have been expected to make up his mind and choose between them, he does not do so, and does not even formulate the question to which of the two categories objects belong.

Thus it is not prop- erly experience or knowledge at all [see TLP 5. See Bearn p. Objects are unchanging see TLP 2. Bearn makes this point on p. Fahrnkopf argues that Wittgenstein's objects include uni- versals. He points out p. He certainly seems to be talking about the universal redness rather than a particular red sense-datum here.

Hintikka p. Hintikka see p. That is, they are what is given in immediate expe- rience, but they are not only the contents of our consciousness. We have immediate experience of physical reality which still remains to be defined , not only of the contents of our own minds. Page 31 of the Blue Book refers specifically to the Tracta- tus and the idea that a fact is a "complex of objects. Talk of facts as combinations of objects, Wittgenstein writes, springs from the following confusion: And perhaps he already thought this way in the Tractatus, given what he writes at 6.

So they cannot be within the world, for if they were within the world they would be accidental, facts see 6. What is accidentally the case, the world, depends on the non-accidental. If things can occur in states of affairs then this [possibili- ty] must already be in them. Something logical cannot be merely possible. Logic deals with every possibility, and all possibilities are its facts. As we cannot conceive of spatial objects at all without space, or temporal objects without time, so we can conceive of no thing without the possibility of its uniting with other ob- jects.

If I can conceive of an object in the context of a state of affairs then I cannot conceive of it without the possibility of this context. It is impossible for words to appear in two differ- ent ways: That is to say, each particular that there is in the world does not in any way logically depend upon any other particular. Each such possibility must be in the nature of the object. A new possibility cannot be found later.

I can conceive of this space as empty, but I cannot conceive of the thing without the space. A spatial point is an argument-place. The speck in a visual field of course need not be red, but it must have a color: The note must have a pitch, the object of the sense of touch a degree of hardness, etc. Leibniz Monadology 1, where simple is defined as meaning without parts.

Fahrnkopf p. Complexes cannot be treated as entities or objects. According to 2. White pp. One starts from the need for the world to have sub- stance, while the latter is based on the demand that sense be determinate. Each concludes that there must be simple ob- jects.

There- fore they cannot be composite. What is contingent is whether it is true or false. But in order to be true or false a proposition must already possess a sense. The sense of a proposition, in short, must be independent of whether it is in fact true or false. Con- sequently, there must be a contact between language and the world which is prior to the truth or falsity of what we say. Such a contact is to be found in the relationship between a simple name and a simple object, the relationship being such that the name just stands for the object independently of de- scription.

Hence, if there is no such object, the name will be meaningless, and the sentence in which it occurs will have no sense. But if a name is supposed to stand for a complex ob- ject, the decomposition or non-existence of that complex is a real possibility. So to ascertain that the original proposition does have a sense, one would have to check whether the com- plex in question did in fact exist, i.

Because these [material properties] are presented only by propositions -- are only pro- duced by the configuration of objects. Nordmann p. McManus p. In what sense could colors be colorless? On the other hand, those complexes which have a spatial quale among their constituents do have a spatial location, and likewise all those complexes which have a temporal quale among their constituents all concrete com- plexes, as we shall see shortly do have a position in time.

Of course different things are red than are blue, but these are external differences between red and blue. Apart from these, the only difference between them is that they are different colors. Because if a thing is not distinguished by anything then I cannot distinguish it, because otherwise it really would have been distinguished all along. But what holds together the links of a chain? Nothing, except their fitting into one another. Their fitting into one another is how they hold together.

The same point applies to the combination of objects in a state of affairs. That they hold together in a determinate way shows something about their logical form. But logical form is not a further fact about them, that which holds them together. See 5. Black p. Form is the possibility of structure]. On pp. Indeed, it would appear to be the reverse: The object is, we might say, a primitive notion.

This makes interpretation problematic. An existing state of affairs, the realization of that possibility set, is a fact. See 2 and 2. Ostrow p. Dover Publications, p. Facts should not be reified. They are uses of pic- tures. His conclusion is that a picture presents [vorstellt] existent and non-existent atomic facts, and represents [darstellt] a possibility of such facts, a choice made from among the facts that it could be used to depict.

For a mathematician talks of picturing in cases where a painter would no longer use this expression. Schopenhauer Fourfold Root p. We must apply it. A spatial picture [can represent] everything spatial, a col- or one everything colored, etc. On the oth- er hand, for instance, not every picture is a spatial one.

It is hard to see how anything could be a picture in this sense without being a com- plete recreation of what is pictured. McManus argues against this view on p. What is thinkable is also possible. We say a sentence expresses a thought.

The mentalistic misreading of the Tractatus relies heavily on proposition 3.

Tractatus pdf wittgenstein

The German can be understood either as explaining what the method of projection is, namely thinking the sense of the proposition, or as explaining what thinking the sense of the proposition is, namely the method of projection, but without specifying what this method is.

On this see Schroeder p. McGuinness, pp. This is for three reasons: The mentalist thesis is supported also, according to its proponents, by the following passage from a letter written by Wittgenstein to Russell Wittgenstein, Cambridge Letters, p.

I don't know what the constituents of a thought are but I know that it must have such constituents which correspond to the words of Language. Again the kind of relation of the consti- tuents of thought and of the pictured fact is irrelevant. It would be a matter of psychology to find it out. Does a Gedanke consist of words? But of psychical constituents that have the same sort of relation to reality as words. What those constituents are I don't know. In that they are pictures in a space, the possibility of the representing picture in the space has internal to it the possibility of the represented situation in that space.

The logical notion of depiction then explains in PT 3. The sort of projection involved in our use of proposi- tions is thus tied to the notion of picturing, which itself is a basically projective notion: And a proposition is a propositional to- ken in its projective relation to the world. A proposition is not an entity distinct from the propositional sign: Thus the possibility of what is projected belongs to it, but not it itself.

Its sense is therefore not yet contained in a sentence, but the possibility of expressing it is. The form of its sense is contained in a sentence, but not its content. A propositional token is a fact. A proposition is articulated. Because in a printed sentence, e. This is how it was possible for Frege to call a sentence a complex name. In fact, although one can see what led Wittgenstein to say what he says here, the thought is a bad one.

There is no mode of expression that would obviate the potential confusion between viewing the propositional sign as a complex object and viewing it as a fact. There is no good reason to suppose that if we used bits of furniture to form propositional signs, people might not take the propositional sign to be the complex object whose parts were those bits of furniture.

The reciprocal spatial position of these things then ex- presses the sense of the proposition. That the painting stands in the relation of hanging to the wall says that the painting is hanging on the wall. The sense of a propo- sition is to be found in an arrangement of physical signs; it is not to be found in something that corresponds to that ar- rangement, some entity over and above it, whether in the em- pirical or some quasi-empirical world. Fahrnkopf discusses a nominalistic interpretation of this passage and a realistic one.

Nominalist readings e. Copi's and Anscombe's take the key point to be that 'R' would have no place in an ideal symbolism. Thus relations are not real, and whatever 'aRb' tells us might just as well be expressed by, say, 'ab' or 'ba'. On my interpretation, then, the purpose of 3. Names are like points, whereas propositions, having sense, are like arrows. The object is its meaning. Signs stand for them. I can only speak of them, I cannot express them.

A proposition can only say how a thing is, not what it is. See Basic Laws of Arithmetic , v. Bearn discusses this on pp. As Frege understands it, the logical law, Either Fx or not Fx, refutes the existence of a concept that lacks sharp bounda- ries. See also Notebooks p. A complex can only be given through its description, and this will match it or not match it. A proposition, in which there is mention of a complex, will, if this complex does not exist, be not nonsensical [unsinnig] but simply false.

We know by this proposition that something is not yet definite [determinate]. The notation for generality indeed contains a prototype. The abbreviation of the symbol of a complex in the form of a simple symbol can be expressed by a definition. The world cannot be indefinite, even though language can be.

Two signs, one primitive and one defined by primitive signs, cannot signify in the same way. One cannot analyze names through definitions.

Tractatus Logico-Philosophicus by Ludwig Wittgenstein

Nor any sign that has meaning on its own, independently. See Letters to Ogden p. What signs slur over, their appli- cation speaks out. The former applies only to mea- ningful propositions, while the second can apply to nonsense. McManus also mentions this issue in footnote 8, p. The application of a sign is here linked with its meaning.

They can thus only be understood if one is already acquainted with the meanings of these signs. Anscombe p. Logical signs, as Wittgenstein in- dicates elsewhere, are not primitive signs.

But see Anscombe p. And from 6. Anscombe concludes that elementary propositions are not simple obser- vation statements, and that this explains why Wittgenstein did not refer to observation in connection with them. What they are he cannot say, but they must exist. See, for instance, 5.

The proposition itself is an expression. The expression is all that is essential for the sense of a proposition that propositions can have in common with each other. An expression marks a form and a content. It is the common characteristic feature of a class of propositions. Moreover in this form the expression is constant and eve- rything else is variable.

In the limiting case the variables become constants, the expression a proposition. Every variable can be taken as a propositional variable. Even a variable name. This class still depends in general on what we, by arbitrary agreement, mean by the parts of that proposition. But if we convert into va- riables all those signs whose meaning is arbitrarily determined then a class like this will still always remain. This however is now dependent on no agreement, but only on the nature of the proposition.

It corresponds to a logical form — a logical proto- type. In the Investigations, he thinks of logical form as being a kind of formalization of the rules of language and these arise out of its use; they do not underlie and guarantee its intelligibility. Common to both works, however, is the view that meaning is not some special entity or psychological process.

The fixing of the values is the variable. The fixing is a description of these propositions. The fixing will therefore deal only with symbols, not with their meaning. And the only thing essential to the fixing is that it is only a description of symbols and tells nothing of the symbolized.

How the description of the propositions occurs is unessen- tial. Because the sign is in- deed arbitrary. One could thus also choose two different signs and where would then be what was common in the symboliza- tion? A symbolism then that obeys logical grammar — logical syntax. The concept-script of Frege and Russell is one such lan- guage, though admittedly it does not yet exclude all errors.

In Letters to Ogden, p. If everything behaves as if a sign had meaning, then it has meaning. The theory of types is explained in the introduction. Rus- sell himself was not completely happy with it: Classes are logical fictions, and if they are treated as be- ing real objects, whose names have real signification, then the sentences in which they are treated this way will be devoid of meaning.

Ramsey, following Wittgenstein, objects to this theory. Propositional functions are symbols, while individuals are objects. But the range of arguments to a function of functions is a range of symbols, all symbols which become propositions by inserting in them the name of an individual.

Mounce p. But then it will be evident that one cannot construct a proposition which refers to itself. For, given such a misguided attempt, it will be evident that what one has is not one proposition, referring to itself, but different propositions.

In short, a theory of types is entirely unnecessary. Any such description already presuppos- es the grammatical rules. That is to say, if anything is to count as nonsense in the grammar that is to be justified, then it can- not at the same time pass for sense in the grammar of the propositions that justify it etc. The what will already have been settled once the how is established. The accidental are those features that come from the par- ticular way of producing the propositional sign.

The essential are those which alone enable the proposition to express its sense. And likewise in general the essential in a symbol is that which all symbols that can fulfill the same purpose have in common. The actual name is that which all symbols that signify an object have in common.

It would then follow that no composition at all is essential for a name. This stems from the essence of the notation. And it is like this in philosophy generally: Every right sign-language must allow of translation into every other by means of such rules: This is what they must all have in common. It is common to them that they all— e. This shows [gekennzeichnet] the way that a specific possible notation can give us general insight. The existence of this logical place is guaranteed by the exis- tence of the constituent parts alone, by the existence of the meaningful proposition.

That is the logical place. Otherwise negation, logical sum, logical product, etc. The logical scaffolding around a picture reaches through the whole logical space. The proposition reaches through the whole logical space.

Ordinary language is a part of the human organism and not less complicated than it. It is humanly impossible to gather the logic of language immediately from it. Language disguises thought. Indeed so much so that from the outer form of the clothes one cannot infer the form of the thoughts they clothe; because the outer form of the clothes is made for a wholly different purpose than to let the form of the body be known. The unspoken, silent agreements for understanding ordi- nary language are enormously complicated.

See Weiner, p. From Frege to Wittgenstein. Weiner gives the reference to Frege as Begriffsschrift, p. So we cannot answer questions of this kind at all, but only ascertain their nonsensicality. Most questions and propo- sitions of philosophers are based on our not understanding the logic of our language. They are of the same kind as the question whether the good is more or less identical than the beautiful. And it is not surprising that the deepest problems are real- ly no problems.

See Nordmann pp. For Mauthner, language is conventional and based on metaphor, so it can never really grasp the real world. See Stokhof pp. Schroeder writes see p. A proposition is a model of reality as we think it is. But so too do written notes seem at first glance not to be a picture of music, nor our written signs for sounds letters to be a picture of our spoken language. And yet these symbolisms prove to be pictures — even in the ordinary sense of the word — of what they present.

Here the sign is obviously a likeness of the signified. Because even these irregularities picture what they are meant to express; only in another way. The logical form is common to all of them. As in the fairytale with the two youths, their two horses and their lilies. They are all in a certain sense one. See Nordmann p. And the rule is the law of projection which projects the symphony into the language of the musical score.

It is the rule of translation of this language into the language of the gramophone record. See Letters to Og- den p. And from it came the alphabet, without losing the essence of picturing. Presumably, Proops argues, Wittgenstein inserted other material without noticing that he needed to change the wording of 4. So Wittgenstein has not made a mistake after all. Because I am acquainted with the state of things it presents if I understand the proposition. And I understand the proposition without its sense having been explained to me.

A proposition shows what is the case if it is true. And it says that this is the case. Therefore it must describe reality completely. A proposition is a description of a state of affairs. As the description of an object goes by its external prop- erties, so a proposition describes reality according to its inter- nal properties. A proposition constructs a world with the help of a logical scaffolding and therefore one can actually see in the proposi- tion all the logical features of reality if it is true.

One can draw conclusions from a false proposition. One can therefore understand it without knowing wheth- er it is true. One understands it if one understands its constituent parts. And the dictionary translates not only substantives but also verbs, adjectives, and conjunctions, etc. We make ourselves understood, though, with sentences. A sentence communicates a state of things to us, so it must be essentially connected with the state of things. And the connection is just that it is its logical picture.

A sentence says something only insofar as it is a picture. Instead of, This sentence has such and such a sense, one can say, This sentence presents such and such a state of things. It is ambiguous in the German, the first sentence allowing for the interpretation that a sentence puts together a situation experi- mentally, or as an experiment, or for the sake of experiment, or in order to be put to the test. That the logic of facts does not allow of representation.

This indeed is the central doctrine of the Tractatus. Logic differs from all the other sciences because the other sciences say something about the world whereas logic only shows something. After all, its import seems entirely negative.

This leaves Wittgenstein with a question as to what holds a proposition together if not logical forms conceived as objects of acquain- tance? Both must possess the same logical mathematical mul- tiplicity. To the Vienna Station, ed. Linda Wessels, Cambridge University Press, , pp.

If the multiplicity of the sym- bolic system is smaller than that of what it represents, there will be possible circumstances we will not be able to describe. If the multiplicity is greater, the problem is more familiar -- it is called 'philosophy'. All of philosophy up to, and perhaps including, Wittgenstein had consisted of attempts to say things that cannot be said. Good philosophy attempts to say what can be shown, sinnlos; bad philosophy attempts to say what cannot even be shown, the unsinnig, the utter nonsense.

Most philosophy had been bad philosophy, based on confu- sions concerning language. These confusions were roughly of the sort displayed by Russell's paradox: The language we use has a greater multiplicity than what it talks about. We can therefore form expressions whose syntactic appearance is like that of perfectly meaningful claims, but from them we are led to some form of chaos.

In particular, it is relative to the audience. He offers us the analogy with presentations of grammar: If simplicity is relative, perhaps multiplicity is too. In the Notebooks Wittgenstein struggles with the question of what is required to sharply delineate truth-conditions.

He finds that a certain high ideal of precision proves not only unne- cessary but actually inappropriate. If one wants to attain a pre- cise measurement of the length of a room, measurements in angstroms are less and not more precise than measurements in meters and centimeters.

Similarly, what is needed for a sharp delineation of truth-conditions is not an anal- ysis in terms of material points or data points, but merely that sentence, thought, and state of affairs have the same multiplicity, i. One cannot get outside it to make a picture. All these ways of symbolizing do not suffice, because they do not have the necessary mathematical multiplicity.

One could then say, e. In treating the Bedeutung of true sen- tences as an equivalent and distinct object from the Bedeutung of false sentences, Wittgenstein believes that Frege fails to make it clear that each proposition with sense essentially has two poles—a true pole and a false pole—each of which ex- cludes the other.

Just as long as one knows that they are meant to be false. That negation occurs in a proposition is still no characte- ristic [or sign: To the fact that a point is black corresponds a positive fact, to the fact that a point is white not black , a negative one.

If I indicate a point on the sheet a Fregean truth-value then this corresponds to the assumption that is proposed for judgment, etc. The point at which the simile breaks down now is this: The emphasis is on logic, not epistemology.

See comment on 4. Proops p. Proops pp. What has to be added to that yardstick in order for it to assert something about the length of the object? Similarly, an unasserted proposition marked only by a horizontal stroke stands, as it were, ready to be asserted as a proposition, but does not assert itself. We might then wonder what needs to be added to it to make it an assertion, an actual proposition rather than mere content.

But this content must already have sense. I cannot even consider asserting something unless it is already a proposition. And the same goes for negation, etc. Wittgenstein, she says, is attacking this idea. Having a sense means being true or false, so there cannot be propositions that have a sense but are nei- ther true nor false. Frege, Anscombe says and she argues that Wittgenstein agrees , is wrong. He makes it seem as though it is merely contingent if we construct a proposition with sense and find that it has a truth-value.

The negating proposition determines another logical place than does the proposition negated. The negating proposition determines a logical place with help from the logical place of the negated proposition, in that it describes it as lying outside this place. That one can again negate the negated proposition shows already that what is negated is already a proposition and not merely the preliminary to a proposition. Philosophy is not a subject but an activity.

A philosophical work consists essentially of elucidations. Philosophy should make clear and distinct thoughts that, without it, are, as it were, unclear and indistinct.

To say that early Wittgenstein aspired to such a conception of philosophy is not to gainsay that to aspire to practice philosophy in such a manner and to succeed in doing so are not the same thing. Theory of knowledge is the philosophy of psychology.

Does not my study of sign-language correspond to the study of thought-processes, which philosophers held so essen- tial to the philosophy of logic?

Only they got entangled most- ly in inessential psychological investigations and there is an analogous danger for my method. Thus the psychological activity in- volved in correlating a mark with an object is in itself entirely meaningless.

What gives it a meaning, what makes it a ge- nuine correlation, is the logical structure into which the mark enters.

It should limit the unthinkable from inside, by way of the thinkable. At B xxx of the Critique of Pure Reason he says that he has had to suspend knowledge in order to make room for faith Ich musste also das Wissen aufheben, um zu Glauben Platz zu bekommen and the references in Prolego- mena to the limits of reason relate to this idea. We might wonder, therefore, whether Wittgenstein is implying that he limits the thinkable in order to make room for some faith in the ineffable.

Everything that can be said can be said clearly. In order to present logical form, we would have to be able to put ourselves, along with propositions, outside logic, that is to say outside the world. There is, McManus argues, no similarity as such, nor sharing of the same form as such. Things are only ever like or unlike in some or other particular respect.

What is like what then depends on how we look at things, on how we choose to categorize or characterize things. What is reflected in language, cannot be presented by it. What expresses itself in language, we cannot express through it. Propositions show the logical form of reality.

They display it. If two propositions contradict each other then their struc- ture shows this; the same applies if one follows from the other. And so on. Schopenhauer on music: Music, like the phenomenal world, shows, as it were, the nature of the thing-in-itself.

What this is cannot be said or translated into concepts. Nor can it be demonstrated or proved that music does this. The listener must simply hear the music and agree that it expresses the inner nature of the world.

On that idea, cf. Nothing can be said about the simple ob- jects that correspond to the names that are the elements of meaningful language, precisely because they are simple, i. The holding of such internal properties and relations, however, cannot be asserted through propositions, but rather it shows itself in the propositions which present the states of affairs and deal with the objects in question.

In the sense in which we speak of facial features. This blue color and that stand in the internal relation of lighter and darker eo ipso. It is unthinkable that this pair of objects not stand in this relation. However, it is not clear that he held this view at the time of writing the Tractatus, where he seems to suggest that the logical order of colour-space will be revealed through the logical analysis of colour terms see TLP 6.

Schroeder p. It would be equally senseless to ascribe a formal property to a proposition as to deny it. Russell had ar- gued against the intelligibility of internal relations and held that all relations are external. The series of numbers is ordered not by an external but rather by an internal relation.

Equally the series of propositions: If b stands in one of these relations to a then I call b a successor of a. I introduce this expression in order to make clear the ba- sis of the confusion of formal concepts with proper concepts, which runs through the whole of the old logic.

That something is an instance of a formal concept cannot be expressed through a proposition. Rather it shows itself in the sign of this object itself. A name shows that it signifies an object, a numeral that it signifies a number, etc.

Formal concepts cannot, in the way that proper concepts can, be presented by a function. Because of their defining characteristics, formal proper- ties are not expressed through functions. The expression of a formal property is a feature of certain symbols. The sign for the defining characteristics of a formal con- cept is therefore a characteristic feature of all symbols whose meaning falls under the concept. See Letters to Ogden, p.

See also Joan Weiner pp. Future Pasts: Richard L. According to Mendelsohn p. Because each variable presents a constant form, which all its values possess, and which can be conceived as a formal property of these values.

Wherever it is used otherwise, thus as a proper concept word, nonsensical [unsinnige] pseudo-propositions arise. Thus one cannot, e. They all signify formal concepts and are presented in the concept-script by variables, not by functions or classes. As Frege and Russell believed. Thus one cannot introduce as primitive ideas the objects of a formal concept and the formal concept itself.

Thus one cannot like Russell introduce, e. This has been overlooked by Frege and Russell: We can determine the general term of a formal series by giving its first term and the general form of the operation that produces the next term from the proposition that goes before it.

Because no proposition can answer such a question. Thus one cannot ask, e. Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc. He goes on: It is not clear what W. It is a concatenation, a linking, of names. Here the question arises of how the combination of prop- ositions comes to be.

Here perhaps we have instances of irredeemable nonsense. I write an elementary proposition as a function of names, in the form: Or else I indicate it by the letters p, q, r. There, Wittgenstein says that names are signs.

The definition is a rule for signs. If I am acquainted with the meaning of an English word and of a synonymous [gleichbedeutenden] German word, then it is impossible that I do not know that they are both syn- onymous; it is impossible that I cannot translate them by each other.

This will be shown later. The world is completely de- scribed by the statement of all elementary propositions plus a statement as to which of them are true and which are false.

All combinations of states of affairs can exist and the oth- ers not exist. Indeed the under- standing of all propositions depends palpably on the under- standing of the elementary propositions.

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Wittgenstein him- self computes this at TLP 4. The absence of this sign means disagreement. A proposition is the expression of its truth-conditions. Frege quite rightly therefore put them first [vorausge- schickt] as an explanation of the signs of his concept-script. Only the explanation of the concept of truth that we get from Frege is false: The argument turns on the extensionality of functions. In such a case each compound proposition mere- ly expresses the thought that the False falls under the concept of negation.

For each such proposition determines the True as the value of the same function for the same argument. A proposition cannot possibly assert of itself that it is true. If the order of the truth-possibilities in a schema is fixed once and for all by a rule of combination, then the last column by itself is already an expression of the truth-conditions.

If we write this column as a row, then the propositional sign will be: The number of places inside the brackets on the left is determined by the number of terms in the brackets on the right.

Proops see pp. But, accord- ing to Black, this is unnecessary, as the difference is already clear, and so the effect is that the sign indicates simply that the authors are putting the proposition forward as true.

The groups of truth-conditions that belong to a number of truth-possibilities can be ordered in a series. In one case the proposition is true for all truth- possibilities of the elementary propositions.

We say that the truth-conditions are tautological. In the second case the proposition is false for all truth- possibilities: In the first case we call the proposition a tautology, in the second case a contradiction. A tautology has no truth-conditions because it is uncondi- tionally true; and a contradiction is true under no condition. Tautology and contradiction are senseless [sinnlos]. Like a point from which two arrows go out in opposite directions to one another.

I know nothing, e. They are not gibberish because there are rules for constructing truth tables that yield tautologies and contradictions, but not for gibberish. What does it show? Mounce tries to answer this question: One is aware, by means of it, of rules which reflect logical form and that enable one to construct out of the symbols which constitute it propo- sitions that do say something.

Is such a thing thereby revealed? Was it not already apparent? So there are rules for constructing gibberish, namely the rules we must follow if we are to make sense. To construct gibberish one need only violate these rules. They present no possible states of things. Because one lets every possible state of things be, and the other none. In tautology the conditions of agreement with the world — the presenting relations — cancel each other out, so that it stands in no presenting relation to reality.

A proposition, a picture, a model, are in a negative sense like a solid body that restricts the free movement of others; in a positive sense [they are] like a space limited by solid sub- stance wherein there is room for a body.

Tautology leaves to reality the whole — endless — logical space; contradiction fills the whole of logical space and leaves reality not a point. Neither of them, therefore, can determine reality in any way. Notebooks November 14th Certain, possible, impossible: And the same applies to tautology.

Thus that prod- uct is identical with the proposition. Because one cannot change the essence of the symbol without changing its sense. That is to say, propositions that are true for every state of things cannot after all be combinations of symbols, because otherwise only definite combinations of objects could corres- pond to them. And there is no logical combination to which no combi- nation of objects corresponds.

Tautology and contradiction are the limiting cases of the combination of symbols, namely their dissolution. That there is a general propositional form is indicated [bewiesen] by the fact that there may be no proposition whose form one could not have foreseen i. The gen- eral form of the proposition is: Things are thus and so.

And those are all sentences and thus are they li- mited. So this is not a mathematical truth. Now, if I say, 'The probability of my drawing a white ball is equal to the probability of my drawing a black one', this means that all the circumstances that I know of including the laws of nature assumed as hypotheses give no more probability to the occurrence of the one event than to that of the other. What I confirm by the experiment is that the occurrence of the two events is independent of the circumstances of which I have no more detailed knowledge.

The circumstances--of which I have no further knowledge--give such and such a degree of probability to the occurrence of a particular event. It involves a general description of a propositional form. We use probability only in default of certainty--if our knowledge of a fact is not indeed complete, but we do know something about its form.

A proposition may well be an incomplete picture of a certain situation, but it is always a complete picture of something. A probability proposition is a sort of excerpt from other propositions. These operations I call truth- operations. Negation, logical addition, logical multiplication, etc. Negation reverses the sense of a proposition. It gives expression to the difference between the forms. And what the bases of an operation and its result have in common is just the bases themselves.

There is only one way of expressing this: Indeed, no statement is made by an operation, but only by its result, and this depends on the bases of the operation. Operations and functions must not be confused with each other. Russell and Whitehead did not admit the possibility of such steps, but repeatedly availed themselves of it. In a similar sense I speak of successive applications of more than one operation to a number of propositions. This bracketed expression is a variable: Operations can cancel one another.

A truth-operation is the way in which a truth-function is produced out of elementary propositions. It is of the essence of truth- operations that, just as elementary propositions yield a truth-function of themselves, so too in the same way truth-functions yield a further truth- function.

When a truth-operation is applied to truth-functions of elementary propositions, it always generates another truth-function of elementary propositions, another proposition. When a truth-operation is applied to the results of truth-operations on elementary propositions, there is always a single operation on elementary propositions that has the same result.

Every proposition is the result of truth-operations on elementary propositions. And it is easy to see that the propositional sign in 4. The interdefinability of Frege's and Russell's 'primitive signs' of logic is enough to show that they are not primitive signs, still less signs for relations. And it is obvious that the 'z' defined by means of 'P' and 'C' is identical with the one that figures with 'P' in the definition of 'C'; and that the second 'C' is identical with the first one; and so on.

And it is no less remarkable that the infinite number of propositions of logic mathematics follow from half a dozen 'primitive propositions'. But in fact all the propositions of logic say the same thing, to wit nothing. For example, an affirmation can be produced by double negation: Does 'PPp' negate Pp, or does it affirm p--or both?

The proposition 'PPp' is not about negation, as if negation were an object: And if there were an object called 'P', it would follow that 'PPp' said something different from what 'p' said, just because the one proposition would then be about P and the other would not.

Pfx', which says the same as ' x. The construction of logic out of its primitive signs must be made clear. If a primitive idea has been introduced, it must have been introduced in all the combinations in which it ever occurs.

It cannot, therefore, be introduced first for one combination and later reintroduced for another. For example, once negation has been introduced, we must understand it both in propositions of the form 'Pp' and in propositions like 'P p C q ', ' dx. Pfx', etc. We must not introduce it first for the one class of cases and then for the other, since it would then be left in doubt whether its meaning were the same in both cases, and no reason would have been given for combining the signs in the same way in both cases.

In short, Frege's remarks about introducing signs by means of definitions in The Fundamental Laws of Arithmetic also apply, mutatis mutandis, to the introduction of primitive signs.

In logic a new device should not be introduced in brackets or in a footnote with what one might call a completely innocent air. Thus in Russell and Whitehead's Principia Mathematica there occur definitions and primitive propositions expressed in words.

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Why this sudden appearance of words? It would require a justification, but none is given, or could be given, since the procedure is in fact illicit. But if the introduction of a new device has proved necessary at a certain point, we must immediately ask ourselves, 'At what points is the employment of this device now unavoidable?

Or rather, it must become evident that there are no numbers in logic. There are no pre- eminent numbers. In logic there can be no distinction between the general and the specific.

Tractatus Logico-Philosophicus by Ludwig Wittgenstein - Free Ebook

Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined--a priori--to form a self-contained system. A realm subject to the law: Simplex sigillum veri. We should also have introduced at the same time the effect of all possible combinations of brackets. And thus it would have been made clear that the real general primitive signs are not ' p C q', ' dx.

Indeed, the use of brackets with these apparently primitive signs is itself an indication that they are not primitive signs. And surely no one is going to believe brackets have an independent meaning. An elementary proposition really contains all logical operations in itself. For 'fa' says the same thing as ' dx.

One could say that the sole logical constant was what all propositions, by their very nature, had in common with one another. But that is the general propositional form. If a sign is possible , then it is also capable of signifying.

Whatever is possible in logic is also permitted. The reason why 'Socrates is identical' means nothing is that there is no property called 'identical'. The proposition is nonsensical because we have failed to make an arbitrary determination, and not because the symbol, in itself, would be illegitimate. In a certain sense, we cannot make mistakes in logic.

Signs that serve one purpose are logically equivalent, and signs that serve none are logically meaningless.

And I say that any possible proposition is legitimately constructed, and, if it has no sense, that can only be because we have failed to give a meaning to some of its constituents. Even if we think that we have done so.

Thus the reason why 'Socrates is identical' says nothing is that we have not given any adjectival meaning to the word 'identical'. For when it appears as a sign for identity, it symbolizes in an entirely different way-- the signifying relation is a different one--therefore the symbols also are entirely different in the two cases: This operation negates all the propositions in the right-hand pair of brackets, and I call it the negation of those propositions.

What the values of the variable are is something that is stipulated. The stipulation is a description of the propositions that have the variable as their representative. How the description of the terms of the bracketed expression is produced is not essential.

We can distinguish three kinds of description: Direct enumeration, in which case we can simply substitute for the variable the constants that are its values; 2. N E is the negation of all the values of the propositional variable E. Only because they are all connected with one another in an infinitely fine network, the great mirror.

Pdf wittgenstein tractatus

Therefore, in the proposition 'Pp', when it is true, 'p' is a false proposition. How then can the stroke 'P' make it agree with reality? But in 'Pp' it is not 'P' that negates, it is rather what is common to all the signs of this notation that negate p. Pp', etc. And this common factor mirrors negation. And similarly we can say that two propositions are opposed to one another if they have nothing in common with one another, and that every proposition has only one negative, since there is only one proposition that lies completely outside it.

Thus in Russell's notation too it is manifest that 'q: These rules are equivalent to the symbols; and in them their sense is mirrored. And this is indeed the case, since the symbol in 'p' and 'q' itself presupposes 'C', 'P', etc. If the sign 'p' in 'p C q' does not stand for a complex sign, then it cannot have sense by itself: But if 'p C p' has no sense, then 'p C q' cannot have a sense either.

Why should it not be possible to express a negative proposition by means of a negative fact? But really even in this case the negative proposition is constructed by an indirect use of the positive. The positive proposition necessarily presupposes the existence of the negative proposition and vice versa.

Frege and Russell introduced generality in association with logical productor logical sum. This made it difficult to understand the propositions ' dx. If elementary propositions are given, then at the same time all elementary propositions are given. The certainty, possibility, or impossibility of a situation is not expressed by a proposition, but by an expression's being a tautology, a proposition with a sense, or a contradiction.

The precedent to which we are constantly inclined to appeal must reside in the symbol itself. This is shown by the fact that in ' dx, O. Ox' we have to mention 'O' and 's' separately. They both, independently, stand in signifying relations to the world, just as is the case in ungeneralized propositions.

It is a mark of a composite symbol that it has something in common with other symbols. And the range that the totality of elementary propositions leaves open for its construction is exactly the same as that which is delimited by entirely general propositions.

If an elementary proposition is true, that means, at any rate, one more true elementary proposition. Difference of objects I express by difference of signs. This becomes very clear if one considers, for example, the proposition ' x: What this proposition says is simply that only a satisfies the function f, and not that only things that have a certain relation to a satisfy the function, Of course, it might then be said that only a did have this relation to a; but in order to express that, we should need the identity-sign itself.

Even if this proposition is never correct, it still has sense. And the proposition, 'Only one x satisfies f ', will read ' dx. P dx, y. All the problems that Russell's 'axiom of infinity' brings with it can be solved at this point. What the axiom of infinity is intended to say would express itself in language through the existence of infinitely many names with different meanings. In fact, this happens when one wants to talk about prototypes, e. Thus in Russell's Principles of Mathematics 'p is a proposition'--which is nonsense- -was given the symbolic rendering 'p z p' and placed as an hypothesis in front of certain propositions in order to exclude from their argument- places everything but propositions.

It is nonsense to place the hypothesis 'p z p' in front of a proposition, in order to ensure that its arguments shall have the right form, if only because with a non-proposition as argument the hypothesis becomes not false but nonsensical, and because arguments of the wrong kind make the proposition itself nonsensical, so that it preserves itself from wrong arguments just as well, or as badly, as the hypothesis without sense that was appended for that purpose.

But even if this were a proposition, would it not be equally true if in fact 'there were things' but they were not identical with themselves? Particularly with certain forms of proposition in psychology, such as 'A believes that p is the case' and A has the thought p', etc. For if these are considered superficially, it looks as if the proposition p stood in some kind of relation to an object A.

And in modern theory of knowledge Russell, Moore, etc. Indeed a composite soul would no longer be a soul. Russell's theory does not satisfy this requirement. This no doubt also explains why there are two possible ways of seeing the figure as a cube; and all similar phenomena. For we really see two different facts. If I look in the first place at the corners marked a and only glance at the b's, then the a's appear to be in front, and vice versa. Elementary propositions consist of names.

Since, however, we are unable to give the number of names with different meanings, we are also unable to give the composition of elementary propositions. And if we get into a position where we have to look at the world for an answer to such a problem, that shows that we are on a completely wrong track. Logic is prior to every experience-- that something is so.

It is prior to the question 'How? We might put it in this way: But between what numbers? And how is this supposed to be decided? There is no pre-eminent number. Can we set up a form of sign without knowing whether anything can correspond to it? Does it make sense to ask what there must be in order that something can be the case?

But when there is a system by which we can create symbols, the system is what is important for logic and not the individual symbols. And anyway, is it really possible that in logic I should have to deal with forms that I can invent?

What I have to deal with must be that which makes it possible for me to invent them. We can foresee only what we ourselves construct. The limit also makes itself manifest in the totality of elementary propositions. Hierarchies are and must be independent of reality.

Our problems are not abstract, but perhaps the most concrete that there are. What belongs to its application, logic cannot anticipate. It is clear that logic must not clash with its application. But logic has to be in contact with its application. Therefore logic and its application must not overlap. So we cannot say in logic, 'The world has this in it, and this, but not that. We cannot think what we cannot think; so what we cannot think we cannot say either.

For what the solipsist means is quite correct; only it cannot be said , but makes itself manifest. The world is my world: The microcosm. If I wrote a book called The World as l found it , I should have to include a report on my body, and should have to say which parts were subordinate to my will, and which were not, etc.

You will say that this is exactly like the case of the eye and the visual field. But really you do not see the eye. And nothing in the visual field allows you to infer that it is seen by an eye. Whatever we see could be other than it is. Whatever we can describe at all could be other than it is. There is no a priori order of things. The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it.

What brings the self into philosophy is the fact that 'the world is my world'. The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world--not a part of it. This is the general form of a proposition. This is the most general form of transition from one proposition to another.

The concept of number is the variable number. And the concept of numerical equality is the general form of all particular cases of numerical equality. This is connected with the fact that the generality required in mathematics is not accidental generality. They are the analytic propositions. One might think, for example, that the words 'true' and 'false' signified two properties among other properties, and then it would seem to be a remarkable fact that every proposition possessed one of these properties.

On this theory it seems to be anything but obvious, just as, for instance, the proposition, 'All roses are either yellow or red', would not sound obvious even if it were true. Indeed, the logical proposition acquires all the characteristics of a proposition of natural science and this is the sure sign that it has been construed wrongly.

And so too it is a very important fact that the truth or falsity of non-logical propositions cannot be recognized from the propositions alone. The fact that a tautology is yielded by this particular way of connecting its constituents characterizes the logic of its constituents.

If propositions are to yield a tautology when they are connected in a certain way, they must have certain structural properties. So their yielding a tautology when combined in this shows that they possess these structural properties. Pp ' yield a tautology shows that they contradict one another. The fact that the propositions 'p z q', 'p', and 'q', combined with one another in the form ' p z q.

The fact that ' x. Truth-combinations I express by means of brackets, e. Now, by way of example, I wish to examine the proposition P p. Pp the law of contradiction in order to determine whether it is a tautology. In our notation the form 'PE' is written as and the form 'E. This method could also be called a zero-method. In a logical proposition, propositions are brought into equilibrium with one another, and the state of equilibrium then indicates what the logical constitution of these propositions must be.

For example, we see from the two propositions themselves that 'q' follows from 'p z q. Not only must a proposition of logic be irrefutable by any possible experience, but it must also be unconfirmable by any possible experience. The reason is that we can postulate them in so far as we can postulate an adequate notation. There is not, as Russell thought, a special law of contradiction for each 'type'; one law is enough, since it is not applied to itself.

To be general means no more than to be accidentally valid for all things. An ungeneralized proposition can be tautological just as well as a generalized one. Propositions like Russell's 'axiom of reducibility' are not logical propositions, and this explains our feeling that, even if they were true, their truth could only be the result of a fortunate accident. It is clear, however, that logic has nothing to do with the question whether our world really is like that or not.

They have no 'subject-matter'. They presuppose that names have meaning and elementary propositions sense; and that is their connexion with the world. It is clear that something about the world must be indicated by the fact that certain combinations of symbols--whose essence involves the possession of a determinate character--are tautologies.

This contains the decisive point. We have said that some things are arbitrary in the symbols that we use and that some things are not. In logic it is only the latter that express: If we know the logical syntax of any sign-language, then we have already been given all the propositions of logic. And this is what we do when we 'prove' a logical proposition. For, without bothering about sense or meaning, we construct the logical proposition out of others using only rules that deal with signs.

The proof of logical propositions consists in the following process: And in fact only tautologies follow from a tautology. Of course this way of showing that the propositions of logic are tautologies is not at all essential to logic, if only because the propositions from which the proof starts must show without any proof that they are tautologies. Hence the absence of surprise. It is clear from the start that a logical proof of a proposition that has sense and a proof in logic must be two entirely different things.

In logic every proposition is the form of a proof. Every proposition of logic is a modus ponens represented in signs. And one cannot express the modus ponens by means of a proposition. Every tautology itself shows that it is a tautology. Frege would perhaps say that we should then no longer have an immediately self-evident primitive proposition. But it is remarkable that a thinker as rigorous as Frege appealed to the degree of self-evidence as the criterion of a logical proposition.

Logic is transcendental. The propositions of mathematics are equations, and therefore pseudo-propositions. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics.

In philosophy the question, 'What do we actually use this word or this proposition for? But it must be manifest in the two expressions themselves whether this is the case or not. When two expressions can be substituted for one another, that characterizes their logical form. But the essential point about an equation is that it is not necessary in order to show that the two expressions connected by the sign of equality have the same meaning, since this can be seen from the two expressions themselves.

For in order to be able to assert anything about their meaning, I must know their meaning, and I cannot know their meaning without knowing whether what they mean is the same or different.

Calculation is not an experiment. For it is because of this method that every proposition of mathematics must go without saying. For equations express the substitutability of two expressions and, starting from a number of equations, we advance to new equations by substituting different expressions in accordance with the equations.

And outside logic everything is accidental. And just as in mechanics, for example, there are 'minimum-principles', such as the law of least action, so too in physics there are causal laws, laws of the causal form.

Here, as always, what is certain a priori proves to be something purely logical. Let us imagine a white surface with irregular black spots on it. We then say that whatever kind of picture these make, I can always approximate as closely as I wish to the description of it by covering the surface with a sufficiently fine square mesh, and then saying of every square whether it is black or white.

In this way I shall have imposed a unified form on the description of the surface. The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh.

Possibly the use of a triangular mesh would have made the description simpler: The different nets correspond to different systems for describing the world. Mechanics determines one form of description of the world by saying that all propositions used in the description of the world must be obtained in a given way from a given set of propositions--the axioms of mechanics.

It thus supplies the bricks for building the edifice of science, and it says, 'Any building that you want to erect, whatever it may be, must somehow be constructed with these bricks, and with these alone. The net might also consist of more than one kind of mesh: The possibility of describing a picture like the one mentioned above with a net of a given form tells us nothing about the picture. For that is true of all such pictures. But what does characterize the picture is that it can be described completely by a particular net with a particular size of mesh.

Similarly the possibility of describing the world by means of Newtonian mechanics tells us nothing about the world: We are also told something about the world by the fact that it can be described more simply with one system of mechanics than with another.

For example, it will never mention particular point-masses: The network, however, is purely geometrical; all its properties can be given a priori. Laws like the principle of sufficient reason, etc. There are laws of nature. But of course that cannot be said: Hence we can describe the lapse of time only by relying on some other process.

Something exactly analogous applies to space: And if such an asymmetry is to be found, we can regard it as the cause of the occurrence of the one and the non-occurrence of the other. Indeed, it exists in one-dimensional space in which the two congruent figures, a and b, cannot be made to coincide unless they are moved out of this space. The right hand and the left hand are in fact completely congruent.

It is quite irrelevant that they cannot be made to coincide. A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space. It is clear that there are no grounds for believing that the simplest eventuality will in fact be realized.

The only necessity that exists is logical necessity. And in fact both are right and both wrong: Let us think how this contradiction appears in physics: It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The statement that a point in the visual field has two different colours at the same time is a contradiction. In the world everything is as it is, and everything happens as it does happen: If there is any value that does have value, it must lie outside the whole sphere of what happens and is the case.

For all that happens and is the case is accidental. What makes it non-accidental cannot lie within the world, since if it did it would itself be accidental. It must lie outside the world. Propositions can express nothing that is higher. Ethics is transcendental. Ethics and aesthetics are one and the same.

So our question about the consequences of an action must be unimportant. For there must be something right about the question we posed. There must indeed be some kind of ethical reward and ethical punishment, but they must reside in the action itself. And it is also clear that the reward must be something pleasant and the punishment something unpleasant.

And the will as a phenomenon is of interest only to psychology. In short the effect must be that it becomes an altogether different world. It must, so to speak, wax and wane as a whole. The world of the happy man is a different one from that of the unhappy man.

If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present. Our life has no end in just the way in which our visual field has no limits.

Or is some riddle solved by my surviving for ever? Is not this eternal life itself as much of a riddle as our present life? The solution of the riddle of life in space and time lies outside space and time. It is certainly not the solution of any problems of natural science that is required. God does not reveal himself in the world. Feeling the world as a limited whole--it is this that is mystical. The riddle does not exist. If a question can be framed at all, it is also possible to answer it.

For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something can be said. Of course there are then no questions left, and this itself is the answer. Is not this the reason why those who have found after a long period of doubt that the sense of life became clear to them have then been unable to say what constituted that sense?

They make themselves manifest. They are what is mystical. Although it would not be satisfying to the other person--he would not have the feeling that we were teaching him philosophy--this method would be the only strictly correct one. He must so to speak throw away the ladder, after he has climbed up on it. He must transcend these propositions, and then he will see the world aright. Thus, we usually do not keep eBooks in compliance with any particular paper edition.

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