Defining CPT functions with the use of Gödel’s incompleteness theorem

By Rob Dinh

Introduction

In order to describe a person’s being, the most succinct and true way would be to state “I am”. However that isn’t helpful for anyone wanting to draw meaning out of that statement. One must be more descriptive, detailing “who I am” to be more compelling and interesting: “I am John, a 45 year old carpenter from South London.” But that doesn’t fully describe John as a whole human being. For any true statement to be as descriptive as it practically can be about John, there’s always more that we don’t know about John.

This approach parallels Gödel’s incompleteness theorem. No matter how much we understand about a given system, there’s more we don’t understand about it. In other words, there is no theory of everything. As well, if everything is true, everything itself can’t be proven with consistency. How much we know about ourselves and our existence cannot be fully determined. Life finds a way to remind us we are always more than the known and proven sums of our parts.

CPT’s way to personality typing initially posits a human being can fluidly shift into any type using any functions. It recognizes that archetypes and metaphors cannot fully encapsulate one’s whole universe. We are first and foremost whole human beings before we are personality types. We are both introverted and extraverted, thinkers and feelers, sensors and intuitives, and more. However contrasting between archetypes and function dichotomies can help us understand one’s cognition and experiences. The map is not the territory, but it’s still a good guide.

The purpose of this blog is to conjoin CPT with Gödel’s incompleteness theorem and how that shapes our perceptions of reality. We don’t see all of the truth because our “incompleteness” enables us to savor our humanly limited experiences. Slicing reality is more practical and useful, like the John example above. We do this implicitly and explicitly with idioms like “from my experience,” “as far as I know” or “in my opinion.” This same limiting effect happens with our egos in terms of the Jungian cognitive functions. Using the theorem, making distinctions between the functions helps draw insight inside the psyche of a personality type.

Application of Gödel’s incompleteness theorem

First we must disclaim that lending Gödel’s incompleteness theorem outside of its nature of mathematics for the use of personality theory is crude. Jungian based systems are composed of metaphorical archetypes and functions. They are not considered formal systems nor syntactically defined. However the theorem states that a well developed consistent and effective system of first-order axioms can prove truths within it, yet there will always be other truths that it cannot prove. This closely relates to the universe in which humans interact with their own limited perceptions. For as much as someone believes what is true, they cannot prove all is true.

Using CPT’s system, we identify that the dichotomous spectrums are constructed similarly to Gödel’s incompleteness theorem. One end is a set of axioms in a system arranged to derive truth proving theorems. The other end is any truth that cannot be proven by the axioms in that system. An agent’s life experience as an axiomatic system is the sum of the set of provable truths and the set of unprovable truths. For the rest of this blog, the determined provable set is expressed within the brackets. The probable unprovable set will be without them, or abstractly outside of them.

Here’s where we start to deviate from the incompleteness theorem. Axioms can mean knowledge, experiences, and impressions. These values can be loosely considered self-evident, tautological, and either logical or non-logical. In other words, we account that the agent’s worldview is shaped by what they perceive and experience as fundamentally true. An axiomatic system is the collection of axioms the agent holds. It is with the use of these axioms that one creates higher order perception and judgement. We equate these as truth statements that lead to the conceptualization of self. Thus proving truths is synonymous with working towards self-realization.

Considering the agent’s progress in life, we allow the agent to dynamically change their set of axioms and develop their system. Gödel’s model shows that we can strengthen the system by adding new axioms in an attempt to uncover the truth of everything, but it won’t ever truly uncover everything. We’re a curious and ever developing species. We progressively learn more about ourselves and about the reality we live in. Yet we won’t ever reach total self-realization.

To reiterate, two assumptions are made:

  • Humans cannot consciously and unconsciously experience all of truth at once
  • Humans consciously and unconsciously attempt to reconcile with the truth

This means that one’s ego manages their axiomatic system by either operating primarily with the closed provable set or with the boundless set of unprovable truths. One will seek to maximize the number of proven truths by doing both the following, while focusing primarily one or the other:

  • Deriving truth statements from the set of current axioms inside the system
  • Integrating new axioms into the system to uncover unprovable propositions

The ego that mainly upkeeps their system as a framework of provable truths examines axioms deterministically with deductive reasoning. If not seeking new information, one would disregard what’s “out there” staying within their closed perception. The ego converging to experience new unproven truths, on the other hand, explores for new axioms to fit with their system probabilistically with inductive reasoning. Without psychologically anchoring to their system, one would aimlessly wander tentatively grasping onto the infinity space without anything absolute to fall back on.

More on ego management

The ego generates information from one set while it can still acknowledge information from the other set. Both sets serve equally important and complementary roles, in which the ego assumes a cogitating role for one and an observant role for the other. The realization of thought from the other role is outsourced. Under our assumptions that the agent inherently needs to reconcile with reality, information from both sides need to be in accordance with the ego to synergistically integrate them. The dynamic interaction between those two dichotomies is where the agent arbitrates to best interpret reality.

Ideally, one has the mindfulness to assess their situation and judge on which reasoning serves them best for processing. We allow that the ego may spend most of its conscious capacity observing information from the other side, instead of generating thoughts from its residing side. We also consider that the ego can switch sides, shifting the generating and observing roles accordingly. Experience and motivation of the ego moving along the spectrum between the two factors will be further explored in another blog.

Lens-codec function

In the following sections, we will declare casual associations with the two factors summing reality and the four Jungian functions such that their definitions analogous to effectiveness, completeness, richness, and consistency are akin to the provable set of an axiomatic system. Other definitions that don’t meet those deductive qualities are akin to the realm of unprovable truths. As CPT asserts, the functions are contrasting ends of a spectrum:

Reality[a1,a2,a3,a4,a5, …]U
Lens spectrumSensing (atomistic)Intuition (holistic)
Codec spectrumThinking (cognitive)Feeling (affective)

Both ends of each spectrum would collect more data over time. Note that during this contrasting exercise, we reiterate that humans need to process both ways even if there’s a convergence of one over the other. One’s life journey is a reconciliation of both embracing and exploring experiences. Personal growth is directly correlated to the attainment and realization of truth. We can’t fully appreciate the present without the context, just as we can’t fully appreciate the context without the present. Our thoughts affect our emotions, just as our emotions affect our thoughts.

In fact, we’re really talking about a unified two dimensional perception-cognition function. Combining the dichotomies leads to four modes the lens-codec function can form, i.e. where the ego converges to:

  • Intuitive-feeler
  • Intuitive-thinker
  • Sensor-feeler
  • Sensor-thinker

For now we consider Introverted and Extraverted versions as part of a common function, recognizing that each type has all eight unit functions as popularly prescribed in Jungian based systems. How each archetype uses these eight unit functions depends on the predisposed temperament of their dominant function. These differences will be detailed in the next section.

Sensing vs Intuition

When paying full attention and taking in as much of reality as one possibly can, one comes quickly into a paradox because to intensely experience the present means to ignore the broader context around it. Getting immersed in the moment also means getting lost in the moment. Total perception of reality of seeing a picture that is both detailed and broad is deemed singularly impossible. The provable set here is the view of a discretely categorized and boundary defined world where the sensor can extract and examine its content. The provability lies in the explicitness of what’s observed. The sensor analyzes an object and breaks it down as an assembly of components at the atomic level illustrating their elemental properties.

The sensor dissects the object in focus and differentiates its components to observe the mechanisms between them. Each component is contrasted and amplified to diminish ambiguity, therefore appreciating the complexity of the content-rich system. However committing to a “deep dive” analysis means the sensor declares their locality to the system. To confine it within their concentrated focus, one would risk failing on perceiving the system as part of a whole. Breaking the system down renders its explicit definition as the face value sum of its mechanisms and nothing more. Seeking meaning beyond the content helps the sensor broadening their attention to the implicit truths related to the context of the object. Hence defining the system’s purpose with reality at large.

Contrast to the sensor’s disambiguated and bounded perception, that of the intuitive is blended and boundless. Rather than analyzing the object’s explicit content, the intuitive observes its implicit context that plays part of an all-encompassing abstraction. Therefore they’re assembling the object into it. Any dynamic change to this holistic system will affect all objects integrated to it. To manageably perceive this sheer amount of data, objects are reduced to their principal structures that serve the big picture. The intuitive continues to synthesize other objects to perceive one unified message.

However the intuitive can lose the object’s relationship with the abstraction when they overly ignore the details of the object. Their abstract set then becomes unprovable if there’s no concrete content to test against. Ignoring details makes the intuitive’s worldview overgeneralized and inconsistent. Thus dissolving it of any practical relevance. There’s no meaning without purpose. Valuing the object’s contents provides insightful depth to the object’s context, and therefore helps intrinsically define the abstraction’s meaning.

A popular misconception is that higher abstraction translates to higher complexity, which isn’t the case for our application. Humans budget their limited perception of their broad worldview by simplifying the complexity. We like to see reality parsimoniously afterall. Additionally, the initial level of abstraction for the system in focus is irrelevant. It can be a work organization, beauty standards, historical context, philosophical stances, a mechanical assembly, etc. Being a sensor or intuitive is whether one primarily observes the object with an atomistic or a holistic approach respectively.

Thinking vs Feeling

While the lens spectrum is about how implicit and explicit the axioms are perceived, the codec spectrum is about the conceptions based on the axiom’s encoding. This is about the cognition itself, whether it’s processed through the cognitive or affective perspective. Thinking is associated with the provable set of the axiomatic system, as it’s most directly related to the mathematical roots of Gödel’s theorem. A thinker creates impressions through a systematic framework by deductively proving effective and consistent truths. One generates statements that stand valid in the face of any argument. The thinker analyzes any given object mechanistically such that any event related to the object can be algorithmically conceived. Thus, one can accurately anticipate the object’s actions and behavioral patterns.

The scientific method can be appropriately considered as the thinker’s modus operandi. Seeking consistent objective results requires a critical thinking process, filtering out the instinctual subjective influences related with the brain’s limbic system. Meaning the thinker ignores unprovable inconsistent truths in order to formalize the structures of reality. Intellectualizing to get to the bottom of a situation, the thinker can fail to consider beyond what’s “actually” happening. Evidently, humans are not machines and cannot divorce themselves from bias. Our views of truth are distorted by our intentions– and objectivity as an idea is a fully intentional endeavor. Incorporating biases, desires, and emotional interpretations improves the thinker’s decision making and emotional regulation, encompassing a more human and complete truth.

Living outside of the deterministic thinking framework, the feeler deals with the erratic and immeasurable information of emotions. Instead of modeling the constructs of an event, the feeler inquires about the experiential effects sprouted from the affective landscape mixed of pleasure and displeasure. Motivations, meaning, and identity conjured up from these experiences are entirely unique and subjective. Impressions from repeated events may be similar, but none are identical. They are heavily influenced by reflections from past episodes, understanding about the situation, and context of the mental state. Plus, no two agents go through life as exact mirror copies.

A lot of literature has proven how emotions serve as signals for survival. While they play a key role in life, relying solely on impulsive emotions is too incoherent and volatile to make high quality heuristics. We don’t just live instinctually, we also reason and channel our emotions to live happier. Understanding our circumstances, we’re able to control and optimize quality of life. Lacking emotional intelligence, the feeler’s thoughts become overly malleable and readily conforming to passing temperamental moods. Embracing the unvarying protocols of the environment through rational thinking leads to a more harmonious connection and relationship with the self and the environment.

Dominant temperament

CPT describes this “stack” as the central domain of the ego where it occupies the most conscious space within one’s mind. This is where one has the most agency for taking control of their environment. Let’s emphasize to look at the dominant function as a temperament rather than one of the unit functions. It’s a two dimensional concept of whether a type is a codec or a lens dominant; and whether they are introverted or extraverted. Incorporating the dominant temperament with the lens-codec function forms the dominant function. A lens dominant introverted intuitive thinker, the INT-F (INFJ), possesses the dominant function of NiTi for example.

As this blog is about working towards the truth, the dominant temperament firstly presents how an individual gathers knowledge rather than what:

Reality[a1,a2,a3,a4,a5, …]U
Rationality spectrumCodec dominance (epistemic)Lens dominance (perceptual)
Orientation spectrumIntroversion (mental)Extraversion (physical)

These traits influence the roles of the other functions, thereby integral to defining the individual’s overall personality and type. Combining the dominant function with the lens-codec function leads to a four dimensional archetype. There are four modes the dominant function can form, i.e. where the ego converges to:

  • Introverted-codec
  • Extraverted-codec
  • Introverted-lens
  • Extraverted-lens

Because of its predispositional extensiveness, the dominant function’s role is a sort of “meta-function.” Cognitive output can be formed beyond one’s awareness and deliberate cognition. Yet information out of the dominant function is provable in terms of our exercise with Gödel’s incompleteness theorem. More of this claim can be expanded in another blog. When focused deliberate cognition is needed to realize experiences, the dominant function as a meta-function is its own primary means to interact with reality. Thus this function can also be called the agency function when employed volitionally.

Here we cite some psychology and philosophy concepts to help distinguish the differences between the dominant traits. As emphasized in the functions section, we remind that these dimensions are continuums an individual navigates in between. Humans acquire knowledge for the stimulation of both utility and novelty. And with that knowledge, they create experiences in both their internal and external worlds.

Codec dominance vs Lens dominance

One of the two aspects of the dominant function is whether it’s a codec or a lens dominant. Being a codec dominant means one holds to maintain order in their system. One mainly works within their provable framework, and could theoretically generate infinite distinct impressions using their current knowledge vault. However nobody possesses all existing axioms. And if the codec dominant rejects unprovability, they would neglect the vast potential world of knowledge. The codec dominant can look out with their agency lens function to introduce new axioms into their system, thereupon to be excavated by their deductive rules.

A lens dominant, in contrast, spends more time in the realm of unprovable truths dispositionally gathering knowledge. One explores for potential axioms and figures how to fit them into their codec set. A lack of codec framework development would render the lens dominant aimless, ineffectively inducting unproven data. To further develop their framework, the lens dominant can create new impressions cogitating with the axioms using their agency codec function, providing proven certainty as an anchor for better focus.

The driving force for gaining knowledge is curiosity. That is the underlying motivation for gathering information to reconcile with truth. We can borrow Daniel Berlyne’s work about types of curiosity here, where he distinguished them as epistemic and perceptual curiosity. A codec dominant is related to having an epistemic curiosity trait. It’s a drive aimed to acquire new knowledge for its own sake. The codec dominant has the cognitive stimuli to reach understanding to solve problems at hand, learn new concepts, and close information gaps.

Perceptual curiosity then relates to being a lens dominant. Being more experiential, the lens dominant is motivated to explore for the sake of novelty. One gathers information because they are reactive to sensory rather cognitive stimulation. Novel stimuli diminishes with continued exposure, thus people with perceptual curiosity traits are prone to exploratory behaviors. Further research shows that one can also be motivated to explore without purpose, but also not necessarily involving oneself in risk-taking.

Since humans aren’t born with a developed axiomatic framework, we can naturally assume that children are more lens biased exploring novelty before they may set into being codec dominant. This means internalized axioms are largely experiences based on one’s cultural rules. Therefore the codec dominant is more formalistically influenced by their environment than their lens counterpart. A lens dominant on the other hand keeps a mediating position by considering the happenings of their surroundings as advisory.

Introversion vs Extraversion

The second main aspect of the dominant function is whether it’s introverted or extraverted. The provable set in this section is defined as one’s framework of subjective experience, thus an introverted system. One who mainly works within that set would be recalling information to create original impressions. The important point is these impressions originate from the mental realm that doesn’t require space nor time. They’re thoughts generated to create a set which the self has full control and can personally prove. Independent from the spatiotemporal realm, the introvert is proactively resistant from acquainting with events native to the ever changing physical landscape of the external world.

Note that the initial primary set of axioms, giving birth to original insights, is previously absorbed from the physical realm. It’s a list of values retained from the past allowing time for reflection and development of insights. An introvert who stops interacting with the physical realm would be entertaining musings out of stale information. Short of periodic revision or reconfirmation would decontextualize one’s worldview from the present. Therefore in need to upkeep their framework, the introvert must externally consult for more axioms. These axioms will be examined at their discretion for adoption into their set.

The extrovert primarily works in the unprovable realm absorbing information. The physical world progresses in time and space, so no two events are absolutely identical. Without valuing their introverted set, one would compare others’ proven experience irrespective of their own. No truth in the now is consistent unless it is entrusted that they won’t change. They would be enslaved to react with the flowing present in need to continuously catch up with it. To ground oneself, the extrovert asserts and controls the present with the influence of their consistent introverted proven set.

To summarize, the axioms’ relation with space and time reflect how the two egos process their thoughts. The introvert interacts with the mental world formulating proofs and predicting outcomes independent of the present context. Insights projected out to the external carries an unvarying past and long term future orientation. The extrovert, in contrast, interacts with the physical world building practical methods and controlling outcomes in the context of the present. Living in the shared universe that incessantly moves on, the data absorbed ad-lib to the self carries a circumstantial present and immediate future orientation.

Additionally, the contrast between CPT’s definitions of introversion and extraversion is similar to the philosophy of mind’s two directions of fit. The introvert has a belief driven “mind-to-world” direction of fit, reformulating their mental state in accordance with the world to seek the truth. The extravert has a desire driven “world-to-mind” direction of fit, changing the world in accordance with their mental state to seek realization. Congruent with CPT, the individual regularly undergoes both directions of fit in real life. While one direction may be more predominant, one expresses both mental states of belief and desire to individuate for what’s personally best fit between oneself and the world.

Nature of axioms

We’ve now presented all four dimensions making up the eight cognitive functions and the sixteen CPT archetypes. If we group the ends of the four spectrums such that the end which the ego converges to and formulates truth is tautologically the provable set within the conscious mind, i.e. the dominant function, we get the following expression:

The oppositional function, also known as the divergent function, is then the unprovable and observed set of truths. Both functions are two dimensional composed of unit function pairings that oppose each other via law of opposites, for the ego to account for both ends of all four dimensions. Much like the dominant function, the oppositional function is best looked at as a temperament and meta-function. The INT-F would have an oppositional function of SeFe.

So far in this blog, we’ve expressed provability with the use of brackets to illustrate how information consciously emerges; the conscious mind being the axiomatic system. The individual formulates experiences from what they observe in life. We can reinterpret this in our exercise by associating the axioms, which are self-evident and fundamental, in the same nature as the information observed from the unprovable set. They’re propositions one acknowledges first before reflecting upon them. Within the ego complex, we define I(x) as a function used to realize an experience:

I(x) being the ego construct is dependent of the observed set of axioms a. What’s realized through the dominant function is the emerging experience based on the oppositional function’s axioms. The INT-F cogitates about reality expressed in NiTi based on SeFe data:

Any derivation by I(x) starts with the axioms. SeFe is a constant value domain that independently emerges into the INT-F consciousness, in which NiTi is codependent on. In other words, the oppositional function as a domain of axioms is a non-ego native set of inputs the ego must adhere to develop an experience.

Going back to the meta expression of our type example, we can rewrite it as such:

The unconscious is included to present an individual’s whole mental landscape as an axiomatic system. Evidently it fits as unprovable since we’re not consciously aware. Revealed is how SeFe wields foundational power in order to build a consistent and effective conscious set. To have working realizations in the conscious set, NiTi must compliment and abide to the SeFe constant. Desiring to create experiences with our own agency relies on the basis set by the oppositional function. Thus this function is monikered the authority function. NiTi is the INT-F’s agency to SeFe authority.

As CPT states, the oppositional function is experientially a reality check. The codec dominant reconciles with their lens authority function to search for missing data in order to close information gaps. They’ll continue until they meet their perfectionistic value standards set by their oppositional codec function. The lens dominant explores for data relevant to their codec authority function for as long as they receive novel stimuli. They’ll continue until they reach a state of perceived completeness set by their oppositional lens function.

Conclusion

Gödel incompleteness theorem is conveniently, and admittedly crudely, applied to help us further distinguish the differences between the Jungian based functions and archetypes. My hope is that introducing the concept of provability sheds an insightful perspective in how one deals with randomness in all four dimensions when facing reality: one end is of control who is deductive, deterministic, and cognitive; and the other is of chaos who is inductive, probabilistic, and experiential. And while these dimensions are orthogonal, these traits form together layered archetypes who have their own unique ways to reason and experience.

Through these metaphorical heuristics, we grasp on what we value as truths to shape our reality. Alas we’re limited by what the ego allows itself to perceive. Our minds process cognition more than the ego realizes. To use Freudian rhetoric, not acknowledging what goes on outside of the Ego would lead to a disharmonious relationship between itself, the Id, and the Superego. If we don’t train our awareness to shift along the lengths of these cognitive spectrums, we’re navigating through a distorted reality. Cognitive fluidity helps us to metacognize for higher quality perceptions of true reality.

If I may add my personal take, bringing ourselves closer to true reality equates to the path of individuation. Uniting in harmony our subjectivity and objectivity, our ego and unconscious, our identity and belonging leads us to the truth about ourselves. Embracing and embodying what we truly are and our existential nature is the process for personal growth. And like Gödel incompleteness theorem suggests, truth itself is a journey that never ends. If we feel we’ve figured it all out, there’s still more to know about ourselves. As such, individuation itself is a journey that never ends. One which CPT is a truly viable tool to carry along with.

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