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Revising the Claims of Function Axes Theory

By Lee Morgan

Several weeks ago, I wrote an article that introduced new definitions for the four function axes, and their eight constituent cognitive functions. With my definitions, I attempted to elucidate the secret principles that tie together a function axis. But that article derived its content from another that I wrote. Its original source resulted from my attempt to apply Ludwig Wittgenstein’s Tractatus Logico-Philosophicus to Carl Jung and his typology. That original meditation appropriated the obscure and “even Delphic” style of Wittgenstein’s first treatise. And I wrote with questionable clarity at that. With this article, I aspire to present more or less the same content, but written in a style that is perhaps a tad more palatable. But before we return to the familiar and to the typological, we must first review Wittgenstein’s work.

Kelly L. Ross states that Wittgenstein presented his philosophy “with little argument or exposition.” And regarding their first meeting, Rudolf Carnap’s provides in his autobiography a similar assessment of the young philosopher’s character. Together these sentiments hint at the compelling obscurity of Wittgenstein’s work and at the difficulty that its decipherment presents its interpreters.

But Wittgenstein anticipated our struggle. The introduction to the Tractatus disclaims to its readers that it “will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it – or similar thoughts.” What a stark disclaimer, indeed! With that in mind, I admit that what follows might very well differ from Wittgenstein’s desired exegesis. So please forgive me for what could offend your academic sensibilities.

Wittgenstein starts his meditation with a sort of ontological workout. “The world,” writes Wittgenstein, in proposition 1.1, “is the totality of facts, not of things.” But Wittgenstein’s sense about our world differs from conventional wisdom. As he writes in proposition 1.13, “the facts in logical space are the world.” Together with its neighboring propositions, proposition 1.13 hints that Wittgenstein’s world refers not to the noumenal world of actual objects but to a “bracketed off” world of perception. In that respect, Wittgenstein continues the Kantian tradition of dividing reality into noumenal and phenomenal categories.

Furthermore, in expanding upon Schopenhauer’s conception of world-as-representation, Wittgenstein’s theory of cognition states that objects contain within their essence the potential to arrange themselves about other objects (2.011), and that it is through these arrangements, and only through these arrangements, that objects enter into our cognition (2.0121).

These arrangements are what Wittgenstein terms facts (2.0122). For an example of the cognitive necessity of facts, consider proposition 2.0131, where Wittgenstein writes, “a spatial object must sit in infinite space.” That is to say that we cannot cognate an object without reference to its syntactic circumstances, that is, to its logical relation to other objects. Yet that “a spatial object sits in infinite space” is senseless. Sure, the fact defines a specific relationship between objects. But so what?

The sense of a fact, Wittgenstein argues, shows itself in the mental pictures we create when we think (3, 3.1, 4.022). To build upon our exemplary fact, readers might represent that spatial object as a white sphere rested on top of a vast Cartesian plane. Just like a photograph “the elements of the picture stand, in the picture, for the objects” (2.131). That is to say that we recognize our white sphere as that spatial object and that our ability to do so hinges upon the structural similarity between fact and picture.

Wittgenstein then connects his picture theory to a propositional logic that he develops throughout the Tractatus. “The thought,” writes Wittgenstein in proposition 4, “is the significant proposition.” From there he connects our previous points, writing in proposition 4.022 that “the proposition shows how things stand… and it says that they do stand.” Moreover, he adds, “what can be shown cannot be said (4.1212).” To reiterate, that is to say that I cannot show you in words how that spatial object sits in its infinite space. Only the sentence itself can show you.

That leaves us with two more pertinent propositions. The first comes in proposition 5.6, where Wittgenstein writes that “the limits of my language mean the limits of my world;” the second comes in proposition 5.632, where Wittgenstein states, “the subject does not belong to the world but is a limit of the world.” The former reaffirms Wittgenstein’s theory of object cognition, whereas the latter reminds us that the world is a function of our perception and that we therefore cannot be found in it.

Now, let us apply Wittgenstein to Jungian typology; rather than defining personality as an object, let us instead consider it to be a picture. So, turn inward, adopt that solipsism that results from proposition 5.632, and let us meditate on our picture theory of type.

Because the subject, that is the self or the ego, is not a worldly object, but is rather alien, even otherworldly in its nature, we must not speak of it as though it were (2.01, 7). That is to say that we must not incorporate it into our language. And it is with that sentiment in mind that, in proposition 5.541, Wittgenstein proves that propositions of the form “[person] RELATION p,” wherein p represents a propositional variable, must dissolve into the simpler propositional form “p,” as the former form’s subject lacks sense, and is therefore subject to Wittgenstein’s definition of Occam’s razor (3.328). Therefore, propositions of the form “I have such and such a personality type,” must simplify into to the propositional form, “personality type.” That much returns us to our original shift from object to proposition.

But what then is meant by the values of the propositional form “personality type?” Before we answer that question, let us first consider its propositional form. As a proposition, we cannot point to its form as we might an object’s, but rather must define its form as a specific type of relationship between particular objects. But what objects, and in which way do they relate? From the deductive way we have approached the problem, we could pick any set of objects, and then consider any relationship they form to be apt. But in keeping with our typological tradition, let us define our propositional form in terms of the cognitive functions and their tiered relationship in the four-function, standard model of personality. Thus the form of the proposition “personality type” may be defined loosely as “[Dominate (Axis A (Temperament X), Auxiliary (Axis B (Temperament Y), Tertiary (Axis B (Temperament X), Inferior (Axis A (Temperament Y)].”

But by proposition 4.1212, we cannot reduce our personality to its constituent functions, or their relational hierarchy. Without sense, we have no personality. And so, to answer what is meant by propositions of the form “personality type,” we must let the proposition to show us. And this, and this alone is the transcendental character of personality; it is why a personality is more than its constituent functions. But, as a picture, personality may only be shown and seen; unlike its functions, it may never written and read. Their difference is identical to that of that spatial object and our imaginary sphere.

But what about those cognitive functions, just how do they relate, and why? In my article “The Facts of Personality,” I attempted to outline the functional structure of our propositional personality. Now, with both proper information and mindset, we can revisit and clarify my earlier ideas.

I maintain my earlier claim that functional atoms, cognitive functions of specified class and temperament, introverted intuition, extroverted feeling, etc., are the simplest objects of personality, and that they are the objects in our proposition.

My first point of revision comes with the language I use to describe them. In my original article, I argued that the functional atom shows its form, its function class, intuition, feeling, etc., and proclaims its temperament, introversion, extroversion, etc. I misspoke. What I ought to have said is that temperament and function class are internal properties of a functional atom, and that in conjunction with that functional atom’s potential to relate to another functional atoms, those qualities constitute its essence.

But, to draw upon the work of another guest writer, Sam Levey, who in his article “Process Vs. Orientation: A Local Formulation of Typology,” and in his responses to my article “Determining Function Axis Part 9,” argued that function axes need not pair opposite functions, I hereby renounce my previous argument that functional atoms need pair with their opposites, as I now believe that a functional atom contains within its essence the potential to pair with any other functional atom (2.0122).

With that renunciation in mind, we need not obey Heraclitus’s law of opposites. Therefore, if, for some arbitrary reason, we continue to restrict ourselves to two functional atoms per axis, we will now have twenty-eight possible axes, only four of which we are familiar with, those being the four I defined in “Determining Function Axis Part 9.”
And this raises another question. What is a function axis? Rather than holding to my previous conception of them as complex ideas, let us instead term them too to be propositions (2.021). And, to again borrow from Wittgenstein’s schema, let us term our new function axes, “elementary propositions,” as their objects are the atomic constituents of our propositional personalities. As with our personalities, our function axes must be both defined, and given the reverence to show us their mysteries; they too must paint us portraits. But again, our personalities are not to be reduced to their constituent parts; not even a picture is made of smaller pictures.

Let us end our reflection where we began, that is, with the world. Since our world is phenomenal, so too are our interactions with others, and with our own selves. All our abstractions forgone, perhaps we could indeed type our egos, or the egos of others, for that matter. But those objective egos that we could type could never be our true egos, and so one must wonder just how meaningful our results would be?

To be true to typology, should we type at all, we must, as was outlined in “Can Anyone Become Good At Typing?” argues, assume an alien, even otherworldly empathy. But, in doing so, we must not pretend to be scientists, for our pictures belong in galleries and not laboratories.

The tragedy of Ludwig Wittgenstein is that it was this very sort of strange empathy that he yearned for in philosophy, not that cold behaviorism that would pick away at work like a vulture its prey.

But alas, Wittgenstein more than any of us knew that “whereof one cannot speak, thereof one must be silent.”

Published in Lee Morgan