Two issues are involved here : (1) Wittgenstein's account of the 'end of philosophy' and (2) the consistency of this account with his own practice.
Wittgenstein and the end of philosophy - his account
Daniel D. Hutto's Wittgenstein and the End of Philosophy: Neither Theory nor
Therapy attempts to trace a continuous line of thought running from the Trac
tatus through all of Wittgenstein's subsequent work. The basic thesis is that
Wittgenstein's early conception of logic?in particular, the claim that there are
no logical facts or objects?leads inevitably to the view that there can be no
philosophical theories and that philosophy should aim at description alone.
This is an intriguing reading of his work, and while much of what Hutto says
in the course of developing it is of great interest, in the end it remains some
what unclear what it means to say (and whether) Wittgenstein's work does not
advance anything that might be called a theory, and how the impossibility of
philosophical theorizing is supposed to follow from the early insight on logic.
Most likely what he means is that just as propositions' logical properties and
relations, which might seem fit subjects for description, cannot be described
but only shown, so (in the later work) certain psychological and semantic
states and properties that might seem fit for theoretical elaboration cannot be so treated, but rather are 'shown' in how we act and speak within a form or life. (John Koethe, 'Wittgenstein and the End of Philosophy: Neither Theory nor Therapy
by Daniel D. Hutto', Mind, New Series, Vol. 118, No. 469 (Jan., 2009), pp. 178-181 : 178.)
Wittgenstein and the end of philosophy - his practice
Whatever Wittgenstein said about the end of philosophy in the Tractatus, philosophical argument is plainly present in the Philosophical Investigations (1953, rev. 1958). Take these remarks on epistemic privacy, which clearly amount to a philosophical argument :
[I]t is obvious that one of Wittgenstein's major concerns in the
Philosophical Investigations is the examination and criticism of the view
that sensations are private ...
In the Investigations, Wittgenstein pays particular attention to two
distinct senses in which sensations may be said to be private - the epistemic
sense, and the sense in which they are privately owned. It is only with the
former, epistemic, sense of privacy that I shall be concerned. The view that
sensations are epistemically private is the view that only I can really know
if I am in pain; others can merely conjecture about it. Wittgenstein's most
direct characterization of the doctrine of privacy is this:
In what sense are my sensations private? - Well, only I can know
whether I am really in pain; another person can only surmise it.-
In one way this is wrong, and in another nonsense. If we are using
the word 'to know' as it is normally used (and how else are we to
use it?), then other people very often know that I am in pain. - Yes,
but all the same not with the certainty with which I know it myself!
Having formulated the doctrine of epistemic privacy in terms of the special
status of one's knowledge of one's own sensations, Wittgenstein continues:
It can't be said of me at all (except perhaps as a joke) that I know am in pain. What is it supposed to mean - except perhaps that I am in pain?
Other people cannot be said to learn of my sensations only from
my behaviour, - for I cannot be said to learn of them. I have them.
The truth is: it makes sense to say of other people that they doubt
whether I am in pain; but not to say it about myself. (PI, 246)
In this succinct passage, Wittgenstein not only characterizes the privacy
of sensation in terms of its epistemic expression, but also indicates his rejection of the view. (Jack Temkin, 'Wittgenstein on Epistemic Privacy', The Philosophical Quarterly (1950-), Vol. 31, No. 123 (Apr., 1981), pp. 97-109 : 97-8.)
This critique of the privacy of sensations - this argument - connects with other arguments about the impossibility of a logically private language and about rule-following. If Wittgenstein isn't doing philosophy here, I don't know what he is doing.