Synthesis and analysis: Jean Nicod as a mediator between Bergson and Russell

ABSTRACT

This paper presents Jean Nicod (1893–1924) as a mediator in the dispute between Bergson and Russell. In La géométrie dans le monde sensible (1924), Nicod extensively discusses Bergson’s epistemology focusing on those aspects that Russell critically discusses in The Philosophy of Henri Bergson (1912) and Our Knowledge of the External World (1914). His aim is to establish a middle ground between synthesis and analysis: to show how most of the disagreements between Bergson and Russell can be resolved without compromising the central principles of their thought. Throughout this paper, I explicate Nicod’s exposition of two points of contention between Bergson and Russell: (1) the nature of sense-data and analysis, and (2) the relation between geometry and the sensible world. I will also show that his attempt to reconcile synthesis and analysis results in an innovative account of representation inspired by an early reading of Wittgenstein’s Tractatus. In the conclusion, I reflect on how Nicod’s proficiency to engage with two increasingly diverging philosophical programmes, namely early analytic philosophy and the French epistemological tradition, could have affected the development of early twentieth-century philosophy.

KEYWORDS:

• Jean Nicod
• Bergson
• Russell
• Wittgenstein
• representation

1. Introduction

In this journal, there has been much attention lately for the reception of Henri Bergson’s work among French epistemologists, primarily Gaston Bachelard, and British analytic philosophers, such as Karin Costelloe-Stephen and Susan Stebbing, writing in the wake of Bertrand Russell’s jarring critique of the “anti-intellectual”, “practical philosopher” (PH 321, 337).¹ In this paper, I will consider the contribution of another participant to the early twentieth-century debate on Bergson’s epistemology: Jean Nicod (1893–1924). Because of his dual education in Paris and Cambridge, Nicod was at home in the French epistemological tradition of Jules Lachelier, Pierre Duhem, and Henri Poincaré, while at the same time being deeply immersed in the new mathematical philosophy of Russell, Alfred North Whitehead, and Ludwig Wittgenstein. His grasp of these two diverging traditions enabled him to discern the merits as well as the shortcomings of Bergson’s epistemology and Russell’s critique, prompting him to try and conciliate in the dispute by establishing a middle ground between synthesis and analysis.

Nicod received his initial philosophical education in Paris at the Sorbonne, became an agrégé in 1914, and thereafter went to Cambridge to study with Russell, ultimately becoming a close friend and interlocutor. After Louis Couturat’s passing in 1914, he became the principal promoter of mathematical logic in France and one of the country’s earliest appraisers of the philosophy of G.E. Moore, Wittgenstein, and C.I. Lewis. Tragically, Nicod died of tuberculosis in 1924 at the age of thirty, leaving only a handful of publications.² Today, he is primarily remembered for two technical achievements: (1) a formula that can function as the sole axiom of a complete system of propositional calculus, widely known as Nicod’s axiom, and (2) a principle of induction, which states that something that is not the case cannot serve as evidence for something which is the case, named Nicod’s criterion by Carl Hempel in 1946 (Hempel, “Studies”). Symbolic logic and induction, however, were not his only interests. As we will see, Nicod’s (meta)philosophical concerns are much more comprehensive than his renown for his technical work suggests.

In 1923, Nicod defended his primary thesis, La géométrie dans le monde sensible as well as a secondary thesis called Le problème logique de l'induction, to a jury at the Sorbonne composed of the mathematician Élie Cartan and the philosopher of science André Lalande.³ As Russell explains in his introduction to the 1930 English translation, the aim of the primary thesis is to examine how geometry can be constructed out of perceptual data: “starting from data of perception, it tries to attain the various geometries that can be built on them” (FG 7). The work consists of three parts: Part I is devoted to formal geometry, Part II intends to identify the elementary terms and relations of the sensible world, and Part III shows how we can built formal geometries on the elementary terms and relations of the sensible world described in Part II.

Throughout Part II and III, Nicod scrutinizes Bergson’s views as set out in Essai sur les données immédiates de la conscience (1889) and Introduction à la métaphysique (1903). In his analyses, he explicitly focuses on those aspects of Bergson’s epistemology that Russell critically discusses in The Philosophy of Henri Bergson (1912) and Our Knowledge of the External World (1914). Although previous work has shown that Russell misinterprets Bergson’s philosophy, I want to argue that Russell’s critique, as reformulated and developed by Nicod, does reveal serious shortcomings for the arguments of the Essai (Čapek, “Bergson”; Vrahimis, “Bergsonism”). At the same time, however, I will show that Nicod’s critique does not involve a repudiation of Bergson’s philosophy: on the contrary, his polemical reflections aim to ameliorate Bergson’s arguments by introducing novel concerns. Nicod’s position is best described as a mediator: his aim is to show how many of the disagreements between Bergson and Russell can be resolved without compromising the central tenets of their thought.

In this paper, I will explicate Nicod’s discussion of two points of contention between Bergson and Russell, namely (1) the nature of sense-data and analysis, and (2) the relation between geometry and the sensible world. I will also show that his attempt to reconcile synthesis and analysis results in an innovative account of representation inspired by an early reading of Wittgenstein’s Tractatus. In the conclusion, I will reflect on the place of Nicod in the history of twentieth-century philosophy.

2. Sense-data and analysis

2.1. The elementary relation of interiority

In the Introduction of Part II, Nicod sets about defining the “elementary terms of nature or relations that nature presents to us in perception” (51). At the outset of his inquiry, however, he emphatically warns us that this approach is not uncontroversial: “to speak of nature as a network of terms and relations seems to arouse all our philosophical scepticism”. With implicit reference to Bergson’s reflections, he writes: “Are we not accepting a considerable postulate? What gives us the right to apply to the flux of sensation the categories of logic?” (51). In the Essai, Bergson had raised this perennial question with new force. He argues that when we apply categories, whether mathematical, linguistic, or logical to our qualitative experience, we come to distort and miscomprehend it. To be able to address this challenge, Nicod says that we need to use the Russellian method to “advance to the details of analysis, by gradually defin[ing] the issue more exactly”. In this way, we might “perhaps remove the objection” (FG 51).

Following Russell, Nicod conceptualizes elementary terms as sense-data. A sense-datum is “the that of anything immediately present to our senses” (51). As examples, he names “that is a tree, that is a penny, or again, that is a falling star, that is the song of the nightingale” (51).⁴ Anything that can be “designated as this” is a potential sense datum (FG 51). Next, Nicod undertakes an investigation into the elementary relations that we can discern within experience. It is these relations that determine how we experience sense-data. They explain why a sense-datum is perceived as a unitary whole, how two sense-data relate or why two sense-data appear as parts of one term. According to Nicod, one of the simple and fundamental relations present in the immediate data of consciousness is interiority. He writes that when we see “an eagle crossing my field of vision with a slow and continuous swoop”, the event of the eagle flapping his wings is experienced as interior to the flight of the eagle (FG 52). The two sensations together form a simple term. The same relation is present when hearing a sequence of words or glimpsing a brush stroke of a landscape painting. In these instances, one sense-datum is experienced as being interior to the other: the words are interior to the sentence, the brush strokes are interior to the painting.

But to Nicod, this analysis of interiority is not yet exhaustive. We may still ask: what are the conditions that occasion interiority? Are there more elementary relations that determine the occurrence of interiority? In subsequent paragraphs, he questions whether interiority consists of two more simple relations, namely temporal inclusion and spatial inclusion. He defines these two as follows. There is temporal inclusion, when one event is enclosed in the duration of the other – think of the flapping of the wings of an eagle during mid-flight. There is spatial inclusion when a sensation is enclosed within the extension of another – we are asked to think of the ashes left after a fire, both occupy the same extension, although they have a different duration. After providing these definitions, Nicod wonders whether the conjunction of these two relations does not “constitute the necessary and sufficient condition for interiority” (FG 53).

Nicod’s negative answer to this question is crucial for understanding the foundations of his critique of Bergson. If the conjunction of these two relations constitutes the necessary and sufficient condition for interiority, then interiority is not an elementary relation, perceptible before any other, but would instead consist of two more simple relations grounded in the more fundamental distinction between space and time, extension and duration. This is what Bergson argues in the Essai. In his philosophy, all relations are subordinated to the elementary distinction between space and time. He argues that before being able to perceive any relation between sense-data, we first need to break down our qualitative experience into distinct and discrete parts. It is only after distinguishing between extension and duration, that we can forge relations between sense-data. Accordingly, the distinction between extension and duration is primary, and relations such as interiority are derived and secondary: it is only after applying categories to experience, after rendering sensation extensive and confusing time and space, that we can come to consider one sense-datum as interior to another (TF 1–6).

For Nicod, however, the distinction between time and space is neither the most fundamental distinction discernible in our experience nor are the relations of spatial and temporal inclusion elementary. On his account, interiority is a primary relation, irreducible to spatial and temporal inclusion. To argue for this point, he turns to the distinction between fixed and moving sense-data. A sense-datum is perceived as fixed when it “retains a constant extension or the same position in the sense field during its whole duration” (54), whereas a moving sense-datum “varies [its extension] in the course of its duration, either by deformation or by displacement” (FG 54). Fixed and moving sense-data are unified by interiority, this relation determines individuation.

In what follows, Nicod sets out to show why the conjunction of temporal and spatial inclusion, in the case of moving sense-data, cannot explain why we perceive a single, moving whole. Temporal inclusion cannot do the work, because all sense-data endure in the same way, this relation cannot be of any aid in distinguishing movement from rest. Spatial inclusion, on the other hand, may account for our perception of fixed sense-data, but cannot account for the fact that we continue to perceive an eagle as a distinct datum when its extension varies continuously. We could say that its extension is the whole field that it has covered during its movement, but this would make “the extension of a falling star … the whole line traced by it in my visual field” (FG 55). If this were the case, a shiny star briefly piercing through a moving cloud would appear interior to it, yet we perceive them as distinct.

Consequently, it is only the relation of interiority, independent of the conjunction of temporal and spatial inclusion, which can explain why, although the shiny star and moving cloud share extension and duration, we do not perceive one as part of the other. Nothing except the relation of interiority can explain our direct perception of fixed and moving sense-data. Therefore, Bergson is wrong to consider the distinction between extension and duration as fundamental. It is secondary; it only comes after a perception of terms being interior to one another. As Nicod concludes:

Facts, like intuition, seem to lead me to say that the interiority of sensed terms is a simple relation which entails spatial and temporal inclusion but is not implied by them, for it is antecedent to the separation of relations into extension and duration.

(FG 56)

2.2. The false dilemma between synthesis and analysis

Nicod continues his examination of interiority by raising another, related question that finds its origin in Bergson’s epistemology: “[d]oes it [interiority] not involve the logical relation of component and composite?” (FG 56). In the opening pages of the Essai, Bergson answers this question in the negative. He argues that the immediate data of consciousness do not consist of simple components that together constitute composites or syntheses of sensations: it is a whole that cannot be analyzed without losing its defining qualities. According to Bergson, there is no logical relation of component and composite between sensations, a complex term is not constituted by more elementary parts: synthesis is irreducible.

By contrast, Russell argues that interiority does involve a logical relation of component and composite. He contends that “the complexity or simplicity of a sensory term will depend upon how many interior terms it contains” (56). The smallest terms are constitutive of the larger terms: “composites are only real through their elements” (FG 56). Through logical analysis, we can reduce every composite to its components without any loss. In this way, however, every possibility of acknowledging Bergson’s irreducible wholes is precluded. For Nicod, this antinomy lies at the very heart of the antagonism between synthesis and analysis: it is one of the pivotal points of contention between Bergson and Russell.⁵

To assess whether analyzing experience in terms of components and composites indeed presupposes a reduction of complex wholes to simple constituents, Nicod first puts forward a criterion for logically simple terms: a term X is simple when I can give it a predicate without at the same time ascribing this predicate to any other term x.⁶ To illustrate this formal definition and its ramifications for his argument, he notes that it is possible that “a common part of our lives to which we refer by the same name, such as a walk taken together, may have been for one of us a succession of events, for the other a unique event” (57). Even in retrospect, one can come to recognize in the succession of events an “aesthetic aspect of integral unity” (FG 57). Since a walk can have such a quality, the term walk (X) can have a predicate, in this case, an aesthetic quality, that cannot be ascribed to any other term (x) interior to it, namely all the different steps, sights, and scenes.

Nicod’s next example, often used by Bergson, displays his position more clearly (TF 111). He considers a chime consisting of a series of notes. For him, it is obvious that there are judgements that hold true of the melody that do not pertain to the individual notes. When we listen to a melody, hearing the quality of the melody does not equal hearing a succession of single notes. Instead, the melody possesses an “irreducible quality” (58) which cannot be predicated the terms interior to it, namely the single notes. The term ‘melody’ thus satisfies the aforementioned criterion for a logically simple term. In Nicod’s words: “the most extended and prolonged sense data of the richest internal diversity may be simple terms in the light of reason” (FG 58–59).

At this stage of his argument, it seems as if Nicod radically breaks with Russell’s scientific philosophy. By opting for a view in which simple terms can be “extended”, “prolonged” and have “the richest internal diversity” (FG 51), he appears to renounce the viability of Russell’s logical atomism, which presupposes “the impossibility of explaining complexity without assuming constituents” (OK 118). If we cannot break down our experience of a melody, or the event of taking a walk in the forest into more elementary terms, then Russell’s method would seem to lose all its force. It seems difficult, almost impossible, however, to reject the principal uptake of Russell’s method. Even if Nicod wishes to reject it, should he not at least admit that a sense-datum, such as a melody, consists of the more elementary sense-data of the striking of the bells?

Surely, Nicod admits that a melody consists of a succession of single notes. At the same time, however, he denies that there is a relation of identity between the conglomerate of single notes and the melody; the single notes do not together constitute the melody. While a macroscopic term, such as a melody, can consist of a number of microscopic terms, in this case, several single notes, this does not mean that it can be reduced to its elementary parts, the melody can still have an independent reality. The microscopic terms, here the single individual notes, only “ideally determine but do not actually constitute” the macroscopic terms, here the melody (FG 60). During our philosophical investigations, so Nicod argues, we must sharply distinguish between determination and constitution as two distinct modes of inquiry and sources of justification, with the first pertaining to experience and the second to logical analysis.⁷

Logical analysis, as an inquiry into the constituents of systems, does not require elementary parts as its point of departure. It can make do with any term or experience. Reason and logic can never be the judge of what are the fundamental parts of perception, for it is impossible to determine a priori that a given term must consist of more elementary components. From the viewpoint of “abstract reason”, all “the conglomerations of macroscopic and microscopic data” are “real and simple essences on the same plane” (60). It is experience, as an inquiry into the components of perception, which should guide us when determining whether a leaf, appearing as a simple term to reason, in reality, consists of multiple parts, i.e. a midrib, venules, and veins. Even though the principle that simple terms, such as a leaf, commonly consist of more elementary parts can only receive empirical justification, no rational justification, Nicod argues that this is still a good ground: “we should be more astonished to find it false than to hear a tree speak” (FG 60).

According to Nicod, distinguishing between empirical and logical grounds allows us to reconcile Bergson and Russell’s views and resolve an age-old conflict: the dilemma between the “philosopher, who defends the integral realities of life and art, and the scientific logician or physicist” (61), who reduces composites to constituents. The distinction between determination and constitution elucidates a profound confusion of those who hold that “the reduction of natural and vital terms into a mass of sensible minima” comes at the cost of a synthetic vision of experience: “[o]nly if we assume that a sensible term cannot be interior to another in extension and duration without forming one of its essential parts, and consequently, a more fundamental reality, do we have to choose between restricted and comprehensive data” (61–2). With this understanding of synthesis and analysis at hand, we can, with Bergson, come to “conceive [of] my whole sensible past as constituting one and the same event, and my whole experience as forming one single object which is continually growing” (61) while at the same time availing ourselves of Russell’s method of analysis and breaking down our experience into elementary terms and relations. There is no longer any opposition between the two perspectives:

But it is only we who are causing the trouble by making reason intervene in a situation to which it is indifferent. This mystery of the sensible whole which is not the sum of its parts vanishes as soon as reason points out that these are not true parts, and that interiority in extension has no rational relation to duration.

(FG 61–62)

As Nicod astutely remarks; even Bergson sometimes realizes that one does not need to choose between these two alternatives, that it is “reason itself [which] impos[es] upon us a deceitful choice” (FG 62). Bergson’s shortcoming, however, lies in his insufficient development of the ramifications of this insight. In the end, Nicod aims to rectify Bergson’s philosophy by employing an amended version of Russell’s distinction between logical and empirical grounds: with this shrewd move, he ameliorates Bergson’s epistemology using Russell’s philosophy to make it impervious to Russell’s critique.

2.3. Distinct but not discrete

In what follows, Nicod extends his analysis to include three other relations that can be perceived prior to the distinction between extension and duration. These relations, namely interpenetration, exteriority, and continuity, play a crucial role in Bergson’s epistemology. After defining these three relations, Nicod remarks that we can also consider them, like the relation of interiority, as “simple and irreducible relation[s] independent of extension and duration … factual relation[s] without intrinsic rational value” (FG 63). His subsequent analysis is intended to show that just like “a sense-datum can be a logically simple term although it comprehends many others, so a sense datum can also be logically distinct although it actually interpenetrates many others” (FG 63).

In the Essai, Bergson argues that the immediate data of consciousness do not consist of distinct terms. Instead, all conscious states interpenetrate: within us, there is a continuous progression of heterogeneous, indefinite phenomena. It is only through the act of spatialization, by which our experience is objectified, that we come to conceive of our conscious states as a “discrete multiplicity”, rather than a “qualitative multiplicity” (TF 122). Spatialization renders our conscious states discrete, that is distinct, with no interpenetration of sensations, external to one another, with no overlap between them, and discontinuous, with all sensations strictly separated. In Bergson’s philosophy, distinctness and discreteness are strictly related, in order to ascribe (logical) individuality to a sensation, we must render it discrete.

In contrast, Nicod argues that a term can be distinct without being discrete. To clarify his argument, he resorts again to the example of a moving cloud. For him, a moving cloud is a prime example of an indiscrete or indefinite term. It might overlap with other clouds, interpenetrate other sense-data, and have varying boundaries during its course. Nevertheless, it has a logical individuality. It can be designated as a simple ‘this’. Notably, designation does not require being able to determine whether a certain spot in our visual field belongs to it or being able to delineate the exact boundaries of a moving cloud: discreteness is not a necessary condition for (logical) individuality. As Nicod playfully observes: “No matter how indefinite the object may be, which I discern by remarking: ‘What a beautiful cloud!’, I still know that this sea-shell is exterior to it” (FG 63).

Accordingly, we can relate two terms, however indefinite they might be. We can say that two terms interpenetrate, that one is external to another or that they overlap, while also recognizing their logical individuality. Here, Nicod employs the same argument he used in his discussion of simple and complex terms to relations such as interpenetration; they must also be conceived as empirical rather than logical. By understanding the discernment of relations within experience as an empirical process, which requires no pernicious abstraction or logical analysis, we come to see that our sense-data can be indefinite yet be related to each other through interpenetration, exteriority, continuity, and interiority.

Hence, Bergson’s worry that by conceiving of our conscious states as a discrete multiplicity we come to disregard the nature of experience as a qualitative, heterogeneous multiplicity turns out to be unfounded. Our lived experience can remain unitary, our sensations can remain indefinite while also becoming susceptible to the scrutiny of logical analysis: “[r]eason no more circumscribes sense-data in distinguishing them than it destroys their unity in doing so; it accepts their lack of sharp limits in extension and duration” (63). Contrary to what Bergson believes, the method of logical analysis keeps the data of immediate consciousness intact: “When I say this, when I distinguish such and such a datum in order to predicate something of it, I do not cut it off from the continuous stuff of my experience, I do not stop it from changing, I do not elevate it above the flux of which it remains a passing wave” (FG 63–64).

From Nicod’s point of view, the source of Bergson’s confusion is his misunderstanding of the nature of abstraction and logical analysis. His conviction that analysis distorts our immediate qualitative experience “rests on an inadequate idea of logical abstraction” (64). When, during analysis, we distinguish a datum and give it a predicate, when we conceive of it as a logical term, we do not ascribe to it more reality, more unity, than I do when I conceive of my qualitative experience as a heterogeneous multiplicity. We can ascribe logical individuality to a sensation, refer to it as simple and distinct, while also recognizing that our sensations are indefinite. Taking up Russell’s critique of Bergson in Our Knowledge of the External World, Nicod insists that logical analysis does not change the nature of our experience: “[t]here is no falsification involved in the procedure by which I discern in the bosom of the sense-flux terms related by the relations of interiority, exteriority, and penetration” (FG 64).

Near the end of this argument, Nicod unexpectedly changes target. He no longer criticizes Bergson but an opposing position, strongly resembling the one adopted by Russell in his critique of Bergson’s concept of interpenetration. He finds fault with those who argue that Bergson’s view of experience as consisting of interpenetrating entities is incompatible with a conception of perception as composed of distinct sense-data. According to Nicod, these philosophers falsely believe that recognizing that our sensations interpenetrate would preclude the possibility for a logical analysis of sense-data. He objects to Russell that acknowledging that our immediate experience is a sense-flux, a qualitative, heterogeneous multiplicity “does not require a kind of miraculous vision and abandonment of reason” (FG 64).

Although Russell recognizes that our immediate experience is as Bergson describes it, namely an indefinite, interpenetrating whole, he still maintains that our perception is “composed of mutually external units” (OK 118).⁸ For this conviction, he draws on the distinction between logical and empirical grounds: “this view, if it is held, must be held on logical, not on empirical grounds … logical grounds are adequate to the conclusion” (OK 118). Yet as we have seen, Nicod’s interpretation of this distinction leads him to the opposite conclusion: logical grounds cannot justify the view that our perception is composed of mutually external units, only experience can determine the nature of sense-data. To Nicod, Russell’s appeal to logical instead of empirical grounds is indicative of a confused understanding of the distinction between constitution and determination.

Rather than solely criticizing Bergson for his misunderstanding of abstraction and logical analysis, Nicod then also reproaches Russell for being too pessimistic about the prospects of Bergson’s epistemology: with a number of additional distinctions, its flaws can easily be rectified. It is Russell’s own understanding of logical analysis that induces him to believe that we cannot conceive of our immediate experience as one synthetic interpenetrating whole without forsaking science for mysticism.

At the end of the day, Nicod believes that both Russell and Bergson are misguided in thinking that they hold two fundamentally opposing views. Just like the choice between a synthetic and analytic understanding of experience turned out to be a false one, with the right understanding of abstraction, we come to see that there is also no conflict between synthesis and analysis in the identification of distinct terms and the discernment of relations between terms. In these matters, the logician and the artist also do not need to interfere with each other's work.

2.4. The two senses of analysis

In the next section, Nicod responds once more to Bergson, this time even granting him the previously refuted premise used to justify his assertions: “Suppose we admit that there is falsification in the discernment of distinct and related sense data” (FG 64–65). Would this not restore Russell’s critique and defeat the preceding analysis? What if reason’s involvement in the mapping of experience did affect the immediate data of consciousness? Would this not be detrimental to the dissolution of the dilemma?

Nicod argues that it would not. Even if reason’s involvement would affect the immediately given, the new data would – regardless of their artificiality – still be data of consciousness: spatialization and symbolization remain basic tendencies of the mind. Even Bergson needs to, and does, admit that “there are in a certain sense distinct and related sense terms in perceived processes since the physicist, the astronomer, and the chemist observe them”. He simply argues that in their own interpretation of their work, there is something erroneous – although not erroneous in the usual sense, but in a “metaphysical sense of spiritual deficiency” (FG 65).

As Bergson explains in the Introduction, scientists do not understand the nature of abstraction and therefore do not recognize the limits of their results: their propositions are only relative, never absolute, they only give a partial view of reality (CM 48). If only scientists would understand this, there would be no conflict: scientific inquiry would simply be delegated to its proper place. To be sure, Bergson does not deem their work as idle or invalid, but as “artificial, superficial, symbolic instead of false” (FG 65).

Nicod’s response to Bergson’s illustrious move is simple yet astonishingly ingenious:

Since, according to what you say, it is not true that there are distinct and related sense-data, for it is not true that lightning precedes thunder but true only in a certain sense, understand whatever we say in that sense whatever that may be, for we mean to use words only in that sense.

(FG 65)

Immediately thereafter, Nicod raises the question whether this “detachment of meaning” is possible, whether understanding the distinctness of sense-data in a sense different from how we usually consider it, is justifiable (FG 65). As he certainly realizes, for Bergson, this separation of beliefs would itself be parasitic upon abstraction. In order to distinguish these two senses, one would first need to abstract from immediate experience and, in this way, once again, fall victim to a confusion of time and space. Ultimately, this concern with preserving the quality, unity, and integrity of experience is one of- if not the - principal concern of the Essai.

At this juncture, the two philosophers part ways, as Nicod’s metaphilosophical concerns are profoundly Russellian. For Nicod, the concern with the overall coherence of our beliefs is secondary to clarification: philosophy is too abstract and encompassing for all its questions to be considered or discussed simultaneously. We first need to analyze and resolve basic philosophical problems before even beginning to consider how all our beliefs hang together. This becomes especially pertinent in the concluding remarks of the chapter, where Nicod explicitly aligns his work with the development of the method of analysis in philosophy, in one of the rare endorsements of one of the principal precepts of analytic philosophy by a French philosopher prior to the Second World War:

The idea is spreading today that philosophy will progress only by becoming more piecemeal like the sciences. The philosopher must learn to treat certain ideas abstractly without regard for his own doctrines as far as possible whenever he deals with a particular question. His solution should be presented in terms, and if possible in an attitude, as independent as possible, of all his other beliefs.

(FG 65–66)

3. Geometry and the sensible world

3.1. The origins of geometry

In Part III, Nicod critically examines Bergson’s views on the origins of geometry. Contra Bergson’s psychologism, Nicod endorses logicism: geometrical truths are logical truths. Similar to Russell in his critique of Bergson’s understanding of mathematics in The Philosophy of Henri Bergson, he contends that Bergson uses obsolete definitions of mathematical objects throughout his critique of spatialization. While Russell only reviews Bergson’s definition of number, Nicod starts off criticizing Bergson’s definition of a line, to then thoroughly reconsider Bergson’s account of the relation between geometry and the sensible world. He intends to show that Bergson’s account is partial at best, his is only one hypothesis to explain the origins of geometry.

Nicod begins his examination with a reiteration of a thought experiment in the Essai:

If we limit ourselves to the case of a geometry reduced to the properties of order in a line, we raise again, although from a different viewpoint, a little problem stated by Bergson in these terms: “ . . . imagine an indefinite straight line and on this line a material point A which moves. If this point were to become self conscious, it would feel itself change since it is in motion; it would apprehend a quality of succession; but would this succession assume for him the form of a straight line?”

(FG 97)

In his effort to think pure duration, Bergson had introduced this thought experiment. His aim was to distinguish between two kinds of succession: one that finds its origin in the juxtaposition of distinct and discrete sensations in an ideal, homogeneous space, and one intrinsic to the experience of time as duration, as a continuous flow of indefinite sensations. According to Bergson, the conscious material point A, due its inability to “rise … above the line which it traverses and perceive simultaneously several points of it in juxtaposition”, would only be acquainted with the second, purely temporal kind of succession: “the succession of states through which it passes could not assume for it the form of a line” (TF 103).

Right away, Nicod notes that “the question, in fact, is not the same for Bergson as it is for us … we are seeking in observable nature cases obeying the axioms of linear order, and not a certain aspect serving alone as a line” (97). The conditions of the emergence of the concept of a line cannot be determined by a single thought experiment, since a line is an abstract and complex concept: “[w]e call line a class of terms connected by a relation obeying the axioms of linear Analysis Situs” (97).⁹ What exactly is to be understood by a line is to be determined by the results of topology: we, philosophers, might have “a certain mental image” (97) of what a line is, but this intuitive idea cannot and should not guide us in our effort to explicate the definition of a line: “we must remember that this image is only one instance of what we are after, and that the other instances need not resemble it at all” (FG 97).

According to Nicod, Bergson’s error is that he proceeds the wrong way around. He adopts a concept of a line on the basis of a mental image generated by a single thought experiment, and then uses this concept to explain and critique the mathematical definition, instead of examining the definitions of lines in use among mathematicians and then trying to determine all the diverse ways in which these concepts can be grounded in experience. On Nicod’s reading, Bergson never considers the various definitions of a line by mathematicians. He never questions whether there might be other possibilities to form the geometrical concept of a line than through a juxtaposition of sensations in an ideal, homogeneous space: “Bergson creates for himself a tyrannical image of the appearance a line should have … [h]e limits the form of a line to one particular appearance” (98). As a result, he remains “unaware that there may be still others [definitions] altogether different which are formed out of other elements and other relations” (FG 98).

In the following paragraphs, Nicod broadens his critique to cover Bergson’s hypothesis of the origins of all of geometry. He argues that Bergson here too commits the error of founding his hypothesis on a single mental image: “Bergson believes that these laws [of geometry], wherever they present themselves, can only be thought in terms of the particular image of simultaneous multiplicity which he calls the idea of space” (FG 98). According to Bergson, the origins of geometry are to be found in a faculty of perceiving or conceiving a space without quality, which allows us to map experience, to discern terms and relations, in brief, to practice geometry: “the mind functions only by the aid of some sort of instinctive or deliberative representation of its objects and their relations on something like an ideal blackboard” (FG 137). What Bergson calls spatialization is, essentially, the construction of this blackboard.

While Nicod admits to Bergson that the existence of such a faculty is a simple and captivating hypothesis to explain the origins of geometry, he believes it is only one possible solution. As he shows throughout Part III, there are other ways in which geometry can be built on experience and we can construct geometries from senses other than sight – including sound and touch, as well as from relations other than of position, for example, simultaneity. In this way, Nicod intends to rectify Bergson’s account of geometry, to argue that it is neither conclusive nor definitive and that we should continue to explore other hypotheses to further our understanding of the relation between geometry and the sensible world. Thus, even in his critique, his commitment to reconciliation remains.

From the perspective of Bergson’s philosophy, however, Nicod’s demonstrations in Part III amount to a refutation. For Bergson, the ideal blackboard is a necessary presupposition of doing geometry: if there are other ways to extract formal geometries from the sensible world, then his critique of spatialization is severely compromised.¹⁰

3.2. The scope of naturalism symbolism

In “The Scope of the Hypothesis of a Natural Spatial Symbolism”, Nicod continues his discussion of Bergson’s account of the origins of geometry, this time addressing the critique that spatialization alienates us from the immediate data of consciousness and engenders an abstract, symbolic discourse dissociated from the concrete nature of perception. In Nicod’s view, this critique rests upon an erroneous conception of representation: by reconsidering our understanding of symbolization, we can come to see that the application of geometry to experience does not affect our apprehension of the immediate data of consciousness, but instead increases our appreciation of its wealth, scope, and structure.

As Nicod makes clear, in Bergson’s view, any analysis involves the construction of the ideal blackboard. Analysis can take place “only by the projection of this reality upon the plane of a visual imagination which presents an intuitive order of immediate place” (FG 137). However, as Bergson ardently argues throughout the Essai, experience of itself does not have this structure: the immediate data of consciousness are qualitative, indefinite, and interpenetrating, and cannot be reduced, without loss or distortion, to abstract objects and relations posited in an ideal, homogeneous space (TF 128–130). Therefore, projecting experience upon the ideal blackboard is imposing an imaginary order.

Although Nicod agrees with Bergson that the construction of the ideal blackboard is a figment of our imagination, he rejects the idea that the order of experience derives from it (FG 185). Like Russell, he argues that Bergson mistakes “a personal idiosyncrasy” for “a necessity of thought” by equating mental laws with objective laws (PH 337). Even though spatialization enables the mind to discern the laws of geometry, this is a mere psychological artifact, it does not affect the validity of these laws. But in contrast to Russell, Nicod does not think that this objection suffices to refute Bergson’s conclusions. In his view, the failing of Bergson’s argument lies elsewhere: “the conception whose limits we are studying rests entirely on the notion of representation or symbolism” (FG 138).

Throughout his argument, Bergson assumes that “imagining any fact by means of a symbol [is] the same as thinking in the presence of a certain ideal spatial background” (138). In other words, the ideal blackboard is not only a necessary presupposition of geometry and analysis, but also of representation: when symbolizing a property of experience, we install our experience upon the ideal blackboard and inadvertently come to substitute our experience for a symbol. Whenever we believe we are analyzing experience, we are, in fact, only “investigating the laws of this imposing medium of representation” (FG 138).

In Bergson’s philosophy, this distinction between presentation and representation is decisive. It is the fundamental premise for his argument that the substitution of an experience by a symbol inevitably distorts our grasp of the immediate data of consciousness. He warns us time and time again that representations.

will never give us anything more than an artificial recomposition of the object of which they can symbolize only certain general and, as it were, impersonal aspects … alongside the illusion, there is also a very grave danger. For the concept generalizes at the same time that it abstracts. The concept can symbolize a particular property only by making it common to an infinity of things. Therefore it always more or less distorts this property by the extension it gives to it.

(CM 195)

But according to Nicod, “this is hardly the case” (138). Representation should not be conceived of as an attempt to substitute a symbol for an experience, to identify representation with presentation: “[e]very kind of symbolism is partial, or again, abstract” (138). For example, in the case of the letters, “the form alone is symbolic of the sound: the colour of the ink, the dimension of the marks do not mean anything” (FG 138). Whenever we represent an experience through symbols, the symbol represents only a particular property of experience, never the full experience itself: “the thing symbolized is not altogether symbolized, but only in certain of its properties” (139). A symbol, then, is “only a symbol in such properties as the mind distinguishes” (139). While “we are often tempted to extend a symbolic system” – in Bergson’s words, to generalize by abstraction – by employing the Russellian method of definition and analysis, we can make sure that symbols do not deceive us, that they represent only those particular properties which we intend them to represent (FG 139). In this way, we can make sure that symbolization remains “an instrument of reason … the servant and not the master of reason” (FG 143).

According to Nicod, this conception of symbolization undermines Bergson’s critique of symbolization, it falsifies his assumption that representation is an attempt to substitute symbol for experience and thereby rebuts his claim that spatialization alienates us from the immediate data of consciousness. Representations neither alter nor distort qualitative experience, symbols merely picture properties present in perception:

Therefore, the introduction of any schematism, visual symbolism for instance, only produces the following changes: instead of thinking: ‘There is in my experience a relation which I name succession and which is an asymmetrical, transitive, and connected relation,’ we shall think: ‘There is in my experience something that I name succession and which may be correctly symbolized by an asymmetrical, transitive, and connected relation’; and so forth for all the rest.

(FG 141)

3.3. The abstract relation of formal analogy

The question remains, however, how symbols represent experience; wherein lies the correspondence between a symbol and the experience it represents? In Nicod’s words: “What relation between two properties makes one a possible symbol of the other? Or else, to remain in the realm of symbolism itself: what relation is there among all the possible systems of the same real property?” (FG 140). At this point in the text, we find the first reference to Wittgenstein’s Tractatus in French philosophy. Nicod, who together with Russell and Dorothy Wrinch had read and discussed a manuscript of this work during a stay in Lulworth in 1919 (PT 49), uses Wittgenstein’s book as a source for the claim that the correspondence between a symbol, and what it is a symbol of, is founded on “an abstract relation of formal analogy” (141). On his reading of Wittgenstein, symbols represent by fashioning formal properties analogous to the properties of the sensible world, they represent through structural equivalence:

In order for the relation R’ to symbolize the same thing as the relation R, it will be found in all cases necessary and sufficient that these two relations be equivalent, that is to say, that they have the same formal properties, or else again, that one can be replaced by the other, salva veritate, in every proposition containing nothing besides logical or mathematical expressions.

(FG 141)

In a posthumous published paper, “Les relations de valeurs et les relations de sense en logique formelle” (1924), Nicod expands upon this notion of structural equivalence and clarifies his understanding of Wittgenstein’s account of correspondence. He begins this paper by distinguishing between relations of value, that is, relations which only depend on the truth or falsity of the propositions involved, and relations of sense, i.e. relations which determine the relation of value between two propositions: “[f]or example, p or q, not-p or q, not-p or not-q are relations of value; p is the contradictory of q, p is the subordinate of q are relations of sense” (RV 578). According to Nicod, in order to do logical analysis, we only need the relations of value; they dictate the truth or falsity of propositions and thereby the validity of a logical inference from p to q.

As an example to illustrate this point, Nicod takes the algebraic statement ‘(x + y) z = xz + yz’. In such a formal statement, only the relations of value are represented. Nevertheless, we are able to infer the verity of the equivalence between the two parts of the statements, we know that the first proposition entails the second. In other words, even though the relations of sense are absent, they still govern our inferences. Using a phrasing which unmistakably resembles the passage on Wittgenstein’s Tractatus in his thesis, Nicod explains this puzzling fact as follows:

[t]he relations of sense of propositions are, in effect, relations of constitution between complexes. They consist in the fact that such elements, occupying such places in the architecture of one proposal, find themselves in such places in the architecture of another.

(RV 580)

In short, the equivalence between the two parts of the statement is determined by the constitution of the two complexes ‘(x + y) z’ and ‘xz + yz’. The constitution of the two complexes is reflected in the composition of the symbol: since they have the same formal properties, we can substitute every element of each part by elements of the other part.

While in our example, the equivalence between the two parts of the algebraic statement is named by the symbol ‘ = ’, this sign does not reveal to us the correspondence between the two. Even without this indication, we would still be able to recognize that we can substitute any element of the first part of the statement for an element of the other. On Nicod’s account, the abstract relation of formal analogy determines the relations of sense. The relations of sense, in our case, the equivalence between the two parts of the algebraic statement, but more generally, the correspondence between any symbol and experience, or representation and presentation:

spreads out before our eyes without any word evoking it. It is signified in the most perfect way by the simple bringing together of the two sentences … It is not named by an arbitrary proper sign, but shown to the mind, by a natural symbolism, in the returns and the arrangement of the other signs.

(RV 580)

On Nicod’s reading, this distinction between naming and showing is the decisive contribution of Wittgenstein’s book: “[t]his duality of the symbolic function in all language is the discovery of M. L. Wittgenstein, which makes it the basis of an entirely new critical philosophy in his singular and admirable Tractatus logico-philosophicus” (RV 581).

Taking his lead from Wittgenstein, Nicod continues by affirming that it is impossible to name, represent or define correspondence. It is inexplicable. In the last section, he drives this point home by arguing that Lewis’ attempt to define determination through strict implication merely results in “a new indefinable” (RV 582). To Nicod, “it is obvious that such a relation does not exist” (RV 582). There is only an indefinite, innumerable set of relations of constitution between complexes and any attempt to group them under one heading – as Lewis’ does – is futile and inane. There simply is no unitary relation that corresponds to the name ‘strict implication’.

By insisting that there is limit to what language can represent, Nicod draws curiously close to Bergson’s notion of intuition in his explication of the abstract relation of formal analogy. In Bergson’s philosophy, intuition has the same epistemological function as showing in Nicod’s reading of Wittgenstein: to connect thought and world. It is what explains our immediate access to the world and our ability to have knowledge of a thing as it is in-itself; it offers us a knowledge that cannot be symbolized. In a word, intuition reveals the world. Since correspondence cannot be symbolized, since it eludes all analysis, Nicod takes recourse to another explanation: the relation of formal analogy can only be shown, only be intuited by the mind.

3.4. Perception as a picture puzzle

In the introduction to Part III, Nicod takes one step further, arguing for a position seemingly opposite to that of Bergson: he contends that symbolization can foster our grasp of the immediate data of consciousness; through symbolization, we can come to discover structures or properties of experience that we had not been able to discern without. He beautifully illustrates this process of discovering structures in experience by comparing perception to a picture puzzle:

As children we have all seen those picture puzzles which represent things that we cannot distinguish at the first glance; where it is a matter of discerning a giraffe or lion in the lines of a landscape deserted when first scanned. When we have “discovered” the picture hidden in them, we have seen nothing new. The contour of this little mountain is now the mane of the lion, and the knot in this tree-trunk is its eye. We had read in this network of lines a certain structure, the landscape, and now, we have just read a second structure, the lion … The pattern that I have before me is sensible nature. The elementary relations that I know how to spell, so to speak, are the original relations of my sense-data.

(FG 93)

In the Introduction, Bergson uses a strikingly similar comparison between symbolization and experience to argue for a different conclusion. He invites us to the following thought experiment:

let us suppose someone puts before me, all jumbled together, the letters which go to make up a poem, without my knowing which poem it is. If the letters were parts of the poem, I could attempt to reconstruct it with them by trying various possible arrangements, as a child does with the pieces of a jigsaw puzzle. But I shall not for an instant think of attempting it, because the letters are not component parts, but partial expressions, which is quite another thing. That is why, if I know the poem, I put each one of the letters in its proper place and link them together without difficulty in one continuous chain, while the reverse operation is impossible. Even when I take it into my head to try that reverse operation, even when I place the letters end to end, I begin by imagining a plausible meaning: I thus give myself an intuition, and it is from the intuition that I try to fall back on the elementary symbols which would recreate its expression.

(CM 201)

The divergence between the two thought experiments is crystalline. On the one side, Nicod claims that we cannot at first glance see all there is to a picture puzzle since the puzzle pieces of perception are not given all at once, we have to analyze our experience to see all of its aspects and thus come to discern its dormant structures. On the other, Bergson maintains that intuition instantaneously gives us the full picture and therefore analysis can never result in creation, it is mere recreation.

For Bergson, symbolization is, at best, a reconstruction of a prior intuition: “it cannot be too often repeated: from intuition one can pass on to analysis, but not from analysis to intuition”. Although he does ascribe to artists, poets, and especially painters the possibility to discover dormant structures in experience (Gandon, “Interpretation”, 26), this is never a discovery of new aspects of experience. The problem with logical analysis is precisely that it cannot recognize novelty: “[logic] sees in a new form or quality only a rearrangement of the old – nothing absolutely new” (CM 27). In the end, Bergson’s primary philosophical commitment is to demonstrating the thesis that radical novelty exists. Therefore, any analysis – regardless whether logical or artistic – can only be subsidiary.¹¹

In Nicod’s eyes, the discovery of unseen aspects of experience also does not lead to novelty: “we have seen nothing new” (FG 93). But for him, this is not a limitation of analysis. On the contrary, it is precisely the merit of analysis: discovering different ways of making sense of the sensible. After all, Nicod remains a realist, a faithful disciple of Russell. Once again, the irreconcilable difference between Nicod and Bergson turns out to be metaphilosophical: while for Bergson recognizing the possibility of radical novelty is the ultimate philosophical concern, Nicod’s attitude is more modest, he simply aims to describe and analyze reality. To him, the world is what it is, only our representations of the world evolve, allowing us to discover different structures in experience. For Bergson, however, this recognition is insufficient: it is not only representations that evolve, reality itself is a “continuous creation of unforeseeable novelty” (CM 106).

4. Conclusion

Nicod’s intervention is a unique effort to reconcile the perspectives of two seemingly disparate philosophers. Regrettably, even though both philosophers were aware of his thesis, neither of them replied to his attempt at mediation. As for Bergson, he referred to the thesis only once. In a paper on contemporary French philosophy, he names Nicod together with Bachelard and René Poirier as representatives of positivist philosophy of science. Unsurprisingly, Bergson does not hold these philosophers in high regard, they deal too closely with the technical problems of science to be even considered “proper” philosophers (Bergson, “Mélanges”, 1178–1179). As for Russell, he too only devotes a summative paragraph to Nicod’s thesis in the revised 1926 edition of Our Knowledge of the External World (OK 93). By the time Nicod’s thesis was published, he had already lost his vehemence for chastising Bergson’s philosophy; he had found new antagonists. After the First World War, Bergson’s fame had started to wane, making it less acute for Russell to further engage with his philosophy. Admittedly, both philosophers rarely engaged with critiques outside their milieu: while Bergson had left the reply to Russell to Herbert Wildon Carr, Russell believed that “explicit controversy is almost always fruitless in philosophy, owing to the fact that no two philosophers ever understand one another” (OK 15).

Due to his early death, Nicod never had the chance to fully develop his (meta)philosophical views and his singular synthesis of traditions makes his work very demanding. Analytic philosophers, such as W.V.O. Quine, thought the thesis to be “rigorous and painstaking, and the matter presented … of considerable interest and unquestionable importance” (Quine, “Review”, 307), but also found “the manner of exposition is lacking in clarity and preciseness … [o]ne misses the skilled pen of a Russell” (Quine, “Review”, 307). Evidently, Quine did not pick up on the references to Bergson: to analytic philosophers, Nicod’s conversing with the French epistemological tradition probably seemed rather alien and abstruse. The thesis also did not find a congenial audience among French epistemologists. In 1923, Russell’s method of logical analysis had only a few adherents in France. Nicod’s analytic approach must have struck French epistemologists, such as Bachelard, Émile Meyerson, and Léon Brunschvicg, as too fastidious, technical, and Aristotelian. In a letter, his supervisor Lalande forewarned Nicod that his thesis was “too original”.¹²

It is intriguing to speculate about how Nicod’s itinerary could have developed, if he had not died at such an early age and had been able to refine his philosophy. Would he have continued his project of the reconstruction of the empirical foundations of science in a way that resembles Carnap’s Aufbau? Undoubtedly, his existing work already shows striking similarities with that of the early Carnap (Moulines, “Die Mathematisierung”). Would the place of Bergsonism in the history of analytic philosophy have been different, if Nicod, upon Russell’s recommendation, had contributed to a journal Moritz Schlick and Hans Reichenbach were attempting to establish in 1923 and thus been able to deepen the Vienna Circle’s engagement with Bergson’s epistemology (PT 48)? Would analytic philosophy have had a more instantaneous impact in France, long before the creation of the Institute Jean Nicod, if he had attained a prominent institutional position at a Paris university? All of this, of course, can only be the subject of speculation.

Nonetheless, it is undeniable that Nicod's philosophical itinerary would have allowed him to continue a dialogue between two traditions that became increasingly more estranged during the first half of the twentieth century. In his eyes, Bergson’s epistemology could not so easily be dismissed, as Russell and many analytic philosophers after him believed. He simply did not share their dismissiveness of other traditions. Inversely, Nicod’s effort to introduce Russell’s philosophy in France reveals his conviction that the French epistemological tradition could have much to gain from the methods of analytic philosophy. In his view, dismissal of traditions through crude categorization is never fruitful; most denunciations stem from misunderstandings. Indeed, vital to his philosophy is a critique of poorly formulated philosophical problems, what Mach before him, Bergson simultaneously with him, and Carnap after him called pseudo-problems: through meticulous analysis of these confusions, he intends to demonstrate the inanity of idle dissension. In this regard, Nicod’s metaphilosophical concerns cohere with his political ideals: as a committed pacifist, he pleaded for rapprochement, accord, and union (Gandon, “Jean Nicod”).

In Les tendances philosophiques de M. Bertrand Russell (1922), Nicod argues that Bergson and Russell are allies precisely in their critique of obsolete problems produced by abstruse metaphysicians, both follow Kant in proclaiming that “there is a common basis of erroneous metaphysics to which a persistent inclination has repeatedly carried the human mind along with it” (PT 58). The difference between the two lies in the location of the source of this metaphysics: while Bergson situated it in “our logical faculty itself” (PT 58), “Russell locates it in the incomplete and simplistic science which prevailed hitherto and which is expressed in traditional logic” (PT 58). Underlying this divergence, however, Nicod discerns yet another common ambition: to temper the lofty, excessive ambitions of logic and to develop a philosophy true to the “actual”, “wide and inexhaustible world” (PT 56). By forbidding logic to “say what the world is” (PT 57) and recovering the “infinitely particular” (PT 61), Nicod conceives of a philosophy in which Bergson’s insights from intuition are discovered through reason by the Russellian method of logical analysis. His philosophy aspires to an impersonal, inhuman universalism, a radical, pure and perfect empiricism combined with a rigorous, scientific rationalism: “the right attitude is a complete oblivion of self, the silence of every inner voice, an inhuman and astronomical curiosity, so to speak” (PT 57–59).

Acknowledgements

I want to thank the following people for feedback on previous drafts of the paper: Miguel Egler, Sander Verhaegh, Andreas Vrahimis and two anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek: [Grant Number PGW.20.021].

Notes

1 See Chimisso, “Intuition and discursive knowledge”, Vrahimis, “Sense data”, and Moravec, “Taking time”.

2 For biographical and bibliographical details, see Gandon, “Jean Nicod”.

3 Cartan to Nicod 14th July 1922 and Lalande to Nicod, 24th April 1922 in Fonds Ignace Meyerson, Archives nationales de France.

4 In a footnote, Nicod refers to Moore’s work in Hicks et al., “Symposium”.

5 In her 1914 paper “Complexity and Synthesis”, Costelloe also argues that this point lies at the heart of the dispute between Bergson and Russell. See Vrahimis, “Sense data”.

6 This criterion obviously needs refinement. Suppose we ascribe the predicate ‘is a complex’ to X. If X is a complex made of simple terms, then X has a predicate, namely ‘is a complex’, that cannot be predicated to its parts. Following Nicod’s criterion, we are forced to the contradictory conclusion that X is both simple and complex. The question whether and how it is possible to refine this principle to evade this problem lies outside the scope of this paper. I want to thank an anonymous reviewer for bringing up this point.

7 For a discussion of Wittgenstein’s assessment of this distinction, see Soutif “La signification”.

8 For a rich discussion of Russell’s recognition of the indefinite, indeterminate nature of experience, see Wishon, “Russellian Acquaintance”.

9 The reference is to Poincaré, “Analysis Situs”.

10 For discussion, see Watt “Bergson on number” and Garner & Noble “Possibility of necessity”.

11 On this, see Sinclair “Bergson on Possibility”.

12 Lalande to Nicod, 17 July 1922 in 19920046/57, Fonds Ignace Meyerson, Archives nationales de France.