I enjoy Wittgenstein's choice of Augustine for a beginning quote because I feel it accurately reflects most people's conceptions of language. "the individual words in lanugage name objects -- sentences are combinations of such names". It cannot be put any better than that.
This concept, which Wittgenstein will later show is flawed, is a fundamental mistake of which even he was guilty. That’s ultimately why I enjoy the quote selection; it isn't just about saying "Augustine is wrong", it is about Wittgenstein saying "I was wrong" as well. Importantly enough though, the larger issue at hand is not the complete wrongheadedness of the concept but of its lacking to capture all that language is. What bizarre place would we find ourselves if we started to ask the question "to which object does the word 'the' refer?"
So by Section 3 Wittgenstein has brought us more fully to an important concept; Augustine's description of language fails to capture what language actually is. As he puts it: " It is as if someone were to say: 'A game consists in moving objects about on a surface according to certain rules...' " This speaks only to board games, not all activities that we rightly call games. So it is with language, words as referents to objects simply is not what language is, it is at best a subset of the overall larger system and even that is of dubious veracity.
Section 6 is full of interesting thoughts on what he calls "ostensive teaching of words" by which the teacher points to an object and repeats the name, in an effort to convey what he or she means. The content of the section is overshadowed by the final sentence where he truly begins to draw the reader into the importance of context:
" 'I set the brake up by connecting up rod and lever.' -- Yes, given the whole of the rest of the mechanism. Only in conjunction with that is it a brake-lever, and separated from its support it is not even a lever; it may be anything, or nothing". So here begins the contextualism. It is important to keep in mind that it is not just contextualism in the sense of what words and usages surround the usage of the specific language we are discovering. It is a complete contextualism that encompasses all of the machine that is language, which includes everything that it means to be human.
Most of the rest of the sections that I've read for commentary today revolve around pointing out how little we are saying when we say that a word siginifies something.