In languages oriented towards systems programming, digital logic and hardware design, it's common to treat boolean as a subtype of integer. In languages oriented towards mathematics and type theory, it's more usual to treat them as disjoint types.

Being from more of a systems programming background, it has always seemed to me appropriate to take the former approach. I would have thought it appropriate even from a mathematical viewpoint, since we already have a hierarchy of numeric types (natural numbers are a subtype of integer which is a subtype of rational etc.) so it would fit neatly at the start of that hierarchy; but then I'm not a real mathematician, so I may be missing something.

Apart from a little bit of extra error checking (catching the mistake if you pass a boolean to a function expecting an integer and you didn't mean to), is there any advantage to having them be disjoint types?