On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory of predication involving three universal categories that Peirce continued to apply in philosophy and elsewhere for the rest of his life. The categories demonstrate and concentrate the pattern seen in "How to Make Our Ideas Clear" (1878, the foundational paper for pragmatism), and other three-way distinctions in Peirce's work. The Categories In Aristotle's logic, categories are adjuncts to reasoning that are designed to resolve equivocations, ambiguities that make expressions or signs recalcitrant to being ruled by logic. Categories help the reasoner to render signs ready for the application of logical laws. An equivocation is a variation in meaning—a manifold of sign senses—such that, as Aristotle put it about names in the opening of Categories (1.1a1–12), "Things are said to be named 'equivocally' when, though they have a common name, the definition corresponding with the name differs for each". So Peirce's claim that three categories are sufficient amounts to an assertion that all manifolds of meaning can be unified in just three steps. The following passage is critical to the understanding of Peirce's Categories: The first thing to extract from this passage is the fact that Peirce's Categories, or "Predicaments", are predicates of predicates. Meaningful predicates have both extension and intension, so predicates of predicates get their meanings from at least two sources of information, namely, the classes of relations and the qualities of qualities to which they refer. Considerations like these tend to generate hierarchies of subject matters, extending through what is traditionally called the logic of second intentions, or what is handled very roughly by second order logic in contemporary parlance, and continuing onward through higher intensions, or higher order logic and type theory. Peirce arrived at his own system of three categories after a thoroughgoing study of his predecessors, with special reference to the categories of Aristotle, Kant, and Hegel. The names that he used for his own categories varied with context and occasion, but ranged from reasonably intuitive terms like quality, reaction, and representation to maximally abstract terms like firstness, secondness, and thirdness, respectively. Taken in full generality, nth-ness can be understood as referring to those properties that all n-adic relations have in common. Peirce's distinctive claim is