by Shinji Ikeda
Leibniz approached the Continuum Problem from multiple aspects. It is his system of boundaries that connects his... more
Leibniz approached the Continuum Problem from multiple aspects. It is his system of boundaries that connects his metaphysics to his geometry. By focusing on the metaphysical and geometrical foundations of boundaries, we consider how his ideas on boundaries contributed to his resolution of the problem. First, we examine his geometrical idea of boundaries, in which he tried to construct a “calculus of situation” by reducing Euclidian geometry into an intensional logic. Our claim is here that boundary is not only defined as “a section of continuum”, but also defined metaphysically as “a place inherent in continuum” and later defined by the relation of “homogonous” (homogona), i.e. the relation of having a same origin. Second, we analyse the metaphysical idea of boundaries. Here, we see his characterization of boundary as “mode of continuum”, which remained throughout in his philosophical and mathematical thought even after he began to develop his geometry.
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