Why is that if P entails not-Q and Q (a contradiction) do we conclude not-P? I understand that this a reductio ad absurdum and that because of the law of bivalence P either has to be true or false so if it entails a contradiction it is proved not true therefore false. But that last step is what I can't seem to justify...why does it become Not-P if it entails a contradiction? If I had to guess it's because contradictions don't exist in real life so if P were true and it entailed something that could never exist then it must be the case that P is not true (and this is true because of modus tollens: not-Q entails not-P). But we are dealing with symbols in the case of formal logic so how does this apply? Is formal logic an analogy of real life? I hope the question is clear after this rant!