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Tractatus Logico-Philosophicus Ludwig Wittgenstein
Representation and Reality in Wittgenstein’s Tractatus
Representation and Reality in Wittgenstein’s Tractatus
José L. Zalabardo
1
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Acknowledgements
I have benefited from conversations or correspondence with Don Berry, María Cerezo, Kit Fine, Marcus Giaquinto, Peter Hanks, Colin Johnston, Mark Kalderon, Michael Kremer, Mike Martin, Michael Morris, and Stephen Read. I am also grateful to three anonymous referees for Oxford University Press for their tremendously helpful comments.
I have presented some of this material at the following conferences and workshops: “Wittgenstein and the Transcendental,” Essex University and Institute of Philosophy, London; “Reading Wittgenstein,” UCL and Institute of Philosophy, London; “Wittgenstein and the Philosophy of Perception,” King’s College, London; “The Viability of Metaphysics,” Durham; “Inferentialism in Epistemology and the Philosophy of Science,” UNED, Madrid, and “The World as I Found It,” University of Fribourg. I have also presented these ideas in my Early Wittgenstein lectures at UCL and in a postgraduate seminar at the University of Valencia. I am grateful to all these audiences for their comments.
Chapter 3 and Appendix I use material from “Wittgenstein’s Nonsense Objection to Russell’s Theory of Judgment,” in Michael Campbell and Michael O’Sullivan (eds), Wittgenstein and Perception (Abingdon: Routledge, 2015). Appendix II uses material from “Reference, Simplicity and Necessary Existence in the Tractatus,” in José L. Zalabardo (ed.), Wittgenstein’s Early Philosophy (Oxford: Oxford University Press, 2012). I am grateful to these publishers for permission to reproduce this material.
Introduction
I.1. Wittgenstein’s Programme
A book is an act of communication. Its author intends to produce with it a certain effect in the mind of her readers. The precise effect that that an author intends to produce with her book varies widely from genre to genre. The authors of novels, poetry volumes, self-help books, and scientific manuals, for example, seek to affect their readers in very different ways.
Scientific manuals and other pieces of academic writing tend to follow a particularly straightforward pattern. These books present facts, theories, or explanations that their authors believe to be correct. The authors’ goal is to get their readers to accept their claims. Success will come about when the reader accepts the claims expressed in the book. If the claims are correct, the reader will have learnt something about the world from the book.
Many philosophy books follow this pattern. They present philosophical doctrines that their authors believe to be correct, with the intention of making their readers accept these doctrines. The author succeeds when the reader accepts the doctrines presented in the book. When this happens, if the doctrines are correct, the reader will have learnt something about the world from the book.
Readers of Wittgenstein’s Tractatus Logico-Philosophicus, especially those who skip the preface, can easily get the impression that it is this kind of book. For the most part, the Tractatus seems to be devoted to presenting philosophical doctrines—about the structure of the world, linguistic and mental representation, the nature of logic and mathematics, and other traditional philosophical subjects. Readers then naturally assume that Wittgenstein believes these doctrines to be correct, and that his goal is to get them to accept these doctrines—that, according to Wittgenstein, we will learn something about the world from the Tractatus if we accept the doctrines that are expressed in it.
However, right at the end of the book, in its penultimate section, Wittgenstein offers an explanation of how he expects his readers to benefit from it that is radically at odds with these assumptions:
6.54 My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)
He must transcend these propositions, and then he will see the world aright.
Wittgenstein, like the authors of other philosophy books, thinks that his readers can learn something about the world from the Tractatus: the book can enable us to ‘see the world aright’. However, the way in which he expects us to attain this goal is not by accepting the doctrines presented in the book. What he wants us to do instead is to ‘transcend’ the propositions that seem to express these doctrines. This process of transcendence will result in the recognition that the propositions of the Tractatus are nonsensical, and hence, in effect, that they don’t actually express any doctrines. This recognition is what will enable us to see the world aright.
These instructions for how to learn from the Tractatus are highly perplexing, and have often failed to make readers abandon the assumption that the book presents philosophical doctrines that Wittgenstein accepts and wants us to accept. Upholding this assumption, without simply ignoring 6.54, requires a creative reading of Wittgenstein’s claim that his propositions are ‘nonsensical’. On this reading, Wittgenstein’s point is not that they are utterly devoid of meaning, but that they don’t express their meanings in the standard way. When read along these lines, the claim is compatible with treating the propositions of the Tractatus as expressing, in some other way, philosophical doctrines that Wittgenstein accepts and wants us to accept.
But surely this line should be taken only as a measure of last resort—if we find ourselves incapable of taking Wittgenstein’s explicit instructions at face value. Hence the first question that we need to pose is this: how would the recognition of the propositions of the Tractatus as nonsensical enable us to see the world aright? Over the last couple of decades, this has been one of the most active areas of research in early-Wittgenstein scholarship but is not the subject matter of the present book.1 Here I only want to make a few basic points about the procedure that Wittgenstein wants us to follow in order to benefit from his book. I shall refer to this procedure as Wittgenstein’s programme. I am not going to defend the details of my construal of the programme. My goal is simply to show that there is at least
1 These issues have been brought to prominence by the work of Cora Diamond and James Conant, among others. See e.g. Diamond 1991; Conant 2002.
one way in which we might in principle learn something important from the book by coming to see its propositions as nonsensical.
Let’s suppose then that we have succeeded in recognizing the propositions of the Tractatus as nonsensical. What, if anything, could we learn from this recognition? One thing we would undoubtedly learn is that certain propositions that seemed to express philosophical doctrines achieve no such thing—that, contrary to appearances, they are complete nonsense. The propositions of the Tractatus seem to us at first sight to make sense. Hence, if they are actually nonsensical, we certainly learn something by recognizing them as such. However, this is hardly a worthwhile discovery for the average reader of the Tractatus who, prior to reading the book, is unlikely to have come across its propositions, or other propositions that strike her as expressing the same doctrines. It is hard to see how we are significantly better off after having been introduced to a set of propositions and then learning that they are nonsensical than before coming across them in the first place.
It is clear, however, that Wittgenstein expects that the recognition of the propositions of the Tractatus as nonsensical will teach us something, not only about these particular propositions, but about the general enterprise to which they seem to contribute before their nonsensicality is recognized. The propositions of the Tractatus seem to provide answers to philosophical questions and solutions to philosophical problems. By recognizing these propositions as nonsensical we are expected to learn something, not just about these answers and solutions, but about the questions and problems they address, and about the enterprise of seeking answers to philosophical questions and solutions to philosophical problems. The recognition of the nonsensicality of the propositions of the Tractatus is expected to expose this enterprise as illegitimate. It will enable us to see that philosophical questions aren’t genuine questions and philosophical problems aren’t genuine problems.
It is not immediately obvious how the recognition of the nonsensicality of the propositions of the Tractatus could have this consequence. We can give nonsensical answers to perfectly legitimate questions and nonsensical solutions to perfectly legitimate problems. So in order to see how Wittgenstein’s strategy is supposed to work we need to consider why in this particular case the nonsensicality of the answers and solutions succeeds in undermining the enterprise of asking the questions and posing the problems.
On this point one thing seems clear: if we haven’t come to accept the propositions of the Tractatus as providing the only correct answers and solutions to the philosophical questions and problems they address, then recognizing them as nonsensical will have no tendency to undermine the status of these questions and problems.
Let’s suppose then that we have come to accept the propositions of the Tractatus as providing the only correct answers and solutions to the philosophical questions and problems they address. It’s not obvious how even now the recognition of these propositions as nonsensical will taint the enterprise of philosophy. If we thought that the propositions of the Tractatus provided correct answers and solutions to philosophical questions and problems, and we now come to the conclusion that they are actually nonsensical, wouldn’t we simply revise our initial positive verdict and resume our search for the correct answers and solutions?
Suppose, however, that after recognizing the propositions of the Tractatus as nonsensical we remain convinced that they are designated by the rules that define the enterprise of philosophy—of seeking answers to philosophical questions and solutions to philosophical problems—as the correct answers and solutions to the questions and problems they address. This will amount to a discovery about the rules—that they compel us to regard nonsense as correct. It is this discovery that is supposed to undermine the enterprise of philosophy. We start off thinking of philosophical questions and problems as perfectly legitimate and, following the rules of the enterprise, we find the correct answers and solutions. But then we discover that what we regarded as correct answers and solutions are nothing but nonsense. We remain convinced, however, that in endorsing these ‘answers’ and ‘solutions’ we didn’t make any mistakes in applying the rules of the enterprise: these pieces of nonsense are the ‘answers’ and ‘solutions’ that the rules designate as correct. The only way out of this impasse is the rejection of the rules and of the enterprise they define, and this is the outcome that Wittgenstein’s programme is intended to produce.
It seems to me that this general approach provides the most plausible construal of Wittgenstein’s communicative intentions, but defending this claim is not among the goals of the present book. As we are about to see, my main claims will not depend on the correctness of this approach, and should also be of interest to those who believe that the goal of the Tractatus is to impart philosophical doctrines somehow expressed by its propositions.
I.2. Within the Diegesis
On the construal of Wittgenstein’s programme that I am recommending, although its intended outcome is the rejection of the enterprise of philosophy, the first step that we need to take in this direction consists in engaging in this enterprise—in doing philosophy. Wittgenstein’s intended audience consists of readers who regard the enterprise of philosophy as legitimate—who accept its rules as effective procedures for selecting the correct answers to genuine questions and the correct
solutions to genuine problems. His goal is to make his readers abandon this enterprise, but for this purpose they first need to accept, by following the rules that govern the enterprise, that the propositions of the Tractatus express correct philosophical doctrines. If philosophy is the ladder that we need to throw away in order to see the world aright, Wittgenstein programme requires that we first climb up it: we need to do philosophy in order to rid ourselves of it.2
In fact, if we don’t come to accept the propositions of the Tractatus as expressing correct philosophical doctrines we won’t be able to recognize them as nonsensical either. Wittgenstein doesn’t establish the nonsensicality of his propositions on independent grounds. What he shows is that they entail their own nonsensicality, since the limits that he defends on what propositions we can produce are grounded in his theory of propositions.3 But clearly this amounts to showing that, if the propositions of the Tractatus express correct doctrines, then they are nonsensical. Unless we come to accept the antecedent of this conditional we will be under no obligation to accept its consequent. We will be able to treat the propositions of the Tractatus as perfectly meaningful, even if the false doctrines that they express entail their nonsensicality.
Notice, furthermore, that the recognition of the propositions of the Tractatus as nonsensical is supposed to come about as a result of philosophical reasoning. Hence, the outcome that will rid us of philosophy is not that its rules compel us to accept as expressing correct philosophical doctrines propositions that are as a matter of fact nonsensical, but rather that its rules compel us to accept, concerning the propositions of the Tractatus, both that they express correct philosophical doctrines and that they are nonsensical. The second result (the nonsensicality) doesn’t enjoy a more permanent status than the first (the correctness). Both will be left behind once the ladder has been thrown away. In fact, even the claim that the rules yield these results may have to be left behind. At this point the construal of Wittgenstein’s programme raises fundamental issues that the present book will not address.
If Wittgenstein believes that his readers will be able to follow his programme, he must expect that its propositions will strike us as expressing correct philosophical doctrines. Why did he think that his propositions could generate this illusion?
2 See, in this connection, Cora Diamond’s insightful remarks on the imaginative activity involved in understanding the demands that the Tractatus makes on its readers (Diamond 2000: 156–8).
3 On this construal of Wittgenstein’s strategy, the realization that the propositions of the Tractatus are nonsensical is supposed to result from arguments for the conclusion that this is so. Resolute readers of the Tractatus have identified other, more subtle ways in which Wittgenstein seeks to promote this realization. See e.g. Goldfarb 1997. My construal could be easily modified to accommodate this point.
What we know about the evolution of Wittgenstein’s thought in the period of gestation of the Tractatus lends strong support to the following answer to this question: Wittgenstein thought that his readers would be likely to see his propositions as expressing correct philosophical doctrines because he himself was once a victim of this illusion. The rejection of philosophy that the Tractatus seeks to promote was not Wittgenstein’s original attitude towards the enterprise. He once thought that philosophical questions and problems were perfectly genuine, and devoted himself to addressing them. Many of the propositions of the Tractatus are very close descendants of propositions that he first formulated as contributions to the philosophical enterprise—as his answers to philosophical questions and his solutions to philosophical problems.
This circumstance is potentially very valuable to those who intend to follow Wittgenstein’s programme. This requires, as we have seen, seeing the propositions of the Tractatus as expressing correct philosophical doctrines, but this is not an easy thing to do. The propositions of the Tractatus are often terse and cryptic. They rarely offer clear arguments in favour of the doctrines that they seem to express, and even the content of these doctrines is sometimes hard to fathom. The Tractatus offers insufficient support to readers who seek to complete the first stage of Wittgenstein’s programme. We need all the additional help we can get. And one possible source of help is Wittgenstein’s own experience as a victim of the illusion he now expects us to fall for. If we could understand the reasons that led Wittgenstein to the conviction that the propositions of the Tractatus expressed correct philosophical doctrines, we might find that they have the same effect on us that they had on him. In fact, it would be a remarkable coincidence if we could reach this point by any other route: our only realistic chance of coming to see the propositions of the Tractatus as expressing correct philosophical doctrines is to identify the virtues that Wittgenstein once saw in them.
This means, in effect, that those who want to complete the first stage of Wittgenstein’s programme will need to adopt the same approach as those for whom the book expresses philosophical doctrines that Wittgenstein accepts and wants us to accept. This approach doesn’t correspond to Wittgenstein’s conception at the time of completing the book of what his propositions achieve, but it does correspond to his conception of his achievement at an earlier point, as well as giving us our best chance of completing the first stage of his programme. This is the approach that I propose to adopt in the present book. In accordance with this approach, I will no longer refer to the doctrines that the Tractatus ‘seems’ to express. At the ladder-climbing stage of the programme, this distance is out of place. I shall simply speak, without reticence, about the doctrines of the Tractatus. Likewise, instead of asking why Wittgenstein thought that we could come to see
the propositions of the Tractatus as expressing correct doctrines, I will simply ask why he thought that the doctrines of the Tractatus are correct.
I.3. Tractarian Account of Representation and Reality (TARR)
I am going to ask this question specifically with respect to a cluster of doctrines providing a systematic account of the structure of language and reality and of how the former represents the latter. I am going to refer to this account as the Tractarian Account of Representation and Reality (TARR). We can characterize TARR as involving three main components.
The first component of TARR is the view that everyday propositions don’t represent the world directly: they represent the world through the mediation of a class of postulated propositions, known as elementary propositions (Elementarsätze). Everyday propositions represent the world by being truth-functions of elementary propositions.
The second component of TARR is an account of the nature of elementary propositions and of how they represent the world. On this account, an elementary proposition is a combination of items known as names. Names are referential expressions. An elementary proposition represents the referents of its names as combined with one another in the same way in which the names are combined in the proposition. The proposition is true if the referents are so combined; false if they are not. The referents of names are simple items known as objects. The combinations of objects that elementary propositions represent as obtaining are known as states of affairs4 (Sachverhalte).
The third component of TARR is an account of the structure of reality, according to which a possible state of the world is constituted by the states of affairs that obtain in it. Two states of the world differ from one another only if there are states of affairs that obtain in one and not in the other. And for every set of states of affairs there is a possible state of the world in which the states of affairs that obtain are precisely the elements of the set.
Thus, according to TARR, elementary propositions and states of affairs provide the interface between language and the world. Propositions represent the world by their truth-functional dependence on elementary propositions. These, in turn, represent states of affairs. This enables propositions to represent the whole of reality, since everything that is the case, and everything that can be the case, consists
4 This is Pears and McGuinness’s translation and the term I shall use. Ogden uses atomic fact (Wittgenstein 1922).
in the obtaining and non-obtaining of states of affairs—what truth-functions of elementary propositions represent.
Taken as an intuitive model, TARR is fairly easy to understand—we can form a conception of what things would have to be like in order for TARR to be correct. A precise, literal understanding of the view is much harder to achieve. And it is even harder to grasp why anyone would think that this is how things are in actuality—that language and reality have the structure that TARR attributes to them and that the former represents the latter as TARR says it does. Specifically, it is hard to understand why Wittgenstein thought this.
Addressing these questions is the main goal of the present book. I am going to put forward a hypothesis as to why Wittgenstein thought that TARR had to be correct. My central contention on this point will be that TARR is the combined result of three separate argumentative strategies for solving different philosophical problems.
First, TARR provides Wittgenstein’s solution the problems that Russell had tried to solve with his theories of judgment and understanding. The strategy that Wittgenstein adopts for solving these problems is based on the strategy that Russell was developing in the period between 1911 and 1913 when Russell and Wittgenstein were in direct contact. Wittgenstein came to the conclusion that Russell’s strategy faced fatal objections. However, he thought he had found a way to avoid these objections while preserving some of the main insights of Russell’s approach. This proposal is the central idea of the Tractarian account of how elementary propositions represent states of affairs.
Second, TARR offers a solution to the problem of understanding how the unity of a fact is produced out of the multiplicity of its constituents, and the correlative problem of how the unity of a proposition is produced out of the multiplicity of its constituents. Wittgenstein’s main contention in this regard is that facts, not their constituents, are the basic units of reality and propositions, not their constituents, are the basic units of representation. I shall argue that this aspect of TARR can be seen as an extension of an idea of Frege’s. The account of the relationship between facts and their constituents also provides a solution to the problem of the metaphysical status of possibilia. According to TARR, what can be the case arises from recombinations of the items involved in what is actually the case.
Third, TARR offers a solution to the problem of our knowledge of logical properties and relations—specifically of how we know that a proposition is a logical consequence of other propositions. The Tractatus contends that whether a proposition follows from other propositions can be seen from their structure. Wittgenstein’s account of how this is possible involves several crucial aspects of
TARR—that propositions are truth-functions of elementary propositions, that for every set of states of affairs the obtaining of the members of the set is a possible state of the world, and that the constituents of states of affairs are simple. Their role in this account of logical knowledge is the main justification for these components of TARR.
My central contention is that Wittgenstein saw these three lines of reasoning as the main sources of support for TARR. Language and the world have to have the structure that TARR ascribes to them, and the former has to represent the latter as TARR says it does, because otherwise these lines of reasoning wouldn’t work. And these lines of reasoning have to work because otherwise, according to Wittgenstein, the problems that they address would go unsolved.
I believe that the basic ingredients of my reading receive considerable support from the available evidence. However, I often develop the arguments that I attribute to Wittgenstein at a level of detail that goes beyond what the evidence could sustain. My justification for taking this licence is that my ultimate goal is not to provide a faithful interpretation of Wittgenstein’s thought, but to complete the first stage of Wittgenstein’s programme, using as a guide what we know about Wittgenstein’s reasons for endorsing TARR. For this purpose I develop the lines of reasoning endorsed by Wittgenstein in ways that facilitate their assessment, even when these developments take us beyond what we are entitled to attribute to Wittgenstein in light of the evidence at our disposal.
I.4. Nonsense
Once we have convinced ourselves that the propositions of the Tractatus express correct philosophical doctrines, we are ready to move on to the second stage of Wittgenstein’s programme—recognizing that these propositions are nonsensical, and hence that they don’t express any doctrines at all, let alone correct ones. As I have suggested, Wittgenstein doesn’t establish this result on independent grounds. What he shows is that it follows from philosophical doctrines that the propositions of the Tractatus seem to express that these propositions are nonsensical. The doctrines that play this role in Wittgenstein’s strategy are all constituents of TARR.
If linguistic representation works as TARR says it does, then there are important limitations to what language can represent. In some cases, the solutions to the problems that TARR addresses arise from these limitations. Thus, for example, as we shall see in due course, the problems that Russell encountered with some paradoxical propositions are solved for Wittgenstein by the fact that, if linguistic representation works as TARR says it does, then it’s not possible to
produce the propositions that would raise the problem. A subsidiary goal of the present book is to understand the aspects of TARR that impose limits on what language can represent. I am going to argue that these limits have two main sources in TARR. One is its account of how elementary propositions represent states of affairs. The other is its account of the relationship between propositions and their constituents. The limits that TARR imposes on what language can represent are ultimately responsible for the nonsensicality of the propositions of the Tractatus, but the resulting implosion of Wittgenstein’s ‘doctrines’ lies outside the scope of this book.
I.5. The Structure of the Book
The book is divided into six chapters, a conclusion, and two appendices.
In Chapter 1, I present the problems that Russell was trying to solve with his theories of judgment and the strategies that he was exploring for dealing with these problems when Wittgenstein came into contact with him. I ascribe a central role to what I call the mode-of-combination problem, the problem of explaining how the judging subject grasps the way in which objects in the world would have to be combined with one another in order for the judgment to be true. I argue that this is the problem that Russell was trying to solve by introducing forms in the theory of judgment/understanding that he presented in his manuscript of May 1913, Theory of Knowledge.
In Chapter 2, I present the Tractarian account of how elementary propositions represent as Wittgenstein’s attempt to solve the difficulties that had made Russell’s project stall. I argue that the claim that pictures in general, and propositions in particular, are facts, is Wittgenstein’s solution to the difficulties that Russell had encountered when trying to deal with the mode-of-combination problem. I then consider Wittgenstein’s claims that a picture cannot depict its own pictorial form and that propositions cannot represent logical form.
In Chapter 3, I consider why Wittgenstein’s account of how propositions represent makes no mention of a representing subject. I argue that the reason for this is Wittgenstein’s conviction that it’s not possible to represent cognitive relations between a subject and the world—to represent a subject as representing the world as being a certain way. I contend that the source of this conviction is a version of the argument that made Russell despair of providing a satisfactory account of judgment or understanding, and that a crucial step in this argument is provided by Wittgenstein’s complaint that Russell’s theory of judgment doesn’t rule out the possibility of nonsense judgment.
In Chapter 4 I move on to the second problem that Wittgenstein expected TARR to solve. I argue that Wittgenstein solved the problems of how propositions and facts are formed from their constituents by rejecting the view that they are composite items. According to Wittgenstein, propositions, not their constituents, are the basic units of representation, and facts, not their constituents, are the basic units of reality. Facts and propositions, on this account, do not arise from the combination of more fundamental items. Nothing is more fundamental. What we think of as their constituents are common features that different propositions and different facts share with one another, always the result of a process of abstraction. I then argue that, with the claim that objects contain their possibilities of combination, Wittgenstein provides a two-step reduction of possible states of affairs, first to the possibilities of combination of objects, and then to the actually obtaining states of affairs in which we encounter these. I consider next how, according to the Tractatus, language makes contact with reality. The chapter closes with a discussion of Wittgenstein’s claim that the world has to have substance and his argument in support of this claim.
In Chapter 5, I consider how Wittgenstein’s account of the relationship between propositions and their constituents imposes further limitations on what propositions can represent. I look at how these ideas result in Wittgenstein’s treatment of Russell’s paradox, in his rejection of self-referential propositions, and in his claim that everything that’s thinkable is also possible. I also consider in this light Wittgenstein’s discussion of formal properties and relations and of formal concepts.
In Chapter 6 I turn to the third family of difficulties that Wittgenstein hoped to address with TARR. I argue that Wittgenstein’s claim that propositions are truth-functions of elementary propositions is motivated by his account of logical knowledge—of how we know that a proposition is a logical consequence of other propositions. We can motivate in the same way some of his main claims concerning states of affairs: that they are independent of one another and that their constituents are simple. I then consider the question of the nature of the truth-functional structure that Wittgenstein postulates for everyday propositions. I develop the proposal that these facts about truth-functional composition are nothing but the precipitate of our ‘logico-linguistic employment’—of our inclinations concerning the logical relations between everyday propositions. I end by considering the difficulties that Wittgenstein encounters when trying to extend to non-elementary propositions his account of how propositions represent. I argue that the difficulties that he faces here provide an important link with some of the central ideas of his later philosophy.
In the Conclusion I outline an assessment of Wittgenstein’s achievement in light of my discussion of TARR.
The appendices contain critical discussions of some prominent alternatives to the reading that I develop here on two specific points: Wittgenstein’s nonsense objection to Russell’s theory of judgment (see 5.5422), in Appendix I, and the argument for substance (2.0211–2.0212), in Appendix II.
1 Russell’s Theories of Judgment
1.1. Introduction
In the Introduction I applied the label Tractarian Account of Representation and Reality (TARR) to a cluster of views expressed in the Tractatus concerning the structure of reality and of language, and how the latter represents the former. According to TARR, propositions represent reality by being truth-functions of elementary propositions. The first component of TARR is an account of how elementary propositions represent reality. The account is expressed by the following slogan:
4.01 A proposition is a picture of reality.
The claim concerns every proposition, but as we shall see in due course, Wittgenstein’s account of what being a picture of reality consists in is primarily applicable to elementary propositions. Elementary propositions, according to Wittgenstein, represent reality by being pictures of it. What does this mean? And why did Wittgenstein think it is true? I shall try to provide answers to these questions in Chapter 2. I am going to argue there that the right answers require seeing Wittgenstein’s account of representation as his solution to problems that Russell had encountered in his attempt to analyse the phenomenon of judgment or belief and (later) understanding.
Wittgenstein arrived in Cambridge in October 1911, aged 22, with the intention of studying under Russell, having had no prior formal training in philosophy. He stayed in Cambridge for two academic years, during which he developed a remarkably intense personal and intellectual relationship with Russell. Wittgenstein completed the Tractatus in 1918, less than five years after he left Cambridge.1 Furthermore, we have proof that some central aspects of the Tractarian account of representation originate in the period during which Wittgenstein was working with Russell: they are already present in the notes that he dictated in October 1913, shortly before leaving Cambridge, known as the “Notes on Logic”.
1 For details of Wittgenstein’s life in this period see McGuinness 2005; Monk 1991.
The influence of Russell’s theories of judgment on Wittgenstein’s account of representation has always been recognized. It is already highlighted in James Griffin’s 1964 commentary, one of whose sections bears the title “Wittgenstein’s Theory of Judgment”, in recognition of this link (Griffin 1964: 112–24). However, the full extent of Russell’s influence on Wittgenstein on this point came to be adequately appreciated only with the discovery in 1967 of the book manuscript that Russell worked on in May 1913, published in 1984 as volume vii of The Collected Papers of Bertrand Russell, with the title ‘Theory of Knowledge: The 1913 Manuscript’ (Russell 1984).
I believe that the theory of understanding that Russell presents in this manuscript holds the key for interpreting the theory of representation that Wittgenstein presents in the Tractatus. For the problems that Wittgenstein thought he had solved with his theory of representation are the problems that Russell had tried to solve with his theory of understanding, and Wittgenstein’s solution arises from a relatively minor albeit inspired transformation of Russell’s original idea. This connection has been seen by others before me, especially by David Pears, in his ground-breaking article “The Relation between Wittgenstein’s Picture Theory of Propositions and Russell’s Theories of Judgment” (Pears 1977). My reading will build on the work of these earlier scholars, but there are important differences of detail between extant interpretations and the reading that I’m going to recommend. In particular, I offer what I regard as a novel account of the precise point at which Wittgenstein saw himself as succeeding where he thought Russell had failed. This will enable us to appreciate the source of Wittgenstein’s conviction that he was offering the only viable account of how propositions represent reality.
The goal of the present chapter is to trace the evolution of Russell’s thought on the problems that, on my reading, Wittgenstein was trying to solve with his account of how propositions represent. My presentation will have many points in common with some of the available accounts of the evolution of Russell’s thought on these issues, but it will differ from other accounts in some respects that are of crucial importance for understanding how Wittgenstein could have come to see his own theory of propositional representation as the only solution to the problems that, as Wittgenstein saw it, Russell’s approach could not overcome.2
1.2. The Idea of a Theory of Judgment
Over the first two decades of the twentieth century, one of Russell’s main philosophical projects was the provision of a satisfactory theory of judgment. The phenomenon to which Russell referred as judgment or belief is a type of mental
2 My reading is closest to Peter Hylton’s in Hylton (1990).
episode in which things are represented in consciousness as being a certain way, with the conviction that that’s how they are. In his lectures on “The Philosophy of Logical Atomism”, of 1918, he gives an example of the kind of episode he has in mind: “If I say ‘What day of the week is this?’ and you say ‘Tuesday’, there occurs in your mind at that moment the belief that this is Tuesday” (Russell 1985: 81). The point that I want to highlight is that what Russell is referring to is not the notion of a state of information playing a certain causal role in the production of behaviour, which seems to many of us to be the most natural referent for the term belief. These informational states are undoubtedly related to the conscious episodes that Russell is discussing, but they are clearly different phenomena.3 Here I shall follow Russell in using the term belief, as well as judgment, to refer to the conscious episodes that he is interested in.
The main goal of Russell’s theories of judgment is to understand the specific way in which the judging mind is related to the world in an episode of judgment. He sought to formulate an alternative to the logical monism advocated by the neo-Hegelian philosophers who dominated the British philosophical scene at the beginning of the twentieth century. According to logical monism, in an episode of judgment the mind is related to the world as a whole. As a consequence, Russell claims, “every possible judgment is partially true and partially false” (Russell 1907: 32). Hence the view “does not distinguish between right and wrong judgments as ordinarily understood” (Russell 1907: 32). Against this, Russell wants to show that individual judgments can be completely true or completely false depending on how things stand in specific respects, with no reference to reality as a whole. Understanding the requisite relation between judgments and the relevant regions of the world is the main goal that Russell expects a theory of judgment to achieve.
In the period that interests us, between 1903 and 1913, Russell developed two main approaches to the analysis of judgment. The first, known as the dual-relation theory, he endorsed, with decreasing conviction, until at least 1907. The second, known as the multiple-relation theory, emerged gradually from about 1905, and had replaced its predecessor by 1910.
1.3. The Dual-Relation Theory of Judgment
The dual-relation theory can be seen as motivated by a prima facie appealing account of how true judgments are related to the world. On this account, a true judgment consists in a relation between the judging mind and a fact. Thus, in
3 On this point see Ramsey 1927: 159.
Russell’s example, if I judge (truly) that Bishop Stubbs used to wear episcopal gaiters, my judgment consists in a relation between my mind and the fact that Bishop Stubbs used to wear episcopal gaiters. On this picture, the world contains a multitude of facts, and when I judge truly my mind is related to one of them. The main problem for this otherwise attractive analysis of true judgment is that it has no obvious extension to false judgment. If I judge (falsely) that Bishop Stubbs was hanged for murder, my judgment cannot be construed as a relation to the fact that Bishop Stubbs was hanged for murder, since this fact doesn’t exist. If it existed, then Bishop Stubbs would have been hanged for murder, and my judgment would be true.
One possible approach to false judgment would be to say that, while in true judgments the mind is related to a fact, in false judgments the mind is not related to anything, but Russell sees no merit in this position:
If a belief may be a content which has no object, then it may be true that, though we believe, there is nothing we believe in; and in this case correct beliefs would be distinguished from erroneous ones by the fact that they have an object, while the others have not. But this possibility seems too paradoxical to be maintained except in the last resort.
(Russell 1904: 218–19)
And again:
Direct inspection seems to leave no room whatever for doubt that, in all presentations and judgments, there is necessarily an object. If I believe that A is the father of B, I believe something; the subsistence of the something, if not directly obvious, seems to follow from the fact that, if it did not subsist, I should be believing nothing, and therefore not believing.
(Russell 1904: 510)
In order to avoid the absurdity of judgments with no worldly relata, Russell postulates a class of entities to which false judgments bear the same relation as true judgments bear to facts: when we believe truly, our belief is to have an object which is a fact, but when we believe falsely, it can have no object, unless there are objective non-facts. The people who believe that the sun goes round the earth seem to be believing something, and this something cannot be a fact. Thus, if beliefs always have objects, it follows that there are objective non-facts.
(Russell 1907: 46)4
He presents these objective non-facts as enjoying the same ontological standing as genuine facts, and uses the term proposition to refer to both types of entity. Facts are true propositions and objective non-facts are false propositions:
4 Russell also argues for objective non-facts from the observation that there are complex facts with false constituents, e.g. negative facts, conditional facts with false antecedents, or disjunctive facts with a false disjunct (Russell 1907: 47–8).
If we accept the view that there are objective falsehoods, we shall oppose them to facts, and make truth the quality of facts, falsehood the quality of their opposites, which we may call fictions. Then facts and fictions together may be called propositions. A belief always has a proposition for its object, and is knowledge when its object is true, error when its object is false.
(Russell 1907: 48)
Thus every judgment has a proposition as its object, and the difference between true and false judgments lies in the object, not in the relation we bear to it when we judge:
And as regards judgments, there seems no difference in the relation to their objects when they are correct and when they are incorrect; the difference is rather in the objects, which are true propositions in the one case, and false propositions in the other.
(Russell 1904: 348)
This assimilation of objective non-facts to genuine facts isn’t mere verbal gerrymandering. Russell’s account of propositions mirrors in all respects his account of facts. A fact, according to Russell, is a complex entity in which a manifold of objects is combined into a unit by a relation:
Given any related objects, these objects in relation form a complex object, which may be called a fact.
(Russell 1907: 45)
Propositions, false as well as true, exhibit this structure. Propositions are complex entities, whose constituents are objects in the world:
a proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words.
(Russell 1903: 47)
And their unity is effected in each case by a relation: “The verb, when used as a verb, embodies the unity of the proposition” (Russell 1903: 50). Thus true and false propositions are, in all respects, ontologically on a par. The only difference is that the former exemplify a property, truth, which is absent from the latter:
True and false propositions alike are in some sense entities […]; but when a proposition happens to be true, it has a further quality, over and above that which it shares with false propositions […]
(Russell 1903: 49)
This property has to be treated as primitive and unanalysable:
Truth and falsehood, in this view, are ultimate, and no account can be given of what makes a proposition true or false.
(Russell 1907: 48)
1.4. The Multiple-Relation Theory of Judgment
In part III of “On the Nature of Truth” Russell sketches an alternative to the theory of judgment that postulates objective non-facts. On this alternative, when I believe that A is B I am not related to a single item—the proposition that A is B—but to a multiplicity of items, namely to A and to B (Russell 1907: 46). But while he concedes that this view is more plausible than the postulation of objective non-facts, he adds that “the difficulties in its way are formidable, and may turn out to be insuperable” (Russell 1907: 49). When he prepared this essay for publication in a collection that appeared in 1910, he replaced part III with a separate essay, “On the Nature of Truth and Falsehood”, in which the contest between the dual-relation theory and the new alternative is resolved in favour of the latter:
Judgments […] consist of relations of the mind to objects. But here a distinction has to be made between two different theories as to the relation which constitutes judgment. If I judge (say) that Charles I died on the scaffold, is that a relation between me and a single ‘fact’, namely Charles I’s death on the scaffold, or ‘that Charles I died on the scaffold’, or is it a relation between me and Charles I and dying and the scaffold? We shall find that the possibility of false judgments compels us to adopt the latter view.
(Russell 1910b: 150)
Russell presents three different sources of dissatisfaction with the view that judgment is a relation of the mind to a single object, for which he uses Meinong’s term objective. The first and most fundamental objection is that the theory seems incapable of making room for false judgment (Russell 1910b: 151). If my judging that Charles I died in his bed consists in a relation to a single item, this item will have to exist. And the only plausible candidate for the worldly relatum of this judgment is the event of Charles I’s death in his bed. But to say that this event existed is to say that Charles I died in his bed. Since Charles I didn’t die in his bed, the event in question didn’t exist. Hence the item to which I would have to be related in order to judge that Charles I died in his bed doesn’t exist. Therefore, I can’t judge that Charles I died in his bed, and false judgment is generally impossible.
But even if we somehow managed to identify items that could play the role of objectives without ruling out false judgment, the view would face further obstacles. The second source of dissatisfaction is the implausibility of accepting the existence of objective falsehoods, whatever we take their nature to be:
If we allow that all judgments have objectives, we shall have to allow that there are objectives that are false. Thus there will be in the world entities, not dependent upon the existence of judgments, which can be described as objective falsehoods. This is in itself almost incredible: we feel that there could be no falsehood if there were no minds to make mistakes.
(Russell 1910b: 152)
The third source of dissatisfaction with the dual-relation theory that Russell adduces is that it goes against the intuition that the truth-value of a judgment depends on the existence, or otherwise, of a corresponding item in the world. Instead, the view is compelled to postulate a fundamental, inexplicable distinction between true and false objectives. “This view”, Russell writes, “though not logically impossible, is unsatisfactory, and we shall do better, if we can, to find some view which leaves the difference between truth and falsehood less of a mystery” (Russell 1910b: 152).
Russell grounds in these considerations the rejection of the view that a judgment is a relation of the mind to a single item, proposing instead that in judgment the mind is related to a multiplicity of items:
When we judge that Charles I died on the scaffold, we have before us, not one object, but several objects, namely, Charles I and dying and the scaffold. Similarly, when we judge that Charles I died in his bed, we have before us the objects Charles I, dying, and his bed.
(Russell 1910b: 153)
This is what is known as the multiple-relation theory of judgment
Notice that the new theory agrees with its predecessor on the items that are ultimately involved in a judgment: in addition to the mind, it involves the constituents of the fact that would have to obtain in order for the judgment to be true (call them worldly correlates). On the dual-relation theory, the worldly correlates were first combined into a propositional unit, and this unit was then combined with the mind to form the judgment complex. On the multiple-relation theory, the preliminary propositional combination is dropped, and the worldly correlates and the mind enter as separate items into the judgment complex.
Now Russell no longer sees the combinations of constituents into facts as a special case of combinations that occur as relata of belief complexes. However, with respect to the unity of facts, of actually existing complexes, his position doesn’t change. It is still effected by a relation:
Wherever there is a relation which relates certain terms, there is a complex object formed of the union of those terms; and conversely, wherever there is a complex object, there is a relation which relates its constituents.
(Russell 1912: 127)
Since each fact has among its constituents a relation that is responsible for producing the unity of the fact, it follows that each judgment complex will have a relation, besides the judgment relation, among its constituents. It is the relation that would be responsible for the unity of the fact, if it existed, that would make the judgment true. Russell refers to the relation that occupies this position in a judgment complex as the subordinate relation.
Judgment requires, on the new account, that the mind is related to objects in the world at two different levels. First, the mind has to bear a relation to each of the worldly correlates separately, which results in our being conscious of these items (Russell 1910b: 153). Russell introduces the term acquaintance to refer to this relation (Russell 1910a). But these separate relations are not sufficient for judgment. Judgment requires, in addition, that there should be a single relation linking the mind and the worldly correlates into a unit:
Nothing that concerns Charles I and dying and the scaffold separately and severally will give the judgment ‘Charles I died on the scaffold’. In order to obtain this judgment, we must have one single unity of the mind and Charles I and dying and the scaffold, i.e. we must have, not several instances of a relation between two terms, but one instance of a relation between more than two terms.
(Russell 1910b: 153–4)
It can be easily seen that the new theory overcomes the obstacles that Russell raised for its predecessor. First, the possibility of false judgment is no longer problematic. Thus suppose that I judge that A loves B:
When the judgment is taken as a relation between me and A and love and B, the mere fact that the judgment occurs does not involve any relation between its objects A and love and B; thus the possibility of false judgment is fully allowed for.
(Russell 1910b: 155)
Second, false judgment is explicated without postulating objective falsehoods. The objects to which we are related in a false judgment, on the new account, “are not fictions: they are just as good as the objects of the true judgment” (Russell 1910b: 153).
Finally, the contrast between truth and falsehood is no longer an inexplicable mystery:
We may […] state the difference between truth and falsehood as follows: every judgment is a relation of a mind to several objects, one of which is a relation; the judgment is true when the relation which is one of the objects relates the other objects, otherwise it is false.
(Russell 1910b: 155–6)
Furthermore, this explanation of the contrast vindicates the intuition that truth and falsehood depend on the existence or non-existence of an item corresponding to the judgment—the complex that would result if the subordinate relation related the worldly correlates:
If A loves B, there is such a complex object as ‘A’s love for B’, and vice versa; thus the existence of this complex object gives the condition for the truth of the judgment ‘A loves B’.
(Russell 1910b: 157)
1.5. Order
The new theory appears to generate the following truth conditions for a judgment complex: it will be true just in case there exists a complex whose (only) constituents are the worldly correlates of the judgment complex. This gives the right result in many cases. If I judge that A is similar to B, my judgment will be true just in case there exists a complex whose constituents are A, B, and similarity, i.e. just in case A and B are similar. However, in other cases, the account yields incorrect results. My judgment that A loves B might not be true even if there exists a complex whose constituents are A, B, and love. B loving A is such a complex, but its existence would not make my judgment true. We will get this problem in every case in which the worldly correlates of a judgment can produce different complexes. I am going to refer to this difficulty as the problem of order. 5
In the 1910 paper Russell made a proposal as to how to deal with this problem. His idea is that when I judge that A loves B, the relation, love, “must not be abstractly before the mind, but must be before it as proceeding from A to B rather than from B to A” (Russell 1910b: 158). He also formulates the proposal in terms of the senses of a relation:
We may distinguish two ‘senses’ of a relation according as it goes from A to B or from B to A. Then the relation as it enters into the judgment must have a ‘sense’, and in the corresponding complex it must have the same ‘sense’.
(Russell 1910b: 158)
This solution to the problem of order was open to a serious objection. If when I judge that A loves B, love is before my mind ‘as proceeding from A to B’, it follows that A’s loving B enters into the judgment complex as a unit—the unit that results from love ‘proceeding’ from A to B. But since I can judge that A loves B even if A doesn’t love B, the proposal reinstates the commitment to objective non-facts. In other words, the solution to the problem of order put forward in 1910 turns the multiple-relation theory into a misleadingly formulated version of the dual-relation theory.
The point was raised by G. F. Stout in a perceptive criticism: it may be argued, from Mr Russell’s own account of the matter, that the manifold items to which the mind is related in judging do have a unity of their own, and are apprehended as having a unity of their own, distinct from that of the whole complex formed by the judging mind and its object. What seems to me decisive on this point is the requirement that not only should one of the items be itself a relation, but that it should have a “sense” or direction with reference to the other terms. The belief that A loves B is different from
5 Nicholas Griffin refers to it as (the narrow form of) the direction problem (1985: 219).
