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: 

• First, that Wittgenstein's 'general form of the proposition' has a specific meaning, a series of propositions in a definite order that consists of the successive negations of the possible combinations of the proposition's elements (there has been, I believe, no adequate explanation of this organization of propositions); and that the Tractatus is itself such a series.
• Second, that the elements that make up the initial proposition in the Tractatus are taken, as commonplaces, from Hertz's definition of the requirements for scientific representations, namely correctness, appropriateness, and logical permissibility; these are used in the Tractatus as the requirements for "that which can be said clearly."
• And third, that the Tractatus is thus a demonstration of the limits of the logic of language; this argument was directed at the extension of logical analysis proposed by Bertrand Russell in the years between 1911 and 1914, while Wittgenstein was his graduate student.

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? 
And what is our view of his work? 

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. 
Wittgenstein's education was somewhat unconventional. He was educated at home, and a very cultured, upper-class home it was. But he was unprepared to attend Gymnasium, an academic high school, at the normal age. So, a year late, he was sent to a technical academy at Linz, where he spent three years. In the following two years, he spent three semesters at the engineering college at Berlin-Charlottenburg. And following that, three academic years at Manchester doing research in aeronautical engineering. During that time, indeed already by 1909 when he was twenty, Wittgenstein was also studying the logical and mathematical questions raised by the work of Bertrand Russell and Gottlob Frege. He even visited Frege and then, in 1911, he went to Cambridge to talk with Russell. There he rapidly became Russell's most important student, the one who would take over Russell's position, even the one who would re-write the early chapters of the Principia Mathematica to meet the new "higher standard of exactness" that he had brought to that work.(2) Russell's trip to America to lecture at Harvard, and then the War, interrupted their work together. But the Tractatus, finished in August 1918, was primarily the result of Wittgenstein's conversations and correspondence with Russell between the years 1911 and 1915. It was, in some sense, the conclusion of Wittgenstein's graduate research under Russell's supervision. 
For some time after the publication of the Tractatus, Wittgenstein withdrew from philosophy. He returned to it, and shortly afterward to Cambridge, in 1929. He worked there with some interruptions until the beginning of the Second World War and again returned for a few years afterward. The result of this later work was the completed text of one book, the Philosophical Investigations, and a mass of other manuscripts, notebooks, jottings, typescripts, and dictations. The publication of the official versions of these other writings is only now reaching its conclusion. 
The significance of Wittgenstein's work can be estimated from Walter Kaufmann's statement that, 

It has been said that every great philospher has given philosophy a new direction, but that only Wittgenstein has done this twice--first with his Tractatus, published right after World War I, and then again with the ideas that found their final form in his Philosophical Investigations, published posthumously after World War II. The early work influenced logical positivism, the later work the analytical philosophy that flourished in the English-speaking world for roughly a quarter of a century.(3) 

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]: 

• Wittgenstein was never a positivist;
• He was never deeply concerned with epistemology; 
• He was not a "linguistic philosopher"; (...). (4)

Philosophy [Ramsey says] must be of some use and we must take it seriously; it must clear our thoughts and so our actions. Or else it is a disposition we have to check, and an inquiry to see that this is so; i.e. the chief proposition of philosophy is that philosophy is nonsense. And again, we must then take seriously that it is nonsense and not pretend, as Wittgenstein does, that it is important nonsense! (7)

(...) It is not at all easy to see what sort of account of Wittgenstein would meet the case, precisely because it is such a glaring contradiction and Wittgenstein was so disinclined to explain himself. The way in which the philosophical profession has coped with the problem is by ignoring it. (11)

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. 
First, let us consider milk jugs. (I apologize to those of you who are accustomed to having philosophy concern itself with arm chairs or jam pots.) With some thought, we can define the requirements of any proper milk jug. It must first of all have some definite structural integrity as a milk jug. It cannot be dissolved by milk or shatter on normal impact with the breakfast table. Secondly, it must be appropriate or purposive, as the philosophers say: that is, it must hold milk and release it as we desire. Finally, a milk jug must be possible: we must be able to make it with existing materials and techniques. 
Now, with this simple list of properties we can do some amazing things. Given that we have a single object which meets all of these requirements, even loosely, we can substitute any object at all, even any conceivable future one, for the milk jug we have, and judge whether the new object would also serve as a milk jug or not. In other words, we can draw a boundary around anything that can be a proper milk jug at all. And, we can show quite clearly, by holding up a series of potential but improper milk jugs, that objects with only two of our 'milk-jug' properties - for example, having structural integrity and holding and releasing milk, but impossible to make - or with only one of our properties - for example, holding and releasing milk but being unsound and impossible to make - or with none of those properties, are definitely not proper milk jugs. We would illustrate part of this series with failed or failing attempts, for example, designs which look good on paper but which are impossible to manufacture. As my ancestors who were architects used to say, "Nur auf Papier läßt sich das machen," "That one is only possible on paper." 
Now, I don't want to belabor this example. The point should be obvious. We can immediately grasp the whole concept of the milk jug, seeing the bounds beyond which an object cannot be a milk jug. This is a clearly arranged representation of the concept of a milk jug. 
Of course the example is a bit too concrete, precisely because there can be no confusion between the requirements for a milk jug and an actual milk jug. The requirement of holding and releasing milk cannot itself hold and release milk. This will not be the case in more abstract examples, since the requirements for logical propositions are, we should hope, themselves logical propositions. 
Let me give you an intermediate case, a link between clearly arranged representations that are concrete and those that are abstract. 

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 in question. 
Of course, again we can avoid the problems which plague more abstract examples. This is so because again it is quite clear that the requirements for scientific representations are not themselves subject to the principles of mechanics, except in so far as they are printed on a physical object. And no scientific theory consists merely of the arrangement of dots of ink on paper. 
In one final intermediate case, this clear separation of requirement and object begins to disappear. Consider a computer program used to evaluate designs for new milk jugs. It must have information about materials and techniques, about milk, and about the normal parameters for the use and abuse of milk jugs. Now consider a meta-program for designing such programs, what's called artificial intelligence. It must represent the requirements of any design-evaluation program: aren't these the same requirements the meta-program must itself exemplify? 
An explanation, a clearly arranged representation, in this case would take me far beyond my topic. So let us just agree that a special form of confusion can result when the requirements which define an object seem to be identical with the object itself: in this case the program and the requirements for the program seem to be the same. 

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 Logico-Philosophicus. 
The title of that work, in German or in Latin, means logico-philosophical treatise, that is, a treatise concerning logic, philosophy and, most of all, their interconnections. Now, Ernst Gombrich once said that there is an element in all art--and I would add, all cultural endeavor including philosophy - 

(...) which might for brevity's sake be called the "cat's cradle" element. Art, as Malraux has stressed, is born of art. The young artist takes over the game from his predecessors and as he does so he introduces variations. In Western communities, at least, art has thus become a social game played among the artists and the pattern that emerges with each move owes at least as much to the moves that have gone before as it owes to the ingenious variation introduced by the present player.(13)

• There are classes of objects and classes of classes (and, indeed, classes of classes of classes);
• Some classes have themselves as members and some do not; for example, the class of all milk jugs is not itself a milk jug, but the class of all objects that are not milk jugs is itself not a milk jug.
• Does the class of classes that do not have themselves as members qualify as a member of itself?

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, 

The charm of extending our knowledge is so great that nothing short of encountering a direct contradiction can suffice to arrest us in our course. (...) The light dove, cleaving the air in her free flight, and feeling its resistance, might imagine that [her] flight would be still easier in empty space.(17) 

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 representation. 
The Tractatus starts from "that which can be said clearly," that is, from the complex requirements for clear, scientific exposition. It then proceeds to show that a proposition cannot be what meets only two of these requirements, or only one of them, or what meets none of those requirements. The latter is that which cannot be said at all, and which must therefore be passed over in silence. This is the same procedure that we used to define the proper milk-jug. Any proposition that only partially meets our requirements can be said even if unclearly. But it can then be corrected or simplified or reformulated logically; it then becomes what can be said clearly; just as every failed milk-jug can be re-structured or re-designed or re-manufactured to produce a proper milk-jug. In other words, the Tractatus proceeds just as we did earlier to draw a boundary around that which can be a milk-jug at all, except that, in the Tractatus, we are drawing a boundary around that which can be said and said clearly. As Wittgenstein says, the whole sense of the book can be grasped in the words: "what can be said at all can be said clearly; and about that of which one cannot talk, one must be silent."(18) He is thus "drawing a boundary to the expression of thoughts." 
Let me just briefly show you the schematic form of the clearly arranged representation in the Tractatus (at the end of this paper). I shall take the main steps in our procedure, apply them now to propositions rather than milk jugs, and show how they correspond to the seven main propositions of the Tractatus. You can follow along in the table. The first proposition of the Tractatus states that the world is a representation of what is not incorrect: a representation of what is incorrect can always be clarified by replacing the incorrect elements with correct ones. The second proposition states that the fact is a representation of what is not inappropriate: the fact with redundant elements can always be clarified by simplifying it. The third proposition states that the picture of a fact can always be clarified by reconstructing it logically: it cannot be illogical. The fourth states that the thought can always be clarified by its application to the appropriate representation of the true facts, giving it sense: it is not logical alone. The fifth, that the proposition can always be clarified by logical representation of the true facts: it is not appropriate alone. And the sixth, that the proposition can always be clarified by reference to its general form as a logical representation of the appropriate elements: it is not correct alone. Thus the Tractatus shows that what can be represented at all can be represented clearly; and what cannot be represented is beyond the boundary of propositional language. 

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. 
In the Tractatus 'unassailable truth' is the property of tautologies, that is, of propositions that can be recognized as true a priori. Tautologies have the same force as well-constructed syllogisms; that is, tautologies have logical necessity: they are apodeictic or proved with certainty. For example, consider this simple tautology: Anything is either a proper milk jug or it is not a proper milk jug. You should be able to recognize that this statement must be true, without even considering any actual milk jugs. Wittgenstein showed that all logical proof involves the same recognition that the asserted proposition is a tautology. So, in claiming that the thoughts communicated in the Tractatus are unassailable and definitive, Wittgenstein is merely claiming that the Tractatus can be recognized as a tautology. And, indeed, he does handle each of the eight discrete cases that are created by the three requirements for clear representations, and in each case he shows what individually must be true a priori. This is the same as showing, one by one, that the positions in the truth-function for an asserted proposition are all true. And this is the method by which we can always recognize a tautology. So, the very arrangement of the propositions in the Tractatus allows us to recognize it as unassailably true. 
The term 'value' in the Tractatus means ethical or aesthetic value. It would be of value in this sense to say that any particular thing was a proper milk jug. And it would be of value to say that it was not a proper milk jug. These would be ethical or aesthetic judgments. But, of course, it would be of little value to assert that any particular thing was either a proper milk jug or it was not, without saying which it really was in this case. In this sense, tautologies are of little value. And that shows how, in Wittgenstein's terms, Russell's contradiction between unassailable truth and having little value was not a contradiction at all: every tautology possesses both properties. 
Indeed, this point connects to one of my main historical contentions. I believe that Wittgenstein produced the clearly arranged representation of the Tractatus primarily as a proof addressed against one aspect of Russell's work in the period between 1911 and 1914. Wittgenstein's purpose was to show that logical propositions could not have ethical or aesthetic value, that they could not express judgments, even empirical judgments, in the way that Russell wanted. 

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. 
In the beginning of this paper, I suggested that the clearly arranged representation was a theme that continues throughout Wittgenstein's work. The point of a clearly arranged representation is that it allows you to grasp a subject immediately as a bounded whole. In giving examples of this concept, I showed how the clearly arranged representation involves a sense of the limits of one's materials and techniques. It is essentially a critical awareness, one which recognizes boundaries and the possibilities that may lie beyond those boundaries. This critical awareness can apply to the production of milk jugs, or to theories of mechanics that recognize the limits of our experience, or to the writing of computer programs. It must also apply to philosophy and to mathematics, where, as Kant says, "the charm of extending our knowledge is so great that nothing short of encountering a direct contradiction [and sometimes not even that, I would add] can suffice to arrest us in our course." Now, if the clearly arranged representation was indeed Wittgenstein's practice, is there a contradiction between that practice and the profession of philosophy? I would say there cannot be, for either philosophy must admit that sometimes it threatens to exceed the bounds of reason or it must relinquish the claim of reason. And that, I believe, disposes of Ryan's attributed contradiction. And it also strengthens the force of his criticism in saying that "the philosophical profession has coped with the problem [of giving a clear account of Wittgenstein] by ignoring it." 

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. 

Footnotes: 

(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)