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This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts. It is therefore not a text-book. Its object would be attained if it afforded pleasure to one who read it with understanding.
The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.
The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).
The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.
How far my efforts agree with those of other philosophers I will not decide. Indeed what I have here written makes no claim to novelty in points of detail; and therefore I give no sources, because it is indifferent to me whether what I have thought has already been thought before me by another.
I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts.
If this work has a value it consists in two things. First that in it thoughts are expressed, and this value will be the greater the better the thoughts are expressed. The more the nail has been hit on the head.—Here I am conscious that I have fallen far short of the possible. Simply because my powers are insufficient to cope with the task.—May others come and do it better.
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 mistaken in this, then the value of this work secondly consists in the fact that it shows how little has been done when these problems have been solved.
1 The world is everything that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by these being all the facts.
1.12 For the totality of facts determines both what is the case, and also all that is not the case.
1.13 The facts in logical space are the world.
1.2 The world divides into facts.
1.21 Any one can either be the case or not be the case, and everything else remain the same.
2 What is the case, the fact, is the existence of atomic facts.
2.01 An atomic fact is a combination of objects (entities, things).
2.011 It is essential to a thing that it can be a constituent part of an atomic fact.
2.012 In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.
2.0121 It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit.
If things can occur in atomic facts, this possibility must already lie in them.
(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)
Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things.
If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.
2.0122 The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)
2.0123 If I know an object, then I also know all the possibilities of its occurrence in atomic facts. (Every such possibility must lie in the nature of the object.) A new possibility cannot subsequently be found.
2.01231 In order to know an object, I must know not its external but all its internal qualities.
2.0124 If all objects are given, then thereby are all possible atomic facts also given.
2.013 Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.
2.0131 A spatial object must lie in infinite space. (A point in space is an argument place.)
A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a pitch, the object of the sense of touch a hardness, etc.
2.014 Objects contain the possibility of all states of affairs.
2.0141 The possibility of its occurrence in atomic facts is the form of the object.
2.02 The object is simple.
2.0201 Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.
2.021 Objects form the substance of the world. Therefore they cannot be compound.
2.0211 If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.
2.0212 It would then be impossible to form a picture of the world (true or false).
2.022 It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.
2.023 This fixed form consists of the objects.
2.0231 The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.
2.0232 Roughly speaking: objects are colourless.
2.0233 Two objects of the same logical form are—apart from their external properties—only differentiated from one another in that they are different.
2.02331 Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them.
For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.
2.024 Substance is what exists independently of what is the case.
2.025 It is form and content.
2.0251 Space, time and colour (colouredness) are forms of objects.
2.026 Only if there are objects can there be a fixed form of the world.
2.027 The fixed, the existent and the object are one.
2.0271 The object is the fixed, the existent; the configuration is the changing, the variable.
2.0272 The configuration of the objects forms the atomic fact.
2.03 In the atomic fact objects hang one in another, like the links of a chain.
2.031 In the atomic fact the objects are combined in a definite way.
2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.
2.033 The form is the possibility of the structure.
2.034 The structure of the fact consists of the structures of the atomic facts.
2.04 The totality of existent atomic facts is the world.
2.05 The totality of existent atomic facts also determines which atomic facts do not exist.
2.06 The existence and non-existence of atomic facts is the reality.
(The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)
2.061 Atomic facts are independent of one another.
2.062 From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another.
2.063 The total reality is the world.
2.1 We make to ourselves pictures of facts.
2.11 The picture presents the facts in logical space, the existence and non - existence of atomic facts.
2.12 The picture is a model of reality.
2.13 To the objects correspond in the picture the elements of the picture.
2.131 The elements of the picture stand, in the picture, for the objects.
2.14 The picture consists in the fact that its elements are combined with one another in a definite way.
2.141 The picture is a fact.
2.15 That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.
This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.
2.151 The form of representation is the possibility that the things are combined with one another as are the elements of the picture.
2.1511 Thus the picture is linked with reality; it reaches up to it.
2.1512 It is like a scale applied to reality.
2.15121 Only the outermost points of the dividing lines touch the object to be measured.
2.1513 According to this view the representing relation which makes it a picture, also belongs to the picture.
2.1514 The representing relation consists of the co-ordinations of the elements of the picture and the things.
2.1515 These co-ordinations are as it were the feelers of its elements with which the picture touches reality.
2.16 In order to be a picture a fact must have something in common with what it pictures.
2.161 In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.
2.17 What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.
2.171 The picture can represent every reality whose form it has.
The spatial picture, everything spatial, the coloured, everything coloured, etc.
2.172 The picture, however, cannot represent its form of representation; it shows it forth.
2.173 The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.
2.174 But the picture cannot place itself outside of its form of representation.
2.18 What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.
2.181 If the form of representation is the logical form, then the picture is called a logical picture.
2.182 Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)
2.19 The logical picture can depict the world.
2.2 The picture has the logical form of representation in common with what it pictures.
2.201 The picture depicts reality by representing a possibility of the existence and nonexistence of atomic facts.
2.202 The picture represents a possible state of affairs in logical space.
2.203 The picture contains the possibility of the state of affairs which it represents.
2.21 The picture agrees with reality or not; it is right or wrong, true or false.
2.22 The picture represents what it represents, independently of its truth or falsehood, through the form of representation.
2.221 What the picture represents is its sense.
2.222 In the agreement or disagreement of its sense with reality, its truth or falsity consists.
2.223 In order to discover whether the picture is true or false we must compare it with reality.
2.224 It cannot be discovered from the picture alone whether it is true or false.
2.225 There is no picture which is a priori true.
3 The logical picture of the facts is the thought.
3.001 "An atomic fact is thinkable"—means: we can imagine it.
3.01 The totality of true thoughts is a picture of the world.
3.02 The thought contains the possibility of the state of affairs which it thinks.
What is thinkable is also possible.
3.03 We cannot think anything unlogical, for otherwise we should have to think unlogically.
3.031 It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an "unlogical" world how it would look.
3.32 To present in language anything which "contradicts logic" is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.
3.0321 We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.
3.04 An a priori true thought would be one whose possibility guaranteed its truth.
3.05 Only if we could know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).
3.1 In the proposition the thought is expressed perceptibly through the senses.
3.11 We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs.
The method of projection is the thinking of the sense of the proposition.
3.12 The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projective relation to the world.
3.13 To the proposition belongs everything which belongs to the projection; but not what is projected.
Therefore the possibility of what is projected but not this itself.
In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it.
("The content of the proposition" means the content of the significant proposition.)
In the proposition the form of its sense is contained, but not its content.
3.14 The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way.
The propositional sign is a fact.
3.141 The proposition is not a mixture of words (just as the musical theme is not a mixture of tones).
The proposition is articulate.
3.142 Only facts can express a sense, a class of names cannot.
3.143 That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.
(For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word. Thus it was possible for Frege to call the proposition a compounded name.)
3.1431 The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.
The mutual spatial position of these things then expresses the sense of the proposition.
3.1432 We must not say, "The complex sign 'aRb' says 'a stands in relation R to b'"; but we must say, "That 'a' stands in a certain relation to 'b' says that aRb".
3.144 States of affairs can be described but not named.
(Names resemble points; propositions resemble arrows, they have sense.)
3.2 In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.
3.201 These elements I call "simple signs" and the proposition "completely analysed".
3.202 The simple signs employed in propositions are called names.
3.203 The name means the object. The object is its meaning. ("A" is the same sign as "A".)
3.21 To the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs.
3.22 In the proposition the name represents the object.
3.221 Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.
3.23 The postulate of the possibility of the simple signs is the postulate of the determinateness of the sense.
3.24 A proposition about a complex stands in internal relation to the proposition about its constituent part.
A complex can only be given by its description, and this will either be right or wrong. The proposition in which there is mention of a complex, if this does not exist, becomes not nonsense but simply false
That a propositional element signifies a complex can be seen from an indeterminateness in the propositions in which it occurs. We know that everything is not yet determined by this proposition. (The notation for generality contains a prototype.)
The combination of the symbols of a complex in a simple symbol can be expressed by a definition.
3.25 There is one and only one complete analysis of the proposition.
3.251 The proposition expresses what it expresses in a definite and clearly specifiable way: the proposition is articulate.
3.26 The name cannot be analysed further by any definition. It is a primitive sign.
3.261 Every defined sign signifies via those signs by which it is defined, and the definitions show the way.
Two signs, one a primitive sign, and one defined by primitive signs, cannot signify in the same way. Names cannot be taken to pieces by definition (nor any sign which alone and independently has a meaning).
3.262 What does not get expressed in the sign is shown by its application. What the signs conceal, their application declares.
3.263 The meanings of primitive signs can be explained by elucidations. Elucidations are propositions which contain the primitive signs. They can, therefore, only be understood when the meanings of these signs are already known.
Excerpted from Tractatus Logico-Philosophicus by Ludwig Wittgenstein, C. K. Ogden. Copyright © 1999 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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