Understanding Completeness – Incompleteness, and the reason behind it, through State[ment]verse
In any framework or structure of ‘consistency’, we, at the limit of this structure encounter inconsistency. At this edge, we encounter the ‘consistency or completeness’ ‘choice’.
This is the case, fundamentally, at the edge of any ‘Space’, be it Logic, reasoning, Mathematics, Physics or any other Sciences, religion, anything, any structure, any space.
In any given structure or space, every thing in or element of that space/set, denoted by the points in that space, has relation between them that is consistent throughout that space upto the very boundary or border of that space.
In the theory of state[ment]verse, every state/statement has ‘Not’ or Not-state(s)/statement(s). Not-statement of any state or statement is the complement of the statement under consideration. And by (the theory of) state[ment]verse, every and any state/statement is the ‘Not’ or ‘Not-state/statement’ of every and any other state/statement. Any state is the ‘other’ of any other state. Any state is the ‘other’ of any other state, and of which it is the ‘other’/’rest’. Any state is the ‘Not’ of any other state, and of which it is the ‘Not’.
Any statement is the Contradiction, and is contradictory, with respect to its ‘Not’/Not-statement. Any Not-statement is the Contradiction, and is contradictory, with respect to any its statement. Any statement is the Contradiction, and is contradictory, with respect to any other or with respect to the ‘other’ statement.
State[ment]verse has states/statements as the unit.
Each state is the space. Each state is the space or the entire universe of existence for or with respect to or relative to that state itself. It is Everything with respect to itself. (And also if you follow other articles, it is Nothing with respect to itself). It is all that exists with respect to itself.
Now, state is its own Basis. It defines itself. Every structure in Mathematics or Logic or any field, can be considered a space or state/statement. The combination of statements or collection of them can be considered and is just another, maybe very long, statement. But it is statement nonetheless.
So, that structure or space/set of things/spaces corresponds just another state/statement in the state[ment]verse.
So, any structure or space or state is its own basis, its own universe, or space of existence. Just as any state has ‘Not’, every structure has ‘Not’ or the ‘other’, with respect to it, and of which it is the ‘Not’.
Now, Contradiction is the or defines the border of any space/state. The statement and its ‘Not’ are contradictory to each other. One is the nonexistence of the respective/relative other. One exists with respect to itself, and does not relative to the other, and vice-versa.
Now, the complete picture is the statement/state — Not-statement/-state. But this involves a statement and its ‘Not’/Contradiction. In general, the ‘Complete’ is statement — Not-statement, is Contradiction. In general, the ‘Complete’ is existence — Non-existence, is Contradiction.
Also, the justification or reason or explanation for any state/statement, a brute fact, is presented by the ‘Not-statement’, by the statement — Not-statement, by the Complete, by the Contradiction:
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Also, because any statement A is the ‘Not’ of any other statement NA or (call it) B or C or any, one is the nonexistence/non-experience of the other. So, A cannot ever ‘know’ or experience B, and vice-versa. So, though B is the justification for A (or for C or D or any), A cannot know B, B cannot Know A. Similar is for any statement(s). The justification for any A is A-NA (or A-B or A-C or so on). Though any A-B (or C-B or A-D or so on or any) is the justification for any A (or for C or D or any), A (or for C or D or any) cannot know A-B (or C-B or A-D or so on or any).
In general, though any A-B is the justification for any A, A cannot know A-B. And though any A-B is the justification for any B, B cannot know A-B.
This is why though a statement in any space/structure, or that entire space as a statement, though has existence i.e. is true i.e. is ‘Brute Fact’, it’s justification cannot be known.
That is why, and therefore, “A statement though is true, but has no proof.” Or, therefore, “There is a true statement that has no proof.” Or, therefore, “A statement though true, might not have a proof”. Or, therefore, “An unprovable true statement exists”. Or, therefore, “A statement though true, might not have a proof within that framework or structure”. Or, you can phrase it any way.
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