Recently I was playing around with how the various functions operate, using my own terminology and viewpoint. I eventually decided I might as well type up a brief summary of my thoughts for posting and comments. [Standard disclaimer - IANAS (I am not a shrink); I've just done some amateur reading.]
Take it with a grain of salt. I'm just trying something theoretical out, to see if anyone else is interested for discussion purposes.
LONG POST AHEAD!
Si & Se
Si seems to be about collecting and storing data for all kinds of various problems: The best kinds of replacement tires for one's car, proper lawn care, when to replace a roof on a house, the best types of cookware, how to lose weight, etc.
Si-Dominant people will also compare sources of data and evaluate how reliable they are so as to choose the best solution. But the main function of Si seems to be about collecting and storing data. That way if a question pops up, the Si-Dominant person has information and solutions at his fingertips.
By comparison, extraverted Se-Dominant people function much the same way by collecting and storing sensations and experience. An accomplished Se-Dominant person can go to a restaurant, take a bite of spaghetti, and tell you from personal experience how it measures up to the spaghetti at every other restaurant at the city. They can go to a club and give you a read-out on how it compares to every other club in town in terms of atmosphere, service, music, clientele, etc. They remember all the best jokes, know the best fishing spots, and know what years were best for each wine.
So ultimately, the Sensing function seems to be about "comparing many to many" (comparing quality and reliability of many different categories of products and situations) in order to have a solution right at one's fingertips for many different kinds of problems.
IOW, Si & Se = solving problems by "comparing many to many"
Ni & Ne
Similarly, introverted Ni-Dominant people seems to enjoy solving problems, but they appear to use the device of "comparing many to one." When faced with a problem, they often have a theoretical model in their head of how the solution should work; then they try out many real-life solutions and compare the results until they find the result that most closely resembles the model in their head. The traditional example is Edison trying many different designs and materials to make a working light bulb.
By comparison, extraverted Ne-Dominant people will do much the same thing aloud with the community around them. Faced with a real-life problem, they'll brainstorm many possible approaches and solutions until they can hone in on a strategy that best addresses the situation at hand.
So ultimately, the iNtuitive function seems to be about "comparing many to one" (generating multiple approaches to be matched up to an internal ideal of how something is supposed to work, or to be matched up against an external problem).
IOW, Ni & Ne = solving problems by "comparing many to one."
Switching gears for a minute, one of the strongest psychological motivators for behavior is the Freudian superego. Thus it's worth playing around with the superego to explain the motivation for N and S behavior. (Modern psychology has kept intact much of Freud's original concept of the superego, along with the unconscious id.)
The most basic model of the superego is the example of housetraining a dog. The owner punishes the dog for going to the bathroom indoors and rewards the pet for going to the bathroom outdoors. Eventually the pet internalizes the lesson to such a degree that the pet will become quite distressed when it has to pee and can't get out of the house.
Similarly, children are punished for various infractions and internalize the lessons. In adulthood, they may feel considerable anxiety and emotional distress when even so much as contemplating some action their parent forbade in childhood. IOW, in adulthood we still carry around an internalized image of a punishing parent in our head, lowering our self-esteem and causing us anxiety when we don't live up an ideal model of behavior. The superego is that portion of our brain dictating punishment (anxiety and emotional distress) or reward (approval and heightened self-esteem) for our actions and intentions, basically acting as our "conscience."
Psychology posits that we each put in a great deal of effort appeasing our superego by avoiding situations that cause us anxiety and seeking situations that quiet our superego or cause our superego to reward us or approve of us.
If the superego (or "conscience") is a prime motivator of behavior, then it's fairly easy to see where N and S problem-solving behavior might be motivated by a desire to appease one's superego. Parents approve of children who are productive and resourceful at resolving problems. So N and S problem solvers may get a jolt of pleasure and reassurance from their superego when they engage in problem-solving behavior: S-Dominant people by storing data for quick access, and N-Dominant people by generating approaches and solutions and comparing them for best fit to a situation or problem-solving model.
Furthermore, as I understand N and S behavior, this data-storage and strategy-generation behavior is a fairly constant, on-going thing; it's a routine, background collection and "churning" of data and ideas in preparation for future challenges; Ns and Ss may actually get in the habit of seeking out problems so that they will have justification and a goal for this constant activity of the mind. Thus, N and S activities are open-ended "Perceiving" activities in the framework of the MBTI.
This sort of constant "churning" of data and ideas seems fairly labor-intensive. The superego would thus serve as justification for this kind of constant labor. Rewarded for problem-solving as children, adult Ns and Ss find that the "churning" of data and ideas generates an approving or pleasurable signal from the superego and/or wards off any punishing signals from the superego due to less-than-ideal behavior elsewhere in their life.
The superego and T/F
I have already stated that the defining characteristic of the S and N functions appears to be a constant collection/generation and then "churning" of data and ideas. The "churning" activity is open-ended and self-sustaining, so it is designated as a "Perceiving" activity in the framework of the MBTI.
In the framework of MBTI, T and F activities are considered "Judging" activities and are geared toward assigning a value judgment to things ("good," "bad," "useful," "useless," etc.). As such, they are closed-ended. Once a judgment is made, the T-Dominant or F-Dominant person moves on. Of course, minor ethical and directional judgments have to be made constantly all day long. But at least T and F activities provide closure so that we can move from one situation to the next, as opposed to getting stuck all day on a single problem, "churning" data and ideas about it (S/N) without judging (T/F).
Judgments require a standard against which to judge. The powerful superego represents an easy internal standard for judgments: It represents a strong compass in the form of an internalized punishing/approving parent image. Furthermore, the superego provides strong motivation for applying judgment to situations in the first place. Faced with a new situation and supervised by the punishing/approving superego, each individual has strong motivation to judge in a way that will cause the superego to approve rather than punish. Given the existence of a strong superego, we really only have two options when faced with a situation or problem: Make a judgment (and risk punishment of the superego) or avoid by running away. And we can't avoid everything in life. So we judge (T/F) and take our chances with the superego.
Hence, in their most basic form, T and F activities represent our interactions directly with the superego. Take the example of the housebroken dog again: Faced with a need to urinate while in the house, the dog "judges" that it is preferable to wait until he is outside rather than deal with the anxiety of urinating indoors. Similarly, faced with an opportunity to have extra-marital sex, an individual may go for it (if the superego prohibition against extra-marital sex is weak and the pleasure of sex will outweigh the anxiety of punishment from the superego) or reject the idea (if the superego prohibition is strong and the anxiety of punishment from the superego will outweigh the pleasure of sex).
Of course, this interaction between superego and our judgments is often more complex than simply reacting to the threat of the superego mechanically like a housebroken dog. For example, the superego is also externalized: Legal prohibitions, authority figures, peer pressure, etc. act as an externalized superego, promising disapproval or punishment in the event of misbehavior. And as adults, our judgments are more complex than mere reaction to pain and pleasure: we can also escape superego-style punishment (internal or external) by rationalizing our actions and building defenses.
Thus, if the superego represents our "conscience," then our rational processes ("churning" of data and then judgment of behavior) represent "free will," in that we get around the dictates of superego and law by rationalizing our behavior.
So the activities of T and F are somewhat more complex than merely mechanically judging situations based on superego dictates of pain and pleasure. Effectively, T and F "wheel and deal" with the superego with the goal of achieving a flexible and nuanced judgment of situations and facts.
Fi & Fe
Superegos are formed in childhood at a time when parents are all-powerful and children are highly dependent on their parents approval/disapproval for simple survival. One's superego will be modified with time and experience; eventually prohibitions and rewards of the legal system and society will supercede the superego in guiding the individual's behavior.
Still, the strongest signals from the superego (the ones that provoke genuine anxiety and pleasure even in adulthood) date back to one's earliest years, when the prohibitions were simplest and most direct: "Share your toys with your brother"; "Don't touch yourself there--it's dirty"; "What's wrong--don't you love me?"
IOW, true superego prohibitions--the ones that are genuinely powerful and anxiety-provoking--tend to be simple and point-blank. Meanwhile, the kinds of ethics conflicts that one deals with in adulthood tend to be some of the most complex and tangled that the individual faces in life. It's the job of Fi to untangle that Gordian knot on a regular basis.
In childhood the introverted Fi-Dominant individual deals with simple dichotomies: Good/bad, nice/not nice. But as the individual grows older, the problems get more complex and muddy. Still, judgments have to be made. So the Fi-Dominant individual hones his "judging" muscles by considering the finer points of good/bad, nice/not nice.
At age four he may simply understand things as good or bad. But at age five he may try wheeling and dealing by asking, "If I do 3 good things, can I do 1 bad thing?" Early in life he may simply rule that war is bad; later in life, with a finer understanding of international politics, he may conclude that war is bad in some instances and good in others.
By comparison, extraverted Fe-Dominant individuals externalize these conflicts. Peer pressure may come to represent a sort of "externalized superego"; the Fe-Dominant individual becomes something akin to a hero on stage rationalizing his actions to a Greek chorus. Wheeling and dealing with the superego on an external basis then comes to represent making one's case to the surrounding community. Judgment is then based on both the standards of the community/Greek chorus and the ability of the Fe-Dominant individual's to make his case and sway the community/Greek chorus.
In the case of both Fi-Dominant and Fe-Dominant individuals, I pointed out that ethical judgments are first made in terms of simple dichotomies (good/bad) and then evolve with time into more sophisticated determinations ("If defending oneself is good, then is war always bad?"). The development of these more advanced determinations isn't haphazard; logic is used and patterns are sought: "If I can argue that A=B and B=C, then can I also argue that A=C?
The overriding consideration for F, however, is to seek harmony between one's judgments and one's superego (to ward off anxiety) in the case of Fi, or to seek harmony between the judgments of the individual and the standards of the community/externalized superego (to ward off external punishment) in the case of Fe.
IOW, Fi & Fe can be summarized as "seeking patterns to achieve harmony" (i.e. harmony with the internalized or externalized superego).
Ti & Te
Much the same considerations apply to T. As the individual grows older and ethical/logical conflicts become more complex, the T individual uses patterns and logic to evolve a more nuanced judging ability. But in T individuals, harmony often takes a back seat to fairness.
A good example would be a T individual who takes an interest in philosophical or legal issues. One of the overriding concerns of philosophy or law is the principle of universal application: Everyone is treated the same under most kinds of rule-based law or philosophy. Science may also have the same appeal: In any given environment, the rules of science apply the same way every time for that environment.
One is tempted to speculate on why T individuals substitute "fairness" in place of "harmony" (in much the same way that N individuals substitute "one against many" in place of "many against many" for S individuals). Perhaps the T individual grew up in a less harmonious (or perhaps even more harmonious) environment than F individuals, and thus had less use for harmony and more need for fairness in their environment to argue their case and placate or appease the punishing superego figure.
Be that as it may, the rules for T and F seem pretty much the same with the substitution of fairness for harmony. The superego is placated when the T individual derives and lives a "fair" life according to the same universal rules that apply to everyone else. The Ti individual generates those rules internally; the Te individual works the rules out in interaction with the community.
Thus, Ti & Te can be summarized as "seeking patterns to achieve fairness" (to placate the internalized or externalized superego).
Thus we have the model for the eight functions:
Si & Se = solving problems by "comparing many to many"
Ni & Ne = solving problems by "comparing many to one."
Fi & Fe = seeking patterns to achieve harmony.
Ti & Te = seeking patterns to achieve fairness.
All of the functions are acting to placate the superego (internalized in the form of a personal superego or externalized in the form of law and community) in some fashion. All are working out a deal in some manner, in the sense that effort is invested for the purpose of deferring punishment and seeking approval.
S-Dominant and N-Dominant individuals (IxxJs and ExxPs) try to stay one step of the punishing side of the superego and earn approval of the rewarding side by racking up achievements and accomplishments; a price is paid insofar as that they get in the habit of existing perpetually in "churning" (perceiving) mode, gathering and storing and categorizing data and ideas against the next challenge. They are the "champions" of the MBTI world, always in training and always striving to deliver products, services, and solutions.
F-Dominant and T-Dominant individuals (IxxPs and ExxJs) try to avoid punishment and win approval of the superego by choosing and judging correctly; the price is that they spend their lives tangled in ethical dilemmas, trying to parse nuances, develop systems, and influence the community around them "to do the right thing." They are the "moralists" and "leaders" of the MBTI world, always honing their systems and striving to know wrong from right.
The danger of this kind of "division of labor" is that all types can become so focused on their one task that they have no energy or interest left over for anything else. They become ascetics in the name of placating their superego and get so caught up in that sole conflict or struggle that their time and space can't be infringed by anyone else. The Fi-Dominant INFP claims that only harmony matters and doesn't care whether it's fair to others; the Ti-Dominant INTP claims that only fairness matters and doesn't care if it results in harmony or not. The Si-Dominant ISFJ knows what's right for his family but doesn't care about what's right for society; the Ni-Dominant INFJ knows what's right for society but doesn't care how it impacts individual families.
A Judging function always works in tandem with a Perceiving function. (Our Dominant and Auxiliary functions work together, and our Tertiary and Inferior functions work together when we are under stress.) But if the Dominant function (ego/superego conflict) becomes all-important), then the Auxiliary function is reduced to little more than a servant to the Dominant and provides no additional useful input from the world.
Ultimately this is why we should aspire to integrate our Inferior function as we mature: It's the direct opposite of our Dominant function and expands our horizons and our adaptability to the world exponentially. It gets us out of our ascetic mode and reminds us that there is more to be achieved in life than merely denying oneself in order to placate the superego. Thereafter, exploration of other functions will widen our world that much more.
Standard disclaimer - IANAS. I'm just brainstorming using some elementary Freudian concepts to try to link together the four functions. It's purely theoretical, and it's just a foundation for further discussion. It's meant to raise more questions than it answers.