خلاصه ماشینی:
Heidegger believes that by addressing the problematic of spatiality of circumspective manipulation within-the-world from the viewpoint of the role played by existential analytic as a kind of (phenomenological) constitutional analysis of meaning, one would give an account of changes in the pre-scientific articulation of spatial contexts of routine practices leading to the need of conceptualizing and formalizing space.
1 Following his scenario of the existential interpretation of science, Heidegger believes that the most extended group of algebraic transformations of geometrical relations has a genesis from contexts of spatializing within the circumspective manipulation of the everyday 7 being-in-the-world, while the more restricted groups (including those of Euclidean geometry and metrical geometry that conserves the property of distance) are arising out through enhancing geometrical idealizations already existing.
2. Spatiality and the Constitution of Meaning To begin with, there is an essential gap between the hermeneutic- phenomenological vocabulary by means of which one describes the spatiality of circumspective manipulation within-the-world and the language expressing the construction (and the epistemological criteria for existence) of space as a theoretically idealized object.
Let me note again that according to Heidegger, there are concepts of space (both in Dasein’s average everydayness and in doing research guided by a theoretical attitude) just because the interpretative appropriation of possibilities within-the-world is constantly making room, uniting thereby the spatiality of circumspective manipulation and the spatiality of being-in- the-world.
It is the tendency for removing privileged directionalities of heterogeneous environments in favor of spatial dimensions that enables one to reflect upon the hermeneutic situation of the existential genesis of idealizations about geometrical and other mathematical spaces.