Way back in my first year of university, as part of a first year discrete maths unit we were taught introductory formal logic. After introducing propositional logic and covering ANDs, ORs and truth tables, we moved on to implications. For this particular lecture we had a fill-in lecturer. I can’t remember why.
In explaining implication to us this lecturer used an example that has stuck with me ever since. This isn’t because it was one of those glorious examples that are like a light being turned on; suddenly it is all clear and new vistas of understanding open up. Oh no, this example was the other kind.
One of those examples that distracts with its own internal errors and inconsistencies; that steers you in completely the wrong direction; and, best of all, pollutes your mind enough that you may never understand the original point.
The bad example:
An implication would be when your mother says to you: ‘If you clean your room, then you can go to the movies.’ So after you clean your room, your mother lets you go to the movies and the statement is true. But if you don’t clean your room and go to the movies anyway, the statement is also true.
Logically, yes, that’s correct. Single implication works like that. But the world doesn’t, and it’s pretty hard to ignore that little detail.
Bonus points if you can work out who the lecturer was.