The Method of the Tractatus
The Method of the Tractatus


In the last years, a small but rapidly growing group of American philosophers tried to convince the world that almost eighty years of Tractarian studies rest on mistake: Starting with Russell and Ramsey, Wittgenstein’s commentators neglected 6.54 which ‘clearly states’ that the propositions of this work are a plain nonsense. My task in this paper is to show that this thesis is mistaken, and that it is mistaken in an important way. Above all, the representatives of this group confuse the method (style) of the Tractarian theories with the method of their exposition. Further, I suggest a new interpretation of 6.54 which differs from both that of this group, as well as from that of Peter Hacker: Wittgenstein’s main problem in the Tractatus was the advancing of a content-less (intuitive) Conceptual Notation and of instructions how to use it. Once we have mastered these two, we must throw them away.

Table of contents

    1. Radical Philosophers

    A few years ago, a group of American philosophers, Cora Diamond and James Conant among them, suggested a resolute, or radical reading of Wittgenstein’s Tractatus. These two authors claim that the Tractatus has a body, and a frame. Wittgenstein minded the frame seriously, whereas all the remaining propositions of the Tractatus, which belong to its body, are written tongue in cheek. To the frame of the work belong the Preface, §§3.32–3.326, 4–4.003, 4.111–4.112 and 6.53–6.54. In it Wittgenstein gave meta-theoretical instructions how to treat the rest of the book. The main idea of the frame is expressed in § 6.54 which reads: “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.).” This was the real message of the Tractatus.

    Further, Diamond and Conant suggest a dialectical reading of the Tractatus. In Conant’s words, this reading discerns, among other things, two doctrines in the book: (1) that the propositions of philosophy are misleading nonsense (it was embraced by the Vienna Circle positivists); (2) that there are many ineffable truths which cannot be articulated but which can be pointed out (it was embraced by Peter Hacker). The propositions of the Tractatus advance such illuminating nonsenses: bits of nonsense that are useful because they nevertheless clarify important parts of reality and language.

    Conant insists that, in fact, “the Tractatus ... aims to demonstrate how each of these conceptions is the mirror image of the other, each feeding on and sustaining the other.” (Conant 2002, 376) They are the product of two different impulses: “The conceptions to which these impulses give rise figure in the work as dialectical way stations that are to be successively recognized as the antepenultimate and penultimate rungs on the ladder that the reader is invited to ascend and – once having ascended – called upon to throw away.” (ibid., 377)

    In other words, Diamond and Conant embrace austere conception of nonsense which claims that the propositions of the Tractatus are plain nonsense and nothing beyond that. They have only therapeutic role, the purpose of which is to cure us from the inclination to embrace philosophical truths of conventional form; once this role is finished, they must be thrown away.

    2. To What Extend Did Wittgenstein Follow Frege in the Tractatus?

    The radical reading of the Tractatus was strongly criticised by Peter Hacker (in Hacker 2000). Hacker is insistent that the propositions of the Tractatus ascribe, above all, formal properties and relations, and these cannot be said but can only be shown. He explains 6.54 so. In this paragraph Wittgenstein means that his propositions are important nonsense. They say nothing; in this sense we can call them nonsense. They, however, demonstrate something about the language and the world; and this something is important – very important.

    Despite this marked difference between the two parties, they have something in common. Both assume that at the bottom of Wittgenstein’s Tractatus lies Frege’s conception of saying/showing. In this, they follow Peter Geach (see Geach 1976). My point of dissent is that, in fact, Wittgenstein’s Tractatus is rather a study of a completely different kind from both Frege’s Grundgesetzte and from Russell–Whitehead’s Principia Mathematica. Its genre is not logic but logical–philosophical meditations, or philosophical reflections on the logical writings of Frege and Russell. This explains, among other things, why typical logicians, such like C.I. Lewis, the Polish logicians, Whitehead, Quine and Hao Wang, didn’t held much of Wittgenstein’s logical–philosophical inquiries.

    The Tractarian theory of saying/showing is also radically different from that of Frege. Above all, the thesis of saying/showing is much more central to Wittgenstein’s system: it determines his whole logico-philosophical thinking in the Tractatus. Specifically, Wittgenstein embraces a radical form of intuitivism which is the right opposite to Frege’s logic that strived to be free from intuition. So in “Notes Dictated to Moore” he sets out: “In ‘aRb’, ‘R’ is not a symbol, but that ‘R’ is between one name and another symbolizes” (Wittgenstein 1979, 109) – i.e. the spatial relation between them. The corollary is a variant of the theory of intellectual intuition which is the heart of the Tractatus: “In a suitable notation [rightly organized geometrically] we can in fact recognize the formal properties of propositions by mere inspection of propositions themselves.” (6.122) This intuitivism made it possible to introduce a most radical form of Ockham’s Razor, which eliminated all superfluous entities in logic and philosophy such like logical constants, logical objects, epistemological subjects, etc.

    Of course, the programme for Conceptual Notation (Wittgenstein widely used this term in the Tractatus), the task of which was to rightly express the logical operations of our thinking, was first set out by Frege. In his hands, however, it was not thus radical as in the hands of Wittgenstein. In short, the latter disparaged the discursive thinking and embraced the intuitive one instead. His conclusion was that the logical symbols in the Tractatus are just means (an instrument) for recognizing the logical properties of propositions of science and everyday life: Logical so-called propositions shew [the] logical properties of language and therefore of [the] Universe.” (Wittgenstein 1979, 108) When we construct the graphically (geometrically) right symbols, all problems of logic are eo ipso resolved. It is in this sense that “we cannot make mistakes in logic” (5.473).1

    A consequence of this position was Wittgenstein’s idea that there are no propositions of logic (ibid.), a position that can be called a ‘redundancy theory of logic’. In the same manner, Wittgenstein declared that in real life we never need mathematical propositions (6.211). So, it is no surprise at all that at the end he set out that there are no philosophical, or logico-philosophical propositions as well.

    3. Our Reading of Tractatus 6.54

    Above all, Conant suggests a mistaken interpretation of the Tractarian term elucidation (and the declared purpose of Conant 2002 is just to discuss this term, plus the term nonsense) which plays a central role in 6.54. My propositions, so Wittgenstein, are nonsense; but they nevertheless serve as something – as elucidations; they are not simply gibberish. “The elucidatory strategy of the Tractatus, so Conant, depends on reader’s provisionally taking himself to be participating in the traditional philosophical activity of establishing theses through a procedure of reasoned argument.” (ibid., 422) Similarly to the process in a psychoanalytic therapy, the reader is elucidated if he actually undergoes certain experience of believing in philosophical perspectives of the conventional form, after which he understands that they were nonsense.

    In contrast, according to my interpretation, Wittgenstein claimed that we elucidate indefinables, or data, of any kind whatsoever. Indefinables are aesthetic, logical, religions, or practical objects. These are things that we wonder at, see sub specie aeternitatis, or simply beyond time. We cannot express or articulate them (we can articulate only states of affairs). What we can do with indefinables is only to comment them – in the same way in which we comment works of art, or historical events. Exactly such an indefinable was the Tractarian Conceptual Notation.

    Now, the propositions of the commentary have not own content: their purpose is simply to bring to light (to clarify) the indefinable under scrutiny, pointing out at new aspects of it. Once we have the new insight into the datum, we do not need these propositions anymore – they are exactly so needless as the ladder with the help of which we have reached a certain height (level) on which we now act and live.

    In short, my point is that Wittgenstein’s Tractarian propositions are elucidations of the Conceptual Notation and thus, of the logic of language. Being such, they train its reader to better see how the propositions of science logically relate one to another, how the logic of our everyday language functions, etc. In this way, they develop our skill to thinking better. They, however, have no own content.

    This interpretation of the Tractatus fits perfectly well its description as a ladder. To be sure, (1) exactly the instrument for training is what we threw away after we have reached a new level in our development – we have no interest in the instrument which brought us up to it. (2) What is important with such instruments is not their content but their form. Perhaps another person should construct a different type of instrument, with the help of which we will be trained in the same skill. In this sense, the propositions of the Tractatus do not express something necessary; they are contingent. Diamond is especially insistent on this point. Unfortunately, from it she made false conclusions.

    My reading of 6.54 also casts light on another difficulty in the Tractatus, widely discussed by Diamond and Conant. Wittgenstein’s insistence (in 4.1272) that objects (but also complexes and facts) are formal concepts evidences that he conceived as part of his task – to set out a right Conceptual Notation – not only the solution of some logical, but also of some ontological problems. This means that the Tractarian ontology is not a pure ontology; it is rather a logico-ontology – a part of Wittgenstein’s new Conceptual Notation. This point is clearly stated in the concluding proposition of Wittgenstein’s Conceptual Notation, set out in 4.5: “The general form of a proposition [which pertains to logic] is: This is how things stand [a statement in ontology].”

    It is exactly this assimilation of the problems of ontology to these of logic that (1) led Wittgenstein to claim that the ontological propositions in the Tractatus are nonsense too – nonsense are not only the logical so-called propositions which are about formal concepts. (2) It made the Tractarian ontology just an instrument for better recognizing the logic of propositions of science and life, and nothing beyond this. After we have grasped this logic, we can cast this instrument aside. – This point rather mesmerizes Diamond and Conant, misleading them to (falsely) believe that the doctrines in the body of the Tractatus are suggested only tongue in cheek.

    4. The ‘Method’ of the Tractatus: How not to Use a Word

    The crisis in the Tractarian Studies, triggered by the recent dialectical reading of this work of Wittgenstein, had a transparent aetiology: for decades the methodological side of the Tractatus, which found expression in 4.1213, 5.473 and 6.12–6.122, was not studied seriously. It is not by accident that exactly these paragraphs peak at the centre of Diamond–Conant’s argument.

    In words, Diamond and Conant investigate ‘the method of the Tractatus’ – this is also the title of Conant 2002. Unfortunately, what Diamond and Conant really do is not a discussion of the method of the Tractarian ideas; not really. Rather, they discuss its style – the strategy of the narrative of the book. At that, they read the remarks on the method of the Tractarian theories as remarks on the Tractarian narrative.

    Indeed, Conant’s interpretation of the ‘method’ of the Tractatus is that Wittgenstein wrote the book as an exercise in Kierkegaardian irony: it advanced theses of the conventional type only in order to laugh at them, saying at the end that they are plain nonsense. His hope was that the experience of going through these conventional-type theses will free the reader from the enchantment with such theses.

    Be this as it may, this reading of Conant is a thesis on the style of the book – on the method of articulating his ideas. It is not a thesis about the method of the conventional-type thesese themselves. They say nothing about the idiosyncratic way in which Wittgenstein treated the problems of logic, philosophy, mathematics and ethics in these theses – even when he minded them tongue in cheek. Even worse, Conant and his friends read the sections which deal with the method of the Tractarian ideas as sections which contain hints about the architectonic of the Tractatus. Here I have in mind above all 5.473 which is quoted by practically all radical readers of the book: “If a sign is possible, then it is also capable of signifying. Whatever is possible in logic is also permitted. In a certain sense, we cannot make mistakes in logic.” Now, both Diamond (Diamond 1991, 196) and Conant (Conant 2002, 421) read this section as meaning: everything in logic is possible; so, any proposition expressed in the body of the Tractatus logico-philosophicus is a plain nonsense.

    In truth, this section expresses the main point of the method of Wittgenstein’s logico-philosophical (conventional) theory: If the sign is well-constructed, it will reveal the logical (formal) properties of the propositions/states of affairs without much ado. This, however, also means that the very possibility of the sign is determined by the proposition/state of affairs itself…


    1. Conant, J. 2002 “The Method of the Tractatus”, in E. Reck (ed.), From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, Oxford: Oxford University Press, 374-462.
    2. Diamond, C. 1991 “Throwing Away the Ladder: How to Read the Tractatus”, in her The Realistic Spirit: Wittgenstein, Philosophy, and the Mind, Harvard: MIT Press, 179-204.
    3. Geach, P.T. 1976 “Saying and Showing in Frege and Wittgenstein”, in J. Hintikka (ed.), Essays on Wittgenstein in Honour of G.H. von Wright, Amsterdam: North-Holland, 54-70.
    4. Hacker, P.M.S. 2000 “Was He Trying to Whistle It?”, in A. Crary and R. Read (eds.), The New Wittgenstein, London: Routledge, 353-388.
    5. Wittgenstein, L. 1979, Notebooks 1914–1916, 2nd ed., ed. by G.H. von Wright and G.E.M. Anscombe, trans. by G.E.M. Anscombe, Oxford: Blackwell.
    My considerations articulated above see 5.473 as a consequence of 6.12–6.122, not vice versa. In contrast, Conant believes that 5.473 is “the heart of the Tractarian conception of logic” (Conant 2002, 421). (On the roots of this confusion see § 4.) Where I and Conant agree is that there is one conception in the Tractatus that can be called its ‘heart’.
    Nikolay Milkov. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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