Then does it appear to you that the psychological functions are all shades of grey? That Fe is really just an extension of Fi?
Or that Te and Fe are essentially the same function varying in degrees of subjectivity? (What is a degree of objectivity anyway?)
Or stranger still, that intuition is some extension of sensing? This would be the hardest for me to grasp though all functions are dependent on sensing to some degree(consider Ti solving a math problem, which seems totally separate from sensing but actually relies on numbers that have been seen and heard), but as a rule, most people use either their five senses or just their sixth sense the vast majority of the time (70%+)
To keep it simple, yes. I've struggled to determine the boundaries of each cognitive function... Especially that for Ni and Ne. The more I talk to Ne dominants, the more I relate to their thinking style. Many of them are also of the opinion that I'm using Ne and not Ni... (I have one tell me he sees me as an INFP). At the same time I'm undeniably Ni dominant. I match all the descriptions given for the use of Ni.
This is pretty much the same for most external and internal aspect of functions... the closer you look at them... the more ways you can see how they relate. One of the previous discussions of how Fi in INTJs can look like Fe is one sample.
On the other perspective, looking at Te vs Fe. Both of these are judging mechanisms. One is supposedly based on logics and the other values. Is there a middle ground where people can use a mixture of both? The answer obviously is
yes. How these people do it though is of interest. What makes up the middle of your continuum?
This leads to the question to the nature of functions. Are all the functions independent from each other and therefore the spectrum is simply due to a mixing of function usage? I.e. Sometimes you use Te more, other times you use Fe? Or is that there is no "real" Te or Fe... the person is using some "function" it's better to call it judging parameter can falls along the whole continuum... and what we call Te and Fe are simply labels for the two extremes for the variation of this parameter usage. I don't know at all. I go with the convention and assume they at the very least provide useful labels for understanding people. Your thoughts on this issue?
Forced categorization of people may only be useful for democracy, but the categorization of the functions is what I am most concerned with. While I do still stand by my original claim, I want to elucidate that although I believe all people can be relegated to a specific type, a taciturn, objective, tactical, sloppy ENFJ is not at all outside the realm of possibility, so it is the percieved boundaries of type that must be extended or in some cases ignored. Thus, the theory is tractable so that reality need not be.
Theory is how you define it.

In other words, it can be either way if it's just a theory... it's made up. My stance is that a theory is only as useful as it can be applied. If it bears little resemblance to reality than I pay no attention to it. However I do see your point in that we need a starting place to describe people. Afterall classification of things is how our minds process most information.
But I think that type is an indicator of the two dominant functions used. Four letters indicate "type" and nothing else. And "type" is only indirectly related to personality in that people of a certain type may have a higher probability of gravitating toward a particular set of behaviors for self-evident reasons, i.e., the introvert, which represents only 25% of the population, will likely be less sociable than the average person (50%).
I emphasize: an impregnable division stands between type and personality. When I say type, I am in no way alluding to a personality, but only to the functions that a person of this type will possess, and more specifically, only to the top two functions which are used without expending energy, since the function theory becomes inconsistent after this point.

Let us for a moment scrap "type" and just look at function pairing. We'll hit the major premises behind the pairing... I.e. a judging function must be paired with a perceiving function of the opposite orientation: JiPe or JePi. I think it's safe to say JiJe or PiPe doesn't work... but why opposite orientation? Many people who put X in their type do so because they feel either internal processing (JiPi) or external processing (JePe) is most natural for them...