  A semantic analysis of formal systems is undertaken, wherein the duality of
their symbolic definition based on the "State of Doing" and "State of Being" is
brought out. We demonstrate that when these states are defined in a way that
opposes each other, it leads to contradictions. This results in the
incompleteness of formal systems as captured in the Godel's theorems. We then
proceed to resolve the P-NP problem, which we show to be a manifestation of
Godel's theorem itself. We then discuss the Zeno's paradox and relate it to the
same aforementioned duality, but as pertaining to discrete and continuous
spaces. We prove an important theorem regarding representations of irrational
numbers in continuous space. We extend the result to touch upon the Continuum
Hypothesis and present a new symbolic conceptualization of space, which can
address both discrete and continuous requirements. We term this new
mathematical framework as "hybrid space".
