Transreal Numbers and Sentient Logic

Abstract

This chapter introduces the basic concepts of Total Semantics based on transreal numbers, a new field of mathematics in which division of zero is allowed. In the logic created from the transreals, it is possible to evaluate non-propositional objects such as sensations or feelings as having truth value. By covering all semantical possibility, transreal semantics enables a “poetical discourse” based on images and an immediate intuition of reality, an intuition that is both sensory and mental. This describes, and defines, a new type of epistemic operation—a sentient one—and leads to the possibility of developing a formal epistemic logic that assesses how we obtain or acquire knowledge from the perspective of sentient agents.