Abstract

The phenomenology of internal time-consciousness, as an analysis founded in part logic and expanded by the pure theory of transfinite continua, clarifies phenomenology as reflective philosophy in distinguishing the essence of comprehensive reflection, its ground, its temporality and its completion despite its possibility of infinite iteration, thus overcoming the Hegelian pronouncement that reflection must die in the ascendance of Reason's absolute identity in totality. ;Hegel acknowledges finite reflection as a part necessary to knowledge, but as nullified by unopposed Reason, which produces the infinite unlimited Absolute of knowledge genuine by its totality of interconnected opposing parts. In stark contrast, Husserl found his phenomenology on reflection, claiming an absolute beginning: science is orderly evident cognition, with first evidences indubitably founding an infinite series. The clarified Cartesian principle of absolute indubitability reveals the ego cogito as in fact the first evidence, accessible by reflection with no nullification by Reason. ;Despite its lack of concrete totality in the absolute of Reason, Husserl's phenomenology lives, sustained by a clarification of essences in the logic of parts, the phenomenology of internal time-consciousness and Cantor's pure theory of transfinite numbers. In the sea analyses reflection is seen as founded in internal time-consciousness, not lost to itself in an infinite regress of directed attention but rather comprehensive as a transfinite limit, in a continuity of continua, simultaneously complete and open. ;Moments of reflection in internal time-consciousness are counted with transfinite numbers and consistently understood, each as a now limit giving the type, order and completion of its past, subsequent yet equal to its past. The particular character of a transfinite number makes possible equality of correspondence and inequality of order: a subsequent now corresponds precisely to its past in comprehension yet follows it in order. In this way the actual now of a reflective comprehension is clarified, as completing a possible infinite regress and as now-original. ;Any now in the double continuity of time is constituted by inseparable parts of varying intentional modes that limit and transcend. Now is never a perfected structure. Open in sequence, the moment 'aware' is yet an absolute abstract basis for all comprehension, as beginning-limitation and founding part, as non-independent of its phases. ;For reflection, totality is essentially an infinite continuity wherein all parts are connected in foundation. By its logic, totality is transfinite and underlying but not concrete and finally limited. For totality, reflection's work presupposes totality and remains incomplete. Reflection has merely symbolized its law, recognized founding order and stated essential part-relation by a beginning-limit which is transcended. ;Reflection and totality are nvertheless both founded in the continuity of the absolute founding now of the innerly aware, not in 'bigness'. Reflection limits; totality transcends. Their now is the limit of each past and the openness to each future. ;Temporal now-continuity is an abstract basis solid enough to sustain science and philosophy. Its beyond means a lack of full apprehension; its now means an absolute basis as limit; its past means comprehension. ;While phenomenological insight is non-independent of the relative independence of concrete lived experience, it achieves absolute knowledge in part, foundation and essence, without requiring total concretion to be phenomenology. An infinite task of self-experience in reflection emerges