1. Historicity and Origin of Geometry1.1 as Prototype of Pure HistoricityIn his lecture about Philosophy and Crisis of European Humanity (1935), also known as Vienna Lecture Edmund Husserl describes development of philosophy and science as an irreversible transformation of human civilization. This transformation was due to introduction of a sense of Along with which established a system of ideal objects and deductive reasoning, there arrived possibility of manipulating universal and infinite objects by 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 first time. But 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 Greek miracle involved a transformation of 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.3The introduction of infinity made possible concept of historicity itself. As Derrida puts it in his commentary on Husserl's posthumous essay concerning of published as an appendix to Crisis, the openness of infinite is only . . . openness of history itself, in 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 infinite realization of human values; it is not realm of delusion and mere appearance against background of absolute being and truth. Historicity is realm in which infinity becomes actual, concrete and true for first time. Historicity is infinite horizon for infinite realization of humanity's true knowledge and absolute value.Husserl's phenomenological investigations into concept of history take as a prototype of science and philosophy in general, and therefore, ultimately, as a prototype of transformation giving rise to new idea of historicity defining European humanity. For that reason, question about origin of geometry, as surprising as it may seem at first sight, must be understood as a question concerning concept of historicity itself. The origin of geometry is origin of historicity, hence 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 general concept of 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 ideality as such, as possibility itself of an idea of infinite progression and infinite task, in sum as methodological basis upon which any historicity of truth is thinkable and therefore any concept of science and of history of science is possible, including idea of science as a cultural practice historically articulated through shift of paradigms that are incommensurable to each other.4 is considered a prototype of 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 origin of geometry is crucial for understanding formation and development of Derrida's early conception of historicity (1989). …
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May 1, 2016
Yi Cui + 4
