Why only 16 Jungian types? Combinatorially it should be 2 * 4! = 48 [closed]

Question

The seeming elegance and symmetry of the table of functions prompted me to use a technical side of my brain to ask a "what if" question about the other possible Jungian functions.

I used combinatorics(math) to calculate all possibilities of arranging letters F,S,T,N as well as adding an alternating i/e "flavor". There are two options for the flavors (once we know the i/e "flavor" of the first function, the rest are determined because they alternate).

For illustration, I enumerated one quarter of all possibilities (only those starting with an F but you can keep going yourself if you like). The original 16 types are listed below that. As you can see, there are many gaps - only 4 of 12 used here and 16 of 48 used overall. So, exactly 1/3 utilization. The mathematical elegance is a tease, makes me think that this theory is based on something real, but is it? Could it be an elegant accident or an elaborate hoax instead? Why are some combinations not possible?

E/I 1   2   3   4   functions   MBTI?
e   F   N   S   T   FeNiSeTi    ENFJ
i   F   N   S   T   FiNeSiTe    INFP
e   F   N   T   S   FeNiTeSi    ?
i   F   N   T   S   FiNeTiSe    ?
e   F   S   N   T   FeSiNeTi    ESFJ
i   F   S   N   T   FiSeNiTe    ISFP
e   F   S   T   N   FeSiTeNi    ?
i   F   S   T   N   FiSeTiNe    ?
e   F   T   N   S   FeTiNeSi    ?
i   F   T   N   S   FiTeNiSe    ?
e   F   T   S   N   FeTiSeNi    ?
i   F   T   S   N   FiTeSiNe    ?
.................................

MBTI    1   2   3   4
INTP    Ti  Ne  Si  Fe
ISTP    Ti  Se  Ni  Fe
ENTP    Ne  Ti  Fe  Si
ENFP    Ne  Fi  Te  Si
ISFP    Fi  Se  Ni  Te
INFP    Fi  Ne  Si  Te
INTJ    Ni  Te  Fi  Se
INFJ    Ni  Fe  Ti  Se
ESTJ    Te  Si  Ne  Fi
ENTJ    Te  Ni  Se  Fi
ESFJ    Fe  Si  Ne  Ti
ENFJ    Fe  Ni  Se  Ti
ISTJ    Si  Te  Fi  Ne
ISFJ    Si  Fe  Ti  Ne
ESTP    Se  Ti  Fe  Ni
ESFP    Se  Fi  Te  Ni

Answer 1

There are not 16 Jungian types. There are 16 MBTI combinations and 16 Kersian (sub-)temperament types. All are related and easily confused.

Jung, in Psychological Types (Collected Works, Book 6), defines two Attitude Types and four functions, splitting the latter into two groups of two.

Attitude Type is Extraversion and Introversion and takes up 9 of the 10 chapters in the work. In the 10th chapter, he explains the four functions: Sensation, Intuition, Thinking, and Feeling. The first two are irrational functions, the second two, rational functions. This makes a total of three groups of two. Though, Jung treats all four functions as one group, it is helpful to remember they can be bifurcated thusly.

Of both the two Attitude Types and the four functions, one is preferred from each. That is, everyone has all the types and functions, but everyone prefers one from each group.

Chapter 10 then explains how the functions play out within the two Attitude Types, leading to 8 explanations, which are Extraversion and Introversion with each of the four functions. He also explains the role of the secondary function. The secondary function will be the opposite of the primary function. That is, if the primary is irrational, the secondary will be rational, and vice-versa.

--

Before Jung published Psychological Types, but based on his works, Meyers-Briggs created the MBTI (Meyers-Briggs Type inventory), a personality inventory based on Jung's functions. The first letter is the preferred Attitude Type, the second letter is the preferred irrational function, the third letter is the preferred rational function, and the fourth letter indicates which function is preferred to be extraverted. Note, the fourth letter does not indicate the primary function. It indicates whether the preferred extraverted function is irrational or rational, which is the inverse of the introvert's primary function.

The combination of one of two Attitude Types, one of two irrational functions, one of two rational functions, and one of two preferred extraverted functions, makes 16 combinations.

In Gifts Differing, Meyers-Briggs defined four function groups (ST, SF, NT, NF) which are like groups to the 16 types.

--

Keirsey, working on Temperament theory (reactions to the external environment), found a connection between his work and the MBTI. Note, he did not find a connection between Temperament and Jung's theory. Indeed, he could not, because Jung did not have the fourth letter defined by the MBTI, which is integral to the connection Keirsey found. He also grouped the letters differently than the MBTI.

Keirsey's groups are SP, SJ, NF, NT, which can be matched to the four historical temperaments: Artisan, Guardian, Idealist, Rational. The history of Temperament theory gives many different names for these groups, so Keirsey, in his main work, Please Understand Me II, says he based it on The Republic. In Keirsey's last work, Personology, however, he focuses much less on those names and uses his own.

With a connection between the MBTI and Temperament theory established, Keirsey extended Temperament theory to include four sub-types for each of the four temperaments. This makes a total of 16 sub-types.

Answer 2

It's because order doesn't matter with the types:

ENTJ == ENJT

When you remove the permutations of order, there are only 16 possibilities.

Another way to think about it is that there are 4 traits, and each trait can take one of two values, so there should be 2 x 2 x 2 x 2 possibilities, which is 16.