Jean Cavaillès: On the Logic and Theory of Science

Ties van Gemert

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).

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