Philosophical and Mathematical Background

This chapter establishes the philosophical-mathematical foundation of Soft logic. We briefly describe Immanuel Kant’s epistemology (Kant 1838), which was revolutionary for its time, especially for his critical distinction between the world of phenomena that our senses perceive and the world as it is in itself, the things as they stand outside the faculties of our consciousness. This distinction in Kant’s epistemological theory entails difficulties which were recognized by Salomon Maimon’s critique of Kant in his “Essay on Transcendental Philosophy” (Maimon 1790/2010). Maimon was a Jewish philosopher who developed the theory of metaphysical infinitesimals, arguing that the world is embodied by human consciousness in infinitely small sizes. Furthermore, we will present a tangible model of the infinitesimal world by distinguishing between the various multiples of the number zero. We conclude this chapter with a survey of the evolution of numbers and the development of the world of infinitesimals in mathematics (Ehrlich 2018).