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"Biddy," said I, after binding her to secrecy, "I want to be a gentleman." (1.17.24)
Here, Pip’s one dream is articulated directly for the first time. So many characters in the novel have specific societal roles with specific societal functions: the tailor, the blacksmith, the clerk, the lawyer, the seedsman, the shipping agent, etc. All of these people seem content in their lives of earning profit and creating things. Even when presented with these possibilities, Pip still vies to become something very vague: a gentleman. What is a gentleman? What does a gentleman do? How will Pip know when he becomes a gentleman?
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. (1.17.74)
Pip is divided here between what is familiar and what is sexy. He knows Biddy well, they talks and interact daily. All Pip knows of Estella is her beauty, her household, and her attitude towards him.
"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." (1.18.63)
Education and gentlemanliness go hand and hand, apparently. However, Pip has already earned many forms of an education – through Biddy, through Joe, through Miss Havisham. In this moment, we realize that certain kinds of education are more valuable than others. Interestingly, we never get to see Pip "learning" in London, though apparently, he’s at it all the time.