Abstract: Jacob Klein's account of the original phenomenon of formalization accomplished by the innovators of modern mathematics, when they transformed the Greek arithmos into the modern concept of number, and his suggestion that the essential structure of this historically located formalization has become paradigmatic for the concept formation of non-mathematical concepts (and therefore the most salient characteristic of the “modern consciousness”), is situated within the context of Husserl's and Heidegger's understanding of formalization. I show that from the perspective of Klein's account of formalization the questions that inform Husserl's and Heidegger's phenomenological responses to the problem of formalization are derivative, insofar as both phenomenologists presuppose that the essence of formalization is something that is knowable independent of its historicity. I then show that Klein's philosophical achievement consists in his account of formalization and the formality of the concepts that it generates as being ungraspable so long as thinking approaches them as something is knowable, independent of its historicity.

Keywords: Jacob Klein; Edmund Husserl; Martin Heidegger; formalization; historicity; concept of number.

Part of the unique philosophical achievement of Jacob Klein is to have both thoroughly surpassed the understanding of his famous teachers Martin Heidegger and Edmund Husserl on important matters and to have remained, for the most part, as unknown in the “world” of the academy and beyond as his teachers, to this day, are known. Accounts by those who knew Klein attest that his lack of fame is not an accident.

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The historical problem underlying Husserl's concept of intentional history

In the foregoing we have indicated that for Husserl the transcendental enquiry into the problem of the intentional history of the categorial formations of the meaning making up an object's identity reveals the essential necessity of its involvement in a history in the usual sense of the term. That is, the transcendental enquiry into the intentional history of the categorial unity of an object discloses an essential connection between the origin of this unity and its historical development within natural time.

For Husserl the connection between the problem of enquiry that underlies historical reflection and intentional history is established when he – in the works that present the final phase of his thought – once again takes up a task that psychologism cannot solve on its own terms but has addressed in its own way: the investigation of the origin of the unity of the meaning formation of any intentional object. In these works Husserl showed that the enquiry into the constitution of any meaning formation as an invariant that transcends the natural time presupposed by psychologism is itself but a mode of “objective omnitemporality” (CM, 156). As such, its identity is an intentional product of the continual accomplishments of transcendental subjectivity, which bring about the combination (Verbindung) constituted through the medium of recollective representations that yields the objectivity belonging to the ideal determinations of the unity of meaning.

The simple givenness of ideality

The account of the origin and development of Husserl's pure phenomenology so far has identified two important contexts for grasping as a “task” the significance of both his formulation of its method and the achievement of its goals. First, his realization of the shortcomings of a more or less orthodox adherence to the principles of Brentanian descriptive psychology for providing an adequate account of the concept of number formation generated the task of reforming these principles in a manner appropriate for the investigation of the ideal meanings that are operative in mathematics and pure logic. Second, his realization that even a reformed descriptive psychology operated with a fundamental presupposition that prevented the proper methodical access to the ideal meanings of mathematics and pure logic generated the task of reformulating the descriptive moment of descriptive psychology as a pure phenomenology dedicated to providing such access. The task-oriented character of “pure phenomenology” thus signals that it is not a finished philosophical system but a method of research and, above all, that a research agenda drives its methodology.

The research agenda of the Logical Investigations is the investigation of the intentional concept formation, or “constitution” (Husserl's preferred word), of the ideal meanings of mathematics and pure logic, the general status of which he termed “ideality”. Rather than focus on resolving the problem in the Philosophy of Arithmetic that led to his rejection of psychologism, the “constitution” of the objective unity of the concept of whole that is characteristic of a multitude, namely, the concept of the collective combination, Husserl's investigations in the Logical Investigations focus on the problem of the constitution of ideality per se.

The two limits of the investigation of the temporal genesis proper to the intentional object

Husserl's account of how the eidetic possibility of an object's intentional unity contains the sedimented history of its own constitution is guided by two limits that are bound up with and therefore indicated by this possibility. These emerge in his critical analysis of the universal eidetic form of the intentional genesis of each such object's unity, that is, in the analysis of internal temporality. The first limit concerns the general substratum of consciousness that the continuous modification of the retentional consciousness approaches, and beyond which the “prominence [Abgehobenheit]” (CM, 80) of the object flows away. The second limit concerns the past history of the original presentation of the object itself. Both limits point to sedimented meanings that can be awakened such that the intentional genesis of the meaning in question is reproduced as the history of its constitution, a history that, of course, does not take place within natural time.

Two “histories”, then, are initially at issue in Husserl's phenomenological account of the eidetic possibility of an object's intentional unity. The first history concerns the possibility of such an object retaining its unity as an enduring “presence” once it has been presented to consciousness. This history concerns the object's intentional genesis as an objective prominence, its persistence throughout the temporality that is the essential characteristic of its (the object's) experience.