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"Biddy," said I, after binding her to secrecy, "I want to be a gentleman." (17.24)
Almost all of the people Pip knows have specific societal roles with specific societal functions: the tailor, the blacksmith, the clerk, the lawyer, the seedsman, the shipping agent, and all of these people seem content in their lives of earning profit and creating things. Not Pip. His goal is much more vague: a gentleman. What is a gentleman? What does a gentleman do? How will Pip know when he becomes a gentleman? And isn't that vagueness kind of the point? If you can't define it, it's easy for someone else to tell you that you're not one.
And now, because my mind was not confused enough before, I complicated its confusion fifty thousand-fold, by having states and seasons when I was clear that Biddy was immeasurably better than Estella, and that the plain honest working life to which I was born, had nothing in it to be ashamed of, but offered me sufficient means of self-respect and happiness. (17.74)
Pip is divided here between the familiar and the, well, sexy. Biddy is familiar, which makes her common in a literal sense: it's common for Pip to see her, because she basically lives with him. Estella is uncommon not because she's beautiful and well-education but because he doesn't spend a lot of time in close contact with her. Learning to value the common is part of Pip's growing up.
"It is considered that you must be better educated, in accordance with your altered position, and that you will be alive to the importance and necessity of at once entering on that advantage." (18.63)
Apparently, certain kinds of education (most likely involving dead languages) are more valuable than others (like how to work a forge). Interestingly, we never get to see Pip "learning" in London, though apparently, he's at it all the time.