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Tractarian Dualism

Robert E. Tully
St. Michael’s College, University of Toronto

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ABSTRACT: While Wittgenstein’s Tractatus keeps issues of metaphysics and ontology at arm’s length, the world it presents seems altogether monistic in character. In Wittgenstein’s account, it is a world of objects and facts, a world which lacks selves, values, cognitive relations (such as belief), and God. I argue that the Tractarian world is nevertheless dualistic. I defend the view that the Tractatus points away from monism towards dualism and that Wittgenstein’s concepts of thought, sense, and understanding are an essential part of its structure. The language Wittgenstein uses was necessitated by his project of giving a sharp account of the nature of description. It is thus ironic that Wittgenstein defends dualism in the Tractatus and does so in the only form in which he thought it could be defended. Along the way, I try to show that his treatment of thought, sense, and understanding is both a continuation and correction of treatments which Frege and Russell had previously given to these concepts.

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The world Wittgenstein describes in the Tractatus(1) excludes any traditional form of dualism, even to the extent of not differentiating types of objects. Neither does it allow for radically different kinds of external properties or "relations proper" [4.122] belonging to Tractarian objects, beyond the observable ones he mentions like space, color, degree of pitch, etc. Properties such as these can be specified. Declaring (without qualification) that "the totality of true propositions is the whole of natural science" [4.11], the Tractatus seems to align itself with if not to defend some form of monism, perhaps with the tradition of atomistic materialism which stretches back to Democritus. Since philosophy is not "a body of doctrine but an activity", part of that activity directs us towards science, away from the lure of philosophical nonsense. "Most of the propositions and questions to be found in philosophical works are not false but nonsensical", he declares, arising from "our failure to understand the logic of our language". [4.002] When the "form of the body" has been duly revealed we cannot identify metaphysical dualities of either objects or their properties. The self or subject is not an object in the world; neither are values; neither of course is God. Thought processes are to be left (it seems) to psychology which, Wittgenstein claims, "is no more closely related to philosophy than any other natural science." [4.11]

Some vestiges of dualistic language remain in the Tractatus, of course. Here and there we encounter references to thought, understanding and sense, particularly in connection with propositions, and Wittgenstein makes no attempt to consign them to psychology. However, in keeping with the idea that the Tractatus radically opposes dualism, one might regard such dualistic language as both innocuous and unimportant. If Wittgenstein describes propositions as 'having sense' and 'expressing thoughts', that could be taken as a concession on his part to enable readers to maintain their bearings part of the outward clothing of everyday language so familiar to everyone. The dualism suggested by such language is a natural byproduct of its own frequent use, dangerous only to the philosopher who might be tempted to take its meaning literally. Perhaps Wittgenstein had this sort of phenomenon in mind when he later wrote in the Philosophical Investigations: "Where our language suggests a body and there is none: there, we should like to say, is a spirit"(2) Alternatively, such dualistic expressions might be treated as examples of the "nonsense" propositions characterized at the end of the Tractatus as part of the ladder which one must ascend in order to see the world aright, the world which does not number propositions, senses or selves among its objects.

If there are suggestions of dualism in the Tractatus, then, they seem to evaporate from language under the heat of analysis, so that what remains in the world portrayed by Wittgenstein are only concatenations of objects. However, while granting that ontology was not his concern in the Tractatus and that traditional questions regarding dualism versus monism seem irrelevant to its purpose or even in opposition to it, one can still ask: is that all there is to the Tractarian world? I am going to present the view that there is indeed something more, that it points away from monism towards a dualism, that Wittgenstein's claims about thought, sense and understanding are not mere embroidery in the Tractatus but part of its weave, that the language Wittgenstein uses was necessitated by his project of giving a sharp account of the nature of description, and that Wittgenstein was in fact ironic though this may seem defending dualism in the Tractatus, and defending it in the only form in which he thought it could be defended. Each of these points I will now try to develop briefly.

I do not claim that defending some form of dualism was Wittgenstein's main purpose in the Tractatus or even a primary one. Given the particular form it takes there, in fact, dualism cannot perhaps even be directly argued for at all, which may help explain why this aspect of the work has been neglected.

1. The Tractarian world holds more than concatenated objects; it holds the possibilities of such concatenations. This point is not trivial and it does not hide behind the ambiguity of the word "holds", for among the concatenations of objects in the Tractarian world are the kind which Wittgenstein identifies as pictures. The elements comprising a picture are related to each other in a determinate way: "A picture is a fact". [2.141] What makes a picture to be a fact is easily stated; what makes a fact to be a picture is much more difficult to express, but Wittgenstein's attempt to render it clearly is well known. A fact would not be a picture unless its elements were representatives of objects and unless the concatenations of these elements represented some way in which those objects could be related in a separate fact. It is essential to any Tractarian picture that it represent. What it represents, however, is a possible fact, at least from the viewpoint of the picture. Representation cannot guarantee the existence of the fact being represented. "A picture represents a possible situation in logical space," Wittgenstein says, it "contains the possibility of the situation that it represents." [2.202 and 2.203] A picture and the situation it represents have something in common, which he calls pictorial form and (more generally) logical form. This relation which binds the two will obtain for any picture whether or not the fact represented exists; so the common relation of logical form is really between the picture, which is an actual fact, and what Wittgenstein calls the sense of the fact it represents. Tractarian pictures have semantical force: they represent that something is the case. (They are not portraits, still lifes, landscapes or battle scenes.) Hence they are not just faithful representations but are either true or false. As long as each element of the picture is made to designate some object, and as long as altogether they concatenate in a way in which the corresponding objects might concatenate in a fact, the picture will succeed in representing, and what it says will be true if the structure of objects is as represented, although the picture's capacity to represent does not depend on its being true. Beyond giving such details, the Tractatus is not concerned with determining the conditions of good representation or with deciding when a fact must forfeit its claim to be a picture. It is enough that there are many non-failures; incontestably, we do "picture facts to ourselves". [2.1]

The example of picturing merges easily with remarks about propositions. "A propositional sign is a fact." [3.14] Words are its elements, serving as names for objects. A proposition projects a possible situation. It contains the form of its sense, he says, rather than its content: it contains "the possibility of expressing" its sense. [3.13]

However, a proposition would only be a propositional sign, and a propositional sign only a fact, were it not for the use to which it is put. Nothing would be a Tractarian picture if we did not cast some fact into a representational role, and no propositional sign would project any possibility at all if it were not our expression of that possibility. The semantical circuit between a proposition and its sense is not closed until a further component is introduced, for what also finds its expression in a proposition is a thought. "The method of projection is to think of the sense of the proposition." [3.11] Wittgenstein seems to have the activity of thought in mind, although he elaborates very little beyond remarking that "a propositional sign, applied and thought out, is a thought", and immediately after that "a thought is a proposition with a sense". [3.5 and 4.0] But he makes the epistemological aspect of the matter evident enough. A proposition can be understood by anyone who understands its constituents (names) [4.024]; these in turn have objects for their meaning

[3.203]; and clarifications of these primitive signs require that their meaning be already known. [3.263] To understand a name and to understand a proposition are not the same. To understand a proposition means "to know what is the case if it is true". [4.024] Although the focus of the Tractatus is on propositions, Wittgenstein includes enough in the periphery of his discussion to indicate that their relation to the world is a dynamic one, not simply because the configuration of objects themselves "is changing and unstable" [2.0271] but because propositions have to be applied and thought if they are to have any sense at all. Tractarian propositions point us towards the

world and, in doing so, they add a dimension to the world. As Wittgenstein prefers to say, these propositional pictures "display" logical form [4.121], they "show" their sense [4.022]. According to grammatical terminology, these verbs take indirect objects; taken formally, they are 3-term relations. Not until later in the Tractatus does Wittgenstein explicitly mention the subject, the "I" to whom the sense of a proposition might be shown. Only grammar is served by this move, however, since a philosophical subject is not a Tractarian object and for that reason at least the mere mention of the third term of the display relation must carry no meaning. Nevertheless, the suggestion of something significant, even if unexpressible, pervades Wittgenstein's talk of sense, thought and understanding. These words introduce an epistemological dimension to that world. The meaning of words cannot be exhausted simply by mentioning the objects they stand for; part of their meaning consists in their being understood to have that role.

2. The Tractatus did not spring forth in a vacuum. Distilled from notebooks Wittgenstein kept over several years, it retains the traces of philosophical struggles he had not only with himself but with the ideas of Frege and Russell, which carried much weight with him. It is worth recalling that the words "sense", "thought" and "understanding" (like "object") common enough in everyday language had acquired a much more technical sense in Frege's writings. Although opposed to psychologism in logical theory, however, Frege had succeeded in preserving an older way of describing propositions which associates them with judgments and with a variety of other mental acts concerned with the so-called contents of propositions. From this perspective, Frege's entire philosophical outlook (not merely his language) reveals various dualistic contrasts: between ideas and experiences evoked by a name on the one hand and its sense on the other, between the sense of a name or phrase and its reference (the object), and between the sense of a sentence (the thought) and its meaning or truth-value.(3) There is nothing deeply exegetical about this observation about Frege's dualism (and certainly no criticism of Frege is intended by it). The point is that the epistemological dimension implicit in the Tractatus is more prominent in Frege's work and trails with it distinctions of Cartesian caliber between an inner mental world of thought and experience and an outer one of objects and events. That Wittgenstein was determined to avoid treating ideas as objects and mental acts as relations is obvious; it seems equally clear, however, that a partiality towards some aspects of traditional dualism lingers in the Tractatus.

As for Russell (in the days before the Great War when he and Wittgenstein influenced each other), the commitment to dualism was more prominent because many of his writings at that time were on epistemology itself. In Russell's case, however, the dualism was between mental acts like acquaintance and understanding and the different sorts of objects and facts with which such mental acts are concerned. Objects are given in acquaintance (according to Russell); they are classified by him as sense-data, whether they would be construed ordinarily as images or as publicly observable features; and they are defined as the meanings of demonstratives like "this". The Tractatus appears comfortable with this approach, at least to the extent of identifying objects as the meanings of simple signs, but in the case of more complicated mental acts such as understanding and believing it offers only reproaches. Wittgenstein's analysis of "A believes that p" is familiar: propositions are not themselves objects of mental acts [5.541-2]. Another charge against Russell's theory of judgment or belief is that it cannot exclude nonsense. [5.5422] Russell's reliance on the mental act of understanding to explain the unity of a proposition has no place in the Tractarian world.

In Russell's uncompleted project known as Theory of Knowledge which Wittgenstein's own criticisms had helped terminate the aim had been to show how the concepts and rules of formal logic rest upon a foundation of acquaintance and understanding, which are the mental acts comprising one side of his dualism. The Tractatus distances itself altogether from that sort of approach to logic. Theory of knowledge (the discipline) is reckoned by Wittgenstein to be no more than "the philosophy of psychology". [4.1121] But he was evidently worried about being drawn into that enterprise. "Does not my study of sign-language correspond to the study of thought-processes, which philosophers used to consider so essential to the philosophy of logic?" he asks; in response he acknowledges that "with my method too there is an analogous risk." [ibid.] More than compensating for this fear of being diverted towards psychology is a near obsession in much of the Tractatus with "a sign-language that is governed by logical grammar by logical syntax." [3.325] This is evident in the demand he makes that it "must be possible to establish logical syntax without mentioning the meaning of a sign: only the description of expressions may be presupposed." [3.33] And it is given an even more forcible expression in Wittgenstein's characterization of the role of

logical syntax in expressing the tautologies of formal logic itself: ". . . logic is not a field in which we express what we wish with the help of signs, but rather one in which the nature of the natural and inevitable signs speaks for itself. If we know the logical syntax of any sign-language, then we have already been given all the propositions of logic." [6.124] What holds these propositions together and makes them part of a system are relations, specifically those he calls internal relations.(4) Such relations cannot be expressed but only shown by the propositions themselves. In this respect the propositions of logic share a family resemblance with humbler varieties like "Fa" and "aRb". The logical form which atomic propositions have in common with the situations they represent cannot itself be expressed by any further proposition but only displayed by those propositions themselves: "What expresses itself in language, we cannot express by means of language". [4.121] And just as the internal relations of formal logic bind tautologies in a system, so also does the relation of representing its sense tie propositions to thinking. The dualistic doctrines of Frege and Russell may have expired in the Tractatus but their spirit hovers near the remains. The suggestion of separation is somewhat misleading, however, for the Tractatus seems intent on establishing an indissoluble connection for propositions between internal and external relations.

3. When a semantical circuit is closed that is, when a non-tautological proposition, which Wittgenstein describes as being "essentially connected" [4.03] with a situation, displays that situation and thus expresses some thought then the current which flows in this circuit is an internal relation. This was not Wittgenstein's way of expressing the matter and it is of course only a metaphor. But so are expressions like "mirror", "display" and "show". They direct our attention (to be sure) to the work that a proposition does. They emphasize the close relationship between a proposition and its sense, and because some situations that are represented are actual these words further emphasize what is required for the truth or falsity of that proposition. There are other ways of describing such work. When a proposition shows or displays its sense, then it has a sense for us; if we say it, then it expresses our thought; and if we understand the proposition then we know what it means for it to be true or false. These latter phrases are not metaphorical (or are much less overtly so), and they are just the ones Wittgenstein has used. Consequently, within the Tractatus, such phrases acquire a somewhat specialized meaning, that is, new rules of use are introduced for them, as the later Wittgenstein might say. The concept of showing, which is an internal relation, helps fix a new rule of use for these old and baggy phrases imported from the epistemology of Frege and Russell.

Wittgenstein's preference for newer words like "show" and "display" is explained by the broader project of "subliming" the "whole account of logic", the attempt "to purify . . . the signs themselves", as he described it later in the Investigations. [I:94] The rules pertaining to the logical structure of propositions are present yet elusive, "hidden in the medium of the understanding" yet known, "for I understand the propositional sign, I use it to say something". [I:102] Individual phenomena such as understanding the sense of a proposition or grasping the meaning of a word conceal something essential which a logical inquiry seeks to expose. The Tractatus was not directly concerned with the phenomena themselves, however. Its stance was to leave their investigation to psychology or to some other field of inquiry. Philosophy, after all, was declared to be not one of the natural sciences but an activity concerned with "the logical clarification of thoughts" [TLP, 4.112] Indeed, that same stance brings everything in the world every object, every state of affairs within the scope of natural science and makes science itself the potential measure of all things. While remaining properly aloof from issues of the actual content of scientific facts, the Tractatus applies rules of description (drawn from Frege and Russell) which specify in a logical sense what an object is and what it is to be a fact. This suggests the possibility of reformulating the structure of one or another science in a way which conforms to these rules of description and of suggesting how individual sciences in turn might be related to one another in a more general theoretical framework. The activity of clarification which Wittgenstein mentions, humble as it might seem, was quite capable of becoming an enterprise and would become so for the positivists. Logical inquiry itself cannot expect a similar fulfillment, however. Something remains hidden, whether in the understanding or in some other medium, for the Tractatus carefully parallels what can be said with what cannot be said. The contrast between fact and sense, propositional sign and the projecting of that sign, external and internal relations, what can be said and what cannot be all these are expressions of the dualism which makes up the fabric of the Tractatus. Silence, therefore, is not a convenience pending further reflection but a permanent necessity. On the other hand, the condition of silence can hardly be so mysterious, if (as Wittgenstein says) there is something which cannot be said even in the case of the most trivial atomic proposition or simple Tractarian picture having a sense. Crystalline purity (cf. PI, I:109) does not begin and end with the propositions of logic. On the other hand, whatever we succeed in making more exact in our descriptions of even the simplest cases of experience becomes potentially something which natural science can measure. That holds for the objects as well as for the cognitive relations required to unite them in acts of understanding or judgment. So Russell's project of portraying the foundations of knowledge as the experience of sense-data, whatever systematic appeal it might have, was not in Wittgenstein's eyes part of philosophy at all; and therefore, if anything favorable is to be said about dualism (specifically, about what is not part of the world of objects and states of affairs), then paradoxically it cannot be said.

4. In the Tractarian world, no dualistic doctrine could be formulated. Whatever can be stated can be stated clearly (cf. 3.251). Consequently, if whatever supposedly lies on the side of the mind or experience can be identified and described, then it falls within the reach of natural science and whatever is withheld from that grasp is not part of the world. If the defender of dualism maintains that the methods of natural science cannot reach the opposite side, then that only seems to create a gulf which the dualist cannot cross either. The abode of experience would then become subjective and the real nature of causal contact between the dualist's inner world and what lies outside must remain as unfathomable as it was for any pure Cartesian. Such a result is philosophically intolerable, not to mention that it renders the claims of dualism irrelevant to science. In different writings Russell tried to grapple with this result. By formulating the paradox of what cannot be said, however, Wittgenstein was proposing a benign solution to the problems facing dualism.

The Tractatus allows space for dualism by making thought, sense and understanding part of the very working of propositions. Without these, language would revert to the status of mere propositional signs. Dualism is present in any Tractarian picture and therefore in every proposition of natural science. What it is to work with language, to understand that p, might of course be studied by science and captured in certain true descriptions of what can be observed to happen when someone understands p. But then what it is to understand those descriptions would be distinguishable though not separable from whatever propositional signs are used for expressing them, because the Tractatus insists that no proposition can express what it has in common with what it represents. For Wittgenstein, a kind of residual inexpressibility belongs to the nature of language, a concomitant feature of any proposition which has meaning. And no meta-language would be able to capture this feature without replicating the phenomenon of our being unable to say what it shares with what it describes. The nature of this paradox may not be clear, but not because it shuns the categories of traditional dualism like self or subject, immediate experience and mental acts. For Wittgenstein, philosophy has foisted these categories on the world at great cost to itself, and even with their help it has succeeded in proving nothing. The Tractatus has pared down dualism to its essential intuition that the world does not live by objects and facts alone.

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(1) Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F. McGuiness (London: Routledge & Kegan Paul, 1963). (Quotations from the Tractatus throughout this paper are from this translation.)

(2) Ludwig Wittgenstein, Philosophical Investigations, tr. G. E. M. Anscombe (Oxford: Basil Blackwell, 1963), I, 36.

(3) These various distinctions are made successively in the first half of Frege's famous essay, "On Sense and Reference". Frege's philosophical outlook is very evident in his 1918 essay, "The Thought", which aroused Wittgenstein's displeasure.

(4) Cf. 4.122. Wittgenstein speaks of internal properties as well as relations. The topic is rich, complicated and obscure. I have space in this paper only to glance off the surface of this topic.

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