This dissertation investigates the internal articulation between world and language - the isomorphy - hold by Wittgenstein in his Tractatus. To do so, I determine using the Set Theory that the tractatian isomorphy functions mapping state of affairs in terms of atomic propositions through a peculiar relation between objects and names. As a result, I demonstrate that it is legitimate to use the mathematical concept of isomorphism to interpret Tractatus. According to this, I also defend that logic, as it is assumed by Wittgenstein, can be held as a regenerated metaphysics in contrast to the illegitimacy of the traditional one.