This paper investigates the two competing ways to conceptualize time in the history of Western thought. There is one which is called phenomenological and the other which is called cosmological. Former is primarily grounded in St. Augustine’s Confessions whereas the latter had its historical source in Aristotle’s Physics. This investigation had its motivation in Paul Ricoeur’s project of Time and Narrative. The main object of this investigation is three-fold. Firstly, it will be argued that neither of the two competing conceptions could be derived from the other. Secondly, none of these two can refute the other. Finally, they are not mutually exclusive, for both of them presume basic theses from one and another. During the pursuit of this threefold-object, it will be become amply clear that cosmological time is the time of nature and phenomenological time is the time of human world or human action. This will help achieve the purpose of this study which is also three-fold: to build an argument towards proposing a critique of human reason that claims autonomy over tradition as discourse, and develop a case against the distinction between natural and human sciences, i.e., social sciences, arts and humanities; inasmuch this distinction requires that there are two separate worlds, the world of man and the world of nature, or that one of them has superiority over other. No solution to the impasse or aporia of time will be proposed, and correspondingly no solution to the problem of exact relationship between natural and human sciences will be recommended. But only an indication towards a possibility of such a solution will be made.