you have to understand how Ti works in the first place to really understand how a experimental conceptual framework of this kind is created, which is to say they take a thing and split it in half and assign semantic coordinates to each half that allows them to now determine their location to a certain degree in relation to the thing. they can do this multiple times forming axes such that you can create x and y and z and t coordinates along any phenomenon. in this way they "grid out" a conceptual understanding of a thing. at its most basic, when there's not much else to go off of, on/off are the coordinates. so they took cognitive function and divided it into phenomenological experience, which was thinking, feeling, intuition, and sensing. then they sub divided it into introverted/extroverted. this was all based on introspection and observation. what defined the content of these semantic notions was the phenomenological experience of them, which means the "what is was like to feel/think/sense/intuit" etc.
so now you have 8 categories and they were defined in terms of when an introverted function is active it cannot simultaneously also be activated in an extroverted capacity, at the very least it has to switch back and forth in time. the same thing goes for thinking/feeling and sensing/intuition
the way socionics was developed was the "dual nature of man" was posited, which was another way to divide, a priori, man into 2, which created the basis for the 16 types. because most people think of duality as something that came after their understanding of MBTI they dont realize it is actually the foundation of socionics, not something added afterward. the idea is everyone has conscious and subconscious valued and unvalued functions, which is a further division based on observation, but the idea is that for every type there is their dual, which is the "other half" in other words no individual human can be strong in both 4d feeling and thinking because humans by definition are split into 2 parts between a dyad, by definition. that is the a priori assumption underlying socionics. that you aren't strong at it all and that the phenomenon of duality is the evidence of that and was inferred from observation then formulated into an axiom which served as the basis for the formal Ti axiom that grounds socionics
fuck I just reread this and its a mess, let me see if I can restate things more clearly. the basis for any Ti structural understanding of a thing is rooted in a binary system: on/off. they took Jung's cognitive functions t/f/s/i x2 via e/introversion and then observed the phenomenon of duality, from which they inferred the fundamental axiom of socionics which is that you cannot be good at everything at once, rather your abilities are evenly split between 2 types (you dual). thus the simplest answer to the question is dimensionality of functions is by definition something that you can only be good at precisely half of the total
reinin dichotomies are derived from the idea that you apply certain formulas that are actually quite simple and are really just variations on how to slice numbers (6 or "half dozen" or 3 x 2, etc), and then they assigned descriptions to what those numbers represented. in other words they took something like sensing + logic in valued blocks (ego or superid) and said hey, we see "aristocratism" as a consistent pattern emerging from those factors we divided up. the reason you cant be both aristocratic and say negativist and decisive and emotivist essentially boils down why you cannot define 10 as (3+3+3+3) it entails a downrange contradiction
duality has religious connotations even though not everyone is aware of it, precisely because God is a symbol of unification and duality is a form of unification. "differentiation" is precondition (or even better, synonymous) to "personality" so at its most basic "personality" is the idea that you cant be good at it all. duality is just an elaboration on the idea via Ti which splits things in 2 in order to make sense of it. this is why there is religious significance to the idea of analytic psychology and why Jung is considered perhaps the greatest 20th century thinker, because he managed to provide a basis for bridging the gap between spiritual and scientific, which had only been widening since the enlightenment
tl;dr: its all definitional