`What can be said', for Wittgenstein, has to do with language,
logic, and the world. His views on all three are interconnected in a very
special way. The
questions he raises in connection with language follow, in the main, Frege's cognitive orientation. What are the essential or necessary conditions, in the
use of factual language, that assure its having meaning, sense, and truth? The concern with logic centers on the question of what explains logical
necessity. Can its source be found in the general form of a proposition, or in the nature of the world, or in both? The concern with ontology-with what
can be said about the world-expresses itself in such questions as: What is the essential nature of the world? What is necessarily true of the world? What
must be its basic constituents?
To answer each of these questions is thereby to give the
limits of meaningful discourse, of logical necessity, of the basic constituents
of the world.
Indeed, an answer to any one of these sets of questions will turn out to be of the same underlying form and to involve at the same time the answers to
the other two. The three (theory of language, theory of logic, theory of the world) are essentially interconnected. They are three different aspects or
versions of one and the same philosophic enterprise. That enterprise (in part) is to give an account of what can be said, and, having given such an
account, to `disappear' as `nonsense'. The theories of language, logic, and the world `exhibit', `make manifest', `elucidate', `clarify' what are the most
fundamental, essential, necessary aspects of what can be said, of what can be known, of what exists. In setting out these fundamental, essential, and
necessary aspects, one is thereby setting out the limits of what can be said in language that is meaningful and true, of what can be known with logical
necessity, of what exists. But in doing all this, philosophy is not using language to give descriptions of some particular matters of fact (to give factual
knowledge and information or to register any factual discoveries). It is not doing what everyday uses of language or the sciences do. It is only pointing
out the `limits', the `domain', within which such particular meaningful use of language can take place, in which specific arguments having logical
necessity can be offered, and in which detailed empirical knowledge can be communciated about what happens to be the case.
The philosophy of the Tractatus is an integrated, carefully
worked out system, covering a large number of topics. It is exceedingly
compressed-only twenty thousand words long. It is written in an unconventional style-numbered statements, mostly short and aphoristic. These are
arranged in such a way that there are altogether seven leading propositions, numbered I through 7. Each of the leading propositions (except number 7)
is followed by others arranged in decimal fashion, e.g., 3.26, 3.261, 3.263. The last digit in any one of these numbered statements marks a comment on,
or application or extension of, the idea contained in the preceding proposition.
Wittgenstein arranged the major divisions of propositions
in an order he considered helpful and important in getting a sense of the
interconnections of his system, and of how it unfolds and develops out of certain basic theses. It is possible surely to read with profit the statements
arranged in this order. Indeed, once one has worked through the book in a variety of ways-after seeing it from various angles and in the multiple inner
interrelationships among its several parts-Wittgenstein's order of exposition is a prime way of examining it. However, for purposes of `getting into' his
network of thoughts, there are several different possible entry points, each of which has its special advantage or insight to offer. It is by no means clear
that Wittgenstein's arrangement offers the best sequence to follow on one's first approach to his thought. Accordingly, while there is no unique,
absolutely preferable entry point among these several possibilities, I shall in what follows choose one such sequence-one line of unfoldment of his
ideas-which, though admittedly not absolutely preferable to all others, has its special advantages.
I begin with two propositions that will allow us to explore,
through the orientation they provide and through an expansion of their
important side of Wittgenstein's thought. They have the advantage of reminding us of how Wittgenstein adapted for his own purposes some key
suggestions of Frege and Russell, thereby illustrating the kind of `stimulation' he owed to their thought.
3.3 Only propositions have sense; only in the nexus of a proposition does a name have meaning.The second half of the first of these statements recalls (it is virtually an exact restatement of) a dictum we encountered in Frege-one of the basic
3.318 Like Frege and Russell I construe a proposition as a function of the expressions contained in it.
Wittgenstein adopts Frege's distinction between sense
(Sinn) and reference (Bedeutung), but applies it differently from
the way Frege did. The term `Bedeutung', as used by
Wittgenstein, is translated by Pears and McGuiness by the word `meaning', and I shall adopt this usage in what follows. `Meaning' (Bedeutung), for Wittgenstein, corresponds to`reference' (Bedeutung) as distinguished from `sense'.
According to Frege, as we had seen, both names and sentences (propositions) have both sense and reference. The sense of a sentence is a function of the sense of its component parts. The sense of a name is the `route' by which one makes reference to an object, where the object is the referent of the name. While all names have sense, some lack referents,although in a scientific or perfected language all names would have referents. According to Frege, the referent of a sentence is its truth or falsity. If it is a compound (molecular) sentence, whose constituents are other sentences, its truth or falsity as a whole is functionally dependent on the truth or falsity of its constituent sentences. Once again, every wellformed sentence must be either true or false. The senses of the constituent parts of a sentence (names, concept-words, relation-expressions) provide the truth-conditions (provide the basis for determining the truth or falsity) of the sentence as a whole.
In the Tractatus Wittgenstein accepts some features and elements of Frege's semantics, just briefly summarized, and rejects others.
Wittgenstein differs from Frege in that for him only sentences have sense; names do not. He agrees with Frege, however, in claiming that the sense of a sentence is the way in which it specifies the truth-conditions of that sentence. By understanding the sense of a sentence we have a way by which to distinguish-among all possible states of affairs-those in which it is true from those in which it is false.
4.063 . . . in order to be able to say, "`p" is true (or false)', I must have determined in what circumstances I call `p' true, and in so doing I determine the sense of the proposition.Names, whose semantic role is to stand for objects, have meaning, i.e., reference. They do not, however, have sense. Since a name is not a sentence it is not either true or false. A namedoes not refer to a state of affairs or to a fact. States of affairs and facts are particular combinations or configurations of objects. They are complex, just as sentences are particularcombinations of names and are also, therefore, complex.
To understand a proposition is to understand its sense. However, this is not tantamount to knowing whether the proposition is true.
4.024 To understand a proposition means to know what is the case if it is true.
(One can understand it, therefore, without knowing whether it is true.)
It is understood by anyone who understands its constituents.
4.032 It is only in so far as a proposition is logically segmented that it is a picture of a situation.(Even the proposition, Ambulo, is composite: for its stem with a different ending yields a different sense, and so does its ending with a different stem.)
What does it mean to say that "only in the nexus of a proposition does a name have meaning"? Are there not situations-for example calling a roster of names, making a laundry list,using names as labels on bottles, and so on-where names are used meaningfully, though not in these circumstances in sentences? The point would be granted both by Frege andWittgenstein. What they are interested in stressing is not incompatible with the use of names in nonsentential roles. Rather, they maintain, it is because we know how to use names (weknow their semantic role) in sentences that we can also use them in nonsentential settings. For example,. if a person's nickname is `Red', we know how to differentiate the use of thisname from the word `red' in the sentence `Red is red', or `Red is a Red (a Communist)' .23 When we call, address, or list the person named `Red' we are not using the word `red' as referringto a type of color, or to a type of political affiliation. Similarly, if a bottle is labeled `Aspirin', and in this context we treat it as a mere label or name, this use also depends on our knowinghow the name `aspirin' can be joined to other words in a well-formed sentence, and how its role in such a sentence is different from, and can be linked with, other terms, for example,`the', `two', `Bayer', `after', and so on.
For Wittgenstein a sentence does not have as its referent truth or falsity, as Frege maintained. A sentence as a whole pictures a particular configuration of objects. A sentence, accordingto Wittgenstein, when fully analyzed, is made up of names. While each name refers to an object, the group of names that make up a sentence depicts the group of objects in somedeterminate interconnection with one another. These objects in their interconnections are in the world. A sentence, as a group of names, is also a group of objects. The special character ofthe names making up the sentence is that these serve as signs for other objects and their configurations.
As we had seen, Frege distinguished names, in the sense
of `singular terms', from concept-words and expressions for relations.
under the heading of `names' he included what we should recognize as ordinary proper names (e.g., `Socrates') and definite descriptions.
On Wittgenstein's view, neither ordinary proper names nor definite descriptions are logically proper names. (We might borrow the
expression `logically proper names' from Russell, to serve as another way of referring to what Wittgenstein simply calls `names'. However,
`names' in Wittgenstein's use are not to be equated with Russell's use of `logically proper names'. Russell takes primarily an
epistemological approach to them, and illustrates them by the use of the demonstratives `this' or `that' in connection with some
sense-datum-e.g., `this red now'. However, Wittgenstein's approach is primarily semantic and metaphysical. There is no reason to believe
he would have accepted Russell's account, or the examples Russell gives, as explicating his own conception of names and the objects for
which they stand.)
A name, for Wittgenstein, is something logically simple.
It is a simple sign; it cannot be analyzed or decomposed into other expressions
as constituents; it cannot be defined. What a particular name stands for (what it represents, the `meaning' it has) is a particular object. An
object, too, is something metaphysically simple, not further decomposable.
2.02 Objects are simple.As already remarked, for Wittgenstein there is a parallel or correlation between the use of simple signs (names) on the one hand, and
2.0201 Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes
3.2 In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.
3.201 I call such elements `simple signs', and such a proposition `completely analyzed'.
3.202 The simple signs employed in propositions are called names.
3.203 A name means an object. The object is its meaning. (`A' is the same sign as 'A' .)
3.21 The configuration of objects in a situation corresponds to the configuration of simple signs in the propositional sign.
3.22 In a proposition a name is the representative of an object.
3.221 Objects can only be named. Signs are their representatives. I can only speak about them; I cannot put them into words. Propositions can only say how things
are, not what they are.
What justification is there, however, for believing that
there are simple objects? Wittgenstein gives an argument (very compressed
its formulation) for this thesis, that we must now examine.
2.021 Objects make up the substance of the world. That is why they cannot be composite.The argument as here presented seeks to establish that there are, in the world, simple objects that make up the substance of the
2.0211 If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.
2.0212 In that case we could not sketch out any picture of the world (true or false).
Let the statement `The world has no substance' be represented
by `p'. Let the statement `Whether a proposition had sense would
depend on whether another proposition was true' be represented by `q'. Let the statement `We could not sketch out any picture of the
world which is true or false' be represented by `r'. Then the entire argument has the form:
If p then q, and if q then r.It is false, in other words, that the world has no substance; on the contrary, it does contain simple objects.
But r is false.
Hence q is false. (By denying the consequent of `if q then r' wecan deny the antecedent q.).
And if q is false, then p is false. (By denying the consequent of`if p then q', we can deny the antecedent p.)
Hence p is false.
The key step in this argument is 2.0211 above: If the
world had no substance (i.e., if there were no simple objects), then whether
tion had sense would depend on whether another proposition was true. If all objects were complex (nonsimple), then given any complex
object its analysis (its description and its decomposition into other objects) would not be terminal. For the complex object or objects
reached at one stage of analysis would require further analysis-into further descriptions and still further complex objects. The process of
analysis would lead to an infinite regress. Under these circumstances the sense of the original proposition could not be given completely. Its sense would not
be completely determinate. And since the sense of a proposition is what specifies the conditions, the states of affairs that allow for the determination of the truth
or falsity of the proposition, the original proposition, in being partly indeterminate in its sense, could not have its truth or falsity established. However, this result
is incompatible with our initial presupposition that every proposition having sense is either true or false. We must therefore give up the belief that there are only
complex, nonsimple objects in the world. The substance of the world must therefore consist of simple objects.
Once having established that the world consists of simple
objects as its substance, various consequences and corollaries follow.
Thus, a simple object,
since it does not contain any parts, cannot undergo any change; it must be unalterable. For change or alterability imply different arrangements of or
modifications in the makeup of something.
2.0271 Objects are what is unalterable and subsistent; their configuration is what is changing and unstable.A man, for example, being a complex object, may have his hair change color or fall out altogether. However, if an object is truly simple, no change can take
The meaning of a logically proper name is the simple object
it designates. Such a name occurs in a fully analyzed proposition. The
sense of the entire proposition
is thus dependent, in part, on the references (the `meanings') of the names in a fully analyzed proposition. To understand what else the sense of a proposition
depends on we must recognize that the objects in the world can belong to various configurations. The way in which particular objects are related to others in
some particular configuration in the world constitutes the basis for determining whether or not the names for these objects are themselves connected with one
another in a proposition to correspond with the configuration of the objects in the world.
Although simple objects constitute the substance of the
world-its content-it is also necessary to take into account their possible
interrelations with one another. The possibilities for combination of any one object with other objects is as necessary to its ontological status as the fact that it is
simple, unalterable, and common to all possible worlds.
2.0123 If I know an object I also know all its possible occurrences in states of affairs.The possibilities of the combinations of an object with other objects is what Wittgenstein calls the form of the object.
(Every one of these possibilities must be part of the nature of the object.)
A new possibility cannot be discovered later.
2.0124 If all objects are given, then at the same time all possible states of affairs are also given.
2.013 Each thing is, as it were, in a space of possible states of affairs.
2.014 Objects contain the possibility of all situations.Each simple object has its distinctive form, its distinctive possibilities for interconnection and concatenation with other objects. Every object exists in its own
2.0141 The possibility of its occurring in states of affairs is the form of an object.
2.013 Each thing is, as it were, in a space of possible states of affairs. This space I can imagine empty, but I cannot imagine the thing without theA speck in the visual field, though it need not be red, must have some colour: it is, so to speak, surrounded by colour-space. Notes must have
2.0131 A spatial object must be situated in infinite space. (A spatial point is an argument-place.)
We can thus conceive that for each simple object there
is a range of possibilities for linkage with other objects. The form of
an object defines its internal
properties, its distinctive range of possible configurations with other objects. The internal properties of an object are such that it is unthinkable that the
object should be without them.
4.123 A property is internal if it is unthinkable that its object should not possess it.What particular, determinate linkages an object has with other objects constitutes its external properties and relations. These belong to the particular configurations (from among allpossible ones) into which an object happens to fall. The internal properties and relations of objects are, however, not explicitly stated in a proposition that contains names for such simpleobjects. The proposition can only explicitly state the relations holding among objects. It thereby shows, at the same time, the internal, formal properties and relations of the objectsinvolved.
(This shade of blue and that one stand, eo ipso, in the internal relation of lighter to darker. It is unthinkable that these two objects should not stand in this relation.)
4.122 In a certain sense we can talk about formal properties of objects and states of affairs, or, in the case of facts, about structural properties: and in the same sense about formal relations and structural relations.It is impossible, however, to assert by means of propositions that such internal properties and relations exist: rather, they make themselves manifest in the propositions that
(Instead of `structural property' I also say 'internal property'; instead of `structural relation', 'internal relation'.
I introduce these expressions in order to indicate the source of the confusion between internal relations and relations proper (external relations), which is very widespread among philosophers.)
2.0231 The substance of the world can only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented-only by the configuration of objects that they are produced.A state of affairs (Sachverhalt) is thus what results from a particular configuration of objects.
2.0232 In a manner of speaking, objects are colourless.
The form of the particular objects involved in a particular state of affairs determines the structure of the state of affairs. Given particular objects, each of which has its own form
(its own range of possibilities for connections with other objects), the way in which those particular objects are connected with one another constitutes a state of affairs having a particular structure.
2.032 The determinate way in which objects are connected in a state of affairs is the structure of the state of affairs.
2.033 Form is the possibility of structure.
2.0272 The configuration of objects produces states of affairs.
2.03 In a state of affairs objects fit into one another like the links of a chain.
2.031 In a state of affairs objects stand in a determinate relation to one another.
Each state of affairs is simple; it is not composed of other states of affairs. It is composed of objects (themselves simple) in a particular configuration. The counterpart, in language, of a state of affairs is an elementary proposition, i.e., a proposition not containing other propositions as its components; an elementary proposition contains only names in a particular configuration with one another.
Among possible states of affairs we can distinguish existing states of affairs from nonexisting states of affairs. As a guide to this distinction let us consider the following pair of possibilities that concern objects in the ordinary, everyday use of the term 'object' (not in Wittgenstein's technical sense). We could say (1) George Washington was elected to be the first President of the United States, and (2) Thomas Jefferson was elected to be the first President of the United States. Both statements describe possible states of affairs. However, only the first statement is true. It describes an existing state of affairs. The second statement is false. It describes a possible state of affairs, but a nonexisting one. In a similar way, in Wittgenstein's ontology the simple objects can enter into various configurations with one another. An existing state of affairs is one containing particular objects in which a certain configuration holds or obtains.
An existing state of affairs is a fact (Tatsache).
2. What is the case-a fact-is the existence of states of affairs.
Since a state of affairs is simple, an existing state of affairs may be thought of as an atomic fact. A true atomic proposition is one that describes an atomic fact. Since, too, an existing state of affairs can be differentiated from nonexisting ones, it may also be considered a positive atomic fact.
Each state of affairs, being elementary, and whether existent or nonexistent, is independent of all other elementary states of affairs within the range of possibilities.
1.21 Each item can be the case or not the case while everything else remains the same.To understand what Wittgenstein means by the independence of states of affairs, let us use the following analogy.24 Suppose we had a world consisting of parallelepipeds of various sorts, each having sides of some particular height, width, and length. For example, one parallelepiped may have a height of 5 feet, a width of 3 feet, a length of 6 feet; another paralleepiped has a height of 9 feet, a width of 6 feet, a length of 10 feet; and so on. The numerical value of any one of the three dimensions of any particular
2.061 States of affairs are independent of one another.
2.062 From the existence or non-existence of one state of affairs it is impossible to infer the existence or non-existence of another.
An elementary state of affairs may be compared to a parallelepiped.
Each state of affairs, composed of its ontologically independent simple
objects, has its
properties determined by the structure into which the objects enter with one another. The objects and structural properties of one state of affairs are logically and
ontologically independent of what holds for other states of affairs. Both existent and nonexistent states of affairs belong to the total range of possibilities. Existing
states of affairs, however, are the only ones to be found in the world. Suppose in your home a certain collection of parallelepiped boxes is to be found. There are, in
`the world' of your home, the actual parallelepipeds (`the existing states of affairs') from among other possible ones. If one enlarged the scope of `the world' to
include a factory making boxes, or even all the boxes in the entire physical universe, these would still be the `existing' boxes (`states of affairs') from among all
The range of all possible states of affairs-existing and
nonexisting-defines the domain of logical space. Logical space is the sum
total of all possible states of
affairs, existing and nonexisting. The world, as the totality of all facts or existing states of affairs, belongs to logical space.
1.13 The facts in logical space are the world.Every existing state of affairs (bestehende Sachverhalt) constitutes an atomic fact. Such atomic facts may form parts of more complex-molecular-facts. The term `fact'
1. The world is all that is the case.The term `the world' (Die Welt) is used by Wittgenstein in its basic meaning to refer to the actual world, the sum total of existing states of affairs, of positive facts-
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by their being all the facts.
1.12 For the totality of facts determines what is the case, and also whatever is not the case.
2.04 The totality of existing states of affairs is the world.
On the other hand, Wittgenstein sometimes uses the term `the world' (as also the term `reality' (Wirklichkeit)) in a broader sense as well. In this use, `the world'
stands for the sum total of existing and nonexisting states of affairs, of positive and negative facts.
2.05 The totality of existing states of affairs also determines which states of cdfairs do not exist.
2.06 The existence and non-existence of states of affairs is reality.
(We also call the existence of states of affairs a positive fact, and their nonexistence a negative fact.)
2.063 The sum-total of reality is the world.
In their broader uses, the terms `the world' and `reality' can also designate what Wittgenstein means by `logical space', for the latter term stands for the sum total of
all possible states of affairs. These broader uses of `the world' and `reality' are not incompatible with the use of the term `the world' to mean the sum total of existing
states of affairs, the sum total of facts, the sum total of what is the case. In standing for these parts of logical space, what is excluded is also thereby determined. In
this way, the world as the sum total of positive facts `includes', in the sense of determining, what is not the case, not in the sense of having `negative facts' or
nonexisting states of affairs as parts of the world. `What is the case' and `what is not the case' are inseparable. In being constituted by the first, the world at the same
time also determines the second."
For Wittgenstein there is a close interconnection between
ontology (what can be said about the most general features of the world),
logic, and language. It is
futile to argue about whether, for him, the nature of the world is the `prior' matter whose `limits' determine the limits of language or of logic, or conversely whether it
is the analysis of the basic features of language and logic that are `prior' and determine what the world must be like. For Wittgenstein, there is no question of `priority'.
In exploring what can be said we are doing both-setting out both what can be said about the world and at the same time setting out what are the necessary features of
any `saying'; what must hold for any use of language as well as the necessary, unavoidable role of logic in any use of language.
Our expository comments thus far have been concerned mostly
with Wittgenstein's ontology-with what can be said about the constituents
of the world, its
objects, states of affairs, and facts. Let us turn to consider, now, what for Wittgenstein is the other side of the coin-what is involved in the use of language and logic. It
is to this `critique of language' that the bulk of the Tractatus is devoted.
We begin, as Wittgenstein does, with some general comments
about pictures and thoughts before coming to the heart of the matter-the
use of propositions. Propositions are
the basic units of language; they constitute special types of `pictures' and express thoughts. The study of propositions forms the core of Wittgenstein's analysis of the
nature of language and logic. In our review of what he has to say about propositions, we shall come upon such topics as his celebrated `picture theory of language',
the thesis that logical `laws' are tautologies, the distinction between a priori and empirical uses of language, and other matters.
Wittgenstein tells us that he obtained an important clue
to developing his theory of pictorial representation in general, and of
propositions as pictures in
particular, by reflecting on the practice in law courts of using small model toy automobiles and dolls to represent the pattern of a street accident. Von Wright, in his
Biographical Sketch of Wittgenstein, reports the following:
Wittgenstein told me how the idea of language as a picture of reality occurred to him. He was in a trench on the East front, reading a magazine in which there wasa schematic picture depicting the possible sequence of events in an automobile accident. The picture there served as a proposition; that is, as a description of apossible state of affairs. It had this function owing to a correspondence between the parts of the picture and things in reality. It now occurred to Wittgenstein that onemight reverse the analogy and say that a proposition serves as a picture, by virtue of a similar correspondence between its parts and the world. The way in which the partsof the proposition are combined-the structure of the proposition-depicts a possible combination of elements in reality, a possible state of affairsAny type of picture (e.g., maps, photographs, representational paintings, diagrams, musical scores, and propositions) presents a certain structure of parts or
2.14 What constitutes a picture is that its element determinate way.It has a sense insofar as it presents a particular structural arrangement. It cannot be a picture without already doing this. Its presentation of a particular
2.15 The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.
Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture.
2.151 Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.
Whether the structure of parts being presented by the pictorial form, as a possibility, actually exists or not in some situation or state of affairs in the world, cannot beread off from the picture alone. One has to go`outside' the picture to determine that. However, even if the picture does not represent some existing structure in the world, the pictur remains as it is with its determinate pictorial form. It depicts the same pictorial form whether there exists such a structural arrangement to correspond to it, or not.
2.22 What a picture represents it represents independently of its truth or falsity, by means of its pictorial form.The logical form of any picture consists in its serving to distinguish the possible existence of a state of affairs from its nonexistence. This is the common
2.221 What a picture represents is its sense.
2.222 The agreement or disagreement of its sense with reality constitutes its truth or falsity.
4.06 A proposition can be true or false only in virtue of being a picture of reality.
Pictures vary in the materials used to convey what they signify.
Some rely primarily on spatial arrangements, others on colors, still others
on sounds, and so on. Also each type of picture will involve its distinctive
mode of `projection', its own representational form or conventions for
relating the elements of the picture to what is being pictured. However,
regardless of the special character of the material medium used and the
conventions that govern the mode of representation, every picture also
has at the same time a logical form
2.18 What any picture, of whatever form, must have in common with reality, in order to be able to depict it-correctly or incorrectly-in any way at all, is logical form, i.e.the form of reality.
2.182 Every picture is at the same time a logical one. (On the other hand, not every picture is, for example, a spatial one.)
3.001 'A state of affairs is thinkable': what this means is that we can picture it to ourselves.
In what does a thought consist? Is a thought necessarily
conveyed by words, by linguistic signs? Russell, in studying the text of
the Tractatus, asked Wittgenstein that
very question. Russell wrote:
But a Gedanke [thought] is a Tatsache [fact]: what are its constituents and components, and what is their relation to those of the pictured Tatsache?2'And to this query, Wittgenstein replied:
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 constituents 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? No! But of psychical constituents that have the same sort of relation to reality as words. What those constituents are I don't know."'Insofar as a situation is thinkable, it can be conveyed by signs that are verbal, by linguistic signs. Propositions are the units of language, the structured ordering of
3.12 I call the sign with which we express a thought a propositional sign.-And a proposition is a propositional sign in its projective relation to the world.We can understand a proposition we never heard before because we can think about possible states of affairs.
A proposition depicts a possible state of affairs. It is thinkable. It can be said. We can understand it because it has sense. Its sense consists in depicting a position in
logical space. This position in logical space is the structure of a possible situation.
4.031 In a proposition a situation is, as it were, constructed by way of experiment.
Instead of, 'This proposition has such and such a sense', we can simply say, 'This proposition represents such and such a situation'.
4.027 It belongs to the essence of a proposition that it should be able to communicate a new sense to us.Another difference between a name and a proposition is this. A name to be meaningful must have an object for which it stands. If there is no object, the putative
4.03 A proposition must use old expressions to communicate a new sense.
Propositions are in this way different from names, for names are not pictures, in the way propositions are. The meaning of a name is established by convention, bycorrelating it with the object it refers to. This correlation needs to be explained or pointed out to us, otherwise we don't know what the name means. However, we dounderstand a proposition we never encountered before, for a proposition presents a concatenation of verbal signs, a structure. It has a sense
we can understand. In having this sense, it need not have a reference in the way a name does.
4.022 A proposition shows its sense.
A proposition shows how things stand if it is true. And it says that they do so stand.
The sense of a proposition has a position in logical space.
When we understand a proposition we understand what it says. What it says
is its sense. Take the
proposition, "Rome is on the same parallel of latitude as New York." Suppose we subsequently discover that what we have understood is in fact true. Or, conversely,
suppose we subsequently discover that what we have understood is false. In either case we have understood the same proposition. It takes only one `saying' to convey
a proposition with sense. Yet, as conveyed, there are two possible truth-values for the same proposition: it is either true or false. However, there are not two different
ways of saying what is true or false; there is only one way. And this one saying is the logical form of what is conveyed by or depicted in the kind of picture that a
A proposition as a composite linguistic sign has a sense
insofar as it depicts a possible state of affairs. It itself is a picture.
4.011 At first sight a proposition-one set out on the printed page, for example-does not seem to be a picture of the reality with which it is concerned. But no more doesmusical notation at first sight seem to be a picture of music, nor our phonetic notation (the alphabet) to be a picture of our speech.What Wittgenstein means by saying that the propositional sign is a likeness of what is signified should not, of course, be interpreted as saying that the letters, words, or
And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent.
4.012 It is obvious that a proposition of the form 'aR6' strikes us as a picture. In this case the sign is obviously a likeness of what is signified.
3.1432 Instead of, 'The complex sign "aRb" says that a stands to bin relation R', we ought to put, 'That "a" stands to "b" in a certain relation says that aRh.'This form is not itself, however, another sign or element among the signs that compose the total propositional sign. It cannot be represented by a sign of some kind in the
The fact that the sign "a" stands in a certain relation to the sign "b", and that this relation is represented in the proposition, enables the entire prop
ositional sign to function as a logical picture of a possible situation. A proposition then has a logical form that is exhibited in the way the words that compose the proposition are related to one another. The form of the wordstheir interconnections-is exhibited by the propositional sign.
A proposition as a logical picture says something. It
has a determinate sense and therefore is either true or false. An ordinary
descriptive or empirical proposition
(whether elementary or compound) is true under certain conditions, for certain situations, and false for others. However, this is not the case with tautologies and
contradictions. A tautology is always true; a contradiction is always false. Thus neither a tautology nor a contradiction is a picture of reality. A tautology cannot be false, and a contradiction cannot be true. A tautology-e.g., `It is either raining or not raining', is always true, and for this reason does not give us any particular information about the weather. Similarly, a contradiction-e.g., `This is black and not black', does not depict a particular state of affairs. It cannot be true, since it cancels itself.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.One of Wittgenstein's most important discoveries was that the socalled `laws of logic' (the rules that guide inferences and determine their validity) are themselves
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense.
(Like a point from which two arrows go out in opposite directions to one another.)
(For example, I know nothing about the weather when I know that it is either raining or not raining.)
4.4611 Tautologies and contradictions are not, however, nonsensical. They are part of the symbolism, just as `0' is part of the symbolism of arithmetic.
4.462 Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and the latter none.
6.1 The propositions of logic are tautologies.Wittgenstein gives examples of the way in which it can be shown that the propositions of logic are tautologies:
6.11 Therefore the propositions of logic say nothing. (They are the analytic propositions.)
6.113 It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone, and this fact contains in itself the whole philosophy of logic. 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.
6.12 The fact that the propositions of logic are tautologies shows the formallogicalproperties of language and the world.
6.1201 For example, the fact that the propositions `p' and `--p' in the combination `--(p . w-p)' yield a tautology shows that they contradict one another. The fact that the propositions `p D q', 'p', and 'q', combined with one another in the form ~(P D 9) ~ (P) : D : (q)' , yield a tautology shows that q follows from p and p D g. The fact that `(x) .fx : D fa' is a tautology shows that fn[There follows a truth table demonstrating that the law of inference known as "modus ponens" is indeed a tautology.]
follows from (x)~ fr. Etc., etc.
Wittgenstein draws the consequences of this analysis of the status of the laws of logic as tautological.
6.124 The propositions of logic describe the scaffolding of the world, or rather they represent it. They have no `subject matter' . . .Insofar as logical laws are tautologies, they exhaust all possibilities; they exhibit what is necessary. They can be known a priori; they are analytic.
6.1251 Hence there can never be surprises in logic.
6.127 All the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived
Every tautology itself shows that it is a tautology.
Elementary propositions consist of names for objects,
arranged in a certain way. If true, they represent the existing states
of affairs (the
`atomic facts') in the world. Propositions other than elementary ones consist of logical combinations of elementary ones. Such logical combinations
make use of various logical constants, for example, `not', `and', `if. . then'. The truth or falsity of a composite (nonelementary) proposition depends
on the particular type of logical constant used to link the elementary propositions that compose it and therefore on the particular combination of
truth or falsity of the elementary propositions so linked. For example, the entire statement `p and q' is true only if both conjuncts are true; on the
other hand, the entire statement 'p or q' is true if at least one of the alternates is true or, otherwise put, `not (not p and not q)'. Propositions other
than elementary ones are thus truth functions of elementary propositions. Logical constants, though used in the formulation of compound
propositions, do not, however, represent either objects or configurations of objects in the world. There is nothing in the world to correspond to `and',
`not', or to `if then'. The only objects in the world are those for which names can be provided in elementary propositions. These are objects that are
configured in states of affairs. The logical constants (e.g., `not', `and', `if then') do not stand for or represent any kinds of special objects or
structures of objects in the world in addition to the simple objects designated by names in elementary propositions and their configurations in states
4.0311 One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole presents a state of affairs.For the same reason, the signs `T' or `F' to mark the truth or falsity of propositions do not stand for any objects in the world.
4.0312 The possibility of propositions is based on the principle that objects have signs as their representatives.
My fundamental idea is that the `logical constants' are not representatives; that there can be no representatives of the logic of facts.
4.441 It is clear that a complex of signs `F' and 'T has no object (or complex of objects) corresponding to it, just as there is none corresponding to the horizontal and vertical lines or to the brackets.-There are no `logical objects'.Let us summarize the main points thus far made about Wittgenstein's views about `what can be said'. The domain of `what can be said'