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Transforming Necessity:

From transcendental logic and back again


Though of historical interest for the reception of Husserl’s phenomenology in post-World War II France, the work of Jean Cavaillès retains its philosophical importance by virtue of its theme, namely the development of logic and its impact on the theory of science. Beginning with Immanuel Kant, proceeding through logical positivism and culminating with Edmund Husserl, Cavaillès demonstrates that as the conception of logic changes the notion of necessity in the theory of science is transformed. Ultimately, Cavaillès claims that logic must be transformed into a philosophy of the concept because only the necessity of a dialectic can describe the scientific progress that a theory of science is to explain. By contrast, I argue that the demand for the necessity of a dialectic is fulfilled by following the dialectic of sense described within transcendental logic.



Cavaillès’s analysis begins with Kant’s transcendental logic. For Kant, the logic is reducible to the a priori structures of consciousness and as such lacks any reference to objects. However, such a theory cannot be a body of knowledge, which by Kant’s account only arises from experience and consequently cannot be a theory of science (Wissenschaftslehre). According to Cavaillès, a Kantian philosophy of science finds its first expression with Bernard Bolzano.


In many ways, Bolzano sets the stage for further considerations of the relation between logic and theories of science. Cavaillès spells out this by pointing to a dual focus in Bolzano’s efforts toward developing a theory of science. Bolzano identified in science’s emphasis on demonstration a twofold impetus: the importance of the paradigm and the impact of theory. The paradigm points to the empirical impulse; for science, explaining and predicting events is central, and so one must look to the exemplar rooted in experience. However, because science is an explicatory enterprise, the impact of theoretical interpretation cannot be avoided. Science does not only observe the world; it makes sense of experience. Herein lays the tension and mutual influence between logic and theory of science. On the one hand, science must explain the travails of experience, that is its contingency, and consequently follow an empirical agenda. On the other hand, the theory of science seeks to explain the necessity of knowledge, and consequently focuses on logic and its role in governing rational thought. Cavaillès argues that this tension structures the two subsequent influential efforts toward explaining the connection between a theory of science and logic, namely logical positivism and Husserl’s transcendental logic. Cavaillès claims both efforts fail to resolve the tension.


In one sense logical positivism is wedded to the empirical: only that which can be directly experienced has meaning. However, in another sense, logical positivism pursues the theoretical impulse too far. Through the guise of analyticity logical positivism seeks to secure the source of necessity, yet does not thereby alleviate the strain redolent in Bolzano’s project. Logical positivism always relies upon the typical, which arrests how a thing is in its development, and so logical positivism’s appeal to the analytic cannot explain the interplay between the progressive nature of science and the necessity adhering to theory. Rather than proceeding directly to the theoretical, Cavaillès asks that philosophers tarry with the object of their investigation and look to the ontological, to ask how things are while keeping firmly in view the desire for necessity. To this end, Husserl’s analysis of logic as a conjunction of formal apophantics and formal ontology appears especially promising.


Husserl takes up the empiricist impulse by describing the import of modern logic’s progress which takes two paths, formal apophantics and pure mathematics. Whereas apophantics focuses on the meaning of propositions, pure mathematics corresponds to the task of traditional ontology. He argues that both must be considered in developing a theory of science that explains the necessity of meaning and the structure of things. Nonetheless, Husserl’s description does not cease at the empirical level, the sphere of the natural attitude, but proceeds to the transcendental. Husserl’s transcendental logic seeks to explain how Bolzano’s tension resides and is sustained in the activity of rational subjectivity. Unfortunately, according to Cavaillès, Husserl’s effort does not resolve the problem as much as it merely embodies it in another guise, for in the end transcendental logic cannot explain how description guarantees necessity. However, one might well wonder about Cavaillès conception of necessity.


For Cavaillès, the notion of necessity in logic stems from David Hilbert’s work in logic and mathematics. Since mathematics was taken to be the discipline most evidently governed by necessity, demonstrating its consistency (that is both its coherence and completeness) would provide an exemplar for a philosophy of science that seeks to explain how the contingency of human thought does not belie the necessity of progress. To address the issue and thus solve Bolzano’s tension, Hilbert’s program calls for an absolute proof. An absolute proof attempts to prove the consistency of a system without reliance upon another system. But, according to Cavaillès, despite Husserl’s laudable attempt to bring the empirical and necessary together within logic as a foundation for a theory of science, the transcendental effort leaves an indissoluble dilemma: either one looks to the subjective, which needs a further explanation of its necessity and hence is not absolute, or one cleaves strictly to logic as a self-justifying discipline that is absolute, but not transcendental. On the basis of this dilemma, Cavaillès calls for the philosophy of science to wed itself to a logic based on the necessity of dialectic. This raises two unanswered questions: what is meant by dialectic and what kind of necessity does it possess.


Dialectic, in one sense, is a term referring to the material progression of things and concepts, on how they propel themselves onward in ways that strain the abilities of analysis. Necessity here, then, refers to the unavoidability of such a transformation, and a logic based on the necessity of dialectic traces out the material transformation of concepts and presents the rules underlying those alterations. To forward a necessity of dialectic, then, is to demand that the logic supporting a theory of science matches the progress that governs empirical sciences. Transcendental logic, properly understood, fulfills such an aim.


For Husserlian phenomenology, the transcendental is an investigation of sense rooted in consciousness. As such transcendental logic in this paradigm does not reduce necessity to the a priori structures of consciousness as did Kant’s earlier effort. Instead, a Husserlian transcendental logic is governed by correlative structure of consciousness, by the necessary connections between thinking and that which is thought. Consequently transcendental logic has a dual focus that explains the necessity of Bolzano’s tension. A philosophy of science is governed by a doubly necessary move. On the one hand, it must attend to the progress of sense that science itself exhibits in a dialectical manner; on the other hand, a philosophy of science exhibits the necessity inherent in the a priori structures of consciousness. Explaining the conjunction between these two demands is the task of transcendental logic.




  • Cavaillès, Jean. Sur la logique et la théorie de la science. 2d ed. Paris: Presses Universitaires de France, 1960.
  • Coffa, Albert J. The semantic tradition from Kant to Carnap. To the Vienna station. Ed. Linda Wessels. Cambridge: Cambridge University Press, 1991.
  • Husserl, Edmund. Formale and transzendentale Logik. Versuch einer Kritik der logischen Vernunft. Ed. Paul Janssen. The Hague, Netherlands: Martinus Nijhoff, 1974.

Kem Crimmins, Curriculum Vitae


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