Propositional calculus is brittle. A contradiction implies everything.

In Set theory, logic and their limitations Machover calls this the Inconsistency Effect. I'm surprised to find that this doesn't work well as a search term. Hunting I find:

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In classical logic, a contradiction is always absurd: a contradiction implies everything.

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Another trouble is that the logical conditional is such that P AND ¬P ⇒ Q, regardless of what Q is taken to mean. That is, a contradiction implies that absolutely everything is true.

Any false fact that you believe acts as a logic bomb. Once you come across the true fact, the combination permits you to construct a logical argument to reach any conclusion. This is just what the monsters from the Id have been waiting for.

The inconsistency effect implies that fallible creatures dare not rely on pure logic.