Logic Of Complementarity As A Synthesis To Completeness And Incompleteness Theorems Of Godel

Abstract

Mathematical logic is central to logic in the modern time. This mounts great emphasis on formal systems and arithmetical laws which are correlational to human reason but less regards to intuition. The aim of this paper is an attempt to draw a logical complementarity as a synthesis to the extremes of completeness and incompleteness theorems of Kurt Godel. Using the analytical method of research, this paper makes a critique of completeness and incompleteness theorems of Godel, hence exposing their limitations/inadequacies in the representation of reality in entirety. The paper studies completeness theorem as a theory which is both consistent and complete while incompleteness theorem demonstrates the fundamental inadequacies of formal systems. In the same vein, this papers studies formalism as the popular stand of logicians in the 19th century with particular concern on Hilbert. Also, the studies reviews the  strength and weakness of both completeness and incompleteness theorems. By appraisal, this paper opines that a true logical position that represents the wholeness of reality and humans is a logical complementarity of both completeness and incompleteness theorems. Thus while completeness theorem shows the strength of formal systems correlational to reason, incompleteness theorem punctures the inadequacies of formal systems to address intuitive capacities of the human person beyond the provisions and provability of reason.