What is the notion of philosophy according to Wittgenstein's works, especially in the Tractatus and Philosophical Investigations? What are the...

In the Tractatus, Wittgenstein argued that all of the problems of philosophy are problems of language. Therefore, all philosophical problems can be solved by addressing the way philosophical problems are stated, reasoned, and thought of. This includes applications of logic, symbolic logic, linguistics, semantics, and how we think. In this latter case, Wittgenstein likened the thinking of language and philosophy as making a logical picture of facts. For Wittgenstein, at this stage of his thinking, language has a logical structure. Anything we can say that has truth and/or meaning, can only be said in language. So, whatever we can not say in language is beyond our understanding and is therefore beyond the limits of philosophy. Anything that is beyond our understanding is meaningless to us. The Tractatus focuses on language but it is also Wittgenstein's way of showing the limits of thought. Language is a fixed, logical structure. 

In Philosophical Investigations, Wittgenstein is still keenly aware of language's role in understanding philosophy, but this work is a departure from the Tractatus in other significant ways. In Philosophical Investigations, Wittgenstein no longer views language as a structure all by itself, separate from humans. At this point, he is more interested in how humans/speakers and language interact. In this shift, Wittgenstein has moved from a mathematical analysis of language in philosophy to something still rigorously logical but more psychological and sociological. Wittgenstein admitted that his thinking in the Tractatus was too simple and general. Thinking only of language as this fixed, self-contained structure of logic ignores the myriad ways humans use and manipulate language. As a result, he changes his thinking and describes language as something more elastic and changeable. This is why he discusses the idea of "language games." Just as there are different rules for different games (sports, board games, etc.), language has different rules for certain contexts, propositions, and so on. So, to address meaning, truth, and philosophy, we have to consider how diverse language is used. In this more flexible philosophy of language, Wittgenstein acknowledges how one proposition could mean two (or more) different things depending upon context and human application. Consider the proposition "King Arthur did not exist." As a mythological character, this is false. The character existed and does exist in a number of literary works. As a historical figure, he may have existed, but probably not as portrayed in those literary works. So, you can see how one proposition can have many different meanings. This is something that Wittgenstein did not consider or address in the Tractatus.