The Joy of Logic BBC Documentary
The BBC made a documentary about logic and how logic relates to computers. As far as I know, this is the only documentary about logic out there and it is decent. Even so, there are a couple of comments that I think are worth making about it that come to mind:
- The documentary says that logic is about proper reasoning. I agree, but it also only talks about formal logic. There’s also informal logic. Formal logic is how computers do things. Formal logic can tell you if an argument is valid — if the form of the argument assures us that true premises can’t be used to get a false conclusion. Informal logic tells us about fallacies, inductive reasoning, hidden premises, and argument interpretation. Unfortunately informal logic is often quite neglected in philosophy and logic classes.
- The documentary says that Godel proved that mathematical/logical systems can’t be complete — there are some thing the systems can’t prove. He actually only showed that finite formal mathematical/logical systems can’t be complete (which are the systems we can give computers). Godel was quite optimistic about the human ability to do math and logic without finite formal systems. He thought we could probably out-think computers for that reason.