This is an exercise I got from the book “First Order Mathematical Logic” by Angelo Margaris (1967). I have never heard of this rule before, the question is whether what Margaris calls the modus moron rule of inference is correct or not and to explain why I think so.
It seems correct to me, my reasoning is that if P\Rightarrow Q and Q it does not matter whether P or \neg P since a false antecedent makes a true conditional, which I would show by the rows of the truth table of (P\Rightarrow Q) where Q is true.
Is this a valid argument?
It’s true that if P is false then P\Rightarrow Q is true. But the question is not asking if P\Rightarrow Q is true, it’s asking you if you can infer P from P\Rightarrow Q and Q.
Let’s be concrete. Suppose “if Mark is drunk, then Mark is happy” is a true statement, because Mark is a happy drunk. Given that Mark is presently happy, may we infer that Mark is drunk? No; there may be other circumstances in which Mark is happy besides being drunk.
(This example is drawn from a real life discussion between friends about putative alcoholism which devolved into a debate about logical implication.)