In The Republic, what is Plato's vision of the relationship between pleasure-pain and reason, and how does he present it?
This analysis of pleasure, pain and reason comes in Book IX of this text, and Plato talks about these topics in the context of his overall argument that those who are just and follow the rules of the state are happier than those who are unjust. Plato argues in his analysis of pleasure and pain that pleasure is of course pleasant, but the pleasures of the body that give relief from pain are not true pleasure in that they are not permanent and are only temporary. The only true pleasure, Plato argues, is derives from understanding, since it can yield permanent pleasure rather than temporary pleasure:
"Which do you think more truly is, that which clings to what is ever like itself and immortal and to the truth, and that which is itself of such a nature and is born in a thing of that nature, or that which clings to what is mortal and never the same and is itself such and is born in such a thing?” “That which cleaves to what is ever the same far surpasses,” he said.
Plato thus argues that the only true pleasure is that which can be found in applying oneself to reason and understanding, or things that are "immortal and to the truth." Plato's argument for living a just life is concluded when he presents a calculation of the greater pleasure a just life receives than an unjust life, which is 729 more pleasurable than an unjust life. It is not clear, however, where this information is taken from or how this precise number was reached. Plato therefore presents his argument about the relationship between pleasure and pain in a rational way up until this point, when suddenly his conclusion becomes a bit more confused.