Was working on this when the forum went down, and waiting for it to come back up.
Here are some new additions to my page on type, which contain the stuff I have been coming to learn that I believe clarify the theories of the functions.
For those who might have read the full version (Temperament Part 2: The MBTI's 16 types and Cognitive Functions), I have been revamping it, to try to improve the flow. I had been adding new stuff as I went along, understanding the concepts better, and it got to the point that the whole flow was interrupted. So now, I have gone back to just building up the type code letter by letter, and moved some of the deeper info on function definitions and archetypes to later.
I hope those who have read it will give it another chance.
As I have been discussing before, the terms that I have found seem to convey the essence of the functions best are:
Sensing: tangible (aka "concrete")
iNtuition: conceptual (aka "abstract")
Thinking: technical (aka "impersonal")
Feeling: humane (i.e. "personal" in a general sense)
Pe: emergent data
Pi: stored data
Je: set standards determined by the object or environment
Ji: variable situation standards internalized by the subject
So we see that the type defining dominant and auxiliary must be JePi or PeJi because:
Emergent data (Pe) produces variable situations (Ji)
Stored data (Pi) is best for set procedures (Je)
Using these definitions of the functions the tandems come together as follows:
SeNi: emergent experience compared with stored conceptualizations (patterns)
NeSi: emergent conceptualizations compared with stored experience (facts)
TeFi: technical (impersonal) considerations are set, so humane (personal) considerations must then be variable in deference to them.
FeTi: humane considerations are set, so technical considerations must be variable, in deference to them.
They've also been expressed as:
TiFe: "I think, we feel"
FiTe: "I feel; we think"
I've never seen this one, but by extension:
SiNe: I experienced, we infer
SeNi: we experience, I infer
Thinking and Feeling function's connection to literal "thinking" and "feeling":
The literal terms are based on the emotionality of the process, with emotion representing more of a deeper personal involvement in the process, in contrast to a detached impersonal pondering of subjects. This is where the confusion about "Feeling=emotions" comes from, but it says nothing about the humane or technical focused content of the process, which is what the T/F functions are about.
Functions and gender roles
At this point, it's probably good to mention the problem of gender and the judging attitudes, and the roles formed around them. Either can gender can be either T or F. But because females are naturally designed to be the mothers, carrying and nurturing the young child, their natural focus has shifted more to the "humane" or "personal" side of life. (Including being more in touch with the emotions). Since males then were the breadwinners, and the strong protectors, they became more focused on the "technical" or "impersonal". The traditional roles of society formed around this, with the typical model of a woman being said to be SFJ or SFP, and the typical model of a man being STJ or at least STP. (Notice how both are S).
Even though modern society has been changing the roles and integrating both genders to the same sorts of careers and family tasks, the associations have stuck. This can cause type confusion for female T's, and both type and "masculinity" problems for male F's. I have noticed particularly that female ITJ's (especially ISTJ's) and ETP's, who both have tertiary Feeling, will look a lot like Feelers. Male EFP's and I imagine, IFJ's (particularly INFJ) will have tertiary Thinking, and are said to look a lot like Thinkers. The tertiary is often carried by a complex that is said to "inflate". This will lead to it becoming very visible in the personality, so a woman's tertiary Feeling, especially, will often be very prominent and color their outward behavior, fitting the traditional roles.