When I first encountered material implication I thought it was just stupid. False implies anything? Everything implies true? That's not what implies means, ther

When I first encountered material implication I thought it was just stupid. False implies anything? Everything implies true? That's not what implies means, there must be some sort of relevancy, surely? The block for me was treating material implication as if it defined what 'if' meant in natural language. But it doesn't. 'If I am a turtle then the president of the United States is Hillary Clinton' isn't a statement about a relationship between whether or not I'm a turtle and who is the POTUS. It's a formal sentence. It's like a regular expression or something. It has no real meaning, it's just symbols. It's just 'Q Y C' or '$ ~ F' or 'A -> B' in a formal language. We give semantics to those symbols by assigning a truth value to 'A -> B' as a function of the truth values we assign to the symbols A and B. It seems silly if we substitute A for something clearly false and B is substituted for something also false and clearly unrelated, but that's because when you read the statement above it looks like natural language, and it is natural language, but logic isn't about natural language. It's about formal language. If you write it as 'I am a turtle -> Clinton is the POTUS' then it becomes a bit more clearly just 'arbitrary false thing -> arbitrary thing'. If you try to divorce the concept of material implication from the natural language construct of 'if..then..' then you shouldn't have a problem. Remember, material implication is truth-functional, which means that the truth value of 'A -> B' is just a function of the truth values of A and B (namely that it's true unless A is false and B is true), not whether they're related or relevant to each other.