'If' and the problems of conditional reasoning

'If' is a puzzle. No consensus has existed about its meaning for over two thousand years. Here, we show how the main psychological theories deal with the seven crucial problems that it raises. These competing explanations treat 'if' as though it was a term in a formal logic, or as eliciting the construction of a mental model of the world, or as an instruction to suppose that a proposition holds. The solution to 'if' would be a major step towards understanding how people reason, and towards implementing a computer program that can reason in a human way. We argue that the mental model theory is closer to resolving the puzzle of 'if' than its competitors.