Weyl's Conception of the Continuum in a Husserlian Transcendental Perspective
Keywords:
actual infinity, completed totality, continuous unity, intuitive continuum, individual, iteration principle, mathematical continuum, restriction principle, temporal consciousness, time-pointAbstract
This article attempts to broaden the phenomenologically motivated perspective of H. Weyl's Das Kontinuum (1918) in the hope of elucidating the differences between the intuitive and mathematical continuum and further providing a deeper phenomenological interpretation. It is known that Weyl sought to develop an arithmetically based theory of continuum with the reasoning that one should be based on the naturally accessible domain of natural numbers and on the classical first-order predicate calculus to found a theory of mathematical continuum free of impredicative circularities (such as the standard definition of the least upper bound of a set of real numbers) only to stumble, to cite a key question, in the evident lack of intuitive support for the notion of points of the continuum. In this motivation, I set out to deal from a Husserlian viewpoint with the general notion of points as appearances reducible to individuals of pre-predicative experience in contrast with the notion of an interval of real numbers taken as an abstraction based on the intuition of time-flowing experience. I argue that the notions of points and of real intervals in the above sense are not by essence related to objective temporality and thus their incompatibility in mathematical terms is ultimately due to deeper constituting reasons independently of any causal and spatio-temporal constraints.
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