  We have published several articles about generalizations and boundary-case
exceptions to the Second Incompleteness Theorem during the last 25 years. The
current paper will review some of our prior results and also introduce an
`enriched' refinement of semantic tableaux deduction. While the Second
Incompleteness Theorem is a strong result, we will emphasize its boundary-case
exceptions are germane to Global Warming's threat because our systems can own a
simultaneous knowledge about their own consistency, together with an
understanding of the $\Pi_1$ implications of Peano Arithmetic.
