Explanation

Creating a filter: in this question, when we read the prompt, we pause at "had been." We're always suspicious of the past perfect, because it's overused. For it to be warranted, the action had to happen before something else. But before what, in this case? Not the "carrying on." He was no more successful, ultimately -- that is, after he had carried on the tradition, not before. Gottlob Frege, similarly, came before the ultimate lack of success, not after. Drawing a timeline with the events on it can clarify this; the past perfect tense has to come to the left of an event in the simple past tense.

Applying the filter: So, fixing the tense, the answer is (B). Choice (E) has the same tense problem as the original sentence. Choices (C) and (D) both distort the intended meaning by messing around with the expression of goals and methods. The correct answer is (B).