Josiah Royce (1855?1916) was, in addition to being the pre-eminent metaphysician at the turn of the 19th century in the USA, regarded as ?a logician of the first rank?. At the time of his death in 1916, he had begun a substantial and potentially revolutionary project in logic in which he sought to show the connection between logic and ethics, aesthetics, and metaphysics. His system was developed in light of the work of Bertrand Russell and A. B. Kempe and aimed (...) to include Russell's logic as a subsystem. This more comprehensive logic, which Royce called system Σ, brought together an analysis of the character of experience and knowledge with the principles which served to organize interests and direct actions. The result was to be a logical theory framed by ?a profoundly ethical motive as well as a genuinely intellectual one? that would serve as ?a theory of the way in which activities must go on if they go on at all?. This paper examines three stages in the development of Royce's logical system, its relation to the logic of Principia Mathematica, and prospects for its further development. (shrink)

This note relates to two recent papers in the journal. The main point was to highlight Kempe's theory of multisets (as we now call them), especially in the background to the start of Peirce's theory of existential graphs.

Josiah Royce (1855-1916) was the leading American proponent of absolute idealism, the metaphysical view (also maintained by G. W. F. Hegel and F. H. Bradley) that all aspects of reality, including those we experience as disconnected or contradictory, are ultimately unified in the thought of a single all-encompassing consciousness. Royce also made original contributions in ethics, philosophy of community, philosophy of religion and logic. His major works include The Religious Aspect of Philosophy (1885), The World and the Individual (1899-1901), The (...) Philosophy of Loyalty (1908), and The Problem of Christianity (1913). Royce's friendly but longstanding dispute with William James, known as "The Battle of the Absolute," deeply influenced both philosophers' thought. In his later works, Royce reconceived his metaphysics as an "absolute pragmatism" grounded in semiotics. This view dispenses with the Absolute Mind of previous idealism and instead characterizes reality as a universe of ideas or signs which occur in a process of being interpreted by an infinite community of minds. These minds, and the community they constitute, may themselves be understood as signs. Royce's ethics, philosophy of community, philosophy of religion, and logic reflect this metaphysical position. (shrink)