「科学作品の現象学」の試み : 量子論における局所性、並びに代数的視点と幾何学的視点の干渉

Abstract

G.-G. Granger considers science as "works", which fix concepts, and which go beyond their authors' consciousness because of their fixed structure. With recourse to his notion of "work", this paper proposes a "phenomenology of scientific works", as distinguished from Husserl's pure phenomenology. "Phenomenology of scientific works" begins with the description of scientific activities and of properties of scientific concepts induced from those activities, while pure phenomenology begins with the description of what appears directly to consciousness. Thus this paper proposes a displacement of the phenomenology that looks for the foundation of all sciences, with a phenomenology that makes possible a reflection on the structure of subjectivity through the description of scientific works. In the history of philosophy, we can find an opposition between intuitive thinking and symbolic thinking. Instead of treating directly the relation between these two kinds of thinking, this paper begins with a description of the interaction between intuitive perspective and symbolic perspective, in theoretical physics, which involves mathematical representations. A great mathematician, M. F. Atiyah, considers geometry as a kind of visual or intuitive thinking, while considering algebra as a consequential calculus which doesn't involve any thinking about meaning. In his view, the problems of meaning and of vision are deeply linked in geometry. A similar link can also be found in Husserl's phenomenology. In shifting this linkage to "phenomenology of scientific works", this paper describes how a reconstruction of "intuitive" concepts of number and space is made through the mediation of "symbolic" operations of algebra and analysis in mathematics. How can theories in physics approach physical reality? What is the relationship between intuition and the approach to reality? This paper affirms that consideration of the "intuitive" geometric perspective in theoretical physics is necessary for answering these questions, even if it is strongly mediated by symbolic algebra and analysis. Moreover, the concept of "locality", which is mathematically expressed in the crossroad of geometry and analysis, accompanies the notion of physical reality. It is well known that quantum physics makes the concept of locality difficult to understand. In order to consider the status of physical reality in the context of the difficulty arising from the notion of locality, this paper analyses the interaction between geometry and analysis or algebra in "local" quantum theory of field. Understanding quantum theory requires the geometric reconstruction of the physical notion of locality, through the mediation of symbolically expressed algebra. Non commutative geometry is a good example for seeing this situation. With this description of scientific works, this paper may open a way to a reflexive approach to such fundamental philosophical notions as understanding, intuition, and reality.