While it's kind of counter-intuitive, we know that the statement "If A, then B" is always correct as long as A is false. For example, both
- If $1 = 2$, then $e + \pi$ is irrational
- If $1 = 2$, then $e + \pi$ is rational
are true, because $1 \neq 2$.
In real life, many statements are based on a false hypothesis. For example,
World War I will never break out without the assassination of Archduke Franz Ferdinand.
My history teacher tells me that this is incorrect, because the assassination is a prelude, rather than the cause. However, from a mathematical perspective, this statement is true, because the assassination did happen, right?
This is weird. Could anyone explain it to me?
Trying to justify this post:
I think this question essentially focuses on the comparison between classic logic and the logic in natural languages, which can help people understanding the former. As I know, many people find it hard to intuitively understand why false implies everything in classic logic, presumably because they are thinking in a natural language, and reading answers under this question would benefit them. According to the help center, questions about "Understanding mathematical concepts and theorems" are welcome on this site.
I admit that it's not entirely about math, so I've tagged it with
soft-question. However, I would argue that it's not particularly related to a specific area, say, history. Here WWI is merely used as an example, and it can be anything else, like rational choice theory in economics and virtually every theory with an assumption.
Plus, based on the positive response from the community (votes and comments), I believe this question would receive some interesting answers if it's re-opened.