|This paper is a really a brief sketch drawn from material for a long
and rather technical project about Wittgenstein's Tractatus. As
in a sketch of a landscape, I will to give you the lay of the land, an
overview, perspective, or panorama of a large piece of territory. This
involves leaving out many details, or only indicating them by the lightest
of strokes. Yet at the same time I do wish to convey something more than
a mere outline, a surveyor's map of the surroundings. I also want to show
some of the local color, the special features and characteristics that
separate this region of the history of thought from all others. The details
have a fascination of their own, but I hope that you will not be lost in
them. For my main point is, indeed, that it is just the overview of the
Tractatus that has been missed--some way of seeing the arrangement
of its main argument. Thus, my title is "The Importance of a Clearly Arranged
Let me say a little more about the larger project. It is tentatively titled, "Drawing a Boundary to the Expression of Thought," a phrase taken from Wittgenstein's own summary of his early work. My project has three interconnected theses:
To accomplish this 'sketch' I will concentrate on a single theme that runs throughout the work of Ludwig Wittgenstein. That theme is the importance of "eine übersichtliche Darstellung", "a perspicuous representation" or, as I prefer to translate it, "a clearly arranged representation". The clearly arranged representation of a subject is an exposition that provides a clear overview, something that can be grasped immediately as a whole. A clearly arranged representation of our ecological situation is, for example, a view of the planet earth from outer space. It shows our ecology as a bounded whole.
As I have said, I shall concentrate on this theme in Wittgenstein's earliest work, his Tractatus Logico-Philosophicus. But let me assert, and this goes beyond my focus here, that the theme is one which continues thoughout Wittgenstein's work and that it is always, as Wittgenstein says, "of fundamental significance." (1)
To begin, let me tell you how I intend to discuss Wittgenstein and his theme of the clearly arranged representation. First, I will briefly sketch Wittgenstein's life and give you some sense of the contradictions that seem to surround our view of his work. Then I will illustrate the concept of the clearly arranged representation with some examples. Third, I will consider Wittgenstein's early work, the Tractatus, as itself an example of a clearly arranged representation of the logic of language. I shall also briefly mention the origin of this concept and its relation to the so-called 'picture theory'. Finally, I will return to those contradictions that cloud our view of Wittgenstein's work. I want to show you how an understanding of Wittgenstein's early work as a clearly arranged representation will resolve many of those contradictions.
Simply put, the beginning of this presentation raises some contradictions in our view of Wittgenstein. The end resolves them. In the middle sections, I will present a simple example of the clearly arranged representation and then apply it to the Tractatus.
First, who was Wittgenstein?
Ludwig Wittgenstein was born in 1889 in Vienna. He died at the age of
62, in 1951, in Cambridge. Until the age of about fifty, Wittgenstein was
an Austrian citizen and during most of that time he probably considered
himself principally a resident of Vienna, although his adult life was always
somewhat nomadic and elusive. At various times he visited Iceland, Norway,
Russia, Ireland, and the United States. His entire philosophical career
was, of course, at Trinity College, Cambridge.
Public reputation has attributed to Wittgenstein half-a-dozen general doctrines, positions and philosophical attitudes which were not at all to his liking; and the first step towards recognising the true nature of his philosophical quest is to see past these false attributions. To summarize [and I give only the first three here]:
Of course, such matters go far beyond my specific topic here. Instead let me focus on some of the contradictions which have been attributed to Wittgenstein that stem directly from the Tractatus. I have chosen four of them. For simplicity I shall refer to each by the name of the philosopher who attributed it to the Tractatus: Russell's Tractatus contradiction, followed by Ramsey's, Ayer's, and finally Ryan's Tractatus contradiction.
Russell's Tractatus contradiction was raised by Bertrand Russell during Wittgenstein's oral examination on the Tractatus for his Ph.D. degree. But it also relates to a witticism of the mathematician, G. H. Hardy, concerning Wittgenstein in 1912. Russell had just told Hardy that Wittgenstein had a real taste for philosophical scepticism and that he was even glad when it is proved that something cannot be known. Hardy replied that he himself would be glad to prove anything; he said, "If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by [my] pleasure in the proof". (5) During the oral exam in 1929, Russell suggested that Wittgenstein had been "inconsistent in stating that little could be said about philosophy and that it was possible to reach unassailable truth". (6) This 'inconsistency' comes straight out of Wittgenstein's own preface to the Tractatus where he indeed makes both of these claims. By the way, Wittgenstein is reported to have replied, "Don't worry, I know you'll never understand it". Yet, while Russell may not have understood fully, it is quite clear that Russell did feel that Wittgenstein had really accomplished something of value to philosophy despite his own apparent claim to the contrary.
In his last papers Frank Ramsey suggested a variant of Russell's contradiction:
More recently, A. J. Ayer rings the final change on these terms when he writes, "What is quite unacceptible is that one and the same series of pronouncements should be both devoid of sense and unassailably true". And later, "(...) Wittgenstein could not have it both ways. It cannot be the case both that his assertions are true and that they are devoid of sense". (8) This is Ayer's contradiction: the contradiction between truth and nonsense.
The final attributed contradiction comes from Alan Ryan's review of the book by A. J. Ayer which I have just quoted. Ryan suggests that Ayer fails to make it clear to the reader why he, Ayer, thinks so highly of Wittgenstein, since he rejects "almost all Wittgenstein's most characteristic claims". (9) Ryan goes on to suggest that "Wittgenstein's hold on the imagination of philosophers stems from [a] strenuously maintained internal contradiction in his life and work". (10) That internal contradiction is between profession and practice--Wittgenstein as the anti-philosophical philosopher, subverting philosophy, its quests and its doubts, in a "strikingly philosophical way." Ryan even says,
I have now completed my first topic: Wittgenstein's life and the contradictions
that surround our view of it. I shall now turn to the clearly arranged
representation as a way of suggesting an account of Wittgenstein that does
not ignore these apparent contradictions. Rather than trying to tease the
notion from a text, let me propose a very simple meaning for this concept
by means of a series of examples. I shall start with the most concrete
example and then work my way through more and more abstract examples until
we have reached the Tractatus itself.
Late nineteenth century German physics was concerned with the principles
of mechanics. How to represent these? What would make for a proper representation
of physical phenomena? Clearly there were contradictions involved in physical
explanations which required an appeal to 'action at a distance' or 'a fluid
ether which is imperceptible and immeasurable'. Such concepts were not
explanations at all since they themselves were inexplicible; they were
'meta-physical' rather than physical explanations. Yet how to represent
the experimentally observable effects of, say, radio waves? Of course the
answer proposed by Heinrich Hertz was that radio waves were electromagnetic
radiation just like light, and as such, they could be propagated through
a vacuum, at a definite rate of speed. There was no need for 'action at
a distance' or 'fluid ether'. Thus the metaphysical problems just disappeared
when one could produce a proper physical representation of the phenomenon
I have now completed my second topic by giving you some examples of
clearly arranged representations, running from the concrete to the abstract.
I shall now continue this series by turning to Wittgenstein's Tractatus
Gottlob Frege had made one of the most significant previous moves at the end of the nineteenth century with his investigation of the logical foundations of arithmetic. Another was made by Bertrand Russell in the first years of the twentieth century when he discovered a paradox in Frege's foundations. Russell's paradox can be formulated as follows:
Between 1900 and 1910, Russell worked with Alfred North Whitehead to produce a new codification of the foundations of mathematics, published as their Principia Mathematica. In this work they used a "Theory of Types" that separates classes of objects from classes of classes and the other orders of classes so as to avoid the contradiction which had shaken the basis of Frege's work. At the same time they had to introduce a problematic axiom, called the Axiom of Reducibility, in order to re-establish a foundation for certain kinds of mathematical reasoning. Without getting into the technicalities, the Axiom of Reducibility says that we can assume that, for every higher order of classes, there is a simple class of objects which corresponds to it. We require of classes defined in this way that it is, under all circumstances, just simply meaningless to suppose that a class can be identical with one of its own members. And that disposes of Russell's paradox.
By 1911, Russell was already working to extend the resulting "logical analytical method" into new realms; indeed by 1913, he had begun a book on the Theory of Knowledge in which he attempted to provide a logical analysis of judgments. That work had to be abandoned under criticisms from Wittgenstein to which I shall return momentarily. Russell then produced a new theory for his Lowell lectures at Harvard in 1914, which was published as his Our Knowledge of the External World as a Field for Scientific Method in Philosophy. This work introduced the logical analysis of sense data which then became one of the hallmarks of logical positivism.
Well, so much for the 'moves that had gone before'. Let me now turn to Wittgenstein's 'ingenious variation'.
Wittgenstein had appeared at Cambridge in October 1911. By the summer of 1912 he had already been assigned the problem of the form and composition of complexes, that is, of configurations of simple objects. As he worked with Russell through 1913, this problem came again and again to the foreground. Ultimately Wittgenstein's work led him to criticize Russell's multiple relation theory of judgment; indeed, Russell scholars have suggested that Wittgenstein found a paradox within it which led to Russell's philosophical 'paralysis' and the abandonment of his Theory of Knowledge book in mid-1913. (14)
Many of the elements of Wittgenstein's 'ingenious variation' were in place by the end of 1913, when Russell forced him to write out some of his conclusions, or at least by early 1914, when G. E. Moore, who was acting as research supervisor while Russell was in America, went to Norway to talk with Wittgenstein and took notes. Two key points in Wittgenstein's pre-War thinking were the recognition that all logical propositions were tautologies and the recognition that Russell's logical analysis of propositions was based on a concept of propositions as 'pictures' or representations of reality.
Now, if you take only one thing away from this presentation, it should be this: Wittgenstein did not invent the 'picture theory' of propositions. The so-called 'picture theory' is a concept out of late nineteenth century German physics and its most important formulation was by Heinrich Hertz. In 1899, for example, Ludwig Boltzmann argued that the questions about whether force or matter was more fundamental were insignificant because "all these concepts are only mental pictures whose purpose is to represent phenomena correctly". He further notes, "This is stated with special clarity by Hertz in his famous book on the principle of mechanics". (15) Indeed, Boltzmann himself wrote an article on this 'picture theory' for the 1902 Encyclopaedia Britannica, under the heading "Model". The 'picture theory' was a development of neo-Kantian philosophy; Stephen Toulmin has described one important result as the shift from inner, mental presentations in Kant to outer, public representations in Hertz.(16)
Wittgenstein, however, did contribute the following original insight: if propositions under logical analysis were representations, this indicated that there must be a boundary to the realm of logic. The reason for this is simple enough: the one thing a picture cannot represent is itself in the act of representing what is depicted. This creates a fundamental limit to the logic of any representational language, a boundary beyond which it cannot extend. And it provides an explanation for Russell's paradox and the special measures that Russell had to introduce to avoid that paradox. Such contradictions had stemmed from an extension of a form of reasoning beyond its essential bounds. As Kant once wrote, with uncharacteristic grace,
Now, you should already know enough about Wittgenstein to judge for
yourself. Would he then proceed to arrange his own treatise as just such
a series of propositions or not? Of course he would. So I am now ready
to give you my two-penny summary of the Tractatus as a clearly arranged
I have now completed my third topic, the Tractatus as a clearly
arranged representation. I shall now turn to my final topic and address
those contradictions that cloud our view of Wittgenstein's work. Our first
task is to understand the three terms that make up the contradictions attributed
to the Tractatus by Russell, Ramsey, and Ayer: unassailable truth,
value, and nonsense. Let me re-examine these terms in light of the Tractatus
seen as a clearly arranged representation.
Let me now turn to the third term, 'nonsense', and its opposite, 'sense'. The term 'nonsense' is somewhat complicated, because Wittgenstein distinguishes between 'not having sense' on the one hand and being 'nonsensical' or absurd on the other. 'Having sense' means having some engagement with reality, that is, possessing definite meanings. A wheel that meets the road has sense; one that spins free does not have sense. Of course, tautologies do not engage reality, they lack sense; that is, they apply to anything and everything at once. This podium, this rug, that arm chair, this room, the city of Chicago, all are either proper milk jugs or they are not, tautologically. (Of course, we know empirically that these things are all not milk jugs, but that's a separate issue.) So again there's no contradiction in Wittgenstein's terms between unassailable truth and not having sense. Indeed all unassailable truths, all tautologies, lack sense just as they lack value. And that disposes of the simplest interpretation of Ayer's attributed contradiction between assertions that are unassailably true but devoid of sense.
Of course, Wittgenstein also says that "he who understands me finally recognizes my propositions as nonsensical when by means of them - [ascending] on them - he has ascended beyond them". (19) Here he means 'nonsensical' in the stricter sense of being absurd. But this too is clarified when you see that the Tractatus itself has violated the fundamental limit to representation by representing the requirements for representation. Like a drawing by M. C. Escher, it pictures the picture depicting what is depicted. In this sense, each proposition in the Tractatus is a failed or failing proposition. And this is as it should be, just as we showed the boundary of what could be a proper milk jug by holding up a series of failed or failing milk jugs. And just as we recognized that the requirements for milk jugs were not themselves milk jugs, so too, the requirements for representational propositions cannot themselves be representational propositions. So, in this way, because the subject matter of the Tractatus is a representational theory of propositions, it's unassailably true propositions about the requirements for representation must, in the end, be recognized as nonsensical. And that disposes of the other interpretation of Ayer's attributed contradiction: that assertions cannot be, at one and the same time, unassailably true and absurd.
Now, in this light, you can begin to see how Ryan's account of the Tractatus must be inaccurate. Actually there is no 'analytical urge' in the Tractatus. Rather it is an effort to reveal that Russell's 'analytical urge' threatened to extend reason beyond its limit when he attempted to analyze the form of judgments. The method by which Wittgenstein does this is to recognize the representational character of Russell's analysis of propositions, and to reveal the true nature of logical propositions as tautologies. Wittgenstein is presenting a critique of Russell's technique, not an endorsement. He is showing the limits to the application of logical analysis. And so, Wittgenstein did not later need to renounce these analytical techniques. He merely turned to the critique of other forms of thought. In this way, the recognition of the true nature of the Tractatus provides a key to seeing Wittgenstein's later work more clearly.
So, let me turn to Ryan's suggestion that there was a contradiction
in all of Wittgenstein's work between profession and practice.
Let me then conclude by discussing Ramsey's attributed contradiction between pragmatic value and nonsense. Ramsey's criticism of the Tractatus has to be taken seriously since Ramsey worked through the Tractatus with Wittgenstein himself as early as 1923. Indeed Wittgenstein later acknowledged Ramsey's help in recognizing grave errors in his early work. (20)
In the quotation I gave, you'll remember that Ramsey suggested that philosophy was either of use in clearing our thoughts and actions, or that it was nonsense, a disposition we have to check, and then it could not be 'important' nonsense, as Wittgenstein pretended. Let me just rewrite Ramsey's remark to illustrate my topic, "the importance of the clearly arranged representation." Thus: Clearly arranged representations (rather than philosophy) must be of some use and we must take them seriously; they must clear our thoughts and so our actions. This is so because they show us the limits of reason. Philosophy, however, may sometimes involve a disposition to extend our knowledge beyond its legitimate bounds; this is a disposition we have to check, and producing clearly arranged representations is an inquiry to see that this is so. Sometimes this means we must admit that our philosophical work is nonsense. Philosophy must be self-critical. And that is the importance to philosophy, indeed to all our thinking, of the clearly arranged representation.
(1) Ludwig Wittgenstein, Philosophical Investigations, 3d ed., remark 122, p. 49. (back)
(2) Russell to Lady Ottoline Morrell, 21 January 1913 (#678) and 23 February 1913 (#707), quoted in Kenneth Blackwell, "The Early Wittgenstein and The Middle Russell," Perspectives in the Philosophy of Wittgenstein, ed. Irving Block, pp. 11, 13. (back)
(3) Walter Kaufmann, "Foreword" to Wittgenstein, by William Warren Bartley III. (back)
(4) Stephen Toulmin, "Ludwig Wittgenstein," Encounter, January 1969, pp. 59-60.(back)
(5) Russell to Morrell, 2 May 1912 (#435), quoted in Ronald W. Clark, The Life of Bertrand Russell, p. 176. (back)
(6) Clark, p. 438. (back)
(7) F. P. Ramsey, The Foundations of Mathematics, p. 263; unavailable to me, so here as quoted in A. J. Ayer, Wittgenstein, p. 30. (back)
(8) Ayer, pp. 20, 30. (back)
(9) Alan Ryan, "Ayer's Wittgenstein," Encounter, November 1985, p. 64. (back)
(10) Ryan, p. 66. (back)
(11) Ryan, p. 64. (back)
(12) Ryan. pp. 66, 65. (back)
13) E. H. Gombrich, "Freud's Aesthetics," Encounter, January 1966, p. 37. (back)
(14) See the articles by Kenneth Blackwell in Perspectives on the Philosophy of Wittgenstein (ed. Irving Block), Stephen Sommerville in Language, Logic, and Philosophy (Proc., Fourth International Wittgenstein Symposium), and Nicholas Griffin in Philosophical Studies (47, March 1985), among others. (back)
(15) Ludwig Boltzmann, Theoretical Physics and Philosophical Problems, p. 104. (back)
(16) Stephen Toulmin, Human Understanding, pp. 192-95. (back)
(17) Immanuel Kant, Critique of Pure Reason, trans. Norman Kemp Smith, pp. A4-A5 (B8). (back)
(18) Ludwig Wittgenstein, Tractatus, Preface, paragraph 2, my translation. (back)
(19) Wittgenstein, Tractatus, remark 6.54, my translation.(back)
(20) Wittgenstein, Philosophical Investigations,
Preface, p. 2. (back)