Here is my attempt:
Attitude (I or E): Energy focus: Intensive vs. Extensive
Perception (S or N): Information type: Concrete vs. Abstract
Judgement (T or F): Reasoning method: Absolute vs. Relative
Orientation (J or P): Primary combination: Pi-Je or Ji-Pe
Making this true:
Ni: Intensive abstract information patterns
Ne: Extensive abstract information patterns
Si: Intensive concrete information patterns
Se: Extensive concrete information patterns
Ti: Intensive absolute reasoning patterns
Te: Extensive absolute reasoning patters
Fi: Intensive relative reasoning patterns
Fe: Extensive relative reasoning patterns
"Intensive" meaning focused on what you have (what is stored in your brain already).
"Extensive" meaning focused on what is out there (what exists in the outside world).
"Relative" meaning what things are in relation to each other (Honesty > Winning).
"Absolute" meaning what things exist. Period. (1+1=2)
"Concrete" meaning what exists in material form (a tree)
"Abstract" meaning what exists as idea (the word "love" in a person's mind)
"Pi-Je" meaning using primarily introverted perceiving and extroverted judging (in any order).
"Ji-Pe" meaning using primarily introverted judging and extroverted perceiving (in any order).
Jung formulated some of his ideas aware of the theory of the unity of opposites first put forth by Heraclitus
All of the functions being some sort of pattern of either information or reasoning was a cool idea to me, but that may just be my intuition-soaked thinking leaking. It would be cool to see what any sensors out there think of that.
This requires some flexibility of thinking when it comes to the actual definition of words, but it helped me to look at the whole typing system as a system of dichotomous patterns.
I'm not fully happy with it, though, so some input would be appreciated!