Mathematical formulation of Leibnizian world: a theory of individual-whole or interior–exterior reflective systems

A world model, suggested by Leibniz’s monadology, is formulated as a mathematical axiomatic system. The purpose of this world model is to provide a general scheme for describing a system of individuals having consciousness or internal worlds that communicate with each other and make a unified whole world, and moreover, the latter is reflected into the respective internal worlds and appears as an external world. Examples of such monadological structure of interior–exterior (or individual-whole) reflection can be observed in bio- or socio-systems and recently in computer networks. Moreover, a most elemental version of this structure can be found in the basic level of quantum physics. The model not only gives a prototype of monadological systems but also has an evolutionary ability to produce a hierarchy of monadological systems, which are interpreted as corresponding to various levels of consciousness.