“Philosophy ought to question the basic assumptions of the age. Thinking through, critically and carefully, what most of us take for granted is, I believe, the chief task of philosophy, and the task that makes philosophy a worthwhile activity.”

Works, VII, 17.
Context: The great thing however is, in the show of the temporal and the transient to recognize the substance which is immanent and the eternal which is present. For the work of Reason (which is synonymous with the Idea) when considered in its own actuality, is to simultaneously enter external existence and emerge with an infinite wealth of forms, phenomena and phases — a multiplicity that envelops its essential rational kernel with a motley outer rind with which our ordinary consciousness is earliest at home. It is this rind that the Concept must penetrate before Reason can find its own inward pulse and feel it still beating even in the outward phases. But this infinite variety of circumstances which is formed in this element of externality by the light of the rational essence shining in it — all this infinite material, with its regulatory laws — is not the object of philosophy.... To comprehend what is, is the task of philosophy: and what is is Reason.

System of Transcendental Philosophy (1800)

Source: Philosophy and the Return to Self-Knowledge (1997), p. 191

Though this has been quoted extensively as if it were a statement of Wittgenstein, it was apparently first published in A Brief History of Time (1988) by Stephen Hawking, p. 175, where it is presented in quotation marks and thus easily interpreted to be a quotation, but could conceivably be Hawking paraphrasing or giving his own particular summation of Wittgenstein's ideas, as there seem to be no published sources of such a statement prior to this one. The full remark by Hawking reads:
: Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of this century, said, “The sole remaining task for philosophy is the analysis of language.” What a comedown from the great tradition of philosophy from Aristotle to Kant!
Disputed

Pt. I, ch. 1, sec. 6.
1920s, Process and Reality: An Essay in Cosmology (1929)
Context: Philosophy is the self-correction by consciousness of its own initial excess of subjectivity. Each actual occasion contributes to the circumstances of its origin additional formative elements deepening its own peculiar individuality. Consciousness is only the last and greatest of such elements by which the selective character of the individual obscures the external totality from which it originates and which it embodies. An actual individual, of such higher grade, has truck with the totality of things by reason of its sheer actuality; but it has attained its individual depth of being by a selective emphasis limited to its own purposes. The task of philosophy is to recover the totality obscured by the selection.

Philosophy : the basics (Fifth Edition, 2013), Introduction

"Philosophy and Fate"
The Protestant Era (1948)
Context: The union of kairos and logos is the philosophical task set for us in philosophy and in all fields that are accessible to the philosophical attitude. The logos is to be taken up into the kairos, universal values into the fullness of time, truth into the fate of existence. The separation of idea and existence has to be brought to an end. It is the very nature of essence to come into existence, to enter into time and fate. This happens to essence not because of something extraneous to it; it is rather the expression of its own intrinsic character, of its freedom. And it is essential to philosophy to stand in existence, to create out of time and fate. It would be wrong if one were to characterize this as a knowledge bound to necessity. Since existence itself stands in fate, it is proper that philosophy should also stand in fate. Existence and knowledge both are subject to fate. The immutable and eternal heaven of truth of which Plato speaks is accessible only to a knowledge that is free from fate—to divine knowledge. The truth that stands in fate is accessible to him who stands within fate, who is himself an element of fate, for thought is a part of existence. And not only is existence fate to thought, but so also is thought fate to existence, just as everything is fate to everything else. Thought is one of the powers of being, it is a power within existence. And it proves its power by being able to spring out of any given existential situation and create something new! It can leap over existence just as existence can leap over it. Because of this characteristic of thought, the view perhaps quite naturally arose that thought may be detached from existence and may therefore liberate man from his hateful bondage to it. But the history of philosophy itself has shown that this opinion is a mistaken one. The leap of thought does not involve a breaking of the ties with existence; even in the act of its greatest freedom, thought remains bound to fate. Thus the history of philosophy shows that all existence stands in fate. Every finite thing possesses a certain power of being of its own and thus possesses a capacity for fate. The greater a finite thing’s autonomous power of being is, the higher is its capacity for fate and the more deeply is the knowledge of it involved in fate. From physics on up to the normative cultural sciences there is a gradation, the logos standing at the one end and the kairos at the other. But there is no point at which either logos or kairos alone is to be found. Hence even our knowledge of the fateful character of philosophy must at the same time stand in logos and in kairos. If it stood only in the kairos, it would be without validity and the assertion would be valid only for the one making it; if it stood only in the logos, it would be without fate and would therefore have no part in existence, for existence is involved in fate.

Lecture "Year of Distraction" http://www.youtube.com/watch?v=ChWXYNxUFdc, at 1:07.