Royce’s sustained interest in technical logic is beyond doubt. One of his first publications, which appeared while he was still teaching at the University of California at Berkeley, was a logic primer, and many of the productions of his later career were articles on logic. Indeed, it can well seem that Royce spent at least ten or eleven years working almost exclusively on logic following his attendance at Peirce’s 1898 Cambridge Conference Lectures, entitled Reasoning and the Logic of Things. During (...) this period he filled dozens of notebooks with minute explorations of Boolean functions and relations, investigating them mostly by using fourcircle Venn diagrams. Less obvious than Royce’s devotion to logic .. (shrink)
In this paper, a game-theoretical semantics is developed for the so-called alpha part of Charles S. Peirce's System of Existential Graphs of 1896. This alpha part is that portion of Peirce's graphs that corresponds to propositional logic. The paper both expounds a game-theoretical semantics for the graphs that seems close to Peirce's own intentions and proves for the alpha part of the graphs that this semantics is adequate.
Writings of Charles S. Peirce: A chronological edition, volume 4, 1879?1884. Editor [in Chiefl, Christian J. W. Kloesel. Bloomington, Indianapolis: Indiana University Press, 1989. lxx + 698 pp. $57.50.