Jean Cavaillès: On the Logic and Theory of Science

On the Logic and Theory of Science Book Cover On the Logic and Theory of Science
Jean Cavaillès. Introductory notice by Georges Canguilhem and Charles Ehresmann. Introduction by Knox Peden. Translated by Translated by Knox Peden and Robin Mackay
Urbanomic/Sequence Press
Paperback $18.95

Reviewed by: Ties van Gemert (Tilburg University)

Why read Jean Cavaillès’ work today? This is the foremost question that we need to address. The history of philosophy pullulates with untimely ideas, obscured innovators, and forgotten precursors: the fact that Cavaillès anticipated decisive developments within French philosophy cannot suffice to revisit his short but dense treatise. Historiographical significance may direct historians to his work, but we need positive, philosophical reasons to convince phenomenologists, philosophers of science, and epistemologists to work their way through a book of which each page demands to be read closely, carefully, and rigorously. To be able to demonstrate the value of Cavaillès’ philosophical pathway, one needs to show how our time calls again for his imagination.

If there ever has been a moment for this untimely treatise. Written while incarcerated by the German authorities in Montpellier and Limoges, Cavaillès did not live to experience its publication, he was executed for his leading role in the French resistance in early April 1944 – just shortly after completing the manuscript. When his friends Georges Canguilhem and Charles Ehresmann published Sur la logique et la théorie de la science in 1947, the moment when one could presuppose acquaintance with Neo-Kantian philosophy, Carnap’s logical syntax, Husserl’s phenomenology, and the debates concerning the foundations of mathematics, had already passed.

The intellectual situation in which the book was conceived had also disintegrated: Cavaillès’ doctoral advisor, the rationalist philosopher Léon Brunschvicg, had died in exile in Southern France; his friend, the philosopher of mathematics Albert Lautman, had been killed for his resistance work; the historian of science Hélène Metzger had become a victim of the Shoah; and the philosopher Gaston Bachelard by then was moving away from philosophy of science to aesthetics. The philosophical positions to which Cavaillès was indebted and the technical debates to which he was responding were reforming: the French epistemology of the 1920’s and 1930’s had lost its compelling force, the fierce disputes regarding the sovereignty of intuitionism, logicism, and formalism in mathematics were tempered, and Kantian, rationalist philosophy had become the target of powerful critiques.

In the 1950’s, the French intellectual scenery underwent profound changes: existentialism came to be fashionable, Marxism became the dominant political ideology, and phenomenology emerged as the dominant philosophical method for studying everything from nausea to wonder. Hegel, Husserl, and Heidegger were the names on the lips and the books of the desks of the agrégés.

Notwithstanding the rather unfortunate circumstances of the book’s publication, Cavaillès’ work still exercised a decisive but ephemeral influence on the young Derrida, the early work of Foucault, and the philosophy of science of Louis Althusser. More lasting was his sway over the work of Suzanne Bachelard, Gilles-Gaston Granger, and Jules Vuillemin, but these philosophers, whose labor was decisive in introducing analytic philosophy in France, never had the same impact on the intellectual scenery as the generation of May ‘68. At the time, there was a particular bias amongst French intellectuals concerning analytic philosophy that leaned too much towards logical positivism: the works associated with the Vienna Circle were considered one-dimensional, politically suspect, and to be lacking in terms of style. In the eyes of philosophers such as Althusser, Cavaillès had adequately portrayed the defects of logical positivism with his critique of Carnap. Consequently, the convergences between the works of the Vienna Circle and that of Cavaillès were overlooked in a climate hostile to scientific philosophy.

Under these conditions, the treatise has come to take up an uncanny place within the history of philosophy. Although Cavaillès’ work is canonized in the French epistemological tradition and now recognized as a critical influence upon the (post-)structuralist generation, the fact that he was ‘thoroughly immersed in the new logical culture’ is often deemphasized or simply ignored (27). The affiliations, conjunctions, and divergences between his work and that of Frege, Hilbert, Brouwer, Carnap, and Reichenbach remain underdeveloped and sometimes even unexplored. While it would be philosophically, but also historically, naive to plead for a restorative rereading of Cavaillès’ work within its autochthonic context, the relevancy of On the Logic and the Theory of Science for this other tradition of doing philosophy certainly deserves further scrutiny.

Indeed, it is precisely the uneasy position of Cavaillès’ work in the history of philosophy that makes rereading the treatise so compelling today. His critique of logical positivism, his elaboration of intuitionism, his conceptualization of Neo-Kantianism, and his divergent reflections on epistemological questions enclose a rich reserve for developing alternatives genealogies of twentieth-century philosophy. At a moment when French philosophers are finally beginning to reconsider Carnap’s contributions to philosophy, analytic epistemologists are exploring the resources of French philosophy for interventions in present-day discussions, and a new generation of French philosophers is reinstalling the fundamental relation between philosophy and mathematics: maybe, the time is finally there to begin to read Cavaillès as a contemporary. Now, more than ever, is his anomalous philosophical trajectory able to generate a conceptual space to assemble estranged thinkers and construct new philosophical itineraries.

To demonstrate this, let us discuss three examples that disclose how Cavaillès’ philosophical imagination may illuminate our current discourse. Together these examples show how his work can, once again, be utilized by philosophers, how his concepts can be put to work, once more, and why we should begin to reconsider and rethink the significance of On Logic and the Theory of Science. In other words, we will use these three examples to re-assess the purport of the treatise.

The first example relates to the role Cavaillès could play in the reconsiderations of Carnap’s work in French philosophy. In his book Carnap et la question transcendentale (2021), Jean-Baptiste Fournier engages extensively with a problem central to French philosophy: the status of the transcendental. Throughout the book, he attempts to reread Carnap’s early work as an exercise in transcendental philosophy – focusing mainly on Der Raum (1922) and Der Logische Aufbau der Welt (1928). In doing so, Fournier not only broadens the breadth of the discussion of Carnap’s relation to Husserl’s phenomenology, Helmholtz’ epistemology, and Neo-Kantianism, but also – implicitly – integrates Carnap’s philosophy in contemporary discussions of the transcendental in French philosophy.

According to Fournier, the early Carnap was fundamentally concerned with the question of ‘how logic could play a transcendental role’ within philosophy (18). He argues that in Carnap’s work the question of the possibility of objective knowledge is transcendental to the extent that it puts at stake the very conceptualization of the world. In what Fournier designates as Carnap’s transcendental analyses, the world has a double meaning: it is both ‘the horizon and correlate of consciousness’ (298). The world ‘thus functions as a Kantian transcendental object’ (298). The crucial difference with Kant’s conceptualization of the transcendental, however, is that in the work of the German philosopher, there is still the possibility of a complete transcendental deduction. In Carnap’s philosophy, the transcendental question ‘does not arise once and for all but must always be revived for each concept and each science’ (301).

Upon a first reading, it might appear that there is no room for reading such a concept of the transcendental in Cavaillès’ philosophy. His remarks on the transcendental are often dismissive (22-24, 120). Kant’s transcendental philosophy is said to obscure any attempt to account for the normativity of logic since it is ‘fundamentally dependent upon the notions of actions and faculty, which are meaningful only in reference to a concrete consciousness’ (20). In a similar vein, Cavaillès’ ambition to found an absolute logic of science leads him to reject the transcendental logic of Husserl. In his view, Husserl’s elaboration of phenomenology is parasitic upon the acts of consciousness and, therefore, lacks the autonomy needed for logic to ground itself.

While Cavaillès critiques the role given to transcendental subjectivity in Kant and Husserl’s philosophy, he does leave open the possibility of a transcendental analysis without a constitutive role of the subject. Sometimes, it seems that this is precisely what Cavaillès is concerned with: ‘[h]ere lies the role of transcendental analysis: to recognise authentic diversities and to establish the relations between them’ (49). Just like Carnap’s transcendental analyses, the analyses that Cavaillès conducts concern the structure of scientific theories and their conditions. But even though Cavaillès commences with a reflection on scientific theories, in his analyses, there is never any given that is presupposed or left unexamined. Each level of analysis is incorporated and related to a subsequent or antecedent one: in this way, his vision resembles that of Carnap’s Aufbau.

The question Cavaillès continually asks himself is also similar to that of Fournier’s Carnap: what are the conditions under which objective or scientific knowledge is possible? For Cavaillès, this question cannot be answered at one moment in time, it must continually be asked in relation to specific scientific discoveries, and it must always be compared with and integrated in previous analyses or theories. Within his philosophy, the transcendental, therefore, undergoes constant transformation: it is no longer possible to deduce all the conditions and ramifications of a single concept in one place and time. If there is a concept of the transcendental in Cavaillès’ philosophy, it is thus thoroughly dynamic – maybe even plastic.

The second example concerns Cavaillès’ anomalous position within the history of French philosophy and how it may be of use in connecting the work of antagonized thinkers. Catarina Dutilh Novaes, in a recent paper titled “Carnap Meets Foucault: conceptual engineering and genealogical investigations” (2020), discloses the similarities between Carnap and Foucault and argues for a reengagement with their work in current discussions on conceptual engineering. Although she tries to reconstruct the historical relations between these two thinkers, she does not discuss or even mention Cavaillès, when in fact, the philosopher is one of the missing links: Foucault probably first encountered Carnap’s work in On Logic and the Theory of Science. More importantly, his philosophy could have brought the concerns and considerations of these two philosophers together – since Cavaillès’ philosophy harbors a plane common to both: a more extensive conceptual space, where the dialectics of history and the complexities of (formal) epistemology come together, a central place to revisit the ramifications of what it means to tinker and ameliorate concepts.

In Cavaillès’ work, there are extensive genealogical analyses of concepts and a methodology of explication. Concepts are contemplated regarding their history and are clarified by rendering explicit the inferences that they imply. Furthermore, the French philosopher does not shy away from ameliorating concepts in order to enlarge their function. Yet throughout these efforts, there is never any reference to an essential constituent of a concept. As in Dutilh Novaes’ account of marriage as well the political aspects of Carnap’s concept of explication, pragmatics plays a crucial role, the function of a concept co-determines its value. At the same time, Cavaillès would never go so far to argue that the value of a concept lies in its use – a danger that seems apparent in Dutilh Novaes’ alliance of Foucault and Carnap. In his philosophy, truth remains the last measure when determining the function of a concept.

The last example bears on the philosophical project of two thinkers: Alain Badiou and Quentin Meillassoux. Both reclaim a Platonic theory of truth, bring renewed attention to the discourse of science in French philosophy, and place mathematics, once more, at the heart of philosophy. Taken together, their work reinvigorates a hybrid of rationalism and materialism in French philosophy. To further delineate and deepen their itinerary, one needs conceptual spaces to perceive the limits of and think through the problems particular to their philosophical project. For this, encounters with precursors such as Cavaillès, who have dealt extensively with questions concerning the nature of mathematics and the dialectics of history, are indispensable.

First, something about Badiou. Even though in his book Figures of Post-War French Philosophy (2009), Badiou discusses the relation between Cavaillès’ philosophy and his life as a resistance fighter, he has never engaged extensively with On the Logic and the Theory of Science. In the third chapter of the book, “Georges Canguilhem (1904—1995) Jean Cavaillès (1903-1944)”, Badiou gives us only a brief summary of Cavaillès’ position, which regardless of its fragmentary nature still reveals a concurrence between their projects: ‘the philosophy of mathematics must rid itself of all reference to a constituent mathematical subject, and should examine the internal necessity of mathematical notions’ (10). The absence of engagement with Cavaillès’ philosophy in Badiou’s work is rather surprising, given the importance that both ascribe to set-theory, their collective embracement of ruptures, and their communal passion for a revised Platonic concept of mathematics.

Needless to say, there are also critical differences between their conceptualization of these three points. While it is only in a complicated encounter between their thought that one could be able to explicate the ramifications of this divergence, a brief and somewhat cursory sketch may already reveal the contours of the paths taken and the advancements that can be obtained from such an analysis.

In their work, Badiou and Cavaillès utilize Cantor’s set-theoretical discoveries to conceptualize an ontology that is open, an ontology that resists totality. For them, set theory represents a break within thought, an event that ruptures the intelligible. Yet whereas both affirm the irreducibility of time within the generative movement of thought, Cavaillès is the only one who has thoroughly studied the fundamental historicity of the scientific event: this constituent of Cantor’s discovery is left entirely unexplored by Badiou. This singular difference characterizes their divergent notion of events: while Badiou’s concept of events leaves little room for describing the origination and construction of a scientific theory, Cavaillès aims to rationally reconstruct the very movement of science. As he puts it in the second part of On Logic and the Theory of Science: ‘by defining a structure of science that is nothing but science manifesting to itself what it is, we specify and justify the preceding characteristics’ (30).

In Badiou’s philosophy, there is no such rational reconstruction of scientific discoveries, there is no effort to define the determinate conditions of scientific progress, as there is no account of the labor involved in the progress in mathematics or science in general. His perspective on the history of science is shaped by the great moments of science, he views science through the eyes and work of aristocratic revolutionaries – not the communal work involved in thinking through theorems, experiments, and demonstrations. For Badiou, it seems that events take place within a vacuum; they are indeterminate, contingent, and original. In this regard, Badiou aligns himself with a century old tradition of French philosophy: the importance he attaches to contingency has been present in French thought ever since Émile Boutroux’s De la Contingence des Lois de la Nature (1874).

Cavaillès, with his commitment to studying the history of science and grounding the necessity of scientific progress, takes a radically different route. From the very beginning of his career, he is concerned with mapping the developments that lead to Cantor’s discoveries and examining the role of other scientists, who assisted in clarifying the ramifications of Cantor’s work. In this way, the event is contextualized, its constituents explained, and its conditions determined. For Cavaillès, this labor is critical. In his view, demonstration is at the heart of science, his aim is always to explicate the progress of science, to apprehend the event: ‘in its generative movement … to recover this structure not via description but apodictically as it unfolds and demonstrates itself’ (31). Ultimately, Cavaillès wants to incorporate the event within science, he aims to ground the development of science within science: ‘a science of science, and hence a part of itself’ (30).

By contrast, Badiou has not shown the least interest in science as a communal enterprise, as a self-illuminating development, or as an ‘Riemannian volume, closed and yet without any exterior’, his view of science is restricted to mysterious breaks within the movement of science that simply shock thought (30). This becomes poignantly clear when he speaks about the difference between truth and knowledge or when he reveals his disdain for normal science. In general, he attaches no importance to the observation, experimentation, and theorizing of scientists working in a settled paradigm. The realm of truth in Badiou’s work is thus restricted to ineffable instants in science, politics, aesthetics, and love. Although these events must be incorporated and related to a world, this work remains one of fidelity to the event – not one of a continuous critical examination of the consequences and limits of a theorem, conviction, style, or commitment.

Crudely put, for Badiou, when the event comes to you, you are immediately enlightened about its significance. For Cavaillès, truths are irreducibly genetic, they inherently involve the labor of explicating its inferences. This labor is, at least, twofold: there is paradigmization, where the demonstration is ‘longitudinal, coextensive with the demonstrative sequence’ and there is thematization, where one inaugurates ‘a new system of interconnection on the basis of the old one, understood no longer as a particular phase within a larger movement, but as an object of reflection in its current configuration’ (71). In Badiou’s philosophy, there is no such distinction, he does not seem to recognize the constructive, laborious activities of scientific communities – only the grandiose seems to deserve being subsumed under the idea. Yet with this gesture, Badiou risks splitting science into the profane and the profound, instead of safeguarding the significance of incorporating events within more expansive webs of knowledge.

Now, something about Meillassoux. In his book After Finitude (2006), Meillassoux aims to reconstruct philosophy through a philosopheme called correlationism: ‘the idea according to which we only ever have access to the correlation between thinking and being, and never to either term considered apart from the other’ (5). For Meillassoux, the modern line of thought that dissolved Locke’s distinction between primary and secondary qualities has obscured the possibility of thinking the thing-in-itself. His aim is to reactivate this distinction by arguing that ‘all those aspects of the object that can be formulated in mathematical terms can be meaningfully conceived as properties of the object in itself’ (3).

In On Logic and the Theory of Science, Cavaillès takes on a similar task: from the very beginning of his book, he is concerned with critiquing the philosophy of consciousness, his worry being that philosophers, such as Kant and Husserl, make science and mathematics dependent upon the acts of consciousness. In his view, science progresses, not consciousness, it might drag consciousness along or happen within consciousness, but certainly does not depend upon it for progress. By distinguishing radically between subject and object, he wants to reinstate mathematics’ autonomy and necessity. As Hourya Benis Sinaceur remarks in her paper “From Kant to Hilbert: French philosophy of concepts in the beginning of the XXth century” (2006): by ‘determining the objective structures of objectivity’, Cavaillès brings about ‘[a] truly Ptolemaic revolution’ (330). It is no longer a question of explicating the constitutive role of transcendental subjectivity, but of explicating the role of conceptual development within the objectivity of mathematics.

For Meillassoux, mathematics plays an equally important role in regaining access to the absolute, but this absolute is one of this world, it is attained through a reflection on the time before or after the existence of human beings. It is at this point that Meillassoux and Cavaillès part ways: Meillassoux wants to make use of the rigorousness of mathematics to say something about the world independent of the correlation between thinking and being and, consequently, about the thing-in-itself, while Cavaillès wants to dissociate subjectivity and objectivity, right now, by founding an absolute logic and science of science, he is determined to never subordinate the autonomy and necessity of mathematics to the ways of the world. For Cavaillès, ‘[t]o know the world, to understand the world – this is a programme that already represents the abandonment of complete creative autonomy, the renunciation of a necessity beholden to nothing other than itself’ (28).

According to Cavaillès, mathematics is never a mere tool for measuring or a medium that helps us access the worldly thing-in-itself, it cannot be subordinated to physics. Although the relation between physics and mathematics remains underdeveloped in Cavaillès’ work, he makes a few profound remarks on the problem of the relation between mathematics and physics. In his view, ‘the concatenation of physics has no absolute beginning, any more than that of mathematics does … experience itself as a system of acts is internally organised in such a way that it is impossible to interrupt its continual unfolding’ (88). It is at the singular intersection of the two sequences that theoretical physics is born. Yet this intersection itself can never be formalized, the correspondence can never be presupposed, and the one can never be incorporated in or reduced to the other. Mathematical physics is hence the name of a problem – not a state of science that we can simply presuppose.

Even if both thinkers endorse a particularly strong concept of logic and mathematics, Cavaillès is the only one who tries to account for this. Throughout Meillassoux’ undertaking, much is put up for grasp: the necessity of the laws of nature, the primacy of consciousness, and the very idea of the transcendental. Nevertheless, the validity of the logic that he uses to construct his philosophy is never questioned, conceptualized, or grounded. Like Badiou, Meillassoux rarely reflects upon the role of logic in his undertaking; he never seems to wonder whether other conceptualizations of logic or the relation between mathematics and the world are possible. Consequently, Meillassoux’ account of the relation of the a priori of logic and the a posteriori of the empirical within science remains somewhat obscure. Crucially, there seems to be no possibility that an event might change the logic he uses to construct his philosophy and thus transform his own conclusive propositions. In other words, Meillassoux’ logic is thoroughly static – whereas Cavaillès’ rendering is thoroughly dynamic.

This difference is also inherent to the conception of their own philosophical projects. In Meillassoux’ work, there is no account of the movement of thought itself. This feature is clearly visible in his philosophical style, which distances itself in the writing from the writing, it considers arguments without considering the dialectics of deliberation. Cavaillès’, on the other hand, never distances himself from the theories or concepts that he is discussing, he constantly closes the gap between his own thought and the thought of the philosopher, logician, or scientist that is discussing. There is a decisive need within his philosophy to give an account of the movement of thought itself. Naturally, this raises the question whether his philosophical project does not end in an infinite regression. His critique of Husserl’s logic using Gödel’s incompleteness theorems as well as his reflections on Spinoza’s idea of the idea suggest that Cavaillès was aware of this problem within his philosophy. Still, the question remains unresolved. A biographical fact may illuminate the two possible pathways that Cavaillès envisioned. In his final days, Cavaillès asked a priest for two books: a copy of the New Testament and a copy of Hegel’s Science of Logic.

Let us end with a few remarks on the new translation. Robin MacKay has, once more, proved to be a great translator. His exceptional ability to render unusually difficult and heterogenous French philosophical texts into stylistically gratifying and elegant English prose has been a more than welcome gift to those unable to read the original texts. His translations of the philosophy and literature of Gilles Châtelet, François J. Bonnet, and Gabriel Catren, not to mention a few short texts by Cavaillès, all have an unprecedented quality. The publishing house, Urbanomic, which MacKay founded in 2006, has been an invaluable source for those trying to renegotiate the limits of philosophical creativity. The series of books published together with Sequence Press is the perfect place for Cavaillès’ treatise to re-appear, his work resonates in a strange but enrapturing harmony with that of Land, Laruelle and Zalameo.

The other translator, Knox Peden, has done much to make Cavaillès’ known in the Anglo-Saxon world. His work Spinoza Contra Phenomenology: French Rationalism from Cavaillès to Deleuze (2014) is an excellent introduction not only to Cavaillès’ work, but also to the French rationalist tradition of which Cavaillès is part. He convincingly argues how we should not only read figures, such as Jean-Toussiant Desanti and Althusser, for historiographical reasons, but for philosophical reasons as well: their philosophical attitude – regardless of its conspicuous shortcomings – remains persuasive. Peden’s introduction adequately narrates Cavaillès’ biography while demonstrating the importance of the concept of necessity in Cavaillès’ work and elaborating upon his position vis-à-vis phenomenology.

Naturally, this is not a perfect translation, and there are choices made by the two translators that are questionable. For example, Peden and MacKay have chosen concatenation as a translation of enchaînement. They choose this word to stress the conceptual continuity between Cavaillès’ philosophy and that of Spinoza and Descartes, but Cavaillès probably picked up this word from Brouwer’s work on the concept of rijen, which is usually translated into English by the word sequences. Footnotes clarifying the obscure references would also have been helpful – especially given the exceptional difficulty and sometimes even obscurity of Cavaillès’ thought.

Still, this new translation is a great opportunity to re-engage with Cavaillès’ treatise. It opens up the possibility of creating a moment that adheres to his vision. A philosopher, whose work breathed cosmopolitanism, and who already at the age of 26 argued in a review of The Second Davos University Conference (2021) that ‘any limitation involves a privation: like those fulgurations with which Leibniz’s God engendered the monads, it is the same spiritual universe that is expressed by French rationalist reflection and German phenomenology’ is one that deserves to be read outside of a small circle of specialists in French epistemology (10). Cavaillès always thought that ‘rapprochement’ between particularisms within philosophy is part of the road to progress (9). For him, it was ‘obvious that they will benefit from coming out of their splendid isolation (like two inland seas), to open up between them channels of communication that will procure for both of them greater movement and fecundity’ (10).

Jean Cavaillès: On the Logic and Theory of Science

On Logic and the Theory of Science Book Cover On Logic and the Theory of Science
Jean Cavaillès. Introductory notice by Georges Canguilhem and Charles Ehresmann. Introduction by Knox Peden. Translated by Translated by Knox Peden and Robin Mackay
Urbanomic/Sequence Press
Paperback $18.95

Reviewed by: Massimiliano Simons (Ghent University)

Why read an obscure, enigmatic and technical treatise on philosophy of science by a half-forgotten philosopher of mathematics, let alone translate it? It seems that there are plenty of reasons to do so. The work of Jean Cavaillès (1930-1944), and especially his final work Sur la logique et la théorie de la science, is typically seen as the starting point of a ‘philosophy of the concept’. Together with Gaston Bachelard, Georges Canguilhem and Michel Foucault, Cavaillès is labeled as one of the main representatives of the French tradition of historical epistemology.

The project of a philosophy of the concept mainly gained fame due to Foucault, who popularized it in his foreword to the English translation of Canguilhem’s The Normal and The Pathological in 1978. Here he claims that to understand Canguilhem, one needs to fall back on the work of Cavaillès. Taking Husserl’s Paris 1929 lecture series as their starting point, phenomenology was developed in France in two radically different ways. On the one hand there is the well-known existential phenomenology, starting with Sartre’s ‘Transcendence de l’Ego’ (1935). But on the other hand there was Cavaillès, who put Husserl’s philosophy of science and mathematics at the center. According to Foucault, these two opposing phenomenological projects shaped 20th-century French philosophy:

It is the line that separates a philosophy of experience, of sense and of subject and a philosophy of knowledge, of rationality and of concept. On the one hand, one network is that of Sartre and Merleau-Ponty; and then another is that of Cavaillès, Bachelard and Canguilhem. In other words, we are dealing with two modalities according to which phenomenology was taken up in France, when quite late – around 1930 – it finally began to be, if not known, at least recognized. Contemporary philosophy in France began in those years. (Foucault 1978, 8)

The source of this ‘philosophy of the concept’ lies in the last few, rather enigmatic pages of Cavaillès ultimate work, here delivered in a new translation by Robin Mackay and Knox Peden for Urbanomic Press. The notion itself is in fact only introduced in the penultimate line of the book: “It is not a philosophy of consciousness but a philosophy of the concept that can yield a doctrine of science. The generative necessity is not that of an activity, but of a dialectic.” (p. 136) The book itself, which is both dense and short, is mainly a critique of the existing philosophies of science in early 20th-century philosophy with a focus on Kant, Carnap and Husserl. Only in the final pages Cavaillès makes some suggestions on what his alternative would be. For sure, Cavaillès intended to develop this alternative elsewhere, perhaps in the intended introduction he wanted to write. These plans did not materialize due to his early death.

Nevertheless, his promise of an alternative to the ‘philosophy of consciousness’ was taken up in French philosophy, in the form of a mythology around the figure of Cavaillès. When I say ‘myth’ I do not so much mean ‘wrong’ or ‘false’, but first of all that it functions as a myth. This means that the truth value of the myth is secondary to its effects – which have been plenty in the self-understanding of a number of French philosophers. The myth consists of three parts: (1) Cavaillès’ essay contains a set of devastating arguments against Husserlian phenomenology, making any phenomenological philosophy untenable; (2) Cavaillès replaced phenomenology with his own alternative, a philosophy of the concept; and (3) this alternative boils down to a form of Spinozism. Let us have a closer look at these three components of this mythology.

The first part is that Cavaillès’ work contains a number of knock-out arguments against Husserlian phenomenology. The final part of the book indeed deals with Husserl’s philosophy of science, as developed by the latter in Formale und transzendentale Logik (1929). Though Cavaillès formulates numerous criticisms, two main objections stand out: the issue of incompleteness and the dilemma of Cavaillès.

The incompleteness issue concerns Husserl believe that it is both possible and desirable to develop a fully-formalized mathematics in the line of David Hilbert’s formalism. That entails that it is capable to articulate and prove its own completeness: any true statement that can be articulated within the formal axiomatic system concerning its object of research can also be proven within that system. And though a common belief when Husserl’s book was published, a few years later it was radically shattered when in 1931 Kurt Gödel published his incompleteness theorems, showing that Hilbert’s program was impossible. Cavaillès was one of the first who saw the consequences of Gödel’s theorems for the Husserlian project, since it too relied on Hilbert’s program, endorsing its ideal of completeness as a central aspect of the phenomenological logic:

For we are familiar with Gödel’s result: any theory containing the arithmetic of whole numbers – which is to say basically any mathematical theory – is necessarily non-saturated. […] For the Husserlian conception of logic and mathematics this affair is particularly serious. In the first place, the very notion of a theory that can be fully dominated and isolated can no longer be maintained. (pp. 128-129)

A second issue consists in a fundamental dilemma that Cavaillès presents to Husserl. The latter aims not only for mathematical completeness, but also for a foundation of science that is both transcendental and absolute. Husserl had the ambition to ground all logical norms in the transcendental subject and its subjective acts. But simultaneously, Husserl hoped for an absoluteness of these norms: they cannot be questioned or relativized in any way. For Cavaillès the trouble arises if one combines both claims: if logical norms are constituted through subjective acts, these acts themselves call for a set of norms to ground them. But these underlying norms would in turn demand a foundation in subjective acts. To avoid an infinite regress, Husserl has to choose between the transcendental and the absolute character of his project. Hence the dilemma of Cavaillès: “If transcendental logic truly grounds logic then there is no absolute logic (i.e., a logic governing absolute subjective activity). If there is an absolute logic it can draw its authority only from itself; it is not transcendental.” (p. 120)

Similar to Husserl and Hilbert, and many other early 20th-century philosophers and scientists, Cavaillès was concerned with the new scientific developments, provoking a foundational crisis of mathematics: if radical historical transformations of mathematics were possible, what then was the foundation of rationality, mathematics, science? In a typical French manner, Cavaillès searched for the answer not in the atemporal, but in the historical: mathematics was rational not despite, but because of its history. The normative force, required to elevate mathematics above contingency, was to be found in its historical developments, where each new result bolstered the past results, but also provoked the next steps. In his primary thesis Méthode axiomatique et formalisme, Cavaillès would define understanding in a similarly dynamic way: “to understand is to capture the gesture, and to be able to continue it” (Cavaillès 1994, 186). Mathematics, and science in general, is understood, not so much as a set of thoughts, but rather in terms of gestures, which Cavaillès often referred to, somewhat misleadingly, under the banner of ‘experience’ (see Cortois 1996).

While terms such as gesture and experience suggests a philosophy of consciousness, this is countered through the third part of the mythology: Spinozism. Cavaillès was the face of a revival of interest in Spinozism, again seen as the alternative to phenomenology. In the words of Gilles-Gaston Granger, another proponent of this myth, it came down to “Jean Cavaillès or the climb to Spinoza” (Granger 1947). Cavaillès, sive Spinoza. The Spinozist reading it provided must have indeed sounded as music in the ears of the anti-humanist turn in the 1960s. Cavaillès, according to this reading, “set out to develop a philosophy without a subject” (Canguilhem 1994, 686).

We thus have a philosophy of science seen from the perspective of gestures. But these gestures are not grounded in a transcendental subject, but, following Spinoza, in the effective development of the successive theoretical concepts. The legitimacy of the concepts is found in these concepts themselves, in the normative force by which they call forth, by a form of necessity, one another. It is in this sense that another famous passage of the book is typically read:

Yet one of the essential problems for the doctrine of science is precisely that progress cannot be a mere increase in volume by juxtaposition, the prior subsisting with the new, but must be a perpetual revision of contents by way of deepening and erasure [rature]. What is after is more than what was before, not because it contains it or even because it extends it, but because it exists from it necessarily and bears within its content the singular mark, each time, of its superiority. There is more consciousness in it – and not the same consciousness as before. (pp. 135-136)

As a result, and especially from the 1960s onwards, Cavaillès’ work was used in French philosophy as an argument for the obsolescence of phenomenology. For instance, when Sartre attacked Foucault’s Les mots et les choses as a reactionary work, Canguilhem responded by invoking the authority of Cavaillès:

Cavaillès assigned the phenomenological enterprise its limits even before that enterprise had exhibited its unlimited ambitions – even in France itself, which is to say, with a certain lag – and he assigned, twenty years in advance, the task that philosophy is in the process of accepting today – the task of substituting for the primacy of experienced or reflexive consciousness the primacy of concepts, systems, or structures. (Canguilhem 1994, 92)

This mythological authority similarly found its way in to the work of many prominent French scholars, ranging from Jean-Toussaint Desanti, Gilles-Gaston Granger, Étienne Balibar to Alain Badiou. Despite the lack of any substantial elaboration by Cavaillès’ of what this philosophy of the concept entailed, his work was nevertheless used as a shovel to bury the philosophies of the past, most notably phenomenology and existentialism. Cavaillès’ alternative was indeed often quite easily equated with the structuralism and anti-humanism of the 1960s. These ideas not only inspired Canguilhem or Foucault, but were central to the Marxism of Louis Althusser as well, who mobilized Spinoza to purge Marxism from any form of Humanism. When Althusser, in his later self-criticisms, turned his gaze to his previous work, he could proudly proclaim that he was no structuralist: “We were guilty of an equally powerful and compromising passion: we were Spinozists.” (Althusser 1976, 132)

But Cavaillès’ biography gave this Spinozism an additional, political dimension. Similar to his friend Albert Lautman and Canguilhem, Cavaillès joined the resistance. While Canguilhem survived, both Cavaillès and Lautman tragically died. In the case of Cavaillès, he was first arrested in Narbonne in 1942, by the French police and ended up in a prison camp in Montpellier. It was during this imprisonment that he wrote this book, which partly explains the dense character of the text and the often liberal quotations, since Cavaillès was restricted in time and resources (though Lautman brought him several books). But with the manuscript in hand, he soon escaped from the prison camp though, due to betrayal, he was arrested again in August 1943 and eventually shot. The book On Logic and the Theory of Science was thus only published posthumously in 1947, by Georges Canguilhem and the mathematician Charles Ehresmann, who also picked the generic title for the book. In a letter of 1941 to Brunschvicg, Cavaillès announced that he was writing a work called L’expérience mathématique, while to Canguilhem and Ehresmann he spoke of a Traité de la logique. The truth seemed to be somewhere in between.

This political dimension of Cavaillès’ biography has been mobilized extensively in this mythology. Raymond Aron, who was a good friend of Cavaillès, later reported how Cavaillès entrusted to him in 1943 that “I am a Spinozist. I believe that we are seizing the necessary everywhere. The necessary in the sequences of mathematics, the necessary even in the stages of mathematical science, the necessary also in this struggle that we lead.” (quoted in Canguilhem 1976, 31) Or, in a variation that Aron cites in his own preface to Cavaillès’ Philosophie mathématique: “I am a Spinozist, we must resist, fight, face death. This is what truth and reason demand.” (Aron 1962, 14) Philosophers such as Canguilhem or Foucault did not hesitate to use this political activism against their opponents. In the same reply of Canguilhem to Sartre, he immediately added:

Shot by the Nazis for his Resistance activity, Cavaillès, who called himself a Spinozist and did not believe in history in the existential sense, refuted in advance – by the action he felt himself impelled to undertake, by his participation in the history that he lived out tragically until his death – the argument of those who seek to discredit what they call structuralism by condemning it to generate, among other misdeeds, passivity in the face of reality. (Canguilhem 1994, 92)

Foucault, in a similar vein, invokes this image in an interview in the 1980s, when he was focusing on Greek philosophy and techniques of the self:

The key to the personal poetic attitude of a philosopher is not to be sought in his ideas, as if it could be deduced from them, but rather in his philosophy-as-life, in his philosophical, life, his ethos. Among the French philosophers who participated in the Resistance during the war, one was Cavaillès, a historian of mathematics who was interested in the development of its internal structures. None of the philosophers of engagement – Sartre, Simone de Beauvoir, Merleau-Ponty – none of them did a thing. (Foucault 1984, 374)

It is thus this triple mythology – Cavaillès burying phenomenology, replacing it with a philosophy of the concept, inspired by Spinoza – that still motivates many philosophers to take up this otherwise challenging and technical treatise on the philosophy of science. The fact that this book is now translated in English (again) testifies to a similar growing interest in the Anglo-American world. There has indeed been a booming cottage industry of Anglophone papers dealing with Cavaillès’ philosophy of the concept, and its criticisms of Husserlian phenomenology (e.g. Hyder 2003; Thompson 2008; Peña-Guzmán 2020). Most of this literature tends to take over this mythology, though often stressing more continuity with phenomenology – an element already found in Foucault. The most exemplary case, perhaps, is an earlier book by Knox Peden, who helped realize this novel translation of Cavaillès and provided it with a helpful introduction. In his Spinoza Contra Phenomenology (2014) Peden repeated this mythology of how Cavaillès is the source of an anti-phenomenological tendency in France, continued by Bachelard, Desanti, Althusser and Gilles Deleuze.

Ironically, while this productive mythology is spreading in the Anglophone world, it is more and more problematized in France. The last decades of scholarship on Cavaillès have further substantiated a number of doubts concerning this triple narrative. First of all, the central role of Spinoza have been questioned, or at least completed with an acknowledgment that Cavaillès’ philosophy of the concept was inspired by other authors as well, such as Hegel (e.g. Sinaceur 2013).

The second main question is whether Cavaillès’ criticisms of Husserl are indeed as devastating as often portrayed. For instance, the young Jacques Derrida already tried to defend Husserl’s project against Cavaillès’ use of Gödel. In his master thesis on Le problème de la genèse dans la philosophie de Husserl (only published in 1990), he suggested that completeness is merely a kind of regulative ideal for Husserl, one that does not need to be realizable. Another option is offered by the daughter of Gaston, Suzanne Bachelard (1957) who suggests that there are multiple notions of completeness at work in Husserl’s philosophy, and that only some of them were refuted by Gödel. Hence, Husserl’s project can remain meaningful, even if one acknowledges the incompleteness theorems.

As part of the secondary literature has noticed, Cavaillès is at many points not that far off from phenomenology itself. It could thus be read, not so much as the destruction, but as a transformation of phenomenology. This is also announced in the lines immediately following Cavaillès’ dilemma: “Perhaps subsequent phenomenological investigations will allow us at least to contest such a brutally posited dilemma.” (p. 120) And to his credit, Peden seems to follow this suggestion in his introduction, playing down his earlier claims in Spinoza contra Phenomenology, and acknowledges that “it is both anachronistic and an overstatement to suggest that there was anything anti-phenomenological about Cavaillès’s work in its original conception. Moreover, criticizing Husserl for his errant steps is par for the course in the phenomenological tradition and Cavaillès is no exception to this tendency.” (p. 11)

And indeed the work of Cavaillès is a reminder of an alternative way phenomenology could have been developed in France, one not focused so much on anthropology and daily experience, but one that continued the Husserlian ambition to explore science in a phenomenological manner. In fact, this tradition exist, but not so much associated with a philosophy of the concept, but rather with authors such as Suzanne Bachelard, Trần Đức Thảo and Jean-Toussaint Desanti. Each in their own way attempted to use phenomenological methods to analyze the methods and products of science.

But even such a reappraisal of Cavaillès as a phenomenologist still risk to fall for another form of anachronism, as if phenomenology was the dominant and only philosophy around in France in the 1930s. This is indirectly suggested by Peden’s introduction (as well as most other Anglophone literature), ignoring Cavaillès’ interactions with other forms of philosophy of science. In the secondary literature, the motivation to focus on phenomenology seems to be one of relevance: given that Cavaillès is nowadays anachronistically classified as continental philosophy, the audience expects a focus on Husserl, not David Hilbert or Rudolf Carnap. This is somewhat surprising, since most of Cavaillès’ essay is focused on other theories, ranging from Kantianism to Logical Positivism. What is therefore perhaps missing in the introduction of Peden, is a sketch of these debates as well.

Moreover, in its current form, the book risks to fall prey not only to a form of anachronism, but also to a typical Anglophone tendency to canonize. The danger is not only to forget minor philosophers (a fate that Cavaillès shared for a long time), but also to immediately canonize newly discovered philosophers in an abstract, contextless hall of fame. This leads to abstract discussions where Cavaillès is compared to Spinoza, Kant, Husserl and Heidegger in a ahistorical fashion, as if they were all part of an eternal and continuous philosophical debate. This tends to forget that the history of philosophy is often more fragmentary.

First of all, it is necessary to ask how the work of the ‘great’ philosophers reached Cavaillès: who introduced him to Spinoza or Kant? The main interpreter of Kant and Spinoza in the early 20th-century was Léon Brunschvicg (1869-1944), supervisor of, among others, (Gaston) Bachelard, Cavaillès, Lautman and Aron. Brunschvicg was the most influential French philosopher at that time, with the possible exception of Henri Bergson (see Terzi 2022). But both Brunschvicg and Bergson were two very divergent products of the French tradition of spiritualism, the specific way how Kant was taken up in France, with a stress on the faculty of judgment and the notion of reflexivity. Though originally opposed to scientific philosophy, it transformed itself at the end of the 19th century, under the name of reflexive analysis (analyse réflexive), represented by authors such as Jules Lagneau and Jules Lachelier, in a Kantian philosophy that developed an interest in science as well, exemplified by the work of Émile Boutroux and Brunschvicg. It was this French Kantianism that fundamentally shaped the thought of Bachelard, Cavaillès and Canguilhem.

Being a clear form of subject-centered philosophy, it is most likely that Cavaillès’ attacks on a ‘philosophy of consciousness’ are not merely aimed at the new, and at that time in France still mostly ignored movement of phenomenology, but at French spiritualism as well. From this angle, the fact that he starts his book with Kantianism appears in a new light, and Cavaillès does extensively engage with the work of his supervisor, Brunschvicg (59-61). Therefore the claim that the philosophy of the concept came into being through a confrontation with phenomenology might be misleading. Quite telling, when Foucault later published a French version of his introduction, he left phenomenology out of the picture and broadened his claims: “Without doubt, this cleavage comes from a long way and we could trace it back through the 19th century: Bergson and Poincaré, Lachelier and Couturat, Maine de Biran and Comte.” (Foucault 1985, 4)

Such a broader history of the philosophy of the concept raises a number of additional questions, well-articulated by Cassou-Noguès and Pascale Gillot (2009): is the philosophy of concept a normative project, to be realized in a future philosophy, or a descriptive claim, referring to an eternal and recurrent constant in the history of philosophy? And against what is a philosophy of the concept precisely opposed? Too often terms such as consciousness, subjectivity, experience and meaning are simply used interchangeably in these often rash oppositions. It becomes especially difficult once one acknowledges that several of the early protagonists of the philosophy of the concept, such as Gaston Bachelard, Alexandre Koyré or the early Canguilhem, defended philosophies that had a clear place for the subject, exemplified perhaps best by Bachelard’s ‘new scientific spirit’ (Bachelard 1934). Only after the Second World War did the anti-humanism and anti-psychologism, that are typically associated with the philosophy of the concept, become dominant.

The originality of Cavaillès resides in the fact that his philosophy was indeed one of the first French philosophies who did – but never as radical as later generations would have it – take a distance from a philosophy of science centered around the subject. Cavaillès’s motivations to do so most likely were linked to the fact that he was one of the first in France to really engage with the new German developments in logic and philosophy of science. But again, it would be misleading to simply assume that this was bound to happen and that France was simply one of the last resisting strongholds doomed to fall for the new logic. The real history of philosophy of science is more contingent. That these developments would become so central for philosophy of science’s self-identity was never a necessity. Cavaillès’ fate could equally have been one of complete oblivion.

This leads us to our second correction of the mythology: there was also an atmosphere of complete ignorance and even dismissal of what was going on in philosophy outside of France. Though it was Brunschvicg who co-invited Husserl to Paris in 1929, he was not that interested. He did not even attend his lectures, but only met Husserl a few days later, when the latter went to the doctoral defense of Alexandre Koyré (who had studied with Husserl). Gaston Bachelard was similarly absent. It highlights how far apart philosophical worlds at that time were.

Cavaillès’ interest in and familiarity with German philosophy was rather exceptional at that time. In 1930-1931 he would stay in Germany on a Rockefeller scholarship to study German Protestantism, during which he met Husserl. He also attended the infamous Davos debate between Cassirer and Heidegger (see Cavaillès 1929) and the Wiener Kreis Vorkonferenz in Prague in 1934, where the Vienna Circle presented itself to the international philosophical scene for the first time (see Cavaillès 1935). Though Brunschvicg and Bachelard were invited, they declined. This highlights another perhaps underappreciated dimension of Cavaillès book, namely that the main perceived threat for Cavaillès was perhaps not so much phenomenology or French spiritualism, but the new movement of logical positivism. More than phenomenology, logical positivism challenged French philosophy, even at home. In 1935, logical positivism held its first international conference in Paris. And despite attempts by French representatives of logical positivism, such as Louis Rougier, to invite Brunschvicg, Bachelard and Cavaillès, most French philosophers responded with indifference and hostility (see Dewulf and Simons 2021). French philosophers of science, exemplified by Brunschvicg, had a distaste for logic, rejecting the idea that science and mathematics could be reduced to them.

Again Cavaillès was the exception in taking this movement seriously. But again this engagement should not be simply understood as the moment when the great lessons of German and British philosophy – Cavaillès discusses Russell and Wittgenstein as well – finally seeped into French philosophy. Cavaillès absorptions of these developments was one that immediately also digested them in order to produce something new. Cavaillès was not the only to do so. In fact, in 1938 Rougier reported to Hans Reichenbach how, in response to the 1935 conference, French philosophers were closing ranks and aimed for a counteroffensive. One first step towards this project was a gathering in September 1938 at Amersfoort in the Netherlands. Ferdinand Gonseth, the central organizer, would write about this conference: «We were quite a large group, from which I still recall Bachelard and his daughter Suzanne, Barzin, Bayer, Dupréel, Destouches, Paulette Février, Ebbinghaus, Tarski, Tatarkiewicz, and especially Jean Cavaillès.” (quoted in Emery 2000, 177-178)

Whether and in what form such a French counter-alliance would have taken shape could never be tested, since it was interrupted, literally during the conference, by incoming news: the first mobilization. Germany and France were at the brink of war. Cavaillès and some others, such Bachelard, decided to leave the conference and return to France. Bachelard returned to Paris and mainly start writing on poetics and imagination; Gonseth went back to Switzerland; both Cavaillès and Lautman joined the war effort and tragically died. No genuine French counter-alliance was formed, but for both Cavaillès and Lautman it was clear that the Vienna Circle was the adversary, and hence the reason why it plays a prominent part in the second part of this book. Especially Carnap was the opponent. While in captivity, Cavaillès would write to Lautman about Carnaps as “their old enemy of the Logische Syntax der Sprache” (quoted in Ferrières, 1950: 164).

Cavaillès’ On Logic and the Theory of Science is thus misleadingly technical in its content, as if what is at stake is nothing but highly specialized arguments in philosophy of science and mathematics. In truth, the stakes were higher and the book is a witness to a genuine struggle for identity: what is the task of philosophy of science? What is the correct way to approach scientific practices and their history? This little book is the battleground of all the major candidates at the beginning of the 20th century: spiritualism, logicism, phenomenology, logical positivism, intuitionism, formalism, and so on. Cavaillès did not pick sides, but attempted to develop his own alternative. In that sense, he practiced what he preached: to understand is to capture the gesture, and to be able to continue it. It is this aborted continuation that, though often shed of its contextual skin, has been the fertilizer for the philosophy of the concept in France and historical epistemology in general.


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Jean Cavaillès: On Logic and the Theory of Science, Urbanomic/Sequence Press, 2021

On Logic and the Theory of Science Book Cover On Logic and the Theory of Science
Jean Cavaillès. Introductory notice by Georges Canguilhem and Charles Ehresmann. Introduction by Knox Peden. Translated by Translated by Knox Peden and Robin Mackay
Urbanomic/Sequence Press
Paperback $18.95