Thus the statement ‘If I am the king of England, the moon is made of blue cheese’ is ‘true’ (assuming I am not the king of England), and so is the statement ‘If I am the king of England, the moon is NOT made of blue cheese’. Thus, ‘B’ AND ‘not B’.
This doesn’t prove B and not B, it proves (~A OR B) AND (~A OR ~B), which is true since A is false (you are not the King of England).
Another way to avoid the mistake is to notice that the implication is false, regardless of the premises. In practice, people’s beliefs are not deductively closed, and (in the context of a natural language argument) we treat propositional formulas as tools for computing truths rather than timeless statements.
This doesn’t prove B and not B, it proves (~A OR B) AND (~A OR ~B), which is true since A is false (you are not the King of England).
Another way to avoid the mistake is to notice that the implication is false, regardless of the premises.
In practice, people’s beliefs are not deductively closed, and (in the context of a natural language argument) we treat propositional formulas as tools for computing truths rather than timeless statements.