The basic premise of the quote
[Paul] "was interested in the triumphs of these cash boys who had become famous, though he had no mind for the cash-boy stage"?
is that Paul's temperament is one moved entirely by the senses; not by the want or need for success, nor by the hopes and wishes of the average warm-blooded individual to "do well" for themselves. Paul's world is one where the good, the beautiful, and the plentiful should be as common and palpable as the air he breathes. Sure, it is great to hear the stories of those who worked hard to succeed but, for Paul, the success part is the only thing he would want to hear about. This does not mean that Paul is a snob. It simply reinforces the fact that he is not a typical human being.
"Paul's Case: a study in temperament" tells the story of a very unique adolescent, not the story of an average kid going through a "phase". Neither is his character meant to serve as a conduit for a moral theme. "Paul's Case" is strictly the analysis of an extremely complex and almost supernaturally sensitive individual who stops at nothing to become a part of the aesthetically-appealing stratosphere where his soul seems to enthrall him to belong.
The quote cited before also shows that Paul's nature is one of enjoying and indulging. He likes to hear and see the "beautiful". He needs the scent and the sensation of everything and anything aesthetically appealing. However, that does not entail that he possesses any inkling to fight and make a goal to acquire those things. That would be too "common". He was not born with the backbone of the average man. He is, simply, a very delicate and different creature altogether.
Let's also consider that the quote cited was rephrased earlier in the story when the narrator explains the effects of the theater in Paul. Although Paul's existence is colored entirely by his presence at the Carnegie Hall, it is clear that he is not inclined to be an actor, nor does he care about the acting world, celebrity, nor even popularity.
It was equally true that he was not stage-struck--... He had no desire to become an actor, any more than he had to become a musician...what he wanted was to see, to be in the atmosphere, float on the wave of it, to be carried out, blue league after blue league, away from everything.
Therefore, here we see in two completely different instances what Paul's tendency is: he is a floater, a dreamer, and a creator of things that are fantastic. His world is not congruent with our own. Hence, it would be impossible to compare ourselves, or our thinking, with that of Paul's.
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