This is known as the paradox of entailment and is part of the reason why people find material implication so weird sometimes. A desire for non-explosive negatio

This is known as the paradox of entailment and is part of the reason why people find material implication so weird sometimes. A desire for non-explosive negation is one motivation for using paraconsistent logic. http://plato.stanford.edu/entries/logic-paraconsistent/ http://plato.stanford.edu/entries/logic-paraconsistent/