What topic can be formed for a term paper that can justify Wittgenstein's philosophy of language?

Wittgenstein wrote his Tractatus Logico-Philosophicus earlier in his career and his other work, Philosophical Investigations, differs from and is critical of some of the views he expressed in the former work. 

In the Tractatus, he argues a proposition that makes logical sense must have a logical form to it. We must think of this logical form as a "picture." But when he says "picture" he really means structure, form, or formula. Wittgenstein means...

Wittgenstein wrote his Tractatus Logico-Philosophicus earlier in his career and his other work, Philosophical Investigations, differs from and is critical of some of the views he expressed in the former work. 

In the Tractatus, he argues a proposition that makes logical sense must have a logical form to it. We must think of this logical form as a "picture." But when he says "picture" he really means structure, form, or formula. Wittgenstein means that the structure of a sensible proposition ("I am alive") will obey logical laws in the same way that a ball thrown up into the air will obey the logical laws of physics. "Socrates is wise" follows a formula, ARB, and its logic depends on the logical sense of the elements placed within that formula. 

Wittgenstein's logical analysis of language is mathematical in this way. Consider the "p and the not-p" formula. "It is raining or it is not raining." This follows a formula, but it is nonsense; it gives no useful information. It is a tautology. Consider "It is raining and it is not raining." This is absurd and a contradiction. It also makes no sense. In these ways, Wittgenstein is trying to show that language can not express anything that contradicts logic. 

His general idea is that which can be expressed in language must be logical. Things that can not be expressed by language must be illogical and we should simply ignore such things. A way to justify this thinking is to say, "if a statement provides no useful information or if it is illogical, then it expresses nothing and should be ignored." 

Consider analogies to justify Wittgenstein's thinking. If you hear a chord made up the notes C, E, and G, then it must be logically represented on the staff. If it is not logically and spatially (in this case) represented on the staff, it will not make sense. Each note must be in a different spot on the staff to make any sense. Just as any expressible thing about the world can be expressed in some logical proposition, any combination of notes can be expressed in a logical form of notes on a staff. In both cases, that which is expressible is only expressible in a logical structure or form. 

(We can't really say how the logical form of C, E, and G on the staff says anything about itself; it only says something about the sound of the chord. Likewise, we can't say how "Socrates is wise" says anything about itself as a formula; it only says something about the fact or idea that Socrates is wise.) 

In Philosophical Investigations, Wittgenstein writes that language is more like an ongoing game, a part of life in which we all play. He doesn't try to boil language down into mathematical formulas of logic. Rather, he discusses how different terms change in different contexts, thus giving a more fluid assessment of language. The commonality between this work and the Tractatus is that Wittgenstein seeks to identify and resolve confusion and contradictions in language.