Deductive Formalism of Jungian Cognitive Functions



Jungian cognitive functions were first came up with by psychiatrist and psychoanalyst Carl Jung in his book Psychological Types in 1921, based on which Isabel Myers and Katharine Cook Briggs created Myers-Briggs Type Indicator (MBTI), which enjoys great popularity in commercial use and causal self-testings by people. While MBTI has been refuted and discarded by academia due to its problematic statistical validity and test validity, the core theory behind it, Jungian cognitive functions, still has profound meaning and serves as an insightful tool in analyzing personalities and understanding people’s motivation and reasons behind their decisions and behaviors.[1] In this article, I attempt to deduct 16 psychological types as described by Jungian cognitive functions using a series of assumptions, which explains why there are sixteen, rather than other numbers of, psychological types, and why these sixteen types are the way they are (as described by certain permutations of Jungian cognitive functions) rather than other seemingly possible permutations. This article is not an discussion of the definition of Jungian cognitive functions, nor does it attempt to prove its validity. Readers are assumed to have prior knowledge in Jungian cognitive functions.

Key words: Jungian cognitive functions, MBTI, psychological types, personality


Here, I will deduct Jungian cognitive functions and corresponding sixteen personality types starting from a series of assumptions. Some assumptions have relatively rigorous theoretical arguments to back them up, while the others only have loose logics behind them.

Assumption 1

Cognitive behaviors of human beings mainly consist of perceiving (P) and judging (J) process. Perceiving is a process of taking in information (input), while judging is a process of making decisions and acting based on the information taken in (output). By mainly, I mean most cognitive behaviors can be well explained by these two process. With this assumption, the cognitive behaviors of human beings are viewed as a constant process of information input (perceiving) and behaviors output (judging); by behaviors, I mean that both internal behaviors, such as judging, making decisions, thinking, feeling, and external behaviors, such as acting, are included.

Assumption 2

There are two perceiving processes: sensation (S) and intuition (N); two judging processes: thinking (T) and feeling (F). Sensation consists of vision, audition, gustation, olfaction, and somatosensation, and only raw input of sensing information are of sensation; by raw input, I mean no further information processing like analysis (e.g., thinking) are involved. Therefore, watching television is not of sensation, while being intrigued by the beauties on the television is of sensation; reading a book is not of sensation, while naturally (other than intentionally) noticing the texture of the paper of the book is very different from others is of sensation. Gaining information by intuition is an instant process that one can generally not control; by instant, I mean the gaining process is usually completed within a very short moment, usually less than a second; by not controlling, I mean the result usually cannot be well reproduced like logical thinking, which generally gives the same conclusions if it is repeated. Thinking and feeling can be understood by just common sense. However, note that by feeling, I mainly refer to the process involving emotions; the feel in “I feel A is right” is not of feeling.

Assumption 3

For each of the above four cognitive processes, there are two directions, one being introverted (I) and the other being extraverted (E). Hence, there are eight cognitive processes in total: Introverted Thinking (Ti), Extraverted Thinking (Te), Introverted Feeling (Fi), Extraverted Feeling (Fe), Introverted Intuition (Ni), Extraverted Intuition (Ne), Introverted Sensing (Si), and Extraverted Sensing (Se). By introverted, I mean the process directs internally (inside of the body; relates to oneself (rather than others); spiritually); by extraverted, I mean the process directs externally (outside of the body; relates to others (rather than oneself); physically); for intuition, however, introversion also indicates convergence (closeness), and extraversion also indicates divergence (openness). For discussion purposes, I will denote Introverted Judging (Fi, Ti) as Ji, Extraverted Judging (Fe, Te) as Je, Introverted Perceiving (Si, Ni) as Pi, and Extraverted Perceiving (Se, Ne) as Pe.

For now, if we record a specific permutation of cognitive functions from the “strongest” to the “weakest” of a person as one personality type (e.g., Alice has her personality as Ti-Fe-Ni-Te-Se-Si-Fi-Ne, which ranks from the strongest to the weakest), the eight cognitive functions can make up 8!=40320 personalities. Here, the definition of strong and weak is unclear, and we will discuss them in Assumption 5-10. Although those many permutations should relatively precisely describe one’s cognitive behaviors, they barely have practical use because of the enormous number of types. Hence, we need to apply appropriate boundary conditions to reduce the number of personality types meanwhile trying to keep the model remaining as effective as possible. Assumptions below serve as this purpose.

Assumption 4

Each of the introverted functions and corresponding extraverted functions have a tendency of suppressing one another. For instance, Ti tends to suppress Te, and Te tends to suppress Ti. Hence, one conclusion that can be drawn from this assumption is that one cannot behaves strong Ti and strong Te simultaneously; by behaving, I do not mean one is prohibited from owing strong Ti ability and strong Te ability simultaneously, but that from an outside observer’s perspective, one cannot show them, namely behave them, at the same time.

This assumption can be well supported by the nature of coupled I-functions and E-functions. Let me discuss them one by one.

Ti-Te. Ti users (who use Ti in their decision making process; similar explanations apply to the rest of this article) tend to think before acting, while Te users tend to act before thinking. Since one cannot think before acting and act before thinking simultaneously, Ti function and Te function suppress each other. Ti users tend to keep order and structure in their internal worlds (e.g., spiritual worlds, ideas, thoughts), while Te users tend to keep order and structure in their external worlds (e.g., physical worlds, surroundings, goals involving external achievements, interpersonal relationships). Since one’s time and energy in thinking process are limited, a priority must be given to one of the thinking functions, which will naturally compete for one’s time and energy. At the end of the day, one of the function will stand out and becomes the dominant function out of the two, while the other well be neglected and of lower frequency use. An analogy is handedness: While there do exist people who have a high proficiency in both of their hands, they still have handedness preferences, at least under specific circumstances, rather than switch their handedness frequently (under the same circumstance). It is becuase the inertial behaviors, i.e., keeping the same preferences, save cognitive energy and are thereby favored in evolution.[2] Similar arguments apply to the rest explanations of Fe-Ti, Se-Si, Ne-Ni duals.

Fi-Fe. Fe users tend to prioritize taking good care of the feeling of the others, while Fi users tend to prioritize taking good care of the feeling of themselves; Fe users tend to put external (i.e., others’) values, evaluations and judgement as their priorities or focuses, while Fi users tend to put internal (i.e., theirs) values, evaluations and judgement as their priorities or focuses. Since one can barely prioritize both external and internal elements simultaneously, a preference will grow and finally one will focus on one side and neglects the other side. The nature of keeping inertial behaviors of human beings will make the preference consistent and stable over time.

Si-Se. Se users tend to be absorbed in their experience at the present, while Si users tend to act based on the experience in the past, hence Se and Si naturally repel, for one cannot both enjoy the present experience meanwhile acting based on the past experience (since past experience will inevitably restrict the present experience that can be experienced).

Ni-Ne. Ni users tend to draw a conclusion when facing a problem, while Ne users tend to not draw a conclusion but get as many possibilities as possible when facing a problem; Ni users favor convergence while Ne users favor divergence. Therefore, Ni and Ne naturally repel each other.

Assumption 5

There are two properties of the usage of cognitive functions: frequency and proficiency. If we use dichotomy, there will be four scenarios: frequently used proficient functions, frequently used unproficient functions, rarely used proficient functions, and rarely used unproficient functions. In the functions that are frequently used, it is natural to assume that there are more frequently used functions and less frequently used functions, and that the proficiency of those functions should have positive correlation with their frequency of use.

Assumption 6

The suppressed functions, which are discussed in Assumption 4, are the rarely used functions; the unsuppressed functions are the frequently used functions. The reason for this is that people have inertia in their preferred functions of use, just as most right-handed people  tend to always mainly use their right hands, unless involvement of their left hands are necessary or of great help.

Assumption 7

It is mainly the frequently used functions that determine one’s personality.

Assumption 8

Out of the four frequently used functions, one must have a strong perceiving function and a strong judging function, and a weak perceiving function and a weak perceiving function. By strong, I mean proficient; by weak, I mean unproficient. This can be well understood as the followings: As discussed in Assumption 1, the cognitive behaviors of human beings are viewed as a constant process of information input (perceiving) and behaviors output (judging). For a normally functioned person, he must have a relative preference to, also relative strength in, one of the perceiving functions and one of the judging functions, leaving the other perceiving function and judging function relatively weak and unfavored. Bound the two strong ones together and the two weak ones together, with Assumption 7, one’s personality can be described as function (strong) – function (strong) – function (weak) – function (weak) (Formula 1).

Assumption 9

Out of the four frequently used functions, one must have a strong introverted function and a strong extraverted function, and a weak introverted function and a weak extraverted function. There are two ways to understand this: One is that there must exist a stronger function out of two introverted functions and a stronger function out of two extraverted functions, and the rest are the weaker functions; the other is that to cope with internal and external issues well enough, one must develop a strong function (totally two) for each direction, leaving the other two relatively weak. The argument for the differentiation of strong and weak function can be explained by the analogy of the appearance of handedness, which has been discussed in the text above. Bound the two strong ones together and the two weak ones together, with Assumption 7, one’s personality can be described as function (introverted/extraverted) – function (extraverted/introverted) – function (introverted/extraverted) – function (extraverted/introverted) (Formula 2). Note that the order in the parentheses matters.

Assumption 10

To keep cognitive balance, the overall strength of one’s perceiving functions should be as close to one’s judging functions as possible. The conclusion from this assumption is that one’s personality type can only be of either J-P-P-J or P-J-J-P (Formula 3). All other permutations, namely J-J-P-P, J-P-J-P, P-J-P-J, P-P-J-J, break cognitive balance, for the personalities formed by those permutations either have too strong perceiving functions or too strong judging functions. Recall that in Assumption 1, the cognitive behaviors of human beings are viewed as a constant process of information input (perceiving) and behaviors output (judging); too strong perceiving functions or too strong judging functions break the equilibrium of the input-output process — how can one output healthily with little input, or have a lot inputs but very little outputs? Note that there is another assumption (or you may call it a fact) that I have not yet mentioned: One’s dominant function (F1) far outperforms one’s auxiliary function (F2), which far outperforms one’s tertiary function (F3), which far outperform one’s inferior function (F4). Under mathematical language, it can be denoted as F1>>F2>>F3>>F4 (rather than use >).

Note that Assumption 10 can also be expressed as following: The two perceiving functions one has must be of different directions, so it is with the two judging functions. While this expression gives to equivalent conclusion as the original one, it is less intuitive and hence unfavored.

Conclusion 1

By Formula 1-3, one’s personality type can only be one of Je-Pi-Pe-Ji, Ji-Pe-Pi-Je, Pe-Ji-Pi-Je, or Pi-Je-Ji-Pe. Any other types will violate Formula 1-3.

Conclusion 2

There are sixteen types in total. To reach the conclusion, suppose someone’s dominant function is, say, Ti, then he is of Ji-Pe-Pi-Je type. There are only two Pe: Se and Ne. If he has Ne, then the Pi of him must be Si, since Ni is suppressed by Ne and cannot appear in his frequently used function stack. Then his Je can only be Fe, as Te is suppressed by Ti. Hence his personality type is Ti-Ne-Si-Fe. Apply the same analysis for Pe being Se, we get two types in total (the other is Ti-Se-Ni-Fe). Apply the same analysis for the rest seven dominant functions, we can get 8*2=16 types in total.

By applying proper boundary conditions, I have successfully reduced the number of types from 8!=40320 to 8*2=16, the simplicity of which gives much greater applicability of the model.


For simplicity, the sixteen types can be denoted as the followings, as used by MBTI test:

INTP: Ti-Ne-Si-Fe

ENTP: Ne-Ti-Fe-Si

INTJ: Ni-Te-Fi-Se

ENTJ: Te-Ni-Se-Fi


INFP: Fi-Ne-Si-Te

ENFP: Ne-Fi-Te-Si

INFJ: Ni-Fe-Ti-Se

ENFJ: Fe-Ni-Se-Ti


ISTP: Ti-Se-Ni-Fe

ESTP: Se-Ti-Fe-Ni

ISFP: Fi-Se-Ni-Te

ESFP: Se-Fi-Te-Ni


ISTJ: Si-Te-Fi-Ne

ESTJ: Te-Si-Ne-Fi

ISFJ: Si-Fe-Ti-Ne

ESFP: Fe-Si-Ne-Ti

Note that the differences between an introverted person and an extraverted person become ultra-clear using cognitive functions language: For a given type, say, NTP, the differences between INTP and ENTP is just that they enjoy different orders for their function stack; if we move each of the extraverted functions of INTP one step left, then it becomes the function stack of an ENTP. This fact can help introverted people understand and “become (if they wish)” their corresponding extraverted versions, and vice versa.


Readers should keep in mind that the deductive formalism discussed in this article provides only one possibility; other interpretation of the assumptions, and even very different assumptions, might also be possible. What is more, readers can come up with their own boundary conditions, with which a totally different model is possible. However, readers should also keep in mind that a model allowed in principle might not reflect the reality.

Some may argue that although the application of a series of boundary conditions greatly reduce the number of personality types, it also make the model too simple to describe the complex reality, as some people’s personality types may not be well described by the sixteen types confined by the boundary conditions. While this argument can be true to some extent, there is yet another assumption that I have not talked about: the natural tendency of the development of personalities. Though even I myself do believe that there are people whose personality types do not belong to one of the sixteen types, I also do believe that good boundary conditions (e.g., the ones I discussed in this article) are in great agreement with the natural development of personalities, i.e., most people developed, are developing, or will develop their personalities in a way which aligns with the assumptions above. Even if there might be some limited number of people who have psychological types beyond the sixteen types, do keep in mind that the failure of the boundary conditions on them is the necessary trade-off for the simplicity of the model — nobody wants a model of 40320 different types! Human beings’ psychology *per se* are very complicated, and nobody will expect there exists a model that can describe people precisely like laws of physics. A psychological model that can explain as much as 95% of people’s cognitive behaviors is actually more than an excellent one.

[1] If you do not agree the above sentences, it does not matter and I do not bother to provide you relevant citations, for they are not the focus of this article.

[2] This is my personal explanation/hypothesis.

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