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:
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.
“Ex falso quodlibet” or “principle of explosion” might be the search term you are looking for. Relevance logic and other nonclassical logics are not explosive in the same way.
The inconsistency effect implies that fallible creatures dare not rely on pure logic.
They can’t consider themselves manifestations of logic, but since they are reasoning about the infallible logic, not about themselves, there is no problem.
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:
One page
Another page
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.
“Ex falso quodlibet” or “principle of explosion” might be the search term you are looking for. Relevance logic and other nonclassical logics are not explosive in the same way.
They can’t consider themselves manifestations of logic, but since they are reasoning about the infallible logic, not about themselves, there is no problem.