Douglas J. Huntington Moore

This paper presents a formal reconstruction of central structural themes in Leibniz’s Monadology and related mathematical writings. Its sole axiom is First-Classness (\FC): no entity is privileged. Applied to the Generic Entity, understood as concrete and of undetermined attribute and undetermined cardinality, this axiom excludes the usual asymmetries of formalisation. Number, origin, container, external standpoint, and fixed identity do not survive as primitive terms. What remains is the first articulation of the Generic Entity: the complementary opposition between toHave and toBe, expressed as feminine and masculine dispositional modes. From this opposition there emerges a monadological field of perspectives in which each monad expresses the whole, while no monad occupies a privileged centre. In this way the paper gives formal expression to themes long associated with Leibniz: monads, perspective, combinatorial generation, and the search for a characteristica universalis. The paper also develops the qualitative binary {F, M}, a fourfold dyadic articulation, and the beginnings of a calculus adequate to monadological organisation. The mode of reasoning is not analytic in the usual sense. It proceeds from candidate structure to ground, closer in spirit to Stoic logical testing than to modern axiomatic construction. The paper is a Leibniz-oriented reformulation of themes originally developed in Dispositions of the Quantum Object (DQO), directed to readers in Leibniz studies, early modern philosophy, and philosophy of mathematics.

This paper presents a formal reconstruction of central structural themes in Leibniz’s Monadology and related mathematical writings. Its sole axiom is First-Classness (\FC): no entity is privileged. Applied to the Generic Entity, understood as concrete and of undetermined attribute and undetermined cardinality, this axiom excludes the usual asymmetries of formalisation. Number, origin, container, external standpoint, and fixed identity do not survive as primitive terms. What remains is the first articulation of the Generic Entity: the complementary opposition between toHave and toBe, expressed as feminine and masculine dispositional modes. From this opposition there emerges a monadological field of perspectives in which each monad expresses the whole, while no monad occupies a privileged centre. In this way the paper gives formal expression to themes long associated with Leibniz: monads, perspective, combinatorial generation, and the search for a characteristica universalis. The paper also develops the qualitative binary {F, M}, a fourfold dyadic articulation, and the beginnings of a calculus adequate to monadological organisation. The mode of reasoning is not analytic in the usual sense. It proceeds from candidate structure to ground, closer in spirit to Stoic logical testing than to modern axiomatic construction. The paper is a Leibniz-oriented reformulation of themes originally developed in Dispositions of the Quantum Object (DQO), directed to readers in Leibniz studies, early modern philosophy, and philosophy of mathematics.