Wittgenstein’s philosophy (or rather both of them – that contained in the Tractatus and that contained in his later writings) is unusual in that it does not set out to give answers to any of the great philosophical questions that drive most people to philosophy (including perhaps even Wittgenstein himself). ”So what?”, you might say. Wittgenstein came to see philosophy as involving a lot of conceptual confusion, so he developed a method to help people avoid confusion. In the process philosophy stops being a search for answers and because a matter of becoming more proficient at understanding how our concepts really work. It stops being grand but empty and becomes modest and practical.
From a philosophical point of view, it is quite reasonable to leave it at that. However, it is interesting to ask what drove Wittgenstein to end up with sort of conception of philosophy. Here we enter the realm of speculation about the personal, and we do of course risk projecting our own concerns onto the person we are talking about. It seems clear that Wittgenstein was a man of great inner turmoil and philosophy certainly seemed to function as an escape for him. He wanted certainty and if the price of that was bracketing out the personal, it was a price he was prepared or even happy to pay. The Tractatus sought to capture what little one could say with certainty only to conclude that this amounted to little (or possibly nothing). The structure, style and tone of the book was (like Wittgenstein’s architecture) stripped of anything personal, and yet there was a sense that the truly important was somehow in there but hidden – therefore we cannot speak, thereof we must remain silent. The latter Wittgenstein’s work is not so frighteningly austere, but it involves an approach to philosophy that focusses on what no one could possibly deny. There are no great answers to learn or life-changing insights to grasp. If you only knew the latter Wittgenstein from his writings, this might change the way you think, but unlike any other great philosopher there is no danger (and no hope!) that it will change the way you live. Whether you are an atheist or a devote believer, a hedonist or an altruist, a capitalist or a communist, understanding the private language argument (or anything else Wittgenstein wrote) is not going to have implications for the views that shape your life.
There certainly is a paradox to this, since Wittgenstein was a passionate man and he had very firm beliefs about all sort of things and certainly about how people should behave. And yet his philosophy is neutral. It is as it were a holiday place – somewhere we can (in principle) escape conflict and emotion and doubt and uncertainty and just concentrate on the practical business of resolving confusions and sorting out conceptual relations. Of course, when we have done that, we are left with the real tough aspects of life with which Wittgenstein struggle as most of us do, although perhaps not all with the intensity with which he did. I do not think it makes philosophy the parlour game that Russell claimed it did, since I think it can still be a powerful and necessary tool. But it is not the kind of philosophy that those who are drawn to philosophy have dreamed of. Wittgenstein rightly had full confidence in the power of his intellect, but he had enough humility and self-doubt to hold back from presenting himself as a fount of wisdom. Perhaps appropriately, the restraint is purer and clearer in the later philosophy than in the earlier one