—the "in-order-to", the "for-the-sake-of", and the "with-which" of an involvement—is such that they resist any sort of mathematical functionalization; nor are they merely something thought, first posited in an 'act of thinking.' They are rather relationships in which concernful circumspection as such already dwells. This 'system of Relations', as something constitutive for worldhood, is so far from volatilizing the Being of the ready-to-hand within-the-world, that the worldhood of the world provides the basis on which such entities can for the first time be discovered as they are 'substantially' 'in themselves'. And only if entities within-the-world can be encountered at all, is it possible, in the field of such entities, to make accessible what is just present-at-hand and no more. By reason of their Being-just-present-at-hand-and-no-more, these latter entities can have their 'properties' defined mathematically in 'functional concepts.' Ontologically, such concepts are possible only in relation to entities whose Being has the character of pure substantiality. Functional concepts are never possible except as formalized substantial concepts.
In order to bring out the specifically ontological problematic of worldhood even more sharply, we shall carry our analysis no further until we have clarified our Interpretation of worldhood by a case at the opposite extreme.
B. A Contrast between our Analysis of Worldhood and Descartes' Interpretation of the World
Only step by step can the concept of worldhood and the structures which this phenomenon embraces be firmly secured in the course of our investigation. The Interpretation of the world begins, in the first instance, with some entity within-the-world, so that the phenomenon of the world in general no longer comes into view; we shall accordingly try to clarify this approach ontologically by considering what is perhaps the most extreme form in which it has been carried out. We not only shall present briefly the basic features of Descartes' ontology of the 'world', but shall inquire into its presuppositions and try to characterize these in the light of what we have hitherto achieved. The account we shall give of these matters will enable us to know upon what basically undiscussed ontological 'foundations' those Interpretations of the world which have come after Descartes—and still more those which preceded him—have operated.
Descartes sees the extensio as basically definitive ontologically for the world. In so far as extension is one of the constituents of spatiality (according to Descartes it is even identical with it), while in some sense spatiality remains constitutive for the world, a discussion of the Cartesian ontology