Proof Theory and Enlightenment a.

Evidencing necessity is probably based on to anybody easily convinced premise which is absolutely correctly evidenced appropriately regarded truth. That definitive interpreting is necessary as the idea is installed there.

Meantime, Enlightenment necessity is mainly dependent on to anybody easily interpretable own circuit prepared, with it, anybody easily tries to inquire any difficult proposition. Then this necessity means more helping demand's educating ones' reaction. 

Then, proof is asked to more state of the art idea condensed own Formula, then, necessarily, Evidencing necessity is equivalent with Excluding any Contradiction and in it, we can find the absolutely reliable knowhow and in it, anybody can easily prove, the mission is there. 

Then, proof is not enlightening necessary own interpreting, but definitely Absolutely Correct Law and method, thereby it intends to verify in proof inquiry, meantime, Enlightenment is rather pushing any asking one and studying one forward to obtain new formula so usefully and conveniently. 

And University or any kind of education site necessity needed in 20 Centiry and this Centiry first quarter period around Proof Theory is left on Analytical Philosophy mainly pioneered by Flege or Russell or so, on the other hand, Enlightenment is left on Phenomenology mainly pioneered by Husseral and Melreau Ponty or so. 

By the way, Proof theory needs very well dividable Enlightenment, on the other hand, Enlightenment needs more Generalized own devise and smart Interpreting for enlightening students. 

Then, after all, former Proof Theory intended to more definitely excluding idea's error and minute trustworthy idea should be picked up, the mission was there, then,  ecesarily many Mathematicians and Logicians had been mobilized at this mission task study genre.

On the other hand, verifiable thinking circuit as former is left could be so often, very sharpened for evidencing, thereby somehow not that popularized understanding circuit is prone to be neglected, thereby, after all, the supplement necessity had been left mainly by Phenemenology. 

And upper all those things after all, can evidence that we all are having mutually very seen contradictory mutually symmetrical two typed thinking circuitsin our own brain, the thing is relatively trustworthiky said, we can conclude for the time being now. 

(Irregularly continued)

Apr. 20th.   2025

Appendix; Data File necessity means Analytical Philosophy and Interpreting necessity in Generalizing means Phenemenology, the interpreted truth can be as well so properly thought.