From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

Introduction

Ever since its publication, the form and numbering system of Wittgenstein’s Tractatus Logico-Philosophicus (1922) has been the subject of comment, reflection and speculation. Reviewing the work in 1923, F.P. Ramsey noted his reservations about the book’s terse sentences and “systematic” organization. The following year, T. de Laguna, having pointed out inconsistencies in the book’s numbering system, concluded, “it is to be hoped that Mr Wittgenstein’s example will find few imitators”. On reviewing an Italian translation of the work some thirty years later, P.T. Geach expressed unreserved admiration, claiming that “there has hardly ever been written a philosophical work with a greater degree of organic unity”.

These reactions anticipate later assessments of the Tractatus’ form and not least its numbering system. At the one extreme we have Max Black’s sceptical assessment, that the book’s numbering system (its “system and order”) “is so misleading here as to suggest a private joke at the reader’s expense”. At the other extreme (and most recently) we have L. Bazzocchi’s unreserved approval of the numbering system, which he describes as “the fundamental key […] to the deep structure of the book”. Between these two extremes we find several judgements and interpretations that vary in their appraisal. Joachim Schulte, for example, feels that “the Tractatus’ numbering is useful in gaining an overview of themes; otherwise it is to be regarded with suspicion”, a view that G. Pitcher foreshadowed in saying that the numbering system is neither as rigorous nor as consistently applied as first impressions suggest (“it is only a rough guide to the structure of the Tractatus”). A classic representative of these intermediate positions is Brian McGuinness, who says that, superficially, the Tractatus gives the impression of a meticulously worked-out structure, yet “in detail, it retains many of the features of the Zibaldone”. In this context, McGuinness hypothesizes that the book’s fourth section is of central significance, in that the work can be regarded as “a kind of systole and diastole around proposition 4”. At the same time, McGuinness reconsiders D. Favrholdt’s suggestion that the book’s use of the numbering system is justified by the practical advantages it brought during the work of selecting and ordering remarks from earlier manuscripts. McGuinness writes “For composition this method of numbering […] has the merit that a number, an afterthought, can always be inserted between any two existing numbers”. V. Mayer has examined this “genetic explanation” and finds that “the numbering system of the Tractatus reflects primarily a method of composition”. Numerous other assessments could be adduced (K. Gibson, C.-A. Scheier, E. Stenius, …). But the above are sufficient to make the point.

What many of the cited authors have in common is that, in hinting at a presumed point of connection behind the Tractatus’ form and its numbering system, they allude to A.N. Whitehead and Bertrand Russell’s Principia Mathematica from 1910. Black points out that the organization of the Tractatus is reminiscent of “the similar system of reference in Principia Mathematica”. McGuinness is of the same opinion: “It will be remembered that Russell wanted Wittgenstein to rewrite the first chapters of that work”. R. Goldstein, on the other hand, believes that the numbering system is borrowed from G. Peano, while E.M. Lange argues that the real place to start when seeking to understand the Tractatus’ form and numbering system is Schopenhauer’s ideas concerning an “organic” philosophy and the difficulties of communicating the like.

But might there not be other possible influences?

1. “… a magnificent work”

The abovementioned attempts to explain the Tractatus’ form and numbering system ignore what is supposedly one of the work’s essential sources of inspiration, namely L. Tolstoy’s Gospel in Brief (Kurze Darlegung des Evangelium = KD) from 1892. It is well known that Wittgenstein’s early thought was influenced by Tolstoy. We are all familiar with Russell’s account of the book that Wittgenstein bought in a partially abandoned bookshop in Tarnow in August-September 1914. We all remember that his fellow soldiers referred to him as the man with the Gospel. And we have all read his diary notes from October 1914 in which he writes that he has been carrying “the ‘Gospel in Brief’ by Tolstoy around with me constantly, like a talisman”. Tolstoy’s “magnificent work” features prominently both in Wittgenstein’s efforts to come to terms with himself and in his work on the Tractatus.

The Gospel in Brief (like the Tractatus) is a book compiled from a selection of texts. Based on the four Gospels and the first epistle of John in the New Testament, Tolstoy seeks to (re)construct Jesus’ message. In this work, Jesus proclaims the vision of a universal philosophy of life, Tolstoy’s alternative to the theology of the established Russian Orthodox church. In his preface, Tolstoy describes the theme of the book and explains its composition, progression and inherent structure. It is these “structural” considerations that I wish to focus on and to tentatively propose as a key to understanding the Tractatus’ form and numbering system. But to begin with we should recall the introductory “catalogue” of the Prototractatus (PT 3), which contains a list of fifteen numbered statements. This list consists of the “system’s” first six “main propositions”, sentences with single-place numbers, together with a selection of sentences to which two-place numbers are ascribed. These numbered propositions form “the scaffolding of the Prototractatus system”, constituting what Wittgenstein would later call “a perspicuous representation” of the manuscript’s content.

Turning now to Tolstoy, in his preface to the Gospel in Brief we find three similar “catalogues” or “perspicuous representations”. Firstly, Tolstoy mentions that the overall structure of his work “came about spontaneously” through working with the book’s content. There are twelve chapters, and the content of the book, namely the essential elements of Jesus’ teaching, is summarized as a list of propositions numbered from 1 to 12. Each numbered proposition corresponds to one chapter and announces in succinct form the content thereof. Tolstoy goes on to state in more precise terms that the twelve chapters are linked in pairs, the elements of which are related “as cause and effect”(KD 7). He then details the content and function of this first list in two subsequent twelve-part “catalogues”. Concerning the chapter titles he explains (with regard to the second “perspicuous representation”): “At the beginning of each chapter, besides a brief description of the content, I had put words from the prayer […] such as corresponded with the content of the chapter”(KD 8). The justification for introducing the words of the Lord’s Prayer is that: “At the conclusion of my work I found, to my astonishment and joy, that the Lord’s Prayer is nothing less than Christ’s whole teaching, stated in most concise form, and in that same order in which I had already arranged the chapters, each phrase of the prayer corresponding to the […] sequence of the chapters”(KD 8). Accordingly, Tolstoy arranges and cites the text of the Lord’s Prayer divided into twelve numbered sections, which, he maintains, correspond to the preceding twelve numbered statements (which essentially reiterate Jesus’ teaching). Thus what the preface’s first and second “catalogues”, each consisting of twelve numbered statements, present us with are two parallel and, in Tolstoy’s view, corresponding lists of the contents of the book’s twelve chapters: 12 main propositions concerning Jesus’ teaching = 12 sections of the Lord’s Prayer. - Allow me to point out that, by adducing the words of the Lord’s Prayer in the headings of the Gospel in Brief, Tolstoy is asserting a relationship between the statements of the prayer (between their potential to bring to light questions to which they themselves provide the correct answers) and a reading of his Gospel in Brief. This reading constitutes both a clarification of the questions about the meaning of life and an imparting of answers to those same questions. And here we can ask, is it not the case that the Tractatus seeks to apply and achieve a similar “rhetorical” objective or “invocative” aspect? I shall leave this question as it stands!

All considered, what we can conclude from the foregoing, namely Tolstoy’s assertion in the preface to his Gospel in Brief that in terms of its content (and despite its compilatory nature) his book constitutes a unified and coherent whole, is that the book’s fundamental ideas are capable of being summarized in the form of twelve numbered “brief descriptions of the content”, or chapter headings. Accordingly, Tolstoy sets up two “perspicuous representations” in his preface, in which he supplements each content description with two parallel formulations, which in principle merely restate the content description in greater detail. In other words, what we have is, first, the “content description”, or heading of the respective chapter, followed by an elaboration of the description concerning Jesus’ teaching, and finally a section of the Lord’s Prayer. The concluding and final “catalogue” of the Gospel in Brief, which is likewise reminiscent of the Prototractatus’ introductory “catalogue”, reiterates the three-part headings of the twelve chapters in summary form. The first four items read:

• I. Chap. The son of God. Man, the son of God, is powerless in the flesh, and free in the spirit. (Our Father!)
• II. Chap. Therefore man must work, not for the flesh, but for the spirit. (Which are in Heaven.)
• III. Chap. The life of all men has proceeded from the spirit of the Father. (Hallowed by Thy name!)
• IV. Chap. God’s Kingdom. Therefore the will of the Father is the life and welfare of all men. (Thy Kingdom come.)(KD 203)

Within the book, the three-part heading of each chapter is followed by the actual text, which consists, firstly, of Tolstoy’s own paraphrased interpretation of a selection of Gospel texts, secondly of a full citation of the selected texts (with chapter and verse references), albeit in Tolstoy’s own translation. In other words, Tolstoy’s recurrent structural principle is such that it encompasses, to begin with, a movement from an introduction in a gnomic title of the main content, to a short subheading, to a section of the Lord’s Prayer, to the increasingly explicit descriptions and explanations in each chapter’s two-part elucidation. Thus there is a movement from a laconic introductory formulation to a progressively more detailed description. Moreover, this structural principle encompasses an organization of the book’s linear development as “cause and effect”.

Linked to this general structural principle, which seems to correspond in various ways to the text of the Tractatus, is a notion of “form as evidence of the content’s validity”. Tolstoy says that the structure of the Gospel in Brief is a consequence of the distinct and inherent logical structure of Jesus’ teaching. And for Tolstoy, this structure (the book’s coherent arrangement) amounts to nothing less than a powerful indicator and corroboration of the validity of the teaching he presents. Tolstoy writes that he has omitted text-critical, philological, historical and dogmatic arguments precisely so as to allow the distinct and inherent validity of his subject matter to be heard. The arguments to which he refers are “omitted; because […] they cannot carry conviction as to the true understanding of the teaching”. Because “The main evidence for the truth of this teaching is its uniformity, clarity, simplicity and unity”(KD 10).

It is tempting to infer that Wittgenstein’s organization of the (Proto)Tractatus amounts to an endorsement of Tolstoy’s idea of “form as evidence of the content’s validity”. This assumption could form the first step in explaining why neither work offers much argumentation or reasoning in support of central tenets; clarificatory remarks would only weaken the impression of unity, in other words, they would counteract the logical, architectural form at which the authors aim – and thus undermine the content’s claim to validity. In his 1923 review, Ramsey may well have been thinking along these lines when he remarked that the Tractatus’ “attractive epigrammatic flavour […] seems to have prevented him [Wittgenstein] from giving adequate explanations of many of his technical terms and theories”.

2. “… as the heading of a chapter”

With these comments in mind we can now ask whether Tolstoy’s introductory remarks to the Gospel in Brief and his thoughts concerning the composition, progression and inherent structure of the “Gospel’s harmony” are of any relevance in seeking to understand the form and numbering system of the Tractatus. Maybe. Maybe not. But despite this uncertainty, I shall briefly indicate a few of the “perspectives” that might result from this approach to the Tractatus. Here the overall working hypothesis (in a more rigorous formulation) will be this: the composition of the Tractatus, its form and numbering system, constitute a modified version (a more formalized implementation) of Tolstoy’s compositional strategy in the Gospel in Brief. Or put another way: when, after his initial reading of the Gospel in Brief, Wittgenstein describes it as “a magnificent work”, is he also thinking about the abovementioned “structural” considerations described in the work’s preface?

If we answer in the affirmative, then a number of implications would appear to follow. Firstly, we have the genetic implication, to the effect that Wittgenstein’s idea for the Prototratactus’ introductory and text-structuring “catalogue” is attributable to his familiarity with the three synoptic and numbered “perspicuous representations” of the Gospel in Brief. Secondly, we have the implication of textual economy, to the effect that Wittgenstein’s choice of remarks in compiling and laying out the (Proto)Tractatus is indebted to Tolstoy’s idea of “form as evidence of the content’s validity”. Some of the remarks in the Tractatus can indeed be read as (meta) comments on this theme, remarks in which Wittgenstein indicates his support for the idea, as for example when he writes: “If a sign is not necessary then it is meaningless”(TLP 3.328). On top of this there is a third implication concerning detailed structure, to the effect that, to the extent that the numbering system in the (Proto)Tractatus is indebted to and to be understood in light of the numbered “catalogues” of the Gospel in Brief (and possibly the last of them in particular), we have to conclude that the Prototractatus’ “catalogue” does indeed constitute a sketch for a table of contents. More precisely, the implication is that the list in the Prototractatus presents, first, the title of the individual chapter in terms of a brief content description (marked by the single-place numbers (1, 2, 3, 4, …)), followed by supplementary subheading(s) (indicated by two-place numbers (1.1, 2.1, 2.2, 3.1, 3.2, 4.1, …)), which (as in the Gospel in Brief) repeat the substance of the content descriptions, albeit in greater detail. According to this pattern, the text sections that follow these subheadings (marked with three-place numbers in the Prototractatus and the Tractatus) have to be regarded as the actual chapters (distributed among the individual subheadings), whereby the content descriptions and the supplementary subheadings are elaborated to make them explicit. In brief, what we have is, first, the content descriptions, in other words the chapter headings (e.g. PT 3), then the supplementary subheadings (e.g. PT 3.1 and 3.2), and finally the text of the actual chapters (e.g. PT 3.11-3.164 and 3.210-3.2531). Accordingly, there is the content description / chapter heading: “A logical picture of facts is a thought”(PT 3), followed by the supplementary subheadings: “The perceptible expression of a thought is a propositional sign”(PT 3.1) and “A propositional sign with its mode of depiction is a proposition”(PT 3.2), followed by the actual text of the chapter (distributed among the individual subheadings) (PT 3.11-3.164 and 3.201-3.2531). Some two decades after completing the Tractatus, Wittgenstein remarked to M.O’C. Drury that C.D. Broad “was quite right when he said of Tractatus that it was highly syncopated”, to which Wittgenstein added that each proposition in the Tractatus “should be seen as the heading of a chapter, needing further exposition”.

In adhering to the proposed juxtaposition of the Gospel in Brief and the (Proto)Tractatus, several other questions arise concerning the actual chapters of the Tractatus. For example, why does Wittgenstein ascribe numbers to these text sections / chapters? Tolstoy does not do the equivalent in the chapters of his Gospel in Brief. One answer might be that Wittgenstein didn’t actually need this expansion of the numbering system, an answer which would imply (and can be justified by referring to the chapters’ numerous “internal inter-textual” comments and elaborations (see TLP 3.201, 3.312, 3.313, 3.325, 3.331, 3.341, 3.3411)) that the chapters of the Tractatus do in fact meet the criterion for a form of presentation that Wittgenstein wanted (but failed) to achieve in the Philosophical Investigations. Namely, a form of presentation in which “the thoughts […] proceed from one subject to another in a natural order and without breaks”, with words and remarks “hang[ing] one in another, like the links of a chain”(TLP 2.03) in a straightforward and self-evident manner. – In order to count as reasonably plausible, this reading must of course be able to answer the following obvious question: if the arrangement and wording of the chapters render the guidance of the numbering system superfluous, then why is it used? Here the answer might be that the numbering system is merely intended to mark the inherent structure of the “teaching”; the use of the system does no more than emphasize the logical connections of the “teaching”, thus reinforcing the convincingness / validity that the “teaching” itself is assumed to possess in virtue of its coherence. Seen from this angle, the introduction and use of the numbering system in the chapters of the (Proto)Tractatus is motivated by the idea of “form as evidence of the content’s validity” elucidated in the Gospel in Brief. Tolstoy writes: “The main evidence for the truth of this teaching is its uniformity, clarity, simplicity and unity”.^*