  But this first proof does not explain why the distinction in  pleasures is made; the appeal to the philosopher’s authority as a  judge gives no account of the philosopher’s reasons for her judgment. Moreover, the first pleasure proof does not say that the  philosopher’s pleasures are vastly superior to those of the  money-lover and the honor-lover. So Glaucon—or anyone else  tempted to avoid the mathematical studies of Book Seven—might  think that the superiority of the philosopher’s psychological justice is slight, and given the disrepute heaped on the philosophers (487a  ff.), Glaucon or anyone else might decide that the  less-than-perfectly just life is better overall. Socrates needs to  show that the philosopher’s activities are vastly better than the  non-philosopher’s activities in order to answer the challenge  originally put forth in Book Two by Glaucon and Adeimantus. So it is  for very good reason that Socrates proceeds to offer a second  pleasure proof that he promises to be the “greatest and most decisive overthrow” for the unjust (583b6–7).