He's saying, "we mathematically figured out a long time that trying to look at a computer program and predetermine what it will do before running it is a task that reduces to the halting problem."
That this is a stupid way to look at the antivirus problem is besides the point here.
You don't need to figure out what a program can do ahead of time if you limit what it can do at run time. You don't even need to let the user do anything at run time.
What's the difference between 'rm -rf foo', for example, and 'run-virus'?
I can't think of an especially usable uber-paranoid defensive system, although I'd definitely love to be proven wrong. Essentially, the problem isn't a totally technological one. The core of the problem is that the user can effectively be convinced to be their own attacker.