In Looking For Alaska, Miles Halter leaves his home in Florida and heads to a boarding school called Culver Creek on a search for The Great Perhaps. One thing Green (the author) introduces to you right at the beginning of the novel is that Miles is OBSESSED with memorizing the last words of people, as well finding The Great Perhaps, whatever that is. After doing further research, I was able to piece together these things.
At the beginning of the novel, we see Miles as a gawky, anti-social nerd who has little to no idea of who he is, and is looking to fulfill his life. As I said, Miles goes to Culver Creek in pursuit of finding The Great Perhaps. When Miles arrives, he meets his roommate Chip "Colonel" Martin, and his friend Alaska Young. Not long after Miles arrives, Colonel and Alaska give him the loving nickname "Pudge", ironically, because he is described to be very lanky.
Soon after Pudge makes friends with Colonel and Alaska, he is doing something he has never done before and is completely out of his comfort zone- smoking. This was not the only time in the book that Pudge smoked, in fact, it was only the first of many, MANY, times that he would smoke. Not long after he smoked, he also drank cheap pink wine with Alaska, his first time drinking alcohol, and again, not his last by a long shot.
Not only that, but before Pudge arrived at Culver Creek, he had barely ever talked to a girl before, let alone getting a girlfriend. A girl named Lara was not only his first girlfriend, but also his first kiss, and also the first person he had gone to third base with. In fact, he was so new to the whole sex thing, that he had to ask Alaska what oral sex actually was.
Getting to the point, I feel like the primary conflict in LFA was man vs. self. My reasoning for this is that Miles started out as a shy, naive, and anti-social kid, who really had on idea about who he was. Miles decides to go to Culver Creek in pursuit of The Great Perhaps- what could be, and what the future could hold for him. The reason that he decides to go after The Great Perhaps so early in his life is because Francois Rabelais, whose last words were "I go to seek a Great Perhaps", died basically saying that he was going to find out one of humanities biggest questions- whether there was an afterlife or not. Of course, we can't find out his answer because, you know, he's dead. Miles wanted so seek The Great Perhaps before he died.
Miles arrives at Culver Creek and becomes a different person. At Culver Creek Miles turns into Pudge. Pudge dates girls, he smokes, he drinks, and is fun-loving and adventurous. Miles/pudge is trying to discover himself. He's trying to figure out who he is within these two conflicting personalities that he has. Ultimately, he is Pudge, but the shy, anti-social Miles still resided within him.
I think Miles/Pudges' pursuit of The Great Perhaps is summed up by "Thomas Edison's last words...: It's very beautiful over there. I don't know where there is, but I believe it's somewhere, and I hope it's beautiful" (pg 221).