SuttaCentral
It is more like the distinction between:
I am pointing out that a formal and rigorous logical distinction can be made between the above. Doesn’t the above seem reminiscent of the conversation in this thread? 
In fact, I’ll go even further: it is impossible to prove #1 from #2 logically without assuming the Law of the Excluded Middle. And the LEM cannot be proved logically. This all follows from Gödel’s incompleteness theorems. So if you adopt #1 you are necessarily relying upon an unproven assumption. That does not sound to me like direct and complete realization.
I don’t understand your reasoning here. Granted, it’s been almost 10 years ago since I took formal logic in college. At my uni, I remember that if you took all the logic classes each semester for an entire bachelors degree, the last semester of that degree, the final logic class would culminate in proving Gödel’s incompleteness theorems.
I’ve always been fascinated by the theorems but I was never motivated to take 2.5 years of prerequisite classes to really understand it. I only took what I needed for my bachelor which was mostly math.
AFAIK, the point of Gödel’s incompleteness theorems is that all systems rich enough to do basic arithmetic must contain assumptions that cannot be proven (by that system). Before this, very smart people were looking for an absolute foundation for mathematics; a set of basic axioms from which all of math would flow.
So like, isn’t the point of the theorems precisely that when we do any sort of sophisticated reasoning, we are necessarily taking on unproved assumptions?
I mean, it’s good to reason in a valid way, it’s nice to have a set of rules that people agree on to make communication smooth, but it can only take you so far?
One consequence of Gödel’s incompleteness theorems is that, “it is not, in general, possible for a logical system to have a formal negation operator such that there is a proof of “not” P exactly when there isn’t a proof of P” for all P. That is exactly what is assumed by the Law of the Excluded Middle; that for all statements P; either P is true or P is false. Consequently, one way of understanding Gödel’s result is that no logical system will ever be able to prove LEM.
To logically prove all things are not self you would need a logical system where it would be possible to have a formal negation operator such that there is a proof of “not” P exactly when there isn’t a proof of P for all possible P.
Deriving “not” P in a logical system without assuming LEM implies assuming P and then deriving a contradiction aka “refutation by contradiction.” However, this is short of an existence proof of ~P; rather it is a non-affirming negation. NOTE: the five fold analysis that the Teacher employed again and again falls short of even this.
Another difficulty I’ve experienced is the incredible plethora of purported proofs of self that sentient beings assume. It turns out there are many many different purported proofs of self that different sentient beings employ. That is why it is necessary to employ myriad refutations by contradiction for all the various rube goldberg machines sentient beings dream up as possible true selves.
Gödel’s incompleteness theorems are more profound than this. The first says that for any consistent logical system, there exist truths that are knowable as truth by us and yet are not provable by that logical system. The second theorem shows that no consistently logical system can prove its own consistency.
What you’ve stated. that there must always exist assumed axioms, I think was never a surprise to those very smart people looking for an absolute foundation. However, they thought there would exist some combination of assumed axioms that would render every non-trivial truth about the natural numbers. Gödel showed that is not the case.
This is not quite right.
The point of the theorems is that there are true statments of arithmetic that cannot be proved by a given Formal theorem, regardless of the assumptions made.
So if you have constructive logic it is possible to define a polynomial the answer to which cannot be proven by constructive logic. If you “upgrade” your logic with more assumptions to classical logic then you can prove the answer to that polynomial, but we can construct another polynomial that cannot be proved by classical logic and so on.
So the incompleteness theorems basically say that there is always more true math than any logical system can capture.
Its a pretty wild thing to think about.
Also not as difficult as your post implies, Raymond Smullyan has a couple of excellent books demonstrating the theorems that anyone with first year university maths experience should be able to work through.
Just wanted to point out that this isn’t restricted to math. Any logical system has the same limitations; not just mathematical systems, but I’m sure you know this. Just wanted to make it explicit.
I think that most people at some moment in time see that the khandha’s are impermanent, changing, liable to arise and cease. Some moment in time we see that we are not in control too. We see, how our desire to be in control, and to have all according our wishes, makes us even feel more bad and only contributes to me misery. That is all part of commen sense, or common human experience, i believe.
We see and understand that clinging to the body, feelings etc as me, mine, my self , mind, existence is not helpful. Also this is common human experience. Many people who become ill see that there is no use in desiring for what once was, health, power etc.
I believe this basic life lessons we all make in life. We do not need a Buddha to let us understand all this. It is like life and suffering forces us to become more realistic and change our expactation, attitues, passions and views. Otherwise we only suffer more. Also therapist go this Path.
I believe many people do this. Maybe not as buddhist, but for humans it is normal to investigate suffering and its causes. We do not wish to suffer. Ofcourse we all know and see at any moment that our attitude, tendencies, wishes, desires, personality, views, identity, attachments plays a major role. We do not need a buddha to figure this all out.
Not always but still it is also quit common and natural that becoming older, one becomes more realistic and more dispassionate. It is quit normal that one day one stops feeding all those inner fires. It is natural for many people to take suffering as a lesson. This Dhamma, as it were, is not difficult to see and also one will do this is quit naturally.
But i do not believe that all these people who have had life and its suffering as a teacher and have not fed the demons, the inner floods, fires, are nobles. For me this is all to much common sense. To rational. For all this we do not need a Buddha, i feel.
I also do not think that we need a Buddha to know and see that emotions, thought etc are insubstantial. It is common human experience.
For me the uniqueness of Dhamma lies in asankhata, the knowlegde of that what has no characteristic to arise, cease and change in this very life. I believe that is what is really ignored or stays unknown or unseen by us. Anicca, dukkha and anatta are not really supra mundane. Such ideas are also common for worldlings, certaintly to some degree.