1 Introduction

The work of Jean Nicod (1893–1924), who died prematurely at the age of 31, has not received the critical attention it deserves. Nicod began by studying mathematics and physics, then switched to philosophy. He successfully passed the prestigious agrégation examination in 1914–just before the war. His frail health enabled him to escape military service, and he spent much of the terrible years that followed at Cambridge, doing a master’s degree and collaborating with Russell. Back in France, Nicod began a doctoral thesis under the supervision of André Lalande, but was unable to complete it until 1923, as illness forced him to spend several months in sanatorium. During his lifetime, Nicod published half a dozen articles on topics related to logic, geometry, sense-perception, but also economy and politics (see Nicod 1917, 1919, 1921, 1922a, 1922b, 1924a, 1924b, 1924c).¹

We do not know if Nicod ever met Wittgenstein in Cambridge. But he was certainly one of the first to read him. Indeed, in August 1919 at Lulworth, he took part with Dorothy Wrinch in the reading session of the Tractatus (which Wittgenstein had just sent) organized by Russell.² At first, one might think that the Tractatus had little effect on Nicod. Indeed, in all his writings, there are only two references to Wittgenstein, which are the two earliest references to Wittgenstein in French: one in La géométrie (Nicod 1924a), the other in the article “Les relations de valeur et les relations de sens en logique formelle” (Nicod 1924c). But analysis of each of these references shows that they both play an essential role in Nicod’s thought.

In this paper, I will focus only on Nicod’s first reference, the one he made to Wittgenstein’s picture theory in Nicod (1924a).³ I intend to show that Nicod’s interpretation is different from Russell’s, as presented in the introduction to the Tractatus, for example, and that it is closer to what Wittgenstein himself, at least according to some readings, was aiming for. More precisely, I will explain that Nicod used the Tractatus as part of a response to an objection Bergson might raise against La géométrie’s main line of argument. Thus, it is only by placing Nicod in his original context—the French philosophical scene, then marked by Bergson—that we can grasp the meaning Nicod gave to Wittgenstein’s view of symbolism, and the reason why his interpretation was different (and in some respects opposed) to Russell’s.

In Section 2, I briefly outline the basics of Bergson’s view in the Essai sur les données immédiates de la conscience (Bergson 1888), and, in Section 3, I summarize the main criticism against Bergson in (Nicod 1924a). In Section 4, I explain how Nicod’s argument remains exposed to a Bergsonian riposte. Nicod’s reference to Wittgenstein is specifically intended to counter this argument, and Section 5 explains how it does so. In Section 6, after recalling the main lines of Russell’s interpretation of the picture theory, I will show that Russell’s interpretation is in almost head-on opposition to the one developed by Nicod.

2 Bergson’s Dualism in the Essai

Even if Bergson refined and sometimes even modified some of his early theses, his first published book, the Essai, remains the most decisive formulation of his thought. Nicod (1924a) attacked a fundamental feature of Bergson’s early approach, namely what we could call his dualism. Indeed, Bergson’s thought is governed by two distinctions: first, an ontological distinction between immediate data of consciousness and external things; second, an epistemological distinction between intuition, which provides access to the first realm, and conceptual intellect (intelligence), which provides access to the second.⁴

For Bergson, material things and mental states exhibit two different types of multiplicity. Because material things are juxtaposed in space, one can, according to him, directly count them (“we have only to think them, at first separately, and then simultaneously, within the very medium in which they come under our observation”; Bergson 1888, 86). Spatialization and numbering are thus tightly connected: the former is a condition of the latter (Bergson 1888, 76–80). The data of consciousness are not immediately spatialized and can be counted only indirectly, by being associated with a spatialized symbolic representation.⁵ This doesn’t mean that the mental state contains no multiplicity; it simply means that this multiplicity is of a different nature: it is not a matter of juxtaposition, but of fusion, a blend of elements that cannot be separated and counted. Bergson (1888, 163) thus distinguishes between multiplicity of juxtaposition (“multiplicité de juxtaposition”) and multiplicity of fusion (“multiplicité de fusion ou de pénétration mutuelle”).

Pure duration is a multiplicity of fusion:

Pure duration is the form which the succession of our conscious states assumes when our ego lets itself live, when it refrains from separating its present state from its former states. For this purpose it need not be entirely absorbed in the passing sensation or idea; for then, on the contrary, it would no longer endure. Nor need it forget its former states: it is enough that, in recalling these states, it does not set them alongside its actual state as one point alongside another, but forms both the past and the present states into an organic whole, as happens when we recall the notes of a tune, melting, so to speak, into one another. Might it not be said that, even if these notes succeed one another, yet we perceive them in one another, and that their totality may be compared to a living being whose parts, although distinct, permeate one another just because they are so closely connected? … We can thus conceive of succession without distinction, and think of it as a mutual penetration, an interconnexion and organization of elements, each one of which represents the whole, and cannot be distinguished or isolated from it except by abstract thought. Such is the account of duration which would be given by a being who was ever the same and ever changing, and who had no idea of space. (Bergson 1888, 100–01)

The type of structure found in pure duration is therefore completely distinct from that found in multiplicities of juxtaposition, and it is a serious mistake to confuse what belongs to the one with what belongs to the other.

Yet this “mistake” is made most of the time, and Bergson goes to great lengths to explain why. Each reality is accessed through a different faculty: the multiplicity of juxtaposition (space) is a construct of the human intellect, while the multiplicity of fusion (duration) is reached by intuition.⁶ But the struggle between these two faculties is not equal, and intuition sees its domain regularly overlapped by the forays of the intellect, to such an extent that it takes a great deal of work (precisely that which Bergson’s writings aim to achieve) to realize that the domain of consciousness does not coincide with the descriptions given of it by the intellect. The first reason for this asymmetry is that “our outer and, so to speak, social life is more practically important to us than our inner and individual existence” (Bergson 1888, 130). The intellect has a practical utility that is out of all proportion to intuition. But Bergson also shows that scientific knowledge itself also confuses the two kinds of multiplicity: science privileges juxtaposition over fusion, and one of the aims of the Essai is to criticize a perfect illustration of this mistake, namely Fechner’s quantification of psychological data.⁷ The combination of the practical and scientific factors makes it inevitable that intellect extends its empire to everything it touches.

The aim of the Essai is to reveal the many ways in which the intellect transforms multiplicities of fusion into multiplicities of juxtaposition. By projecting its structures (notably space) outwards, the intellect analyzes (i.e., reduces to a multiplicity of juxtaposition) everything it encounters. Thus, to take one example, just after the passage on pure duration quoted above, Bergson explains that, because we are familiar with the idea of space “and indeed beset by it”, we introduce it “unwittingly into our feeling of pure succession” (Bergson 1888, 101).⁸ The ordinary notion of time results from the projection by the intellect of the idea of space into pure duration. Whereas pure duration is “a mutual penetration,” time “takes the form of a continuous line or a chain, the parts of which touch without penetrating one another”.

Bergson insists on the spontaneous nature of this intellectual projection, stressing that it is a by-product of the use of language. Names, because they are discrete entities that introduce a separation between the states they designate, inevitably lead to the juxtaposition of what is interpenetrated:⁹

Just as we can go on inserting points between two positions of a moving body without ever filling up the space traversed, in the same way, by the mere fact that we associate states with states and that these states are set side by side instead of permeating one another, we fail to translate completely what our soul experiences: there is no common measure between mind and language. (Bergson 1888, 164–65)

The spatial grid is therefore also a linguistic pattern. Language is intrinsically discrete: it juxtaposes words into sentences, and sentences into discourse, and thus, according to Bergson, projects the juxtaposition model into everything it depicts.¹⁰ And this is why Bergson can say that “there is no common measure” between mind (fusion) and language (juxtaposition).¹¹

But why would we want to speak out against the tendency of the intellect to analyze experience? If it is the practical and scientific imperatives that give the intellect its authority, why insist so much on its limits? What do we lose by relying exclusively on the intellect? Bergson answers the question at the very beginning of his preface:

We necessarily express ourselves by means of words and we usually think in terms of space. That is to say, language requires us to establish between our ideas the same sharp and precise distinctions, the same discontinuity, as between material objects. This assimilation of thought to things is useful in practical life and necessary in most of the sciences. But it may be asked whether the insurmountable difficulties presented by certain philosophical problems do not arise from our placing side by side in space phenomena which do not occupy space, and whether, by merely getting rid of the clumsy symbols round which we are fighting, we might not bring the fight to an end. When an illegitimate translation of the unextended into the extended, of quality into quantity, has introduced contradiction into the very heart of the question, contradiction must, of course, recur in the answer. (Bergson 1888, xix)

The misuse of the intellect is at the root of philosophical problems, which can only be solved, according to Bergson, by restoring the rights of intuition.¹² The “illegitimate translation” constituted by the conceptual analysis of sensible experience is the original confusion that plunges the mind into philosophical embarrassment. Thus, the third part of the Essai, devoted to the problem of free will, aims at showing that “all discussion between the determinists and their opponents implies a previous confusion of duration with extensity, of succession with simultaneity, of quality with quantity”, and that “this confusion once dispelled, we may perhaps witness the disappearance … of the problem of free will itself” (Bergson 1888, xvii–xix).

This is not the place to summarize Bergson’s discussion of human freedom. But it is important to understand how the philosopher articulates his defense of free will in the third part of the Essai with his epistemological and ontological dualism. Bergson’s general idea is that opponents, but also common-sense advocates of free will, replace action in progress with action already performed, in the same way that pure duration is replaced by time. The instrument by which this operation is carried out is geometrical symbolism. Here’s a typical passage:

[Common sense], being essentially a devotee of mechanism, [loving] clear-cut distinctions, … will picture a self which, after having traversed a series MO of conscious states, when it reaches the point O finds before it two directions OX and OY, equally open.

These directions thus become things, real paths into which the highroad of consciousness leads, and it depends only on the self which of them is entered upon. In short, the continuous and living activity of this self, in which we have distinguished, by abstraction only, two opposite directions, is replaced by these directions themselves, transformed into indifferent inert things awaiting our choice. But then we must certainly transfer the activity of the self somewhere or other. We will put it, according to this hypothesis, at the point O: we will say that the self, when it reaches O and finds two courses open to it, hesitates, deliberates and finally decides in favour of one of them. (Bergson 1888, 176–77)

What Bergson emphasizes is the role played by the schema of the bifurcated line. In a sense, it is perfectly legitimate, when a self is hesitating between two actions X and Y, to divide the states it passes through into two groups, accordingly as it inclines more towards X or Y. But, according to Bergson, when we use the “invariable signs X and Y”, we need to recall that those signs do not denote any tendencies or states themselves, but “the two different directions which our imagination ascribes to them for the greater convenience of language” (Bergson 1888, 175). As he makes clear, “in reality there are not two tendencies, or even two directions, but a self which lives and develops by means of its very hesitations, until the free action drops from it like an over-ripe fruit” —in reality, action is in progress, time is flowing. But by confusing the symbols themselves with the data of consciousness, common sense is led to replace “the continuous and living activity of [the] self” by the symbols X and Y, denoting two directions “transformed into indifferent inert things awaiting our choice” (Bergson 1888, 177). Worse, in the schema, the activity of the self is completely crystallized at point O. The common-sense defender of the free will insists that if we stop at point O, before the action X (let’s say), then the two paths are still open, whereas the determinist maintains that once X has been performed, there is only one branch left, and that the Y branch must be seen as the product of an ego’s delusion of its own omnipotence.¹³ In the first case, the action is seen as something yet to be done, while in the second, it is seen as something that has been completed—in neither of the two alternatives is there any room for action in progress.

Let me summarize the main lines of Bergson’s reasoning. The intellect has a natural tendency to analyze (i.e., to distort) sensitive experience by projecting a spatial grid onto it. This tendency stems from the successes the intellect encounters in practical life, but also in the advancement of scientific knowledge. It’s only when it comes to philosophy that this inclination manifests itself for what it truly is: an abuse of the prerogatives of reason that leads to the obscuring of a part of reality, the inner realm of the data of consciousness. Note that, in the genesis of philosophical confusion, Bergson attaches central importance to language, which, by naming them, separates things that originally merge.

3 Nicod’s Main Argument

La géométrie can be seen as the unfolding of a single sophisticated argument against Bergson’s idea that the intellect’s projection of a spatial grid into sensible experience betrays it. A detailed presentation of this argument would require an article of its own, so I will limit myself here to giving an overview of the main stages, referring to Gandon (2023a) for complements. My aim is to show that this argument, powerful as it is, has a weak point (Section 4), and that it is to remedy this shortcoming that Nicod turns to Wittgenstein (Section 5).

Nicod’s main argument can be broken down into three parts. The first intends to give a theoretical description of sensible experience viewed as a Bergsonian multiplicity of fusion. The second one aims to give a precise meaning to Bergson’s notion of the intellect’s projection of a geometric pattern into sensible experience. The third seeks to establish that, contrary to Bergson’s claim, the said projection does indeed teach us something about the immediate data of consciousness. Let me explain the three stages in turn.

As I said, in the Essai, the different epistemic modalities (intuition versus concept) determine the types of multiplicities to which the mind has access. In particular, for Bergson, no conceptual theory (only intuition) can grasp the multiplicity of fusion that the sensible experience is. In the second part (Nicod 1924a), Nicod breaks with the idea of a univocal correlation between epistemic modalities and multiplicities, arguing that the sensible world, considered as a fusion, can be described as the model of an axiomatic theory. In this section, however, Nicod does not explicitly confront the Bergsonian alternative between intuition and intelligence. He merely presents a sketch of formalization and defends the idea that the model of sensible experience thus axiomatized is indeed a multiplicity of fusion. Thus, Nicod introduces in his theory T_E of the sensible world E a primitive relation of interiority between sensible terms, which he distinguishes from the part-whole relation: to say that a flapping of the eagle’s wings is interior to an eagle’s flight does not mean that the eagle’s flight can be broken down into the flapping of its wings and other elements—from a logical point of view, the flight is as simple as the flapping that is interior to it. In the same vein, Nicod claims that “just as a sense datum can be a logically simple term while containing many others, so a sense datum can be a logically distinct term although it interpenetrates many others” (Nicod 1924a, 46). The elements of the sensible world E have thus exactly the properties that Bergson ascribed to the elements of pure duration: they merge into each other. So even if Nicod acknowledges that his development is not faithful to the letter of Bergson’s doctrine (because T_E is a conceptual scaffolding), he considers it to capture its spirit. In La géométrie, the sensible world is viewed as a multiplicity of fusion, not as a multiplicity of juxtaposition as in Russell.¹⁴ Note, however, that this first stage of reasoning does have a weak point: Nicod does not take into account Bergson’s idea that the simple fact of using a language (and a formalized language for that matter) leads to “project” into what is described features that are not there. We will return to this question in Sections 4 and 5 below.

From this first phase, it follows that it is possible to describe sensible experience, seen as a multiplicity of fusion, in a theoretical system, just as we can describe geometrical space. An axiomatic theory T_E of the sensible world E can be thus compared to an axiomatic theory T_G of the Euclidean space G. Now, Nicod agrees with Bergson that the sensible world can be described without resorting to any geometrical concept. The two theories T_E and T_G are completely distinct, and their “models” E and G are not the same. But in part I of La géométrie, Nicod explains that a theory T, which, even if it does not adequately describe a specified structure M, can be said “to be about” M in the sense that one can define in M a substructure M′ that satisfies T. For instance, set theory is different from Peano arithmetic, but in ZFC one can still define several models of Peano’s axioms. The universe of set (M) is not adequately described by Peano arithmetic (T), but one can nevertheless say that Peano’s arithmetic “deals with” sets, in the sense that one can define in the universe of sets a model (M′) which satisfies Peano’s postulates. In model theory, we would say that Peano arithmetic is interpretable into set theory. Now, according to Nicod, Bergson’s notion of projection can be given a precise meaning here: instead of saying that Peano’s arithmetic is interpretable into ZFC, one could say that Peano’s arithmetic can be projected into ZFC. This analysis of Bergson’s projection is quite sophisticated. Indeed, even if it explains the connection between the projected structure and the structure on which it is projected, it preserves the idea that the two structures are not the same—sets are not numbers, even if one can find an interpretation of arithmetic in set-theory.¹⁵

According to Nicod, to say that the spatial grid is projected into the sensible world E is nothing other than to say that geometry is interpretable into the theory T_E. This only means that there is a definable substructure of E that satisfies the axioms of a geometry T_G. The final Part III of Nicod (1924a) shows how several different geometries can be extracted in the way just described from the sensible world E (axiomatized in Part II of Nicod 1924a). This attempt to clarify what Bergson means by “projection” thus runs through the whole book. Note however that this analysis is not yet an argument against Bergson. To say that geometry is interpretable into the sensible world does not mean that the sensible world is akin to a geometrical space. This only means that we can “group” the sensible terms in such a way as to obtain a model of geometry—a space. Bergson is not himself opposed to such a conclusion. On the contrary, he claims that the intellect never ceases to perform such an operation, which is in reality nothing more than a betrayal of sensible experience. And regarding this last point, Bergson could be right: if sensible experience E can be completely described without recourse to geometry, and if geometry is not an adequate description of E, what does it matter to us that, once restructured, the sensible world can give rise to geometrical substructures? Do we really learn anything about the sensible world when we recognize that geometric substructures can be artificially extracted from its theoretical description?

In a beautiful passage, Nicod meets the challenge:

As children, we have all seen those drawings that represent something other than what you can see at first glance, where you have to make out the giraffe or the lion in the lines of a seemingly deserted landscape. When we "discovered" them, we saw nothing new. The outline of this hillock was the lion’s rump, and the knot in this tree trunk its eye. We had read into this network of lines a certain structure, the landscape, and we have now read into it a second structure, the lion. As for the lines themselves and the elementary relations—angles, distances, intersections—that ultimately determine the whole drawing, they are the substance of everything else, the very arabesque in which we can read a landscape, by noticing that its elements, grouped in a certain way, make a certain order appear,—and also a lion, by noticing that a different grouping highlights a second structure. The drawing before me is sensible nature. The elementary links that I can spell out, so to speak, are the primitive relations among my data. The form I try to read into it is, for example, the geometry [T_G]. Which groups, taken as elements, make this [geometrical] structure appear in the relations which stem from their composition? (Nicod 1924a, 85)

The arabesque of lines corresponds to the sensible world E and the lion hidden in the drawing corresponds to a space G, described by a geometry T_G. The arabesque can be described completely without mentioning the presence of the lion figure; similarly, the sensible world E can be fully described by T_E, without mentioning G, and more generally without mentioning any spatial notion. But it would be wrong to say that when we use the lion figure to indicate the drawing hidden in the original, we are describing something other than the arabesques in the picture. What we discover when we see the lion is a new aspect of the figure itself. And the same applies to the sensible world and geometry: when we apply spatial notions to the sensible world, we are not betraying what sensible perception presents us; we are discovering an aspect of sensible reality that we have not been able to detect until now. Bergson is thus too rigid. He fails to make room for the idea that objects of knowledge may have implicit properties that do not immediately reveal themselves. In a sense, it is true that the spatial grid, by separating initially merged data, distorts what is presented; but the fact that it is possible to distort data in this way manifests the presence of substructures unseen in the initial target. Even if there’s nothing missing from a description of the arabesque, which does not mention the lion hiding within them, the fact remains that the lion is indeed in the picture, and that we learn something about the figure when we discover its presence within it.

To sum up, what we have called Nicod’s main argument consists in showing that the spatialization of the sensible world, denounced by Bergson, far from being a vicious projection that betrays experience, enables us to identify characteristics implicitly contained within it (step 3 of the argument). The crux of reasoning revolves around the clarification of Bergson’s notion of projection, assimilated to an interpretation of one theory into another (step 2). Nicod’s argument presupposes, however, that the sensible world can be the subject of an axiomatic theory in exactly the same way as geometric space can (step 1). We will now see that this last point is the Achilles’ heel of the whole argument.

4 A Bergsonian Rejoinder

Convincing and sophisticated as it is, Nicod’s reasoning has a weak point. The young philosopher admits without discussion that geometric space can be defined as a structure described in certain formal theories. This means that, for him, space is a semantic notion; it is something that is described by a linguistic device. But in Bergson, as we have noted, space is not always “on the side” of reality, it is also “on the side” of the symbolic device used to represent this reality. Recall what Bergson said in the introduction of the Essai: “language requires us to establish between our ideas the same sharp and precise distinctions, the same discontinuity, as between material objects” (Bergson 1888, xix). Recall also the role that the MOXY diagram plays in generating the confusion that leads to the opposition between defenders and opponents of free will: the spatial figure is not used there as something described by language, but as a part of a symbolic device. Now, in his main argument, Nicod does not say anything about Bergson’s “syntactic” use of the notion of space. So there is a dimension to Bergson’s thought—the one which links the “projection” of the spatial grid to the use of language—that Nicod did not address. Note that this difficulty is linked to that already highlighted above concerning Nicod's assumption that it is possible to describe a multiplicity of fusion in a formal language: if the use of symbols were in itself spatializing, as Bergson thinks, then the development Nicod elaborates in Part II of his book would be threatened (see Section 3).

In La géométrie, Nicod tackles this issue by discussing what he calls “positional space”. The notion is introduced at the beginning of Part III of Nicod (1924a). Commenting on a strange passage from the Essai in which Bergson wonders how a point would become aware of its motion were it placed on a straight line, Nicod remarks:

What does the “form of a line” mean to us? It is a property as abstract as it is complex. We call line a class of terms linked by a relation obeying the axioms of linear Analysis situs. We have no idea which terms, which relations, will satisfy this definition. … We cannot therefore restrict in any way the nature of the elements and relations that form a line in the sense of analysis …. Bergson [on the other hand] conjures up a tyrannical image of what a line should look like. He imagines a set of simultaneous elements offering a certain original order, which he calls juxtaposition; and seeing that this is indeed a line that satisfies the geometer, he doesn’t dream that there may yet exist quite different ones, made up of other elements and other relationships. (Nicod 1924a, 77–78)

Instead of seeking to formally characterize the spatial structure of a line, Bergson “conjures up a tyrannical image” of what it must be: he gives himself a particular model, a simultaneous juxtaposition of positions “offering a certain original order”, which he considers to be the space. Of course, from Nicod’s point of view, the notion of positional space (i.e., a space made of positions) is just one of countless models that satisfy geometric axioms, and there is no justification for Bergson’s attachment to this model rather than another. But precisely, Nicod clearly sees that Bergson’s definition of space as a network of positions has an extra-logical justification: it allows one to take space as a grid applicable to different materials. Indeed, one and the same position-point can be occupied by different entities:

A visual term does not disappear, like a sound, in its entirety: it leaves behind an heir to one of its characters. Its sensitive locality survives it in a new term. This takes something away from the absoluteness of becoming. The appearance or disappearance of a datum merely realizes or undoes a certain possible arrangement, of which one of the two factors—the sensible place, the here or there—always remains present to me. (Nicod 1924a, p 128)

The positional space is a model described by a formal theory; but because its elements are positions that can be occupied by different entities in turn, this model is also a form that can be applied to sensible experience. And when the data of consciousness are structured according to the positional space, then the sensible world atomizes into a dust of elementary grains, which, because they are perceived in the simultaneity of an instant, become disconnected from each other, and all together from their becoming. Positional space is not just one geometric model among many, it also plays the role of a symbolic medium in which the multiplicities of interpenetration are transformed into combinations of separate positions.

Nicod recognizes the dual (semantic and syntactic) function of the positional space in a passage which immediately follows the one about the “form of the line” quoted above:

True, M. Bergson considers that, wherever they may be found, [the laws of geometry] can only be thought of by means of this particular image of a simultaneous multiplicity [positional space] he calls the idea of space; and he appears to think that, conversely, a being endowed with this idea and using it in his thoughts as a kind of blackboard cannot fail to transmit [transporter] the intuitive order it presents him to everything he conceives with its aid. … But the first of these assertions does not concern sensible laws, but only the mental means required for thinking about them. As for the second, according to which the use of these means would determine the laws themselves, we shall see that it is untenable (Part three, Chapter V). (Nicod 1924a, 78)

Bergson’s first assertion (that positional space gives the word “space” its semantic content) is, as we have just seen, erroneous. But there is a second assertion, more difficult to criticize, according to which space is a kind of blackboard, a medium for description, in short, that it is part of a representational device. In this passage then, Bergson does not denounce the artificial extraction of a model (a geometric space) from a certain domain (the sensible world), as explained above—but the use of a certain symbolism, the blackboard language that positional space is. This second claim is not addressed in Nicod’s main argument, which always considers space as a semantic notion, and not as part of symbolism. This is why Nicod, at the end of the quoted passage, refers to a dedicated chapter for an answer: Chapter 5 of Part III, precisely the one that includes a mention of the Tractatus.

The mention of Wittgenstein in such a context should come as no surprise. As we said (see Section 2), Bergson draws a strong connection between the use of language, spatialization, and the emergence of philosophical difficulties. Indeed, insofar as it has a discrete structure (i.e., it juxtaposes words to form utterances and utterances to form discourse), language itself is for Bergson a positional space, which plays a crucial role in the development of philosophical troubles.¹⁶ This seems close to this passage from the Tractatus:

Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language. (Wittgenstein 1922, sec. 4.003)

Bergson does not speak about the “logic of our language”, but he suggests that the treatment of the philosophical confusion should be viewed as a “fight” against language.¹⁷ For a reader as imbued with Bergson as Nicod was, it is hardly surprising that Wittgenstein’s remarks on the philosophical problem rang a Bergsonian bell.¹⁸ What is more amazing, however, is that Nicod played the Tractatus off against the Essai.

5 Nicod and Wittgenstein Against Bergson

Part III, Chapter 5 of La géométrie is entirely devoted to what we have called above “the Bergsonian rejoinder”—the idea that it is space as a syntactic device, on a par with language, that is responsible for the tendency to intellectualize experience. Speaking of the geometries introduced in the auditive and kinesthetic world (Part III, secs. 1–4), Nicod asks:

Suppose then that the analysis of an auditive or kinesthetic reality … cannot be performed directly but only through the projection of this reality into the midst of a visual imagination [of an ideal blackboard] which presents an intuitive order. Does it follow from this that the analysis which has … exposed a manifestation of geometry in the succession of data … really applies to the field used as a background? Would it have extracted only the laws of this obligatory medium of representation? (Nicod 1924a, 109)

Nicod immediately stresses the generality of the issue:

The concept whose significance we are studying rests entirely on the notion of representation or symbolism, and it is through this that we must examine it. (Nicod 1924a, 110)

And he pursues, describing Bergson’s view as following:

If … the relation between the symbolized thing—by hypothesis inconceivable in its pure state—and the symbol—the only thing imaginable—were to substitute the symbol, in all that it is, for the thing, in all that it is, then the examination of things by means of symbols would in fact be no more than the examination of the symbols themselves. (Nicod 1924a, 110)

Nicod thus attributes to Bergson the idea that symbolizing or representing something means substituting the symbol or representation for the thing itself. Thus, when we use the figure MOXY to represent the process of decision which “develops by means of its very hesitations, until the free action drops from it like an over-ripe fruit” (Bergson 1888, 176), we are in fact replacing the experience by a set of states represented by the schematic sequences MO, OX and MO, OY. According to Nicod, this illustrates Bergson’s view according to which a symbol, “in all that it is,” is always substituted for the thing, in “all that it is.” By the mere use of language, a multiplicity of fusion is transformed into positional spaces, in which states are juxtaposed with other states. The linguistic device, with its discrete structure, is thus entirely responsible for the fundamental philosophical illusion of reducing the “intensive” to the “extensive”.

Now, is Bergson’s view of representation (or symbolization) acceptable? To demonstrate that it is not, Nicod makes three general points. The first one is that any symbolism is abstract: “in any symbol, the aspect which symbolizes something is accompanied by other aspects which symbolize nothing” (Nicod 1924a, 110). Thus, in the letters of the alphabet, “the form alone is symbolic of the sound: the colour of the ink, the dimensions of strokes signify nothing”. The second remark is that “the thing symbolized is not symbolized completely, but only in certain of its properties” (Nicod 1924a, 111). Nicod is not here suggesting that it is possible to access things independently of any symbolism and compare it to what is represented (on this, see Section 6 below). He merely points out that a symbolizing property always represents a very specific aspect of the symbolized thing: “the form of letters in an italicized word indicates the general sound of the word, and the type face indicates a more accentuated intonation”, so that “each of the symbol’s symbolic aspects is incontestably associated mentally with a determinate aspect of the thing symbolized” (Nicod 1924a, 111). But how then are we to understand the connection between the property of the symbol and that of the thing symbolized? This is Nicod’s third, and more important point: there are formal conditions which constrain the capacity of a feature to symbolize another one. The symbolizing property must be appropriate (convenir) to what it symbolizes—for instance, a relation of sensible succession can be represented by the order of a straight line, a parabola, a sinusoid, a helix and many other—but not by a circle. What do the first geometrical symbols have in common that the last one does not? “Nothing apart from the fact that they are all open simple lines” (Nicod 1924a, 112). And Nicod goes on:

We can generalize … as follows. Among all the relations capable of symbolizing accurately the same aspect of the reality studied, there exists an abstract relation of formal analogy. In order for the relation R′ to symbolize the same thing as the relation R, we shall in all cases find it necessary and sufficient that these two relations be similar, i.e. they have the same formal properties. (Nicod 1924a, 112)

The footnote in which Nicod refers to the Tractatus is attached to this passage.

It seems natural to assume that Nicod is here thinking of picture theory. Recall that Wittgenstein explains that the represented facts are complex items composed of objects, and that “to the objects correspond in the picture”, i.e., in the representation, “the elements of the picture” (Wittgenstein 1922, sec. 2.13). This means that a picture is a complex which “consists in the fact that its elements are combined with one another in a definite way” (Wittgenstein 1922, sec. 2.14). Wittgenstein’s key idea is that, in order to have a representing relation (abbildende Beziehung) between a picture and a fact, the possibilities of combination between the elements of the picture should be the same as the possibilities of combination between the objects that these elements designate. The form of representation is precisely the possibility that the elements combine in the way they do to form a picture, and Wittgenstein claims:

What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation. (Wittgenstein 1922, sec. 2.17)

The notion of form of representation is certainly what Nicod has in view when he speaks of the abstract relation of formal analogy between the symbol and what it symbolizes. Note, however, that Nicod tends to “Russellianize” the terminology by substituting relations and similarities of relations where Wittgenstein remained more neutral, talking of objects (constituents of the fact) and elements of the picture—I will come back to this below.

What is important for us now is Nicod’s stress that the representing relation is based on the identity of the forms of variations between symbols and facts. The form of the representation not only guarantees the possibility of the formal analogy that links symbol and reality (point 3 of Nicod’s analysis of representation above), but also the distinction between relevant (symbolizing) and irrelevant (non-symbolizing) properties in the representation (point 1 above), as well as the distinction between symbolized and non-symbolized properties in the reality (point 2 above). This threefold characterization of symbolism helps to defuse Bergson’s idea according to which the intuitive order a symbol presents to us is transmitted “to everything [we] conceive with its aid” (Nicod 1924a, 78). Indeed, not all the properties of the symbol symbolize, but only some of them, precisely those that belong to the form of representation. It is then wrong to claim, as Bergson did, that any property possessed by a symbol is projected into the fact represented—the properties of the symbols that are projected are only those shared by the facts symbolized, and thus, “by the use of the symbols, [the mind] really grasps the thing, and not simply the symbol in place of the thing” (Nicod 1924a, 113).¹⁹ Nicod continues by noting that even if we were to admit that certain facts can only be symbolized “by projecting them into a visual imagination where geometry is expressed by an intuitive order of position, the geometric order discovered in these data would not have been the effect of this projection”. Indeed, “among the properties of this symbolic milieu, geometric order could have symbolized nothing”. So, if the order exhibited by the displacement on a straight line needs to be symbolized, any non-closed curve will do: “the difference in appearance between a straight line and a sinuous line drawn on [the] ideal blackboard, however familiar it may be to [the] imagination, will not represent anything” (Nicod 1924a, 113).²⁰

We could explain things differently by focusing on Wittgenstein’s distinction between symbol and sign. As Wittgenstein explains, what symbolizes in a symbol is not the visual sign (what Nicod calls the “concrete image”), but the sign taken with its significant use (sinnvollen Gebrauch), i.e., taken with its possible occurrences in the proposition-pictures; see Wittgenstein (1922, secs. 3.262, 3.32–3.326). The form of the representation (the possible occurrences of the symbol in propositions) is precisely what makes it possible to recognize the properties that belong to a symbol from those, inessential, that belong to its sign. Now, Bergson’s “positional” approach to symbolism, which emphasizes that language is broken down into separate units that are juxtaposed to form statements, runs completely counter to Wittgenstein’s insight. In some contexts, different signs (the various open lines in Nicod’s example above) can correspond to the same symbol—and conversely, the same sign can be used to represent different things and then becomes part of different symbols. Bergson reduced symbols to signs. He did not see that a symbol is the use of a word in a proposition, not an isolated mark perceived by the senses. On the contrary, Nicod’s emphasis on the abstract character of the symbol is simply a way to assert that, in order to recognize the symbol beneath the sign, we must, in each case, rely on its “appropriate” uses.²¹

6 Russell and Nicod on Wittgenstein’s Picture Theory

In this section, I would like to sketch a comparison between Russell’s and Nicod’s interpretation of Wittgenstein’s picture theory. The first thing to note is that Nicod’s stress on the notion of formal analogy echoes Russell’s emphasis on the notion of structure:

In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. This is perhaps the most fundamental thesis of Mr. Wittgenstein’s theory. (Russell 1922, 8)

It is worth noting that the idea that the representation shares a common structure with the represented predates Russell’s 1919 reading of the Tractatus (even though the subject must probably have been debated in Russell's discussions with Wittgenstein in 1913, see footnote below). This idea is linked to the relation-arithmetic developed in Part IV of Principia Mathematica, i.e., to a theory of structures as sets of similar relations—a theory that Russell suggested applied to the relation between language and reality.²² In the passage quoted above, Nicod elaborated on the suggestion: a relation R′ symbolizes a relation R when they are similar, i.e., when there is a one-one function S from the field of R′ to the field of R such that if any two x and y are such that R′(x, y), then R(S(x), S(y)). When this happens, Russell says that R′ and R have the same structure (Russell 1959, 99–100). This analysis makes Wittgenstein’s conception of a form of representation more precise, without any loss of generality: all the examples taken in the Tractatus appear to be cases where the symbol and the symbolized share the same structure in Russell’s sense. However, while Nicod uses Russell’s logical tools for interpreting the picture theory, he does not, as we shall now see, endow Wittgenstein’s proposal with the same philosophical meaning as Russell.

Indeed, the lesson Nicod draws from the Tractatus is that it is not possible to determine what a symbol is independently of the relation of formal analogy it has with the fact it symbolizes.²³ This is in direct opposition to Bergson’s view that we can consider what a symbol is independently of what it describes, i.e., independently of how symbols are used. Language and reality are linked by an external relation in Bergson: one can describe what language is (a multiplicity of juxtaposition) without referring to the reality it depicts. For Nicod, on the contrary, what symbolizes in the symbol depends on the form of the representation, and therefore on what is symbolized. In other words, the relation between language and reality is internal. Now, what seems to impress Russell in Wittgenstein’s theory is the idea that the picture is a fact, completely dissociated and separate from the situation it represents—a fact which can be described for its own sake, regardless of what it depicts. This transpires, for instance, in this passage:

What relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other? This … is a logical question, and is the one with which Mr. Wittgenstein is concerned. He is concerned with the conditions for accurate Symbolism, i.e. for Symbolism in which a sentence “means” something quite definite. (Russell 1922, 8)

Here, a sentence is seen as a kind of fact, and Russell’s Wittgenstein would ask what the conditions are for it to become the symbol of another fact. The picture and what it represents are seen as two different items that need to be described independently of each other. Thus, Russell gives himself permission to break away from the connection between the proposition and what it describes, by positing it as an external relation between two (complex) terms that must be described separately. In Russell’s view, the philosopher stands above the representational relation he is examining. He has direct access to both the propositional and factual poles, and can compare them to see whether they share a common structure or not.

A detour through Russell (1919b)²⁴ reveals the gulf between Russell’s and Nicod’s interpretation of the picture theory. In this article, Russell explains that propositions (truth-bearers) are facts that relate to other facts (their truth-makers).²⁵ He then distinguishes between two types of propositions, image-propositions and word-propositions, and maintains the primacy of the former over the latter, in the sense that it is via image-propositions that word-propositions have meaning. While the connection between image-propositions and reality is immediate and straightforward,²⁶ the same cannot be said of the relation between word-propositions and the facts they represent. Talking about the image-proposition of a window at the left of a fire, Russell explains:

Such idyllic simplicity of correspondence is … absent in the word-propositions which mean such simple visual image-propositions. In the phrase “A is to the left of B,” even if we treat “is-to-the-left-of” as one word, we have a fact consisting of three terms with a triadic relation, not two terms with a dyadic relation. The linguistic symbol for a relation is not itself a relation, but a term as solid as the other words of the sentence. … Hence the linguistic statement of a fact is a more complex fact than that which it asserts, and the correspondence of a word-proposition with its objective is never so simple as the simplest correspondence in the case of image-propositions. (Russell 1919b, 38)

As the relation between an image-proposition and the fact it describes is direct, the structure of the former is identical to the structure of the latter. But this does not hold for a word-proposition. Thus “A is at the left of B” has six elements; and not three. Here, Russell adopts the very attitude towards symbols that Nicod, on the basis of the Tractatus, rejects. The number of words in the sentence “A is at the left of B” is no more important for its ability to symbolize than the fact that it is written in red or black.²⁷ The number of words is not an “appropriate property” of the symbol. According to Nicod, Russell falls here into the same error as Bergson: that of identifying the symbol with the sign.

Russell, Nicod and Wittgenstein all agree that representation is based on a structural identity. But Russell always assumes that the philosopher has independent access to the proposition and its structure, on the one hand, and to the fact and its structure, on the other, and that his task is to determine under what conditions the first entity can be said to bear on the second. Russell was, as we know, aware of his disagreement with Wittgenstein on this point. He thus explained that, in the Tractatus, this common structure, which makes the proposition capable of being a picture of the fact, “cannot itself be put into words, since it is a structure of words, as well as of the facts to which they refer” (Russell 1922, 21). While he acknowledged the difficulty of theorizing within a single language how that language relates to the world, Russell suggested at the end of his introduction that it is possible to use a new language to accomplish the task, and to get around the obstacle by positing a hierarchy of different languages. Russell thus presents the Tractatus as the work of a mystical and dogmatic mind, eager to lay down prohibitions and police rational thought. But, as a matter of fact, what Wittgenstein was questioning was Russell’s self-granted ability to describe language independently of the form of representation, and therefore also of the form of the world. Nicod understood the importance of this issue, and saw Wittgenstein’s picture theory as a way of showing that symbol and sign differ from one another.

7 Conclusion

The reference to Wittgenstein plays a central role in the organization of La géométrie. It enables Nicod to rebut the idea that the properties of the symbol (notably the fact that signs are juxtaposed with one another in the sentence) are always “projected” into the reality described. Nicod does not reject the Wittgensteinian and (perhaps) Bergsonian claim that philosophical problems stem from a misuse of language. He does, however, refuse to condemn language, as Bergson does, simply because sentences juxtapose words as isolated and separate elements. Like Wittgenstein, Nicod considers that the treatment of philosophical confusions requires a patient, case-by-case examination of the workings of specific symbolisms—of the kind Nicod undertakes for the use of geometric and perceptual languages.

His Bergsonian background explains Nicod’s singular reception of Wittgenstein. When Russell read the Tractatus, he had in mind not Wittgenstein’s link between the use of language and the emergence of the philosophical problem, but his own difficulties in elaborating a satisfying theory of the proposition. Before receiving Wittgenstein's manuscript, Russell developed a new conception according to which a proposition is a fact that “corresponds” in some ways to the fact it represents. Russell believed it was possible to construct a general theory of picturing propositions (of symbolism) independently of the representing relation. Exactly what Nicod opposed to in La géométrie.

It is surprising to note that it was his exposure to the anti-intellectual Bergson, often considered a foil by analytical philosophers, that enabled Nicod to understand the intentions of the Tractatus better than Russell himself. To the latter, Wittgenstein wrote (19 August 1919):

[You say:] “The theory of types, in my view, is a theory of correct symbolism: (a) a simple symbol must not be used to express anything complex; (b) more generally, a symbol must have the same structure as its meaning.”

That’s exactly what one can’t say. You cannot prescribe to a symbol what it may be used to express. All that a symbol can express, it may express. This is a short answer but it is true! (see Wittgenstein 1995, 99)

Nicod knew that, for Wittgenstein, no general theory of symbolism was possible, and endorsed the view according to which one cannot prescribe to a symbol its form of representation in advance.