Explanation

The first two sentences present a contrast between extending our knowledge by discovering “new information about the world” — which we are told philosophy does not do — and extending knowledge through some activity involving “things that are closest to us.” The first blank asks us to identify that activity, and although “attainment” makes little sense in context, both “rumination on” and “detachment from” have some appeal.
However, the clear implication that philosophy attends to things that ordinarily escape our notice eliminates “detachment from” as a correct answer. Blank (ii) requires something that suggests the importance of familiar things as subjects of philosophical rumination, and “utterly mysterious” does just that. “Essentially irrelevant” and “thoroughly commonplace” do not fit logically since they suggest that these “familiar” things are unimportant. Similarly, Blank (iii) needs to be consistent with the description of those things as familiar and close. “Most prosaic” fits that idea while “refreshingly novel” goes in the other direction. “Somewhat hackneyed” has some plausibility but is too negative given the overall tone of the sentence; there is no indication that those things are in any way trite. Thus the correct answer is the rumination on (Choice B), utterly mysterious (Choice E), and most prosaic (Choice G).