I was reading about the principle of explosion and there is one thing I don't get.
Based on my understanding, the principle of explosion goes as follows: Given two statements $P$ and $Q$, and suppose $P$ and $\neg P$ are both true. Then we assert that $P\lor Q$ is true since $P$ is true. Finally, since $\neg P$ is true, it follows that $Q$ must be true for $P\lor Q$ to be true.
How does this form of deduction make sense? What I don't get is that if both $P$ and $\neg P$ are true, then it is a contradiction. At this point, we cannot conclude whether $P$ is true or false. So, it would be meaningless to determine whether $P\lor Q$ is true.