"Modus moron" rule of inference? 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.

$$\frac{P\Rightarrow Q, Q}{\therefore P}\qquad \text{(modus moron)}$$

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.)
This will, in all likelihood, be drowned out by the other answers. But, a mathematical version of this, is as follows:

$$p&gt;3,p\in \mathbb P\implies p\in\{x:\text{Mod}(x,6)\in\{1,5\}\},25\in\{x:\text{Mod}(x,6)\in\{1,5\}\}\over\therefore 25\in\mathbb P$$