Is the Historicity of the Scientific Object a Threat to its Ideality? Foucault Complements Husserl

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Are mathematical objects affected by their historicity? Do they simply lose their identity and their validity in the course of history? If not, how can they always be accessible in their ideality regardless of their transmission in the course of time? Husserl and Foucault have raised this question and offered accounts, both of which, albeit different in their originality, are equally provocative. Both acknowledge that a scientific object like a geometrical theorem or a chemical equation has a history because it is only constituted in and transmitted through history. But they see that history as a part of its ideality, so that, although historical, a scientific object retains its identity as one and the same object. Their account of history thus entails a significant reformulation of what an ideality is. While Husserl appeals to the possibility of reactivating an ideality, thereby repossessing, as it were, its genesis, Foucault emphasizes the role of what he calls a statement and which he considers to be a material unity. While these two approaches may seem irreconcilable, I try to show through a careful analysis of Husserl's and Foucault's methodologies that they complement each other. In the case of Husserl, I will focus on how he understands the transfer of idealities across time in the Origin of Geometry,1 and in the case of Foucault, I wiil appeal to his notion of statement as explained in The Archaeology of Knowledge.2 My main interest is the contrast between the two approaches and I will lay aside the many other aspects of their thought as well as their rather different ontological commitments. The first part of this essay will deal with Husserl's analysis in the Origin of Geometry, in which I will lay out his understanding of the ideality of a scientific object as a reactivatable sense, and distinguish the two modes by which he claims it can be transmitted through history. In the second part of this essay, I will delineate what Foucault understands by a statement. In his Archaeology of Knowledge, he argues that the scientific object is a repeatable materiality constituted by statements and part of a discursive formation. In the final part of the essay, I will contrast the methodological frameworks of phenomenology and archaeology with respect to the question concerning the constitution and transmission of scientific objects and show that there is a way in which we can see these methodological frameworks as complementing each other, despite their divergent responses to the question concerning the nature of idealities. Husserl's Phenomenological Analyses of the Historicity of the Sciences In the Origin of Geometry, Husserl accepts that idealities are historical entities, in the sense that they are constituted in history or in the course of history. While he avoids the problem of how we have access to them, he still has to explain how idealities can retain their identity and validity in the course of history. This will require that he radically reformulate the notion of ideality which, I believe, is precisely what he attempts in the essay on the origin of geometry. In general, Husserl understands tradition as the inheriting of a store of idealities handed down from generation to generation, so that new ideal objects are added to the previously existing store and some older ones are modified. Science in general and mathematics in particular (of which geometry is considered to be a part) is one such ideal product, which we acquire as a tradition through history.3 Husserl explains that geometry has sustained itself as a discipline, and moved ahead at the same time, because the idealities that have been forged at every stage in its history have never lost their validity as such, and newer idealities have always been acquired only on the basis of all the former acquisitions. At every point in the history of geometry, geometers have always found themselves to be a part of a tradition, even if they have not been explicitly aware of all the particular contributions of the past still at work in the present. …