Arguments with INCONSISTENT premises ⟨06,04⟩

Question: what can you do with an argument with inconsistent premises—e.g. (p ∧ ¬p)?

Answer: anything you like! An argument with inconsistent premises entails anything.

Why? Because an argument is valid only if it's impossible that, supposing the premises are true, the conclusion is false. So F to T is invalid. But F to F arguments are valid. And inconsistent premises will always be F. So you'll never go from T to F if your premises are inconsistent.