Whether or not Godel could have foreseen all of the potential applications
for his Incompleteness Theorem is doubtful. In fact, the nature of what he was
proposing suggests that he (nor anyone else) would have been able to do so. The
Incompleteness Theorem states that no formal mathematical system will ever be
able to describe all true assertions – there will always be at least one that
is true despite being utterly beyond the ability of the system to prove
(Penrose). At the time, Godel employed this theorem to describe the limitations
of mathematical systems. Decades of extrapolation have permitted scholars to
use this theorem to make assertions about the nature of the mind – whether
cybernetic or human.
It is clear that Godel’s Incompleteness Theorem has implications for all of
human thought, not simply the disciplines of mathematics. Godel’s theorem is as
much a philosophical argument as it is a mathematical one, especially when
considering the extrapolations that can be drawn from the theory. Godel’s
theorem not only suggests that there are limitations to the minds that human
can create through cybernetic means, it also suggests that the human mind
itself is a finite system that is bounded by rules we ourselves will never be
able to fully comprehend.
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