Husserl thinks of philosophy as a general, fundamental and apodictic science of world. He set out to found transcendental phenomenology as general philosophy or apodictic science, but he ought to explain the possibility of objective knowledge of world as to reach to this point. Concerning about crisis in modern western culture, Crisis projects his view of philosophy and of duty of philosopher in context of a critics of modern philosophy and science concerns about crisis in modern western culture. So he introduces the original concept life-world that is a novel idea for the philosophy as general science. The paper is to consider the Husserl's point of view on relation between philosophy and crisis of modern culture and to review the question if life-world can introduce Husserl's transcendental phenomenology as a fundamental philosophy and general science. We consider the problem of possibility of objectivity of world, a problem that proposed in late philosophy of Husserl in more extensive and innovative form.