Quote Originally Posted by Subterranean
The functions themselves are obviously discrete because they are set in stone.
Well I think this is one of the key issues. Socionics assumes the functions are discrete. However, each function is described in many ways. For example, Se is described as forcefulness, ability to process lots of sensory data, and a number of other things. Te is described as algorithmic logic, productivity, general factual knowledge, and a number of other things.

What if someone is strong in some of those things that describe a function, but not all of them? In theory, this is impossible, because Socinoics assumes that each function is one thing, and that all those behaviors are merely the consequences of the actions of one thing. But how can we be sure?

Maybe each function is merely a cluster of many somewhat related qualities that themselves are correlated but still slightly independent?

In that case, the discreteness of the functions would be in doubt.