What is the objective of philosophy according to the late
The objective of philosophy according to the later Wittgenstein is both to make us aware of the temptation of any a-priori generalization and to show how to overcome it.
(The rejection, which marks the thansition from early to later Wittgenstein is, more generally, addressed to every kind of dogmatism in philosophy and the Philosophical Investigations can be seen as the culmination of all the consequences of this rejection).
The rejecting of any a-priori generalization is also the rejection of the tractarian approach, which did consist in reducing the sphere of the sayable to meaningful declarative sentences which are all of equal value, by virtue of a general form of truth-function ([p-, ξ-, N(ξ-)]), therefore every meaningful sentence is, abstractly and dogmatically, no more than the result of successive application of a formula consisting on a formal operation and one propositional variable (see TLP 6 and following comment).
So, while the Tractatus does construct a systematic edifice which relies on strict formal logic, on the other hands the Philosophical Investigations points out the therapeutic non-dogmatic nature of philosophy, verily instructing philosophers in the way of therapy. Consequently, according to this new viewpoint, a philosophical problem has the form: "I don't know my way about" (PI 123), and hence the aim of philosophy is "to show the fly the way out of the fly-bottle" (PI 309)
(source: see in particular the paragraph 3.7. The Nature of Philosophy here)