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.