Newbie question regarding Godel's Incompleteness Theorem

Hi: Have a newbie question regarding Godel's Incompleteness Theorem.
When Godel constructs the statement G, which is undecidable, why is it
not considered to show an inconsistency? Doesn't the law of the
excluded middle state that either G or ~G must be provable in the
system?

Thanks
Scott
.

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