We can see the first (exclusive-or) result as a limit on learnability. The linear associator's architecture is restricted in such a way that there are some things it just can never learn. Many such results have been derived for individual learning systems, whether connectionist or not: we're now beginning to see general theories of learnability. The idea is that we can see learning as function-building: our system has to learn a certain mapping from its inputs to its outputs. But it only has a certain set of primitive functions available, those provided by its hardware and software. If the function to be learnt can't be built up from these primitive functions, it's logically impossible for the system to learn it.