A translation of elements of Tractatus Logico-Philosophicus by Ludwig
Wittgenstein, the German text being first published in Annalen der
Naturphilosophie, 1921.

Foreword of the Author

This book will perhaps only be understood (by) he who has already of
himself similarly thought the thoughts which are herein expressed-or even
similar thoughts.-It is no textbook.-Its purpose would have been attained
if it had caused pleasure for one who read it with understanding.
The book treats the philosophical problems and shows-as I believe-, that
the issue-position of these problems is based on the misunderstanding of
the logic of our language.  One might gather the whole sense of the book
somewhat in the words:  What could be said altogether, could be said
clearly; and where one cannot speak of it, one must be silent about it.
The book thus desires to draw a limit to thought, or rather-not to thought,
but rather to the expression of thoughts:  Because to draw a limit around
thoughts, we must be able to think of both sides of this border (we must
thus be able to think what cannot be thought).
The limit will be able to be drawn therefore only in language, and what
lies on the other side of the border will simply be nonsense.
How widely my endeavors coincide with those of other philosophies I would
rather not guage.  Indeed, what I have here written makes in detail no
claim of originality; and I also declare no sources, because it makes no
difference to me whether what I have thought has already been thought
before me by another.
However I would like to mention that I owe a great deal to the great works
of Frege and to the labor of my friend Mr. Bertrand Russell for stimulus of
my thoughts.


Logical-Philosophical Treatise
1*  The world is everything that is the case.
1.1  The world is the summation of facts, not of things.
1.11  The world is identified by means of the facts and since all facts are it.
1.12  For the summation of the facts identifies what the case is and
everything which is not the case.
1.13  The facts in logical space are the world.
1.2  The world divides into facts.
1.21  The case can be of one or not be the case and everything remaining
(would) remain the same.

*The decimal-listing as ordinals of the individual sentences signifies the
logical weight of the sentences, from out of which spreads the emphasis in
my representation.  The sentences n.1, n.2, n.3, etc. are comments to the
sentences No. n; the sentences n.m1, n.m2, etc. comments to sentences
No.n.m; and so on.


2  What the case is, the fact, is the existence of states of affairs.
2.01  A state of affairs is a union of objects (affairs, things).
2.011  It is essential to a thing to be able to be a component of a state
of affairs.
2.012  In logic nothing is accidental:  If a thing in a state of affairs is
able to exist, the possibility of the state of affairs must already be
predetermined in the thing.
2.0121  It would appear as it were accidental if a circumstance would
subsequently suit the thing that alone could exist of itself.  If things
can occur in states of affairs, then these (things) must already lie within
them.
(In logic, something cannot be only-possible.  Logic deals with every
possibility and all possibilities are its facts.)
Since we are not able to imagine spatial objects without space, nor
temporal outside of time, we can imagine no object outside of the
possibility of its connection with others.
If I can imagine the object in association with the state of affairs, then
I cannot imagine it outside of the possibility of this association.
2.0122  A thing is self-standing insofar as it can happen in all possible
circumstances, but this form of self-sufficiency is a form of associating
with the state of affairs, a form of internal self-sufficiency.  (It is
impossible for words to appear in two different manners, alone and in a
sentence.)
2.0123  If I know an object, then I know all possibilities of its occurence
in states of affairs.
(Every such possibility must lie in the nature of the object.)
It is not possible for a new possibility to be subsequently found.
2.01231  To know an object, I must indeed not know its external but rather
all of its internal properties.
2.0124  All objects are given, thus all possible states of affairs are
given therewith.
2.013  Every thing is, as it were, in a space of possible states of
affairs.  I can imagine this space empty, but not the thing without the
space.
2.0131  A spatial object must lie in limitless space.  (A spatial point is
a premise.)  A spot in the field of vision must not necessarily be red, but
it must have some color:  it has, so to speak, color-space around itself.
A tone must have a pitch, an object of the sense of touch a hardness, etc.
2.014  Objects contain the possibility of all circumstances.
2.0141  The possibility of its occurence in states of affairs is the form
of objects.
2.02  An object is simple.
2.0201  Each statement concerning complexes can be broken into a statement
concerning its components and into the individual propositions which
completely describe the complexes .
2.021  Objects form the substance of the world.  Therefore they cannot be
put together.
2.0211  Had the world no substance, then whether a proposition has meaning
would depend on whether another proposition is true.
2.0212  It would in such a case be impossible to craft an image of the
world, whether true or false.
2.022  It is apparent that even an imagined world, although of the real and
different from it, must have something-a form-in common with the real one.
2.023  This fixed form consists precisely of objects.
2.0231  The substance of the world can only determine form and not material
qualities.  Thus these [materially qualities] are represented only through
propositions-only constructed by means of the configuration of objects.
2.0232  In a manner of speaking: an object is colorless.
2.0233  Two objects of the same logical form are-apart from their external
qualities-distinguished from one another only through their differences.
2.02331  Either a thing has qualities that no other has, in which case one
can distinguish it from the others immediately by means of a description
and point to it; or however there are many things which have the whole
qualities in common, in which case it is altogether impossible to point  to
one of them.  For were a thing distinguished through nothing, then I am not
able to distinguish it because it would then be displayed.
2.024  Substance consists of that which is independent of that which is the
case.
2.025  It [substance] is form and content.
2.0251  Space, time and color [lit. colorfulness] are forms of objects.
2.026  There can be a fixed form of the world only if there are objects.
2.027  Fixity, consistency, and objects are one.
2.0271  An object is fixed, consistent; the configuration [of objects] is
that which changes, the inconsistent.
2.0272  The configuration of objects forms the states of affairs.
2.03  Objects are suspended together in a state of affairs like the links
of a chain.
2.031  Objects interact with one another in a state of affairs in a
determined manner and way.
2.032  The manner and way objects are connected together in a state of
affairs is the structure of the state of affairs.
2.033  Form is the possibility of structure.
2.034  The structure of a fact consists of the structures of the states of
affairs.
2.04  The totality of consistent states of affairs is the world.
2.05  The totality of consistent states of affairs also determines which
states of affairs do not exist.
2.06  The existence and non-existence of states of affairs is reality.
(We recognize the existence of the states of affairs as a positive, the
non-existence as a negative fact.)
2.061  The states of affairs are not dependent upon one another.
2.062  The existence or non-existence of a state of affairs cannot be
determined from the existence or non-existence of another.
2.063  The sum total of reality is the world.
2.1  We make for ourselves images of the facts.
2.11  An image introduces circumstances into the logical space, the
existence and non-existence of states of affairs.
2.12  An image is a model of reality.
2.13  Objects correspond in an image to the elements of the image.
2.132  In an image, the elements of the image represent the objects.
2.14  An image consists of the interaction of its elements with one another
in a definite manner and way.
2.141  An image is a fact.
2.15  That the elements of an image interact with one another in a definite
manner and way [leads to the idea] that matters [Sachen] likewise interact
with one another.
The relationship of the elements of an image is called its structure and
possibility its form of illustration.
2.151  The form of illustration is the possibility that things interact
with one another as elements of an image.
2.1511  In this way is the image linked with reality; it reaches up to it.
2.1512  It is applied as a standard to reality.
2.1512  Only the extreme points of the [standard's] divisions touch (or,
are in common with) the measured objects.
2.1513  According to this understanding, the depicted relationship, which
is what makes the image into an image, itself belongs to the image.
2.1514  An illustrated relationship consists of associations between the
elements of the image and articles.
2.1515  These associations are as it were the feelers of the elements of
the image, with which the image touches upon reality.
2.16  To be related to an image, a fact must have something in common with
what is illustrated.
2.161  Something must be identical in an image and what is illustrated, and
it is thereby that the one can be an image of another at all.
2.17  What an image must have in common with reality in order to be able to
illustrate it concerning its manner and way-correctly or incorrectly-is its
form of illustration.
2.171  An image can illustrate any reality whose form it has.
A spatial image can illustrate anything spatial, a colored image anything
colored, etc.
2.172  But an image cannot illustrate its form of illustration; it exhibits it.
2.173  An image represents its subject from outside (its stand-point is its
form of representation), which is why an image represents its subject
correctly or falsely.
2.174  But an image cannot present itself outside of its form of representation.
2.18  Whatever its form, what every image must have in common with reality
to be illustrate it at all-correctly or falsely-is logical form, which is
the form of reality.
2.181  Since the form of illustration is logical form, an image is called a
logical image.
2.182  Every image is therefore also a logical image.  (In contrast, every
image is not necessarily a spatial image, for example.)
2.19  A logical image can illustrate the world.
2.2  An image has the logical form of illustration in common with what is
illustrated.
2.201  An image illustrates reality by representing a possibility of
existence and nonexistence of states of affairs.
2.202  An image represents a possible circumstance in the logical space.
2.203  An image contains the possibility of the circumstance that it represents.
2.21  An image corresponds with reality or does not; it is right or wrong,
true or false.
2.22  An image represents what it represents independently of its truth or
falsehood through the form of illustration.
2.221  What an image represents is its sense.
2.222  Its truth or falsehood consists in the correspondence or lack of
corresponce of its sense to reality.
2.223  In order to discern whether an image is true or false, we must
compare it with reality.
2.224  Whether it is true or false cannot be discerned from an image alone.
2.225  There is no such thing as an 'a priori true image.'


3.  An idea is a logical image of facts.
3.001  "A state of affairs is imaginable" means that we can fabricate an
image of it.
3.01  The sum of true ideas is an image of the world.
3.02  An idea contains the possibility of the circumstance that it
considers.  What is imaginable is also possible.
3.03  We cannot think of the illogical because, if this were so, we would
think illogically.
3.031  It was once said that god could create anything except for what was
against logical principles.-That is to say, we could not speak of how an
"illogical" world would have appeared.
3.032  It is as impossible to represent something "of contradictory logic"
in language as it is in geometry to represent through its coordinates a
figure contradicting one of the principles of space, or as impossible as it
is to indicate the coordinates of a point that does not exist.
3.0321 We can easily represent a spatial state of affairs that runs counter
to the principles of physics but we cannot represent such a one that runs
counter to the principles of geometry.
3.04  An a priori correct idea would be one whose truth was necessitated by
possibility.
3.05  Only in this way could we know a priori that an idea is true:  if its
truth were recognizable from the idea itself (without a subject to compare
to it).
3.1  In a proposition, an idea shows itself as sensibly perceptible.
3.11  We use the sensibly perceptible sign (phonetic sign or letter etc.)
of a proposition as a projection of the possible circumstance.
The method of projection is the thought of the sense of the proposition.
3.12  A sign through which we express an idea is what I call a
propositional sign.  And a proposition is a propositional sign in its
projective relation to the world.
3.13  Anything that belongs to a proposition belongs to its projection; but
not to what is projected.
Consequently the possibility of what is projected, but not of this itself.
Consequently its sense is not contained in the proposition, but it does
contain the possibility to express it.
("The content of a proposition" is what the content of a sensible
proposition is called.)
The form, but not the content, of its sense is contained in a proposition.
3.14  A propositional sign exists in such a way that its
elements-words-interact in a definite manner and way.
A propositional sign is a fact.
3.141  A proposition is not merely a mixture of words.  (Just as a musical
theme is not merely a mixture of tones.)
A proposition is articulated.
3.142  Only facts are able to express a meaning; a system of classification
cannot.
3.143  That a propositional sign is a fact is disguised by the typical form
of expression of written letters or of print.
Thus in printed propositions, for example, a propositional sign does not
seem significantly different from words.
(Thus it was possible for Frege to designate a proposition as a compound name.)
3.1431  The essence of propositional signs is very clear, if we think of it
as composed of spatial objects (such as tables, chairs, books), rather than
of written signs.
Then the interrelated spatial arrangement of these objects will express the
sense of the proposition.
3.1432  Not:  "The complex sign 'aRb' means that a is connected to b by R,"
but rather: That "a" is related to "b" in a certain way means that aRb.  [A
difficult sentence.]
3.144  Circumstances can be described but not named.  (Names are like
points, propositions are like [geometric] rays [lit: arrows]; they have
sense.)
3.2  An idea can be expressed in a proposition in such a way that elements
of the propositional sign correspond to the objects of the idea.
3.201  Such elements I call "simple signs" and their proposition "fully
analyzed."
3.202  Those simple signs that are employed in a proposition are called names.
3.203  A name signifies an object.  An object is its signification.  ("A"
is the same sign as "A".)
3.21  The configuration of simple signs in a propositional sign correspond
to the configuration of objects in a circumstance.
3.22  In a proposition, a name represents an object.
3.221  I can only name objects.  Signs represent them.  I can only speak of
them; I cannot articulate them.  A proposition can only say how a thing is,
not what it is.
3.23  The requirement of possibility of simple signs is the requirement of
certainty of sense.
3.24  A proposition which deals with something complex is internally
related to a proposition that deals with the components of the complex.
A complex can only be shown through its description, and this will be
either correct or not.
That an element of a proposition indicates a complex can be seen from an
indeterminateness in the proposition in which it occurs.  We know that
everything is not determined through such a proposition.  (Indeed, the
general designation contains an archetype.)
The condensation of the symbols of a complex into a simple symbol can be
expressed through a definition.
3.25  There is one and only one complete analysis of a proposition.
3.251  What a proposition expresses it expresses in a determined manner,
which can be set out clearly:  a proposition is articulated.
3.26  No definition can further analyze a name:  a name is a primitive sign.
3.261  Each defined sign is indicative by way of every sign through which
it is defined; and definitions show the way.
Two signs-one primitive and one defined through a primitive sign-cannot
indicate in the same manner and way.  A name cannot be analyzed through
definitions.  (No sign alone and independent has a meaning.)
3.262  Their application shows what signs do not express.  Their
application pronounces what signs slur over.
The meanings of primitive signs can be explained through elucidations.
Elucidations are propositions that contains primitive signs.  Consequently,
they can only be known if the meanings of these signs are already known.
3.3  Only a proposition has a sense; a name has meaning only in connection
with a proposition.
3.31  Any part of a proposition that characterizes its sense is what I call
an expression (a symbol).
(A proposition itself is an expression.)
Expression is everything instrinsic to the sense of the proposition, and is
what propositions can have in common with one another.
An expression identifies form and content.
3.311  An expression presupposes the forms of all propositions in which it
can occur.  It is the same charactersitic mark of a class of propositions.
3.312  It becomes consequently represented through the general form of
proposition that it characterizes.
And indeed the expression becomes constant in this form and everything
remaining is variable.
3.313  Consequently, an expression is represented through a variable, whose
values are the propositions containing the expression.
(In the limiting case, a variable becomes a constant and an expression
becomes a proposition.)
I call such a variable "a propositional variable."
3.314  An expression has meaning only in a proposition.  Every variable is
regarded as a propositional variable.
(Likewise for variable names.)
3.315  If we transform a component of a proposition into a variable, then
there is a class of propositions all of which are values of the developed
variable proposition.  Generally this class, according to arbitrary
convention, will be dependent on what we mean by parts of each [original]
proposition.  Yet if we transform each and every sign whose meaning is
arbitrarily determined into a variable, then there will be such a class
anyway.  But this [one] is not dependent upon any convention but rather
upon the nature of the proposition.  It corresponds to a logical form-a
logical archetype.
3.316  What values a propositional variable is permitted to take is stipulated.
The stipulation of values is the variable.
3.317  The stipulation of the value of a propositional variable is what a
proposition declares, of which proposition a variable is the common mark.
A stipulation is a description of such propositions.
Thus a stipulation will be concerned only with symbols, not with meanings.
And this only is essential of a stipulation, that it is only a description
of a symbol and does not make a statement about characteristics.
How the description of a proposition occurs is unimportant.
3.318  Like Frege and Russell, I regard a proposition as a function of the
expressions contained within it.
3.32  A sign is what is sensibly perceptible of a symbol.
3.321  Two different symbols therefore can have a sign (a written or spoken
sign, etc.) in common-in such a case, they are indicative in different
manners and ways.
3.322  That we indicate objects by the same sign but through two different
modes of signification can never indicate a common characteristic of the
two.  For a sign is indeed arbitrary.  One could therefore even choose two
different signs, and then where does the commonality in the designation
remain?
3.323  It is particularly frequent in colloquial speech for the same word
to designate different manners and way-and thus belong to different
symbols-or for two words that designate different manners and ways to be
superficially employed in similar ways in a proposition.
Thus the word "is" appears as copula, as a sign of equality, and as an
expression of existence; "to exist" appears as an intransitive verb like
"to go"; "identical" appears as an adjective; we speak of some thing, but
also say by it that something happens.
(In the proposition:  "Green is green"-where the first word is the proper
name of a person and the last is an adjective-these words do not simply
have different meanings, but rather they are different symbols.)
3.324  And so arise the fundamental confusions (of which all philosophy is
full).
To avoid these errors, we must make use of a language of signs, which
excludes them by not employing the same sign for different symbols and by
not employing signs which designate different manners, and by not
superficially employing them in the same way.  Thus a language of signs,
that of the logical grammars-of the logical syntaxes-obeys.

EOF