Academic journal article Philosophy Today

From Ideality to Historicity, What Happens? the Problem of the Origin of Geometry in the Formation of Derrida's Early Conception of History 1

Academic journal article Philosophy Today

From Ideality to Historicity, What Happens? the Problem of the Origin of Geometry in the Formation of Derrida's Early Conception of History 1

Article excerpt

1. Historicity and the Origin of Geometry

1.1 Geometry as Prototype of Pure Historicity

In his lecture about "Philosophy and the Crisis of European Humanity" (1935), also known as "The Vienna Lecture" Edmund Husserl describes the development of Greek philosophy and science as an irreversible transformation of human civilization. This transformation was due to the introduction of a "new sense of infinity" Along with Greek "geometry" which established a system of ideal objects and deductive reasoning, there arrived the possibility of manipulating universal and infinite objects by the finite means of human reason.2 Infinite horizons for universal validity in knowledge, ideas and ideal objects that are not subjected to transformation and becoming, that stand eternally and omnitemporally both outside historical becoming and as regulative horizons for historical progression, were made possible for the first time. But the introduction of infinity not only entailed a shift in science and philosophy. Human values and human art, ethical and political life, also begin to be shaped and guided by infinite horizons. Thus the "Greek miracle" involved a transformation of the way in which human beings produce their own civilization. Human culture became a culture of trans-historical or trans-generational objects, and began producing humanity itself according to such infinite objects, indeed as infinite objects.3

The introduction of infinity made possible the concept of historicity itself. As Derrida puts it in his commentary on Husserl's posthumous essay concerning the "origin of geometry" published as an appendix to the Crisis, "the openness of the infinite is only . . . the openness of history itself, in the utmost depths and purity of its essence" (Derrida 1962: 143; 1989: 131). Historicity is not senseless mortality or senseless finitude; it is not opposed to the infinite realization of human values; it is not the realm of delusion and mere appearance against the background of absolute being and truth. Historicity is the realm in which infinity becomes actual, concrete and true for the first time. Historicity is the infinite horizon for the infinite realization of humanity's true knowledge and absolute value.

Husserl's phenomenological investigations into the concept of history take "geometry" as a prototype of Greek science and philosophy in general, and therefore, ultimately, as a prototype of the transformation giving rise to the new idea of historicity defining European humanity. For that reason, the question about the origin of geometry, as surprising as it may seem at first sight, must be understood as a question concerning the concept of historicity itself. The origin of geometry is the origin of historicity, hence the origin of any possible understanding of historical origins in general. "Geometry" will therefore be treated as being much more than, or something totally different from, a simple mathematical discipline or theory. It will not be taken, for instance, as the general concept of the normal way in which science is practiced, that is, as a 'paradigm' in Thomas Kuhn's sense (Kuhn 1996). It is not even taken as one horizon or one infinite task, among others. "Geometry" is analysed as infinite horizonality, as the ideality as such, as the possibility itself of an idea of infinite progression and infinite task, in sum as the methodological basis upon which any historicity of truth is thinkable and therefore any concept of science and of the history of science is possible, including the idea of science as a cultural practice historically articulated through the shift of paradigms that are incommensurable to each other.4 Geometry is considered a prototype of the ultimate horizon for any trans-generational practice of meaning and for any formation of world-views or world-conceptions capable of providing representations of historical progression (Heidegger 2002; Derrida 2013: 196-202).

The problem of the origin of geometry is crucial for understanding the formation and development of Derrida's early conception of historicity (1989). …

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