A dual identity based symbolic understanding of the Godel's\n incompleteness theorems, P-NP problem, Zeno's paradox and Continuum\n Hypothesis

A semantic analysis of formal systems is undertaken, wherein the duality of\ntheir symbolic definition based on the "State of Doing" and "State of Being" is\nbrought out. We demonstrate that when these states are defined in a way that\nopposes each other, it leads to contradictions. This results in the\nincompleteness of formal systems as captured in the Godel's theorems. We then\nproceed to resolve the P-NP problem, which we show to be a manifestation of\nGodel's theorem itself. We then discuss the Zeno's paradox and relate it to the\nsame aforementioned duality, but as pertaining to discrete and continuous\nspaces. We prove an important theorem regarding representations of irrational\nnumbers in continuous space. We extend the result to touch upon the Continuum\nHypothesis and present a new symbolic conceptualization of space, which can\naddress both discrete and continuous requirements. We term this new\nmathematical framework as "hybrid space".\n