STEFAN BRANDT
In his essay “Being and Being Known” (1963), Wilfrid Sellars attributes to Aquinas and the early Wittgenstein the view that “knowledge involves an isomorphism of the knower with the known” (p.41). He suggests that this view implies that what he calls “intellectual acts” differ in their “intrinsic character as acts” when they differ in content. Sellars claims that this view compares favorably with views according to which intellectual acts do not differ in content by virtue of differences in themselves but “by virtue of being directly related to different relata” (p.41). These relata are traditionally either construed as contents, which have merely “being‐for‐mind” and are the “immediate and primary objects of knowledge” (p.42), or as objects and states of affairs in the “real order” (p.42). Philosophers holding the first variant of the relational view, which Sellars associates with Descartes, typically have difficulties explaining the relation between the contents of intellectual acts and the genuinely mind‐independent objects and states of affairs in the world these acts are supposed to represent, and are therefore naturally tempted by some form of idealism or skepticism. Philosophers committed to the second variant of the relational view, which Sellars associates with early twentieth‐century British and American realism, have notorious difficulties accounting for false thoughts. Since, according to them, the contents of true intellectual acts simply are the objects and states of affairs they represent, the content of false intellectual acts must also be the objects and states of affairs they represent. But if an intellectual act is false then there are no such objects or states of affairs. Hence, it seems as though false intellectual acts do not have content. But that is absurd. Thinking falsely is not the same as thinking nothing. Realists are therefore typically driven to introduce new and ontologically dubious entities: nonexistent but still subsistent objects and states of affairs that are the content of false representations.
At least as far as the interpretation of Wittgenstein is concerned, Sellars perfectly captures a false dilemma that was very much on Wittgenstein’s mind in both his early and his late thinking on intentionality; and he correctly identifies how the early Wittgenstein tried to avoid this dilemma, namely by assuming an “isomorphism of the knower with the known.”
In this chapter, I shall first discuss Wittgenstein’s early account of intentionality in his Tractatus Logico‐Philosophicus as a sophisticated attempt to avoid Sellars’s dilemma for relationist theories of thought. Wittgenstein’s later views will then emerge as a fundamental rejection of central assumptions underlying his earlier account.
As Sellars suggests, in the Tractatus Wittgenstein aims to give an account of intentionality that retains the realist insight that when we represent truly how things are – in thought, language, or by any other means – what we represent is identical with what is the case, while avoiding the mistake of thinking of the contents of false representations as somehow subsistent but not existent objects and states of affairs. And he indeed does so by postulating an isomorphism between our representations and what they represent. All intentional phenomena are pictures of states of affairs, i.e., they model how things are and are therefore isomorphic with the reality they represent (see TLP 2.12, 4.01; see also Chapter 7, LOGICAL ATOMISM and Chapter 8, the PICTURE THEORY). However, before we can properly appreciate how intentional phenomena “picture” or “model” reality we have to understand the nature of the states of affairs that our representations depict. I therefore begin my exposition of the so‐called “picture theory” with a few remarks on ontology.
According to the Tractatus the world consists of facts (TLP 1.1) and a fact is “the existence of states of affairs” (TLP 2). States of affairs are possible combinations of objects (TLP 2.01). The objects constituting states of affairs are ontologically simple (2.02, 2.021) and exist necessarily (2.021, 2.024, 2.027–2.0271). The combinatorial possibilities of objects determine which states of affairs are possible (2.014). Hence, objects make up “the substance of the world” (2.021). The combinatorial possibilities of an object are its “logical form” (2.0141, 2.0233). Thus, the logical forms of the simple objects determine what can be the case. Their actual combination determines what is the case, i.e., what facts obtain.
The pictures with which we represent states of affairs are themselves facts (TLP 2.141). They are existing combinations of elements, which stand for the elements making up the depicted state of affairs (2.131). Wittgenstein claims that a picture can only depict a state of affairs if it has something in common with it, namely its “pictorial form”:
There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all.
What a picture must have in common with reality, in order to be able to depict it – correctly or incorrectly – in the way it does, is its pictorial form.
(TLP 2.161–2.17)
The pictorial form of a picture is a function of the pictorial forms of its elements. It can consist in a multiplicity of commonalities between the elements of the picture and the objects constituting the depicted state of affairs (TLP 2.171) but it at least consists in a shared logical form of the picture and the pictured (2.18). This means that the combinatorial possibilities of the elements of the picture within pictures must exactly match the combinatorial possibilities within states of affairs of the objects they stand for. A picture, which shares a logical form with the states of affairs it depicts, is a “logical picture” (2.181). Since every picture shares at least a logical form with what it depicts “[every] picture is at the same time a logical one” (2.182).
Still, a shared logical form is not sufficient to make a specific picture into the picture of a specific state of affairs. Here is why: it is plausible to assume that the logical form of a pictorial element only suffices to specify a determinate object as its referent if there is no more than one object with that form. For otherwise it would be unclear to which one of the several objects sharing its form the pictorial element referred. So, if we wish to say that the pictorial forms of pictorial elements suffice to determine their referent, we must assume that there are never several objects with the same logical form. If we make the further plausible assumption that an object cannot normally occur simultaneously in all the states of affairs it can potentially occur in, then we must conclude that the occurrence of an object in one state of affairs excludes the possibility that certain other states of affairs obtain, in which this object could occur. That, however, is incompatible with a fundamental commitment of Wittgenstein’s, namely the idea that states of affairs are independent of one another (TLP 2.061–2.062). So, it seems that Wittgenstein assumed that there are normally several objects with the same logical form (2.0233). And this implies that the logical forms of the elements of pictures alone cannot determine their referents (pace Winch, 1987).
Wittgenstein therefore concludes that a picture also includes a “pictorial relationship” to what it depicts. This pictorial relationship “consists of the correlations of the picture’s elements with things” (TLP 2.1514). These correlations Wittgenstein describes as “feelers […] with which the picture touches reality.” Only once they are set up can the picture “[reach] right out” to reality (2.1511) and depict exactly what is the case if it is true.
In TLP 3, Wittgenstein says: “A logical picture of facts is a thought [Gedanke].” The noun “Gedanke,” just like the English “thought,” is commonly used in a psychological or a semantic sense. In its psychological sense it refers to acts of thinking; in its semantic sense, in which Frege famously uses it, it refers to the content of such an act. Wittgenstein does not appear to use “Gedanke” here in its psychological sense. There is no reason to think that he wishes to say that if something is a logical picture then it is an act of thinking. After all, he explicitly says that all pictures are logical pictures (2.182). So he must be using “Gedanke” in its semantic sense. But unlike Frege, he does not conceive of thoughts as abstract objects in a “third realm” of ideas (Frege [1918]1997b), which are the senses of used sentences. He rather employs “Gedanke” to speak about types of pictures. In other words, a picture has a certain thought as its content by instantiating it, and it instantiates a specific thought by having a specific logical form and by standing in a pictorial relationship to a specific state of affairs. It does not have specific content by being related to an abstract Fregean sense.
One form in which a thought in this sense can be instantiated is in a proposition:
In a proposition a thought finds an expression that can be perceived by the senses.
(TLP 3.1)
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.
(TLP 3.2)
Wittgenstein is not saying that in a proposition an inner mental act is overtly expressed nor that propositions express abstract inhabitants of Frege’s “third realm,” but rather that in a proposition a logical picture, i.e., a thought in the semantic sense, can be made visible to the senses. This happens when the proposition is expressed in its fully analyzed form, i.e., when the proposition contains a sign for every element of the thought it expresses. This idea allows Wittgenstein to investigate the nature of intentional phenomena quite generally, i.e., the nature of all those phenomena that have a thought or Gedanke as their content, by investigating the nature of propositions. He thereby realizes the strategy that he announces in the preface of the Tractatus, namely to investigate the limits of thinking by investigating the limits of language. Hence, I shall now turn to the Tractarian account of propositions.
Like all representations, propositions are pictures of states of affairs. Their pictorial form is their logical form; i.e., they are “logical pictures” in the narrow sense that they do not share anything with the states of affairs they depict except their logical form. They are either (so‐called) elementary propositions or truth functions of elementary propositions (TLP 4.51, 5). An elementary proposition is a concatenation of names (4.22). The names occurring in elementary propositions are the fundamental units of linguistic representation; they are the “elements” of propositional pictures. They are indefinable “primitive signs” (3.26), which stand for the simple objects that constitute states of affairs. A name shares the logical form of the object it stands for and the object is its meaning or Bedeutung (3.203).
Wittgenstein distinguishes between “propositions” and “propositional signs” (3.12). Propositional signs are the acoustical and visual signs we use in speech and writing. The propositional signs we employ in ordinary language are not usually composed of simple names (4.002). Hence, ordinary language often disguises the thoughts it is used to express. However, according to the Tractatus, we can express every proposition in its true logical form, i.e., as a truth function of elementary propositions containing only simple names (3.2). If we do so, the propositional sign represents via the simple names that are correlated with the simple objects constituting the depicted states of affairs. For it is one of the central thoughts of the Tractatus that the only other signs occurring in fully analyzed propositions, i.e., the truth‐functional connectives, do not have a representative function: “My fundamental idea is that the ‘logical constants’ are not representatives” (4.0312).
In order for a propositional sign to become a proposition it has to be used as “a projection of a possible situation” (TLP 3.11). The question is: how do we use a propositional sign in such a way? According to Wittgenstein we have to think its sense: “The method of projection is to think of the sense of the proposition” (TLP 3.11).
But what does it mean to think the sense of a proposition? It can be said to involve usually three, but minimally two, different activities. First, if the propositional sign we employ does not reflect the true form of the thought it expresses, we have to accompany the sign with a thought that has this form. If a proposition is expressed in its fully analyzed form, however, this is not necessary. In that case we only have to do two things. First, we have to give the simple names a specific logical form. This is done by the use of a sign within a language (3.327). Second, like all pictures, linguistic pictures include a pictorial relationship to the states of affairs they depict (2.1513). This means that the simple names making up the proposition have to be correlated with the simple objects that are their meaning.
How are these correlations established? In the Tractatus Wittgenstein fails to give an answer. Still, his remark in TLP 3.11 that the method of projecting a propositional sign onto states of affairs consists in “thinking of the sense of the proposition” (my emphasis) intimates how he conceives of these correlations. Since even fully analyzed propositions have to be projected onto states of affairs, this remark might suggest that apart from thinking of the analysis of a propositional sign there is a further activity of thinking involved when we project a sign. This may be the mental activity of correlating simple names with the objects that are their meaning. This is also suggested by remarks Wittgenstein made both before and after he wrote the Tractatus. In Notes on Logic, dating from 1913, Wittgenstein says that the relation between names and their meanings is “psychological” (NB 104) and in a letter to Russell, written after the completion of the Tractatus, he writes that investigating this relation is “irrelevant” since it is “a matter of psychology” (NB 130). And psychology, he stresses in the Tractatus, is not part of philosophy: “Psychology is no more closely related to philosophy than any other natural science” (TLP 4.1121).
But why does Wittgenstein think that investigating the relation of the constituents of a proposition to the constituents of the depicted fact is not part of philosophy but of psychology? A clue to his answer can again be found in the early Notes on Logic:
Just as little as we are concerned, in logic, with the relation of a name to its meaning, just so little are we concerned with the relation of a proposition to reality, but we want to know the meaning of names and the sense of propositions.
(NB 102)
This remark is puzzling. Is not an interest in the senses of propositions and the meanings of names eo ipso an interest in the relations of names to their meanings and propositions to reality? How can Wittgenstein say that the former is a concern of logic but the latter is not? His answer seems to be this (see also Ammereller, 2001, pp.119–20): logic and philosophy are concerned with the role of names and propositions in language. The role of a name is to stand for an object; that of a proposition is to represent a state of affairs. Propositions and names can only fulfill their respective roles if names are correlated with objects. However, the “psychological mechanism” of meaning a specific object by a name or of understanding a specific object as the referent of a name by means of which the “correlations” between names and objects are established is not itself part of logic. The correlations of names and objects, and hence the “pictorial relationship” between propositions and pictures they establish, are indeed a part of every picture, since without them the picture would not depict what it depicts, but they are of no concern to the logician or philosopher who merely wishes to understand the different semantic functions of propositions and names.
According to this interpretation Wittgenstein makes the very natural assumption that in order to use a proposition with a sense we have to understand it or mean something by it. Additionally, he makes the – as he later came to recognize injudicious – assumption that meaning and understanding consist in some kind of mental activity or process of correlating names with objects, whose exact nature ought to be investigated by the sciences rather than philosophy.
We are now in a position to understand the account of intentionality in the Tractatus. Propositions are pictures of states of affairs. They depict states of affairs via the names occurring in elementary propositions, which stand for the necessarily existing simple objects that make up states of affairs. Names stand for objects in virtue of two properties: (a) they share the “logical form” of the object that is their meaning or Bedeutung; (b) they are correlated with this object, presumably by means of some mental mechanism of meaning or understanding. By being analyzable into an arrangement of simple names every proposition presents a possible arrangement of simple objects: “In a proposition a situation is, as it were, assembled by way of experiment” (TLP 4.031, my translation). If the objects making up states of affairs are assembled in the way their names are assembled in the propositional picture, the proposition is true; if not, it is false. Since a shared logical form of names and objects is a condition for the possibility of sense, every proposition represents a possible state of affairs but not necessarily an actual one.
The picture theory goes a long way toward avoiding both horns of the dilemma facing relational conceptions of thought. On the one hand, as realists rightly stress, what a true proposition represents is identical with what is the case. Since every name making up a fully analyzed proposition is immediately correlated with an object in reality that is its meaning, every proposition “reaches right out to [reality]” (TLP 2.1511). The pictorial relationship between picture and state of affairs is part of the picture (2.1513); it is an “internal relation” (4.014). In other words, it is part of the identity of a picture that its elements are correlated with specific elements of reality and the picture as a whole is thereby correlated with a possible state of affairs. Hence there is no content, which as Sellars puts it, has merely “being‐for‐mind,” is the “primary and immediate object of knowledge” (Sellars, 1963, p.42) and somehow indirectly relates our representations to the facts that make them true.
On the other hand, Wittgenstein stresses that a proposition does not stand in the same relation to reality as a name. Whereas names only have a meaning or Bedeutung but no sense or Sinn, propositions have a sense but no meaning:
Situations can be described, but not given names.
(Names are like points; propositions like arrows – they have sense.) (TLP 3.144)
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.
(TLP 3.221)
Names merely stand for objects but do not present them as being a certain way. They merely have a referent or Fregean Bedeutung, but they do not have a Fregean sense (see also TLP 3.3) or “mode of presentation” (Frege, [1892] 1997a). Propositions, on the other hand, have a sense; they represent things as being thus‐and‐so. By being an arrangement of names, which share the logical forms of the objects they stand for, a proposition, as it were, exhibits a possible situation but does not refer to it. Hence, contrary to the “extreme realist” view Sellars criticizes, a proposition can represent a state of affairs although this state of affairs neither exists nor subsists. A false proposition is not directed at some alternate reality of subsisting but not existing objects and states of affairs; it rather represents a possible but not actual combination of actual objects. A false proposition, just like a true proposition, “reaches right out to [reality]” via the names of which it is composed.
Furthermore, with his “fundamental idea” that logical constants do not represent (TLP 4.0312) Wittgenstein does justice to the intuition that a negative proposition denies the very fact that the negated proposition affirms. Since there is no object corresponding to the negation sign a negative proposition represents exactly the same states of affairs as the corresponding positive proposition. It merely says that these states of affairs do not obtain. Wittgenstein puts this as follows: “The propositions ‘p’ and ‘not‐p’ have opposite sense, but there corresponds to them one and the same reality” (4.0621). Negative propositions are not directed at ontologically dubious negative facts, as “extreme realists” might be tempted to argue; they are directed at exactly the same reality as the propositions they negate.
Finally, since Wittgenstein’s account of propositional representation applies to all phenomena that have a Fregean thought as their sense, i.e., to all those mental phenomena that are nowadays subsumed under the label of “propositional attitude,” the picture theory of the proposition can be understood as providing a perfectly general account of intentionality.
While the picture theory goes a long way towards providing a general account of intentionality in terms of linguistic representation and does so in a way that prima facie avoids both horns of Sellars’s dilemma for relationist theories of thought, on closer scrutiny, the early Wittgenstein does not seem to be entirely successful at meeting either of these explanatory goals. First, in his explanation of how we use propositions to represent states of affairs he relies on an unexplained mental activity of connecting names with objects. In order to represent a specific state of affairs with a proposition we have to connect the names making up the proposition with objects making up the state of affairs through an underlying activity of meaning or understanding. It seems that the intentionality of propositions derives from this underlying mental activity. This is at odds with Wittgenstein’s ambition to provide a completely general account of intentionality in terms of linguistic depiction. Furthermore, since he thinks that thoughts are logical pictures, whose elements, as he points out in a letter to Russell, “have the same sort of relation to reality as words” (NB 131), this view has the odd consequence that we have to project our own thoughts onto the reality they represent through underlying activities of meaning and understanding.
Second, Wittgenstein is not entirely successful at avoiding the problems of the view Sellars calls “extreme realism.” Although he does not have to admit subsistent but nonexistent objects and states of affairs, which correspond to false or negative propositions, he is still forced to postulate necessarily existing simple objects, which are the meanings of the names occurring in elementary propositions.
These problems are consequences of Wittgenstein’s conception of the “pictorial relationship.” The first stems from his assumption that the pictorial relationship between names and objects is established by a psychological mechanism, which does not have to be explained by philosophy. The second is a corollary of the idea that all pictures include the pictorial relationship. Since the pictorial relationship between names and objects is part of every proposition with a sense, there has to be an object corresponding to every name occurring in its fully analyzed form. After all, the pictorial relationship has to relate the picture to something.
In his later philosophy Wittgenstein sharply criticized both the idea that the use of propositions with a sense requires the accompaniment of mental activities or processes of meaning and understanding, and the idea that a relation to objects in reality is a part of every meaningful proposition. I shall begin my discussion of Wittgenstein’s later views on intentionality with some of these criticisms.
There is great intuitive appeal to the idea that whenever we use language we have to accompany the use of overt signs by inner activities of meaning and understanding. In his later writings Wittgenstein shows a strong interest in this conception of language and a keen awareness of its attractions. He writes:
It seems that there are certain definite mental processes bound up with the working of language, processes through which alone language can function. I mean the processes of understanding and meaning. The signs of our language seem dead without these processes; and it might seem that the only function of the signs is to induce such processes […] Thus, if you are asked what is the relation between a name and the thing it names, you will be inclined to answer that the relation is a psychological one.
(BB 3)
“There is a gap between an order and its execution. It has to be closed by the process of understanding.”
“Only in the process of understanding does the order mean that we are to do THIS. The order – why, that is nothing but sounds, ink‐marks. –”
(PI §431)
These remarks capture a very intuitive idea about how meaning is at all possible. It can appear puzzling how mere physical things such as sounds and ink marks can be intentionally directed at other things. How can a name, which is, after all, only a sound or a mark on paper, stand for a specific object? How can an order, which seems to consist merely of “dead signs,” determine the action that is its execution? A natural answer is that it is through the mental accompaniments of meaning and understanding that an order determines its execution and a name its referent – just as Wittgenstein thought when writing the Tractatus.
However, it is rather unclear how such a mental accompaniment can fix the meanings of signs, as Wittgenstein brings out with a well‐known example in PI §185 (see also Chapter 24, RULES AND RULE‐FOLLOWING). He asks his reader to imagine a pupil being instructed to develop different series of integers and being given exercises and tests up to 1000. His teacher then tells him to develop the series of even integers. He proceeds correctly up to 1000 and then continues with “1004, 1008, 1012, etc.” When asked to continue to add two, he claims to be doing so. What is it about the teacher’s order that means that the pupil’s continuation of the series after 1000 does not conform to it? It’s difficult to give an answer. For even if the teacher thought of the series of even integers, he cannot have thought of all its instances:
So when you gave the order “+2”, you meant that he was to write 1002 after 1000 – and did you then also mean that he should write 1868 after 1866, and 100 036 after 100 034, and so on – an infinite number of such sentences?
(PI §186)
Obviously, the teacher could not have thought of all these steps. Still he clearly meant his pupil to write “1002” after “1000” and “1868” after “1866” (see PI §§187, 693). As Wittgenstein suggests, one would like to say that although the teacher could not have thought of all these steps, he meant his order in a specific way and from this all its applications follow (PI §186). But how can something that is now in my mind achieve this remarkable feat, which cannot be achieved by mere “dead” signs?
Here it is easy to be led into thinking that facts about meaning are just very special, “inordinate” facts (PI §§191–2); that meaning and understanding are special mental phenomena, which in a “strange way” (§195) already contain the correct uses of the words we are employing. But when we think about meaning in this way we replace a puzzle, i.e., the question of how signs come to have meaning, by a mystery, i.e., the idea that they acquire it through underlying mental phenomena that contain all their correct uses. It is like supposing that in meaning the order to add two “your mind, as it were, flew ahead and took all the steps before you physically arrived at this or that one” (§188).
Trying to avoid this assumption might lead us to think that signs are given meaning by an interpretation. But this is not so (disregarding a small class of special cases such as the interpretation of poems, say). If signs cannot determine their meaning neither can an interpretation. The teacher and the pupil of PI §185 might agree on an interpretation for the order “+2” – e.g., “Write down the series that is determined by the formula n = 2n” – and still disagree about what to do. The teacher might think that the pupil has to write “1398” after “1396” while the pupil believes he ought to write “1400.” Adding further interpretations will not help, as teacher and pupil might again agree on an interpretation while continuing to disagree about what to do, and so on ad infinitum. If the meaning of an order or a rule is determined by an interpretation, no order or rule can determine what one has to do to follow it. This may seem paradoxical. Thus Wittgenstein writes:
This was our paradox: no course of action could be determined by a rule, because every course of action can be brought into accord with the rule. The answer was: if every course of action can be brought into accord with the rule, then it can also be brought into conflict with it. And so there would be neither accord nor conflict here.
(PI §201)
It is possible to give many conflicting interpretations for a rule, such as “+2.” But that means that the rule ceases to tell us anything. Rules divide the space of possible actions into those that accord with them and those that do not; if they generally fail to do so they do not make sense. Furthermore, the problem Wittgenstein illustrates with the example of the deviant pupil is perfectly general. For any statement we can think of we can think of a variety of conflicting interpretations. Hence, we cannot give signs a specific meaning by means of an interpretation.
Some interpreters, most prominently Kripke (1982), have suggested that this means that there cannot be such a thing as linguistic meaning and that Wittgenstein thought as much. Although Kripke’s interpretation is subtle and intriguing, the view he presents is implausible and also mistaken as an interpretation of Wittgenstein. Wittgenstein says explicitly that the “paradox” of PI §201 rests on a “misunderstanding.” It is quite clear that the misunderstanding in question is the idea that signs are given meaning by an interpretation. Hence, we should not interpret him as arguing that since interpretations cannot give signs a sense nothing can. He is rather arguing that meaning is not determined by interpretations. Interpretations should be thought of as substitutions of one expression for another (PI §§198, 201) and we can only give an expression meaning through such a substitution if the substituting expression already has a meaning. Hence interpretations cannot initially confer meaning onto signs.
Rather than by an interpretation the connection between a rule and its execution and a sign and its employment is made by the use of the rule or sign in a linguistic practice (PI §§197–9, 201–2). Quite generally it is the use of signs in “language‐games” that gives them their meaning or “life” and not anything accompanying their employment on a particular occasion, such as the mental activity of interpreting signs, i.e., of translating them into different signs: “If we had to name anything which is the life of the sign, we should have to say it was its use” (BB 4; see also PI §§43, 432).
It is important not to misunderstand Wittgenstein’s invocation of use and linguistic practices at this point. For example, when he says that “the meaning of a word is its use in the language” (PI §43), he does not mean that we can simply give expressions meaning by employing them with certain illocutionary and perlocutionary aims. We can only use expressions that way when they already have a meaning. Nor is he at any point suggesting that the meaning of signs can be reduced to their use, e.g., that we can give a description of the use of a sign in non‐semantic terms from which a description of its meaning follows. It is part of the point of the scenario of the deviant pupil that this is impossible. The actual applications of “+2” understood in non‐semantic terms do not furnish the pupil with a standard of how to proceed after 1000. After all, it is assumed that no applications after 1000 have been made. But if we understand “+2” as being used to express the order or rule to add two these signs do furnish the pupil with such a standard. So when Wittgenstein says that “the meaning of a word is its use in the language,” he is not saying that meaning can be reduced to use, but is merely making the “grammatical” observation that we can only attribute semantic properties to expressions if they have an established use in a linguistic practice. Since “+2” has such a use, it determines what one has to do to follow it. Expressions that do not have such a use, on the other hand, cannot be used to mean anything, regardless of what is going through our mind while producing them. We cannot, for example, mean “If it doesn’t rain, I shall go for a walk” by saying “bububu” (boxed remark after PI §35), although we can think the thought while making the noise.
Just as the use of signs is not anything “co‐existing” with them (BB 5), so understanding signs is not an accompanying mental process either. It is rather a kind of ability:
[Understanding], the knowledge of the language, isn’t a conscious state that accompanies the sentences of the language […]. It’s much more like the understanding or mastery of a calculus, something like the ability to multiply.
(PG 50)
Understanding is not a mental process. It is a kind of potentiality and not an actuality. To understand a statement consists in the ability to do certain things with it, just as understanding how to multiply consists in the ability to perform certain mathematical operations. And just as the latter ability is exercised in the multiplications we perform and does not consist in what goes through our minds while performing them, so our understanding is exercised in what we do with, and in response to, statements and not in what goes through our minds while hearing or making them. Occasionally we may exercise our understanding by translating or interpreting some statement but usually we do not. Furthermore this activity of translating will only be an exercise of understanding if we understand the translation. Hence “there is a way of grasping a rule which is not an interpretation, but which […] is exhibited in what we call ‘following the rule’ and ‘going against it’” (PI §201). The understanding that those who follow a rule thereby display is an ability that is exercised in the very actions they perform and not in what goes through their mind while performing them.
The second mistake informing the Tractarian conception of the pictorial relationship I shall discuss is the idea that this relationship is included in the picture. Wittgenstein brings out this mistake by distinguishing between the “method of projection” and “projection lines” (see PG 213). He says that when describing a worker constructing an artifact from a blueprint we may call “the way in which the workman turns such a drawing into an artefact ‘the method of projection’” (PG 213). We might think of this method as mediating between the picture, i.e., the blueprint, and the artifact, and compare it to “projection lines which go from one figure to another” (PG 213). This, however, can be misleading:
This comparison conceals the fact that the picture plus the projection lines leaves open various methods of application; it makes it look as if what is depicted, even if it does not exist in fact, is determined by the picture and the projection lines in an ethereal manner; every bit as determined, that is to say, as if it did exist. (It is ‘determined give or take a yes or no.’) In that case what we may call ‘picture’ is the blueprint plus the method of its application. And we now imagine the method as something which is attached to the blueprint whether or not it is used.
(PG 213)
If we think of the method of projecting a blueprint in terms of projection lines, we might come to think of the blueprint as in some sense containing lines, which connect parts of it with corresponding parts of the artifact. The only question then left open by the blueprint is whether the parts of the artifact are assembled as depicted. Hence, the blueprint determines the artifact “give or take a yes or no.”
As we have seen, this is the way Wittgenstein thought about the “pictorial relationship” in the Tractatus. There he thought that the simple elements of pictures are connected through the pictorial relationship to the simple objects making up the depicted state of affairs. If the picture has a sense, these simple objects exist and the depicted state of affairs is possible. All the picture leaves open is whether the state of affairs obtains. Hence: “A proposition must restrict reality to two alternatives: yes or no” (TLP 4.023).
Later, Wittgenstein came to think that this line of thought is the result of a “confusion” of the method of projection with the projection lines (PG 213). It confuses the representation of the use of a representation, i.e., the projection lines, with the use of a representation, i.e., the method of projection. We may think of the projection lines as part of the picture (PG 213–14), since they are what Wittgenstein on other occasions calls a “means of representation” (e.g. PI §50), i.e., a means of representing how a picture is to be projected. But such a means of representation is itself a representation and like all representations “leaves open various methods of application.” It does not connect a representation with what it represents, as the “pictorial relationship” is supposed to do. This would even be true if the projection lines consisted of actual strings connecting blueprint and artifact. In that case the artifact itself becomes part of the representation. It becomes a sample (PI §16) of the kind of object that is to be made from the blueprint. The method of projection, on the other hand, does connect the picture and the pictured. After all, it is “the way in which the workman turns […] a drawing into an artifact.” However, it is not included in the picture. It does not precede the use of the picture in a concrete situation: “[If] the method of projection is a bridge, it is a bridge which isn’t built until the application is made” (PG 213).
Ultimately the confusion at the root of the idea that the pictorial relationship is included in the picture, i.e., the confusion of a representation of the use of a representation with a use of a representation, also underlies the idea that this relationship is established by a mental process or activity. Once we have discarded the idea of meaning and understanding as containing in a “strange way” all the ways in which words are and can be used, the only candidates for mental activities that give signs their “life” are interpretations that users of language have in mind. But interpretations, regardless of whether we merely think of them or produce them in speech or writing, are nothing more than specifications of the meaning, i.e., the use, of expressions. An interpretation of what someone said may correctly specify the use she made of the expressions she employed but it cannot replace this use. It must itself have a use before it means anything and this use is given to it by the way it is employed in “language‐games” and not attached to it in an “ethereal manner.”
The idea of a pictorial relationship between thought and language on the one hand and states of affairs on the other is an essential element of the Tractarian explanation of how thought and language reach “right out to [reality].” Since all representations are made up of simple elements that are (a) immediately related through the pictorial relationship to simple objects and (b) share the logical form of these objects, what a thought represents is identical with what is the case if it is true. In his later thinking Wittgenstein holds on to the idea that thought and language “reach right out” to reality. He writes:
“Thinking must be something unique.” When we say, mean, that such‐and‐such is the case, then, with what we mean, we do not stop anywhere short of the fact, but mean: such‐and‐such – is – thus‐and‐so.
(PI §95)
“A thought – what a strange thing!” – But it does not strike us as strange when we are thinking. A thought does not strike us as mysterious while we are thinking, but only when we say, as it were retrospectively, “How was that possible?” How was it possible for a thought to deal with this very object? It seems to us as if we had captured reality with the thought.
(PI §428)
The idea Wittgenstein expresses by saying that “we do not stop short of the fact” in what we say and that our thoughts seem to “capture” reality is clearly the same idea he expressed in the Tractatus by saying that pictures “reach right out” to reality: the ability of thoughts, beliefs, and speech acts to determine exactly at what object, event, or state of affairs they are directed.
Wittgenstein is right about this phenomenon. All intentional acts and states determine exactly what their so‐called “intentional objects” are, i.e., they determine exactly what objects, events, or states of affairs they are directed at. There is a necessary relation between our representations and their objects. If I think that Caesar crossed the Rubicon, it is necessarily of Caesar and of the Rubicon that I think that the former crossed the latter. If I were not thinking of Caesar and the Rubicon my thought would not be the same. However, we might wonder how Wittgenstein can account for this after rejecting the pictorial relationship. If it is wrong to assume that our representations include a relationship to their intentional objects, how can there be a necessary relation between representations and their objects? Wittgenstein’s answer is simple. There is a necessary relation between representations and their objects but it is not a relation between, on the one hand, mind and language, and on the other, the world, but it is a relation within language. He writes:
“The proposition determines in advance what will make it true.” Certainly, the proposition “p” determines that p must be the case in order to make it true; and that means: (the proposition p) = (the proposition that the fact p makes true). And the statement that the wish for it to be the case that p is satisfied by the event p, merely enunciates a rule for signs: (the wish for it to be the case that p) = (the wish that is satisfied by the event p).
(PG 161–2)
“An order orders its own execution.” So it knows its execution before it is even there? – But that was a grammatical proposition, and it says: if an order runs “Do such‐and‐such”, then doing such‐and‐such is called “executing the order”.
(PI §458)
It is in language that an expectation and its fulfilment make contact.
(PI §445)
The necessary relation between our wishes, propositions, and orders and their intentional objects is explained by the “grammatical,” and hence necessary, fact that we attribute and express the former with the same words with which we describe and refer to the latter (see Chapter 14, GRAMMAR AND GRAMMATICAL STATEMENTS and Chapter 21, NECESSITY AND APRIORITY; cf. Chapter 15, the AUTONOMY OF GRAMMAR). For example, if Jack expects Jill to arrive, he can express his expectation with such sentences as “Jill will arrive” or “I expect Jill to arrive,” and we can attribute this expectation to him with such statements as “Jack expects Jill to arrive.” If Jack’s expectation is fulfilled, we can use the same words to speak about the event that fulfills it, namely “Jill arrived,” “Jill is arriving,” etc.
What is true of expectations is true of intentional phenomena generally. We typically attribute intentional acts and states by combining an expression referring to a person with an expression for the type of act or state attributed and with a clause specifying the content of the act or state – typically a declarative clause (e.g., in “A believes that her car has been stolen”), an interrogative clause (e.g., in “A wonders whether her car has been stolen”), or an infinitival clause (e.g., in “A wants to catch the thief”). What Wittgenstein is suggesting is that we can always use the expressions that we use to specify the content of a person’s intentional act or state, and that that person herself might use to express that act or state, to speak about the intentional objects of that act or state.
This grammatical fact not only explains the necessary connection between true thoughts, executed orders, and fulfilled expectations and their objects, it also explains how even false and negative representations can “reach right out to [reality].” If Jack thinks that Caesar did not cross the Volga and Jill thinks that Caesar killed Mark Antony then there are no events at which Jack’s and Jill’s thoughts are directed. Hence we cannot use the sentences occurring in the content‐clauses of “Jack thinks that Caesar did not cross the Volga” and “Jill thinks that Caesar killed Mark Antony” to speak about events, whose occurrence is responsible for the truth of Jack’s negative thought and the falsity of Jill’s positive thought. Still we can use the expressions “Caesar,” “the Volga,” and “Mark Antony,” which occur in these content‐clauses, to speak about actual objects, namely two Roman generals and a river in Russia. And it is because we use “Caesar” to refer to Caesar, “Mark Antony” to refer to Mark Antony, and “the Volga” to refer to the Volga that Jack’s negative thought and Jill’s false thought are still directed at Caesar, Mark Antony, and the Volga. Here is how Wittgenstein puts it:
The agreement, the harmony, between thought and reality consists in this: that if I say falsely that something is red, then all the same, it is red that it isn’t. And in this: that if I want to explain the word “red” to someone, in the sentence “That is not red”, I do so pointing to something that is red.
(PI §429)
In Philosophical Grammar Wittgenstein says: “Like everything metaphysical the harmony between thought and reality is to be found in the grammar of language” (162). We are now in a position to appreciate this remark. In the Tractatus Wittgenstein assumed a complex isomorphism between thought and reality in order to explain how thought can reach “right out to it.” All our representations, he held, are pictures of states of affairs consisting of simple elements that stand for necessarily existing simple objects that are their meaning or Bedeutung, share their “logical form,” and make up the depicted state of affairs. Later, Wittgenstein came to realize that the “internal” pictorial relation that appeared to make this metaphysical harmony necessary is merely a “shadow of grammar.” The ability of thought and language to reach “right out” to reality is explained by the grammatical fact that we can use the same expressions we use to specify the contents of our thoughts and utterances to speak about their intentional objects.
Some may find this conclusion disappointing and might object along the following lines: Wittgenstein may have correctly identified confusions underlying his own earlier explanation of intentionality, but he has failed to provide a more adequate explanation in its stead. It may be a grammatical truth that if A believes that p we may use “p” or some expression therein to speak about or refer to the objects of her belief. But here we are invoking such notions as “speaking about” and “referring,” which we have to explain if we wish to explain how language and thought can be intentionally directed at a reality outside itself. Wittgenstein simply fails to do this.
An adequate treatment of this objection is beyond the scope of this chapter. But in conclusion I shall briefly draw attention to a reply, which is contained in a passage I have already quoted. In PI §428 Wittgenstein writes:
“A thought – what a strange thing!” – But it does not strike us as strange when we are thinking. A thought does not strike us as mysterious while we are thinking, but only when we say, as it were retrospectively, “How was that possible?” How was it possible for a thought to deal with this very object?
The fact that thoughts do not “strike us as mysterious while we are thinking” shows that we are perfectly familiar with the phenomenon of intentionality. We know perfectly well how to speak and think about objects and we also know how and on what grounds we attribute thoughts, beliefs, and meaningful utterances to others and ourselves. There is no need for a philosophical theory to explain something that we already know (see PI §128: “If someone were to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them”). The task of the philosopher is to disabuse us of the confusions we fall into when we think of the phenomenon of intentionality philosophically, e.g., when we start asking such questions as, “How was it possible for a thought to deal with this very object?”
One such confusion is the idea that a necessary relation to their intentional objects is part of all our representations. Wittgenstein himself was subject to this confusion when writing the Tractatus but it is not peculiar to his own early thinking. Wittgenstein is not merely treating the “bumps” that his own understanding has got by “running up against the limits of language” (PI §119). He is dispelling a confusion that is widespread in the history of philosophy and lies at the root of Sellars’s dilemma for relationist theories of thought. Only if we assume that a relation to what they are about is a part of all our representations will we assume that there always is something our representations are about, even if they are false. This will then typically lead, as Sellars points out, either to the introduction of contents that have merely “being‐for‐mind” (Sellars, 1963, p.42) and whose relation to genuinely mind‐independent objects and states of affairs remains obscure, or to the introduction of subsistent but not existent objects and states of affairs that are the contents of false representations. In the Tractatus Wittgenstein avoided these two mistakes, but he still assumed simple, necessarily existing objects that are the meaning of the simple signs of language. In that respect his early work was part of a long and continuing philosophical tradition to which his later criticisms are highly pertinent.