Soft logic and numbers

In this paper, we propose to see the Necker cube phenomenon as a basis for the development of a mathematical language in accordance with Leibniz’s vision of soft logic. By the development of a new coordinate system, we make a distinction between −0 and +0. This distinction enables us to present a new model for nonstandard analysis, and to develop a calculus theory without the need of the concept of limit. We also established a connection between “Recursive Distinctioning” and soft logic, and use it as a basis for a new computational model. This model has a potential to change the current computational paradigm.