Pragmatics & Cognition 23:3 (2016), 473–485. doi 10.1075/pc.23.3.09kle issn 0929–0907 / e-issn 1569–9943 © John Benjamins Publishing Company Soſt logic and numbers Moshe Klein and Oded Maimon Tel Aviv University and Ohalo College Katzarin / Tel Aviv University, Israel 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 soſt logic. By the development of a new coordinate system, we make a distinc- tion between −0 and +0. is 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 soſt logic, and use it as a basis for a new computational mod- el. is model has a potential to change the current computational paradigm. Keywords: Soſt logic, Necker cube, Mobius strip, Nonstandard analysis 1. Introduction Marcelo Dascal (2008) wrote about the mathematician and philosopher Gottfried Wilhelm Leibniz, that as a young researcher he aspired to develop a universal lan- guage with a single symbol. Spencer-Brown (1969) fulfilled this vision in his book Laws of Form. As suggested by Dascal, Leibniz converted his first vision into a new one: to discover and develop a mathematical language that will demonstrate a soſter logic that will overcome the limitations of the dichotomy of truth and falsehood. Leibniz had an ambitious plan to construct a universal language, which will prevent misunderstandings between people as well as serve as a scientific lan- guage that reflects thought. According to Dascal, language is a tool for thinking and influences thinking. Precise formal language, precise expression and think- ing, are necessary to reduce the number of errors and increase certainty, thus al- lowing for the resolution of disputes. However, Dascal argues that Leibniz knew that no rational thinking and no “soſt rationality” could be described by a formal computational model of rationality and computational language. In fact, Leibniz wrote in many occasions that the logic of two states is insufficient to grasp the full meaning of reason.