Function stack

The function stack is a typical ordering of the functions for each type. Type is formed from a "dominant" function and attitude, coupled with an "auxiliary" function, which is of the opposite "rationality" (judgment or perception) and the opposite attitude.
This is due to the need for cognitive balance. We all must take in information, and make decisions with it. So we will have one "strongest" function for each. We also need to be in tune with both the "internal" world of individual impression or reflection, and the external world of the environment of other people and "objects".

So the stack basically starts with the dominant and auxiliary. Beyond that, a common stacking order is widely used, and yet people will often ask why it is so, and why different functions might be "stronger" or "weaker" in relation to others in an order different from the stack. Most theorists only deal with four functions for each type, but some theorists such as John Beebe, Lenore Thomson, and Socionics stack all eight function-attitudes.

The common order, first popularized by Harold Grant, is a sort of "mirror" dynamic, which is due from the way we split reality by choosing one perspective, which automatically suppresses its opposite.
So when the two functions are preferred by the ego, their opposites become suppressed into a less conscious position. Generally, in the opposite order. So the opposite of the dominant becomes “inferior”, and the opposite of the auxiliary becomes “tertiary”. The inferior is also opposite in attitude from the dominant, and the attitude of the tertiary was deemed by Grant to be opposite of the auxiliary. (Jung originally belived the tertiary, like the auxiliary and dominant, would take on the attitude opposite the dominant; the "unconscious" attitudeThe MBTI Manual and other authorities leave the attitude of the tertiary open or uncertain).
Lenore Thomson had stated: "Whatever we habitually put aside to make our willful conscious choices will inevitably make its alliance with the unconscious -- emotions we don't want to feel, desires we don't recognize..." (Lenore Thomson Bentz . . . on Personality Type - Volume 1, No. 3 "Different Meanings of Temperament" http://www.personalitypathways.com/thomson/type3-2.html.

Ego states or archetypal "complexes"

Ultimately, the total “Stack” order (including the positions of all eight possible function attitudes for each type) is set by what are known as “ego-states", or more familiarly “complexes". The ego, which is our main sense of “I” also has many lesser senses of “I”, which are different emotinal states we encounter through the day. Examples can be anything from anger at someone, and another can be happiness, or sadness, amorous, etc. ("Ego Strengthening and Ego Surrender" Diane Zimberoff, M.A. and David Hartman, MSW [1]). These all are kinds of “ruling patterns” (archetypes) connected to the limbic system of emotions. Through them, we can have different expressions of “I” that feel different things.These are separated by a dynamic known as “dissociation”, which we all do, but becomes a “disorder” (leading to “multiple personalities”) when the dissociation is too great.

So for the states regarding the function stack, the dominant takes on a “heroic” connotation, being ego’s “main achiever”. The auxiliary becomes associated with “support“, since it supports the ego with balance, by taking the opposite rationality of function, and the opposite attitude.
This “supporting” ego state (labeled by analyst John Beebe after the classic archetype known as the “Good Parent“) will then be “compensated” (or “mirrored”, basically) by a “child” complex, while will orient the tertiary function in the attitude opposite the auxiliary, or the same as the dominant. This “child" (or “Puer”{m}; "Puella"{f}) will childishly try to maintain the ego’s dominant attitude, through the associated function.
The dominant will be mirrored by an “inferior” complex, combining both the function and attitude opposite the dominant. It will be our weakest standpoint, and yet carry a sense of completeness.

Lenore Thomsons says "The archetypal Hero (the ego identity) who has successfully established a sense of self and assimilated the good, supportive aspects of a Parental figure will be compensated, in the unconscious, by what's been rejected as not part of this self." ("John Beebe & Archetypes" [2])

Since this common stack so far only involves four functions, many have asked "what about about the other four?". John Beebe expanded the common Grant stack to include them.
The way this works, is that all four of these function-attitude-complex combinations are further compensated by having their attitudes reversed, in what’s known as the “Shadow". The shadow was originally Jung’s archetype of an “enemy” we project negative ego-states onto, and it also becomes associated with the unconscious.

So the four functions in the opposite attitude to the first four are associated with four other complexes, called by Beebe, the “shadows”. These deal (respectively) with obstruction of the ego (#5: "Opposing Personality"), feelings of negation of the ego’s dominant standpoint (#6: "Witch"{f}/"Senex"{m}), feelings of being double bound in situations (#7: "Trickster"), and the fear of the ego’s destruction (#8: Demonic Personality).

These ego-states will generally be manifested and felt by the ego through the lens of the four associated function-attitudes (called “shadow functions”) when the ego feels placed into those situations (this can be real or imagined). We tend to project the ego-states onto others, and respond to them in kind. (Hence, shadows often become associated with conflict). They also have good sides to them, that manifest more when the ego becomes mature.

The resulting order, it must be stressed, is not to be assumed to be strength (as many have assumed). And even though we have used "shadow" as the group of bottom four, even that is not a hard division. According to Mark Hunziker and Leona Haas :

Actually, the shadow encompasses all processes that are primarily unconscious in an individual. Which processes these are will depend on that person'a type development and can even include all eight in a very young child. Note also, that the normal hierarchy of preference for processes five through eight has not yet been empirically established, and in practice is likely to vary from person to person. Beebe cautions us not to assume too much on the basis of his numbering, which in many ways is simply for convenience in identifying the various positions. He simply puts it forth as a tool that he has found useful and informative and which at least for the first four functions seems to reflect the order of conscious cultivation of the functions that he has observed. The numbers for the shadow functions are identified merely to mirror the ordering of the first four. (Building Blocks of Personality Type (Unite Business Press, a division of Telos, 2006 Glossary: "Shadow", p. 215, emphasis added)

The resulting order, it must be stressed, is not to be assumed to be strength. And even though we have used "shadow" as the group of bottom four, even that is not a hard division. According to Mark Hunziker and Leona Haas Building Blocks of Personality Type (Unite Business Press, a division of Telos, 2006):

Actually, the shadow encompasses all processes that are primarily unconscious in an individual. Which processes these are will depend on that person'a type development and can even include all eight in a very young child. Note also, that the normal hierarchy of preference for processes five through eight has not yet been empirically established, and in practice is likely to vary from person to person. Beebe cautions us not to assume too much on the basis of his numbering, which in many ways is simply for convenience in identifying the various positions. He simply puts it forth as a tool that he has found useful and informative and which at least for the first four functions seems to reflect the order of conscious cultivation of the functions that he has observed. The numbers for the shadow functions are identified merely to mirror the ordering of the first four. (Glossary: "Shadow", p. 215, emphasis added)

These primary and shadow functions have often eclipsed each other, especially in the older four-process theory, which does not address the opposite orientations of each function. After all, there are really four functions that the ego orients in a particular direction. So most type discussions focus on only the four functions and their associated "attitudes" for each type. All of the attributes of these functions then tend to become associated with the function or "process" notated as "Xe" or "Xi" in the dominant, auxiliary, tertiary or inferior position. So INTP's will often attribute all of their strong emotional reactions to their "inferior Fe".
However, Beebe, ("Understanding Consciousness through the theory of psychological types") quotes James Hillman (Lectures on Jung’s Typology, 1971) in associating "inferior Feeling" with "anger and rage and ambition and aggression as well as with greed and desire" and that it "turns upon itself, morbidly; we are envious, jealous, depressed, feeding our needs and their immediate gratification...", and then later suggests that this "might better be understood as a description of demonic introverted feeling in an introverted thinking type". (emphasis added). So hence, both "attitudes", and the associated archetypes will parallel the same complex, only the "shadow" of the inferior will be even more negative!

ISTJ

ESTJ

ISFJ

ESFJ

ISTP

ESTP

ISFP

ESFP

INFJ

ENFJ

INFP

ENFP

INTJ

ENTJ

INTP

ENTP

1st

Si

Te

Si

Fe

Ti

Se

Fi

Se

Ni

Fe

Fi

Ne

Ni

Te

Ti

Ne

2nd

Te

Si

Fe

Si

Se

Ti

Se

Fi

Fe

Ni

Ne

Fi

Te

Ni

Ne

Ti

3rd

Fi

Ne

Ti

Ne

Ni

Fe

Ni

Te

Ti

Se

Si

Te

Fi

Se

Si

Fe

4th

Ne

Fi

Ne

Ti

Fe

Ni

Te

Ni

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Ti

Te

Si

Se

Fi

Fe

Si

5th

Se

Ti

Se

Fi

Te

Si

Fe

Si

Ne

Fi

Fe

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Ne

Ti

Te

Ni

6th

Ti

Se

Fi

Se

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Te

Si

Fe

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Ne

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Fe

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Te

7th

Fe

Ni

Te

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Ne

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Fe

Si

Se

Fi

8th

Ni

Fe

Ni

Te

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Ne

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Ne

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Te

Ti

Se

Si

Fe

Fi

Se

Familiar "stacking" of the extended Grant/Beebe model for each type

Lenore Thomson's function stack

Lenore Thomson's biggest contribution is her brain lateralization theory, which exposes another path in which we fall into our shadows. Introverted judgment and extraverted perception (Ji/Pe=P) were determined to be controlled by the right brain hemisphere, and introverted perception and extraverted judgment (Je/Pi=J) controlled by the left hemisphere. (And extraversion is front and introversion is back).
In her theory, in certain instances of stress in which your dominant functions cannot solve the problem, you will switch to the functions located in the same hemisphere, which in the Beebe order are actually the last two! (Especially when the tertiary hasn't developed yet, which will later assume this role). So for your dominant, you will maintain the same attitude, and the same rationality of function (j or p), but it will become the opposite function! You also are maintaining your J or P attitude. This way of viewing it is apparently more true to the original conception of MBTI, with E/I and J/P as separate factors (dichotomies) in their own right, apart from the functions. Hence, when an Fe dominant switches to Te in such instances, it is general "J" action, and maintaining a "left brain" orientation.

This has resulted in a different stacking order, called the "lasagna model", where the shadows are placed inbetween the dom/aux and tertiary/inferior blocks. So the block that in Beebe's model is placed last, she calls "Crow's Nest" in a ship crew analogy she has made, and they are usually listed in 3rd and 4th place, followed by "the Double Agents" (the other two shadows; so called, because they are the dom. and aux. in the opposite attitudes, and thus the opposite brain hemisphere also). The tertiary and inferior are listed last.

A lot of people in discussions like this order, because it more closely matches their comparitive strengths, as measured by the cognitive process test. Of course, this can't be made into a hard rule either, and it won't always match in that order. The model is actually not intended to replace Beebe's; it works beside it as another perspective on shadow degradation. (Like function #8 doesn't become the "tertiary" just because it is listed in third place). The order using Beebe's numbers are as follows: 1,2,8,7,6,5,3,4. It's divided as the first four are the same brain hemisphere, and the others, the opposite brain hemisphere.

One example she gives of how the ship model works (Personality Type, An Owner's Manual p.87), is that the dominant, as the captain, is navigating in a particular direction. The auxiliary is the petty officer, who follows orders, but also brings to attention alternative perspectives. Like I imagine he might suggest steering off course to avoid some obstacle. The tertiary water skis behind the ship, thus heading in the captain's direction, yet making rude remarks. The inferior is a castaway given a lifeboat, who ties a rope to the ship, reaches land, and then ties the rope to a powerful truck, and begins driving inland, actually pulling the ship along with him. Of course, these different directions, if you haven't caught it, represent the attitudes.