That’s interesting. I’ll have to read up on that. You’re right, I am thinking about boolean algebra.
In the mean time though, I’ll note that Boolean algebra on Wikipedia also refers to this operation, so I’m not alone:
Material conditional
The first operation, x → y, or Cxy, is called material implication. If x is true, then the result of expression x → y is taken to be that of y (e.g. if x is true and y is false, then x → y is also false). But if x is false, then the value of y can be ignored; however, the operation must return some Boolean value and there are only two choices. So by definition, x → y is true when x is false (relevance logic rejects this definition, by viewing an implication with a false premise as something other than either true or false).
It also uses the second interpretation that I mentioned in my earlier comment (4 above this one), with true being default, rather than the one we’ve been discussing.
The comment you replied to is my response to this. It’s the only boolean operation that works this way. All the others are straightforward.
I think the problem is that you’re thinking in terms of boolean algebra, while implication being implication comes from propositional logic.
That’s interesting. I’ll have to read up on that. You’re right, I am thinking about boolean algebra.
In the mean time though, I’ll note that Boolean algebra on Wikipedia also refers to this operation, so I’m not alone:
It also uses the second interpretation that I mentioned in my earlier comment (4 above this one), with
truebeing default, rather than the one we’ve been discussing.