### More Thoughts on the Republic

What is justice? I want to say that, for Plato, we can simplify the answer to a kind of equation: " justice = reason + will + desire ," except with the immediate caution that we should not misunderstand this as simple addition in the mathematical sense - so, for instance, to borrow a mathematical term here, we could say that the relation between, for instance, reason and will in this formula is non-commutative . That means you can't rearrange the terms of the formula and expect the result to be equivalent. So for example, although it's true for Plato that "justice = reason + will + desire," it is not true that "justice = will + reason + desire," and it is not true that "justice = desire + will + reason." That is to say, for Plato, " justice = reason + will + desire in that order ." Or, to be more precise, for Plato, in order for justice to exist, what matters is that the three elements that make it up - reason, will