There seem to be two distinct aspects to the role played by the Interpretant in Peirce's account of the sign relation. On the one hand, the Interpretant is said to establish the relation between the Sign and Object. That is, the Sign can "stand for" its Object, and thereby actually function as a Sign, only by virtue of its being interpreted as such by an Interpretant. On the other hand, the Interpretant is said to be "determined" by the Sign in such a way that it is thereby mediately determined by the Sign's Object. How can we understand the relation between these two aspects of the Interpretant ? This is the question with which this paper is concerned. I begin by drawing a distinction between what I call the first-order function and second-order function of the Interpretant, and illustrating this distinction using Peirce's example of comparing the letters p and b in & SECT; 9 of the 1867 "On a New List of Categories." I then show that this same distinction can be discerned in a significant passage in the second section of Peirce's 1903 "A Syllabus of Certain Topics of Logic," as well as in his early definition of the Interpretant in the "New List." This double function of the Interpretant has been noted in the Peircean literature, specifically by Joseph Ransdell in his 1966 dissertation, and more recently by Andre De Tienne. However, an important aspect of what I call the second-order function of the Interpretant remains unclarified in Ransdell and De Tienne's approaches, namely, its relation to the logical operation of hypostatic abstraction. I will show that the Interpretant, in its second-order function, plays a role formally identical in the sign process to the role played by hypostatic abstraction in Peirce's demonstrations of the Reduction Thesis. This formal identity will afford us with a way of understanding the relation between the two aspects of the Interpretant in terms of hypostatic abstraction.
