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
2021
Paperback $18.95
128

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
2021
Paperback $18.95
128

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.

Bibliography

Althusser, L. 1976. Essays in Self-Criticism. New York: Schocken Books.

Aron, R. 1962. «Préface.» In: Cavaillès, J. Philosophie mathématique, 11-16. Paris: Hermann.

Bachelard, G. 1934. Le nouvel esprit scientifique. Paris: Alcan.

Bachelard, S. 1957. La logique de Husserl: étude sur logique formelle et logique transcendantale. Paris: PUF.

Canguilhem, G.  1976. Vie et mort de Jean Cavaillès. Les Carnets de Baudasser: Villefranche d’Albigeois.

Canguilhem, G. 1994. «The Death of Man, or Exhaustion of the Cogito?» In: Gutting, G. (Ed.). The Cambridge Companion to Michel Foucault, 74-94. Cambridge: Cambridge University Press.

Cassou-Noguès, P., and Gillot, P. 2009. Le concept, le sujet et la science: Cavaillès, Canguilhem, Foucault. Paris: Vrin.

Cavaillès, J. 1929. «Les deuxièmes Cours Universitaire de Davos.»  In: Die II. Davoser Hochshulkurser. Les IImes Cours Universitaires de Davos du 17 mars au 6 avril 1929, 65-81. Davos: Kommissionsverlag, Heintz, Neu, & Zahn.

Cavaillès, J. 1935. «L’école de Vienne au Congrès de Prague.» Revue de métaphysique et de morale, 42(1), 137-149.

Cavaillès, J. 1994. Œuvres complètes de Philosophie des sciences. Paris: Hermann.

Cortois, P. 1996. The Structure of Mathematical Experience According to Jean Cavaillès. Philosophia Mathematica, 4(1), 18-41.

Derrida, J. 1990. Le problème de la genèse dans la philosophie de Husserl. PUF: Paris.

Dewulf, F., and Simons, M. 2021. «Positivism in Action: The Case of Louis Rougier.» HOPOS: The Journal of the International Society for the History of Philosophy of Science, 11(2).

Emery, E. 2000. «La notion de temps chez Bachelard et Gonseth.» In: Gayon, J. and Wunenburger, J. Bachelard dans le monde, 177-186. Paris: PUF.

Ferrières, G. 1950. Jean Cavaillès, un philosophe dans la guerre 1903-1944. Paris: PUF.

Foucault, M. 1978. «Introduction.» In: Canguilhem, G. On the Normal and the Pathological, xi-xx. Dordrecht: Reidel.

Foucault, M. 1984. The Foucault Reader. New York (N.Y.): Pantheon Books.

Foucault, M. 1985. «La vie : L’expérience et la science.» Revue de métaphysique et de morale, 90(1), 3-14.

Granger, G. 1947. «Jean Cavaillès ou la montée vers Spinoza.» Les études Philosophiques, 2(3/4), 271-279.

Hyder, D. 2003. «Foucault, Cavaillès, and Husserl on the Historical Epistemology of the Sciences.» Perspectives on Science, 11(1), 107-129.

Peden, K. 2014. Spinoza contra phenomenology: French rationalism from Cavaillès to Deleuze. Stanford: Stanford University Press.

Peña-Guzmán, D. 2020. «Not Phenomenology’s ‘Other’: Historical Epistemology’s Critique and Expansion of Phenomenology.» In: Apostolescu, I. (Ed.). The Subject of Phenomenology. Rereading Husserl, 355-380. Cham: Springer.

Sinaceur, H. 2013. Cavaillès. Paris: Belles Lettres.

Terzi, P. 2022. Rediscovering Léon Brunschvicg’s Critical Idealism. Philosophy, History and Science in the Third Republic. London: Bloomsbury.

Thompson, K. 2008. «Historicity and Transcendentality: Foucault, Cavaillès, and the Phenomenology of the Concept.» History and Theory, 47(1), 1-18.

Gregor Schiemann: Lebenswelt und Wissenschaft, De Gruyter, 2021

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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
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Jürgen Renn, Hanoch Gutfreund: Einstein on Einstein: Autobiographical and Scientific Reflections, Princeton University Press, 2020

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Rudolf Carnap: The Collected Works of Rudolf Carnap, Volume 1, Early Writings

The Collected Works of Rudolf Carnap, Volume 1, Early Writings Book Cover The Collected Works of Rudolf Carnap, Volume 1, Early Writings
Rudolf Carnap. Edited by A.W. Carus, Michael Friedman, Wolfgang Kienzler, Alan Richardson, and Sven Schlotter
Oxford University Press
2019
Hardback £70.00
528

Reviewed by: Flavio Baracco (Institut Wiener Kreis)

After the complete collection of the published works of Rudolf Carnap (1891-1970) was accepted to be published by Oxford University Press in 2016, the long-awaited first volume of the 14-volume edition of the Collected Writings of Rudolf Carnap has been finally published. This volume represents the first ever English translation of Carnap’s early writings published from 1918 through 1926, before Carnap moved to Vienna becoming one of the leading figures of the Vienna Circle. Carnap is rightly considered one of the most influential philosophers of the twentieth century. He made contributions in many areas, from the philosophy of science to the philosophy of logic, always stressing the need for a critical assessment of the role logic, mathematics and philosophy should play in scientific knowledge. His works played a key role in the development of Logical Empiricism; one of the main sources of what would become analytic philosophy. Although in the present day a fruitful dialogue between analytic philosophy and other philosophical traditions is not always easily achievable, at that time rather different philosophical perspectives were coexisting. The perspectives shared a common cultural framework and, most importantly, they were used to profitably interact with each other in a way that has since become increasingly difficult and Carnap’s early writings are a perfect example of this. Carnap was an eclectic intellectual whose interests embraced different philosophical ways of thinking to such an extent that his multifaceted interests appeared to some as objectionable or even inconsistent, as he recalls in his autobiography. However, he was proud to claim that he acquired valuable insights from philosophers and scientists of ‘a great variety of philosophical creeds’. Carnap’s early writings indeed shows a clear influence of the main philosophers usually regarded as belonging to the analytic tradition, such as Frege and Russell, but Husserl’s phenomenology and many neo-Kantian thinkers such as Natorp and Cassirer play an important role as well. These essays  represent a fundamental resource for both Carnap scholars and historians of analytic philosophy. Firstly, these writings make possible a better understanding of Carnap’s thought and its development since the early years and, secondly, they shed some light on the origins of analytic philosophy and the multi-faceted nature of the cultural framework around  that time.

I wish now to make a few general considerations on the editorial work. First of all, let’s say the present volume represents an outstanding work in Carnap scholarship both for its great attention to detail and for its richness in several in-depth analyses that furnish all the historical and mathematical background needed to understand Carnap’s writings. The volume is the final outcome of the work of many people and the editors present an  overall picture of all those who have  contributed to the  project. The volume begins  with a brief chronology of Carnap’s life followed by an Introduction edited by Carus and Friedman which presents  an exhaustive overview of the essays that  follow. The editors show the original German alongside the English translation and at the end of volume they accurately report any minimal changes they have made with respect to the original text. Each essay is followed by a section giving further information that carefully helps the reader to contextualize and understand the text, and in places,  the editorial notes are impressively accurate. The editors indeed make  extensive use of Carnap’s Nachlass to furnish us with a clear representation of Carnap’s view. Although, reference to an English translation of much of the literature quoted in the final bibliography would have been useful to the reader. The editors accurately report the corrected bibliographic information for all items cited in Carnap’s texts, but they do not indicate whether  an English translation of each item is available . As  the present volume is mainly addressed to an English audience, this would have been useful even though  it would have resulted in a longer bibliographical list. Finally, I would report a misprint at page 189: towards the end of the page the editors refers to note mm (twice), but it should be note ll. In the following I will briefly show the content of the different essays and give a few remarks on the editorial work on these texts whenever appropriate.

The first essay is entitled Völkerbund – Staatenbund and depicts a young Carnap in his twenties engaged in the social-political life of his country towards the end of World War I. At that time Carnap was actively engaged with the German Youth Movement, particularly the parts of the movement politically engaged against the war, and this text represents his contribution to the first issue of the left-wing political newsletter Politische Rundbriefe, published by Karl Bittel in October 1918. This brief text should have been followed by another text where a few critical considerations on the German’s defeat in the war were addressed; however, this second text was never published. However, in the  Introduction the editors sketch the content of both texts and we can then see how they present  an overview of Carnap’s political world view at that time. According to Carnap, politics is not to be understood in a narrow sense, rather  it refers to everything that has ‘some connection with the public social life of people’. As the editors suggest, this view of politics underlies Carnap’s philosophical work for most of his life, especially with respect to the role that reason, and more specifically ‘scientific’ reasoning should play in a society or a community where all the activities should be regulated and so removed ‘from the realm of chaotic whim’ and subordinated ‘to goal-oriented reason’. On the contrary, an excessive contemplative, quietist, or even mystical approach of mental life, not properly balanced by a politically active life is instead suggested to be one of the main reasons for Germany’s guilt for causing the war. This text represents an important resource in order to understand the interconnection between the political and philosophical reflections that were co-existing in Carnap’s philosophy and more generally, in the ambitious and multi-faced cultural phenomenon represented by the Vienna Circle.

In Wer erzwingt die Geltung des Naturgesetzes? Carnap reviews Hugo Dingler’s Physik und Hypothese where the author defends a conventionalist account of the primary laws of nature. Carnap acknowledges Dingler’s philosophical view as one of the most important influences on his own  thought. In 1920 Carnap even considered writing a doctoral dissertation under Dingler’s direction at the physics department in Munich, and a joint publication was also planned till September 1921. Despite several disagreements, Dingler remained an important influence Carnap’s writings in the early 1920s. At the very beginning Carnap asked himself a question: what if someone comes along and claims that laws of nature are matter of free decision? That’s exactly the kind of question  that Dingler’s book seeks to address. Dingler holds that nature can neither impose a particular choice, nor ever contradict our stipulations, but we are free to choose the primary laws of nature; the spatial and causal laws. Carnap admits that a view of this sort appears  odd, and he is reluctant to  agree with Dingler, (especially with respect to Dingler’s rejection of Einstein’s general theory of relativity), but he proudly claims that this book ‘clears the ground on which an examination of the foundations of physics, and in particular the theory of relativity, could rest’. The present essay is an important resource in order to better understand the genesis of  very distinctive Carnapian notion, i.e. Carnap’s conventionalism. This notion is clearly influenced by Dingler’s view on the conventional nature of the laws of nature that Carnap identifies as critical conventionalism, thereby distinguishing it from Poincaré’s notion of conventionalism. According to Carnap, Poincaré’s conventionalism relies on a free choice that is completely arbitrary, whereas Dingler’s view holds that our choices can be uniquely determined by a certain principle of maximal simplicity. Carnap favours Dingler’s conventionalism over Poincaré’s account and  will reformulate Dingler’s criteria of simplicity in later years. Carnap’s early conventionalism then seems to find its roots in a critical reformulation of Dingler’s conventionalism. Moreover, this essay shows us the  extent to which Carnap’s philosophical considerations rely on an in-depth knowledge of physics and scientific practice. This is  evident from his remarks on stipulations that rely on a critical analysis of physical knowledge, conceived not simply as a study of empirical data, but as a stratified and articulated measurement practice of empirical phenomena.

Der Raum is definitely a fundamental text for Carnap scholars. It is a lengthy and substantial book, it was largely written in late 1920, then submitted in 1921 to the philosophy department as a doctoral dissertation, and eventually published in Kant-Studien in 1922. The book aims to make things clear on the  debate taking place at the time regarding  the source of our knowledge of space and, especially, to what extent an objective knowledge of space could depend on experience. Carnap argues that the many different perspectives advocated by philosophers, mathematicians and physicists are contradictory as their differences rely on confusion over the different meanings of space. Der Raum then aims to show that a proper conceptual clarification of the different meanings of space and their interconnections can shed light on this debate and finally dissolve the controversy.

The first three chapters deal respectively with three different meanings of space; formal, intuitive and physical space, whereas the last two chapters focus on their interconnections and how each space is related to experience. The notion of formal space (formale Raum) is defined in terms of ‘relational or structural system’, i.e. a system fully determined by a set of formal axioms whose objects and relations (holding among them) are indeterminate and not related to any specific intuitive meaning. From this formal system we can obtain the spatial system once we substitute spatial elements (point, line, …) for their indeterminate correlation. Carnap refers to this formal system also in terms of “pure theory of relations” (reine Beziehungslehre). He further claims that the construction of formal space can be undertaken in a different way, which is the only path that ‘makes the complete construction of formal space possible, comprising all the special cases’. Starting from formal logic, i.e. the general theory of classes and relations, Carnap then briefly sketches this construction. He introduces the basic notions of ‘judgment’, ‘proposition’, ‘concept’, ‘relation’, and so on, until he defines the notion of ‘(ordered) series’ (natural numbers, real numbers, etc) and finally he arrives at the most general notion of formal space, called n-dimensional topological space and designated by Rnt. By imposing specific conditions on this structure, Carnap obtains the n-dimensional projective space Rnp and the n-dimensional metrical space Rnm. Starting from these formal structures we can obtain the three different intuitive spaces (topological, projective, metrical) by substituting their indeterminate elements with spatial elements. Carnap explicitly claims that ‘a relation of substitution (Einsetzung) holds between the theory of formal and that of intuitive space’, even though the connection between formal space and intuitive space is not so straightforward since postulates and generalizations also play a role in the construction of the order-structure of intuitive space (for any dimension). However, this kind of connection resembles Husserl’s distinction between formal ontology and regional ontology and Carnap is well aware of this and he explicitly refers to it in order to clarify his perspective. Moreover, Husserl’s Wesenserschauung is mentioned to specify the kind of intuitive knowledge involved, making clear that it is not to be confused with ‘intuition (Anschauung) in the narrower sense, focused on the fact itself’ as it pertains to the essential features that can be grasped within phenomena. In agreement with Husserl’s remarks on Kant’s conception of a priori, Carnap claims that the essential features of intuitive space turn out be ‘the synthetic a priori propositions claimed by Kant’. Therefore, the principles governing the formal space are analytic a priori, whereas the ones governing the topological space are synthetic a priori. These two kinds of space, however, are not enough to give a comprehensive picture of scientific knowledge of space. We need to introduce the physical space that represents the domain of synthetic a posteriori knowledge. The knowledge of physical space, however, other than being based on the empirical results of experiments, necessarily relies on conventions that are based on the choice of metric stipulation we decide to adopt. Carnap further claims that, if we wish, we could impose a different metric geometry and still obtain a physical space that is compatible with all our everyday and scientific observations, even though the final outcome might be far from straightforward. Physical space, therefore, relies on conventions but the choice of metric stipulation should be evaluated in terms of some criteria of simplicity that consider the overall description of nature.

Carnap’s Der Raum shows an impressive richness both from a philosophical and mathematical point of view. Carnap’s appendix ‘Pointers to the Literature’ contains substantial resources to historically contextualize many of the issues raised in the book. Starting from his adherence to the logistic approach of Frege and Russell, then going through the neo-Kantian perspectives of Natorp and Cassirer, on to Husserl’s phenomenology and Dingler’s conventionalism, Carnap’s Der Raum turns out to be a very interesting re-elaboration and combination of different philosophical perspectives. Moreover, the most important mathematical and physical literature of the time is seriously taken into account and the major works of Hilbert, Poincaré, Weyl, Riemann, and many others, are discussed and their results are assimilated into Carnap’s view. Several issues in Der Raum, therefore, should be enlightened by reference to the rich cultural framework that underlies this book. For instance, further investigation into the interconnections between Der Raum and Weyl’s Raum-Zeit-Materie would prove  very interesting and fruitful. Carnap explicitly makes reference to Weyl’s writings several times, and a comparison between Carnap’s and Weyl’s studies on space – the latter being clearly influenced by Husserl’s phenomenology – might shed light on the nature of Husserl’s influence on Der Raum. Similarly, further investigation into Carnap’s re-elaboration of Russell’s and Husserl’s perspectives on logic to construct formal space could be useful in order to clarify several aspects of Carnap’s later notion of rational reconstruction. Carnap’s notion of metrical stipulation is another example. A detailed analysis of Carnap’s account on stipulations could shed light on the development of his  later conventionalism. The editorial work on Der Raum (edited by Michael Friedman) successfully achieves a great deal of this task. It is extremely accurate and several in-depth analyses furnish the historical and mathematical background that a reader needs to properly understand the many issues contained in this book. The editor further includes Carnap’s marginalia (contained in Carnap’s own copy of Der Raum) in the editorial notes at the corresponding points which gives the reader a clearer picture of Carnap’s view on this specific issue.

However, a few critical remarks can be put forward. Friedman does not seem to capture the exact nature of the Husserlian framework underlying Carnap’s view nor how it relates to the neo-Kantian framework that – as Friedman rightly suggests – underlies Der Raum. In the Introduction (edited also by Carus), for instance, the editors charge Carnap with  confusion in respect to his conception of intuitive topological space, which ‘somewhat confusingly’ shares the status of conditions for the possibility of experience with formal topological space. This remark seems to underlie a misconception of Husserl’s philosophy. The introduction of phenomenology is definitely one major difference between the previous Masters dissertation of 1920 and the published version of Der Raum. The published edition of 1922, indeed, is a revisited version of the previous Masters dissertation that Carnap had written for the philosophy department in 1920. In the revisited version Carnap substitutes his previous conception of ‘pure geometry’ with ‘intuitive space’ and this very change marks a shift from a neo-Kantian notion of ‘condition for the possibility of experience’ to a Husserlian reinterpretation thereof. I do not mean that Carnap adheres completely to Husserl’s perspective, but his major interest in phenomenology relies exactly on the Husserlian reformulation of Kant’s synthetic a priori propositions in terms of regional axioms that belong to a certain regional ontology. It is precisely this notion of regional ontology that shapes Carnap’s notion of intuitive topological space, and more generally it is precisely the Husserlian distinction between regional ontology and formal ontology that shapes the overall Carnapian distinction between intuitive and formal space. Husserl’s transcendental phenomenology is a philosophical account that – by the introduction of the notion of categorial intuition (that later develops into the notion Wesenserschauung) – enables Husserl to speak in terms of essential structures intuitively given in a phenomenal domain and playing the role of regional axioms, i.e. conditions for the possibility of experience of this very domain. These regional axioms, moreover, are connected to their correlated abstract structures – free from any intuitive elements and belonging to the domain of formal ontology – by means of relations of formalization and de-formalization (categorical intuitions come into play again). These abstract structures, moreover, share the status of experience-constituting validity since they represent the categorical form of the essential structures governing the given phenomenal domain. Carnap’s intuitive topological space – shaping Husserl’s notion of regional ontology – does not share ‘confusingly’ the status of conditions for the possibility of experience with formal topological space, rather they both have this experience-constituting validity – even though in a different way – in agreement with Husserl’s perspective. Further remarks can be found in the editorial notes that do not seem to capture adequately the nature of the Husserlian framework underlying Der Raum. The editors rightly point out that Husserl’s phenomenology is essentially a descriptive science based on essential insight (Wesenserschauung), but they do not seem to ascribe the role of essences – grasped by Wesenserschauung – directly to the axioms of intuitive space. They designate these axioms as ‘describing the Wesenserschauung’ of our perceptual experience of objects in space, or as ‘codifying certain attributes of intuition’. These remarks seem to underlie that firstly, they keep distinct essences grasped by Wesenserschauung and the axioms describing them, and secondly, they do not ascribe to the axioms any intuitiveness by essential insight. Although the relation between a phenomenological description of a given phenomenal domain and the regional ontology characterizing the domain itself is a complex, multi-faced, and problematic field of phenomenological research, Husserl clearly states that they both have to investigated by Wesenserschauung. Therefore, the axioms themselves are intuitively given and they do not ‘describe’ or ‘codify’ an intuitive knowledge but, at most, we could say that in-depth phenomenological analysis can clarify their meaning-constitution.

It seems to me that this misconception of Husserl’s philosophy undermines their evaluation of Husserl’s contribution to Der Raum in several instances. However, the editors are right not to over-estimate Husserl’s influence on Der Raum over Carnap’s adherence to Kant’s philosophy or neo-Kantian thinkers. Der Raum is arguably a personal re-elaboration of several philosophical perspectives rather than a complete adherence to one specific account. It is not clearto what extent Carnap is fully accepting Husserl’s phenomenology in Der Raum, especially, with respect to the possibility to explore exhaustively a given phenomenal domain by Wesenserschauung in all its essential and stratified connections. Instead he seems interested in Husserl’s perspective only so far as it represents a philosophical account (with a Kantian flavor) within which it is possible – starting from the domain of empirical reality – to avoid the restrictions imposed by a neo-Kantian approach. This would enable him  to freely explore the ‘characteristic structures’ belonging to this domain as without it implies a contingent knowledge and laying the foundations for a structural objective analysis of experience.

Über die Aufgabe der Physik addresses the question of what should be regarded as a criterion for maximal simplicity within a physical theory. Two different possibilities are examined with the aim of clarifying the relevant aspects that should rule the choice between them, even though no decision between these two possibilities is suggested in the paper. This text is an important resource to better understand Carnap’s view on simplicity and stipulations within a physical theory and how they both are related to Carnap’s conception of scientific rationality.

In Dreidimensionalität des Raumes und Kausalität Carnap explores how we construct reality starting from a world of sense impressions. Carnap draws an important distinction between experience that exhibits only necessary formation – or first-order experience – and experience that is processed further – or second-order experience. This distinction echoes the previous one in Der Raum between the necessary topological form and the various metrical conventions that could be imposed on it. In the paper Carnap explores this specific issue in a wider perspective where his conventional view is elaborated in the light of Vaihinger’s pragmatic view. It is no coincidence that the paper was published in Annalen der Philosophie, regarded as the house journal of Vaihinger and his followers. Vaihinger argues that we are able to access only the ‘chaos’ of our world of sense impressions whereas the reality we construct is not genuine knowledge but is rather based on useful fictions that allow us to get things done and live in the world. Carnap agrees with Vaihinger as far as it concerns the role of fictions in constructing the reality, but he argues that such a construction is not completely arbitrary. Firstly, we face a first-order experience that exhibits a basic form of ordering, and secondly, certain kinds of logical connections can be established among fictions shaping second-order experience. The paper aims to show that the fiction of three-dimensionality of space and the fiction of physical causality ‘stand in a relation of logical dependence with each other’, and the former is conditioned by the latter. This text is especially important because it helps us to shed light on the development of Aufbau. The first draft of Aufbau dates back to early 1922 and it was completed in 1925. During these years we can observe an important shift: in the early phase (1922-24) Carnap distinguishes a fixed ‘primary world’ of immediate experience – in accordance with the text we are discussing – from a ‘secondary world’ (or ‘realities’) that could be constructed by quasi-analysis on this intuitive basis. However, sometime during 1924 the distinction between primary and secondary world was dropped. Further investigation of Carnap’s intellectual encounters during these years is required , but the present text is clearly an important resource to better understand the development of his thought from Der Raum to Aufbau, especially with respect to his changing perspective on the epistemic value of intuitive knowledge.

In Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit Carnap argues that statements about the topological structure of physical space can be reduced to statements about temporal or causal order. The paper needs a proper mathematical and physical background to be properly understood and Malament’s appendix satisfies this requirement. Malament gives a detailed reconstruction of Carnap’s account and he further discusses a number of mathematical problems suggesting how they could be fixed. This text is clearly an important resource for understanding Carnap’s efforts during these years not only in logic and philosophy of science, but also in physical and mathematical research of the time.

The last paper, entitled Physikalische Begriffsbildung, is an important paper written shortly before Carnap moved to Vienna in 1926. In the Introduction Carnap outlines what is science: an activity of collecting and organizing items of knowledge with the aim of subjecting the reality ‘to an ever higher degree of control’”. According to this pragmatic view of science, the task of physics is ‘to order perceptions systematically and to draw inferences from perceptions at hand to perceptions to be expected’. Carnap then explores thoroughly the hierarchical structure of physical concept formation, subdividing its formation into three main stages: qualitative stage, quantitative stage, and abstract stage. The present paper gives us an interesting overall picture of Carnap’s conception of rational reconstruction at the very moment when Carnap was on his way to the final version of the Aufbau. The editorial work (edited by Creath and Richardson) is again very accurate and detailed, although a few remarks on the comparison between Carnap’s Begriffsbildung and Weyl’s Begriffsbildung (as well as Weyl’s Konstitution) might have been useful, especially with respect to Carnap’s later conception of Konstitution.

But aside from these last considerations, the editors have done an excellent job firstly, in making all these texts available to English readers for the first time, and secondly, in making them more understandable thanks to their very rich in-depth analysis. This volume enhances the increasing English literature on the early young Carnap, which in turn provides a clearer picture of the development of logical empiricism and early analytic philosophy. The essays provide a fundamental resource to explore the multi-faceted cultural framework of the time where different philosophical movements were used to profitably interact with each other in a way that has become increasingly difficult in the later years. For all these reasons, the present volume is of considerable merit and should be of interest to Carnap scholars, historians of analytic philosophy and to Husserl scholars and researchers working at the intersection between the philosophy of science, logic and phenomenology.

Edmund Husserl: Logic and General Theory of Science

Logic and General Theory of Science: Lectures 1917/18 with Supplementary Texts from the First Version of 1910/11 Book Cover Logic and General Theory of Science: Lectures 1917/18 with Supplementary Texts from the First Version of 1910/11
Husserliana: Edmund Husserl – Collected Works, Volume 15
Edmund Husserl. Translated by C.O. Hill
Springer
2019
Hardback 88,39 €
L, 437

Reviewed by: Matthew Clemons (Stony Brook University)

In a passage (§56) from his 1929 Formal and Transcendental Logic, Husserl expresses frustration at a particular group of interpreters of his Logical Investigations. Fearing the specter of the historical-empiricist move that denies the objectivity of the ideal, these interpreters reject the phenomenological investigations in Volume II of the LI. This rejection  is based on the critiques of psychologism that Husserl provides in Volume I. Presumably, what the interpreters found to celebrate in the LI was its insistence that logical formations—e.g. judgments, proofs, theories—are not mental events, which secured the possibility of a purely formal logic. Their disappointment with the foray into the constitutive acts correlative to the logical formations in Volume II likely persisted in light of Husserl’s subsequent publications. Around the time of the publication of Ideas I (1913), Husserl admits to having cooled to formal logical investigation, preferring instead the examination of transcendental subjectivity.[1]

For this reason, Claire Ortiz Hill’s 2019 translation of Volume 30 of the Husserliana Series entitled Logik und Allgemeine Wissenschaftstheorie may come as a surprise to an English-speaking readership. The volume, with the English title Logic and General Theory of Science, consists of the final version of a series of lectures given by Husserl on the topic of formal logic, its bounds, fundamental formations, and its relation to the Idea of science in general. The lectures date from the Winter Semester of 1910/11 through Winter 1917/18, the same decade that saw the publication of his Ideas I and Ideas II. Given those dates, it would seem that, whatever his interest in the constitutive acts of logical formations, his interest in those objective formations themselves did continue.

The volume is divided into three sections with a series of appendices added to the main text. In Section I, Husserl is concerned with setting the bounds for formal logic. This is a preparatory step for the  formal logical investigations in Section II that seek to develop systematically a theory of the forms of meaning. Section III deals with the Idea of Science, which for Husserl includes formal logic but, as he outlines, encompasses more than just formal logic. The appendices are Husserl’s notes and additions to the lectures. In what follows, I give a brief overview of each of the three sections.

Setting the Bounds of Formal Logic (Section I)

The first section is entitled “Fundamental Considerations for the Demarcation and Characterization of Formal Logic.” Husserl begins the section with a series of reflections on the understanding, which, as the activity that sets norms for both the sciences and extra-theoretical life, serves as a leading clue for the scope of logic. Rather than reflecting on the acts of understanding, those “mental activities and achievements” (§1) at work in the norm-setting, we can inquire into the norms themselves, or the forms that the various acts of understanding imprint on their content. The work of logic, Husserl suggests, is to fix these forms conceptually and systematically.

However, before that work can get underway, it is necessary to distinguish understanding as norm-setting from understanding as a mental event. Interpreting the norm-setting activity of understanding as a mental event would result in subsuming logic under psychology, the science that deals with the “inner sphere.” Note that, just as in the earlier Logical Investigations and the later Formal and Transcendental Logic, Husserl is again careful at the outset to disentangle logical investigation from psychological investigation. The major difference between psychology and logic is that, while the latter is normative, the former is not. In other words, logic strives after normative laws by which to measure if purported knowledge is actually knowledge. The origin of the norms of logic lies in, in Husserl’s own words, “the ideal essence of acts of understanding and their contents” (§4), whereas the understanding figures in psychology only as a mental event to be explained according to natural, i.e., causal laws. One of the major consequences of this distinction is that the logical norms are unconditionally binding and discoverable regardless of any reference to factual, or empirical, existence.

Anticipating the controversy of his position (he predicts that he will be pejoratively dubbed a “Scholastic” or “mystic” (§4)), Husserl retorts that the psychologizing interpretation of logic falls prey to the prevalent naturalistic prejudice in the sciences. By naturalism, Husserl understands the rejection of any sort of any non-natural, i.e., non-empirical, non-spatiotemporal, objectivity. Thus, any ideal objectivity, be it logical norms, cardinal numbers, or self-evident statements is reinterpreted psychologically. In contrast, Husserl insists on the admission that Ideas are genuine objects that merely give themselves differently (“as eternal, selfsame, as non-temporal and non-spatial, as unmoved, as unchangeable” (§8)) than spatiotemporal objects.

This difference in position on the status of Ideas proves consequential for formal-logical investigation. On the one hand, Husserl identifies the failure to recognize Ideas as the basis of a series of errors propagated by traditional logic, a point substantiated more in Section II of the volume. On the other, acknowledging the genuineness of Ideas at the outset opens up an avenue of inquiry in formal logic, namely investigating according to ideal meaning forms rather than empirical contents. To that end, Husserl notes that in these lectures he is foregoing a noetic orientation, i.e., one that takes up the cognitive and related acts constitutive of logical objectivities, for a noematic one. To clarify what he means by a noematic orientation, he points us to a series of distinctions, beginning with that between knowing and known. The former is a cognitive act while the latter leads us towards the ideal. A parallel distinction between judging and judgment (§7) and another between naive judgment as directed at the state-of-affairs and judgment as proposition and Idea (§9-10) help to clarify. Judgments as ideal objects are importantly not determinate, therfore not empirical, and yet they have ideal properties (e.g., all judgments with the form of a contradiction are false). When the idea is made into an object of reflection, it becomes the basis of norms sought in logical investigation.

As far as the demarcation of formal logic goes, the introduction of the Idea of judgment places us in the terrain of apophantics, or the logic of affirmative statements. This harkens back to Aristotle’s original demarcation of pure logic, which he called analytics. Husserl sometimes adopts this term. It is worth noting that he employs several related terms synonymously throughout the lecture, namely analytics, along with pure logic, formal logic, and the mathesis universalis (more accurately, he uses these terms to emphasize different aspects of the same science). In contrast to Aristotle, Husserl’s own demarcation of analytics is not limited to affirmative statements. It includes an underlying level of investigation into more basic forms of meaning. This level both serves as a foundation for a second level of logic and also provides some crucial conceptual distinctions that allows for its expansion. It could be said that one of the ubiquitous features of Husserl’s thinking on formal logic is its effort at expansive unity. The second level of logic, for instance, is not only concerned with the logic affirmative statement (“A is b”), but also with its modifications (e.g. “It is possible that A is b”). Further, in a series of complexifications that occur at the second-level, Husserl further expands the notion of logic to include cardinal and ordinal numbers, sets, and eventually a third level. This third level, the highest of analytics, is the formal theory of manifolds, or the theory of theories (§47).

For Husserl, then, formal logic is a three-tiered science, connecting disciplines and Ideas that were once thought to belong to disparate sciences. Importantly, Husserl’s insistence on the genuineness of Ideas makes this possible. As ideal, the basic meaning forms that constitute the first-level of logical investigation and are the basis of the other two exhibit an ideal structure and conformity to law. These basic meaning structures can then combine in indefinitely many ways in accordance with their conformity to laws, allowing an ideal building up and out of formal logic that itself occurs with lawful regularity. Husserl compares this structure to crystals in that each form exhibits its own structure that is also taken up in the crystal system (§27 B).

The Systematic Investigation into Forms of Meanings (Section II)

If Section I concerns the demarcation of formal logic, Section II jumps into the discipline itself. Husserl’s strategy is to start with the most basic forms of meaning and, insofar as it is possible in a lecture-series, to obtain a systematic overview of the possible kinds. From there, he gradually builds his way up to propositionally simple judgments and beyond to more complex judgments, to inferences, and to theories. My own synopsis of the section is divided into two parts. First, following Husserl, I give a very general outline of the development from the most basic meaning components up to the highest tier of formal logic. Second, I indicate a handful of the concrete ways in which, as I stated above, Husserl imagines that traditional logic’s rejection of Ideas leads it astray.

The point of departure for the investigation of meaning forms is the ideal distinction between independent and dependent meaning (§20). Independent meanings are those which are capable of standing alone, i.e., complete propositions. Dependent meanings, on the other hand, are those that, although they may express something, intrinsically belong to an independent unit as a component. These dependent meanings cannot be put together in any half hazard way, but fall under fixed types governed by laws (e.g., in the proposition S is p, grammatically speaking, p cannot have any kind of meaning (§22)). Any basic component also admits of a conceptual distinction between syntactical form, which refers to its role within the proposition (e.g., the subject-form, object-form, predicate-form), and syntagma, or the “stuff” (§24), the content of the component. The phrase “ethical human beings,” for instance, can function as the subject-form in one case, the antecedent in a hypothetical in another, but in any case retains the same content, namely “ethical human beings.” A further, parallel distinction in the syntagmas between the nucleus-form (e.g. nominal-forms, or adjectival-forms) and the nucleus-stuff gives us the most basic components in our investigation of the meaning of forms. This last distinction is especially important because the nucleus need not contain any definite content and could instead be “an empty something.” For one thing, it allows for the entrance of generality, or universality and particularity. For another, formal logic, says Husserl, is characterized by this emptiness (§26 B), as this emptiness signifies its being ideal rather than empirical.

Equipped with the most basic meaning components, namely the syntagma, Husserl moves on to the basic forms of simple judgments. He arrives at that basic form by considering in what way the fewest syntagmata might unite to form a judgment. Similarly to Aristotle, he decides that the most basic form involves one nominal and one adjectival syntagma (S is p) (§28). This simple judgment-form is then the basis for another series of variations and complexifications. Of note, here, is his discussion of the effect of empty syntagma (§32), of plural judgments (S is p and/or n) as the origin of the Ideas cardinal numbers, arithmetic, and sets (§3437), and existential and impersonal judgments (§40). After the simple judgment-forms, Husserl turns to the propositionally complex judgment-forms (conjunction and disjunction) (§4142), following which is his introduction of modifications (e.g., possibility and probability). This latter topic is of particular note in that it is accompanied by an extended treatment of the Ideas of law, apodicticity, and analyticity (§4445). Husserl insists not only that analytic (apodictic) laws have been crucial in the investigations up to this point in apophantics, but that a proper conception of analyticity allows for the connection between formal logic, formal ontology, and mathematics to emerge (§46). Finally, Husserl turns to inference, whose ideal laws allow for the introduction of the third-level of formal logic, i.e., the theory of manifolds, or the theory of theories (§47, §54), a discussion which spills over into Section III (§4659).

That suffices for a general outline of Husserl’s thinking in Section II. Because he is insistent on the unity of what might seem, from the perspective of the history of logic, like disparate disciplines, it might already be visible in broad strokes how Husserl’s own account differs. Additionally, there are several, concrete, and persistent logical problems dealt with in the course of Section II. In general, if Husserl disagrees with logicians, it is on the grounds of their mistakingly rejecting Ideas, and so of not sufficiently recognizing the ideal as the guide in formal logical investigations. For instance, Husserl accuses logicians of conflating equivalence and identity (§29, §39, §48). Two judgments might be equivalent in their relation to a state-of-affairs, but not identical with regard to their ideal meaning form. Among the errors that Husserl identifies in this regard are:

  1. Traditionally, affirmative and negative judgments (S is p; S is not p) are thought to be coeval. But if analyzed according to their meaning-form, it seems that the negative is a modification of the affirmative, which must then be prior.
  2. Instead of recognizing the difference in meaning-form between determinative judgments and functional judgments (universal and particular judgments), traditional logic takes all judgments to be either universal, particular, or individual.

These are far from the only topics of interest that Husserl treats in Section II, but it suffices to give the examples mentioned above as an indication.

Reflections on the Idea of Science (Section III)

In Section III, the final section of the lecture, Husserl concludes the thorough, systematic investigation of the forms of meaning and begins to consider the relationship of the science of analytics to other theoretical sciences. By theoretical science, he means those that are not normative and practical and whose primary interest is explanatory. Theoretical sciences, insofar as they are applicable to any particular science without that particular science’s forfeiting its unique domain, comprise the general Idea of science. Analytics has priority because, insofar as it deals with those activities present in every science, it is operative in every science. But there are other sciences that can be included in the Idea of science as well, and even those that deal with a particular region of being can be included insofar as they deal with it in an a priori manner. Among these sciences are pure natural science, which deals with objectivity and spatiotemporal being in general (§61), the science of consciousness, both individually and communally (§63-64), and formal axiology (§61). The final chapter in the Section offers some reflections on noetics, which, as mentioned above, Husserl has set aside in these lectures in favor of a noematic analysis. Central in this chapter is the question of justification of knowledge and the relevant concepts of Evidenz and givenness.

Husserl, of course, says much more than I am able to relay here, but the above should suffice as direction for further inquiry. Those who do delve into the volume further will find it  readable, and well-edited and translated. As Ortiz Hill mentions in her introduction, that these are lectures make them clearer and more transparent than some of the writings published during Husserl’s lifetime. For any given point, Husserl offers a variety of examples, and approaches it from several directions. Further, Ortiz Hill provides a lucid translation of an already well-edited volume. There are a handful of pesky German terms that are difficult to translate, which she either alerts readers to or leaves untranslated. She decides on “presentation” for Vorstellung, but points to its ambiguity in Husserl’s writing (xliv-xlv)—Husserl himself also notes the difficult ambiguity of the term. I should also note that, in the case of terms like “nucleus-stuff,” the “stuff” is presumably translating Stoff, which more generally means material in German (der Stoff des Mantels—the material of the coat). Given that terms like “nucleus-stuff” are often contrasted with something formal, it might seem more appropriate to translate Stoff as material. However, Husserl does use the latinized Materie sometimes making it seem worthwhile to translate Stoff differently. Only in the case of the terms Geist and Gemüt do I hesitate with the translation. The former, she translates as “mind” (l), which might seem strange in the context of the discussion of community and culture in Section III. For Gemüt and its variations, Ortiz Hill employs adjectival expression with the word “inner.” Although I think this doesn’t quite capture the emotive connotation that translations like “heart” do, this term plays almost no role in the volume. The few passages in which it  could cause some confusion, such as its being contrasted with will and understanding at the beginning of Section I (§1), do not interfere with the trajectory of Husserl’s thought. Beyond these terms, there are a handful that Ortiz Hill leaves untranslated, e.g. Unsinn, Widersinn, and Evidenz. In each case, I appreciate the choice to leave the terms in their original German. In the case of the first two, no English equivalents readily suggest themselves that capture their contrast. In the case of Evidenz, the English cognate “evidence” suggests something like external proof, which is different than the “consciousness of fulfillment” that Husserl has in mind.

In closing, I offer a few words on the significance of the volume. For those primarily interested in Husserl or more broadly in phenomenology, the edition offers an interesting link between different periods of Husserl’s thought. Many of the topics that he addresses in Section II, for instance, harken backward to his Logical Investigations (which he himself notes on occasion) and also point forward to the concerns of Formal and Transcendental Logic (such as the preoccupation with the unity of disciplines thought to be disparate under the banner of formal logic). This is especially significant for those who, as I suggest above, accuse Husserl of abandoning formal analyses in favor of transcendental ones. For those primarily interested in formal logic, or in topics predominately discussed in analytic philosophy, the volume represents a significant overlap of concerns. In both the translator’s introduction and a review of the German edition, Ortiz Hill does a remarkable job at indicating the overlap and ultimate differences between Husserl and the school of thought that emerges from Frege and runs through Russell, Carnap, Hilbert, and Gödel.[2] At any rate, readers of all kinds may be surprised to find Husserl undertaking a systematic survey of formal logic in the decade of the 1910’s, and that makes the volume a welcome contribution to the scholarship.


[1] See Ursula Panzer’s “Einleitung” in the original German volume, quoted in Ortiz Hill’s “Introduction.”

[2] Ortiz Hill, Claire. “Review of E. Husserl, Logik Und Allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, Mit Ergänzenden Texten Aus Der Ersten Fassung 1910/11.” History and Philosophy of Logic, 1998.

Rudolf Carnap: The Collected Works of Rudolf Carnap, Volume 1, Early Writings, Oxford University Press, 2019

The Collected Works of Rudolf Carnap, Volume 1, Early Writings Book Cover The Collected Works of Rudolf Carnap, Volume 1, Early Writings
Rudolf Carnap. Edited by A.W. Carus, Michael Friedman, Wolfgang Kienzler, Alan Richardson, and Sven Schlotter
Oxford University Press
2019
Hardback £65.00
528