A commonly shared image of convergence is that of arrays of light aiming at a focus―a projected vanishing-point to which all empirical inquiry strives to converge or the Kantian regulative ideal that reason aims at beyond the boundaries of all possible experience. Such an intuitive image of convergence is not completely foreign to Peirce's view, but a predominantly optical model of convergence fails to capture the generality and flexibility of the idea that Peirce wished to advocate. This paper formulates Peirce's convergence theory of truth based upon his mathematical insights and examines a number of criticisms leveled against the theory including that of Quine. I argue that Peirce's understanding of convergence is far more sophisticated than what critics have often assumed and that simultaneous convergence to multiple elements is not excluded from his picture.