++++Contextual Distinction as Proto-Ontological Grounding
Posted: Wed Jun 03, 2026 2:40 am
Contextual Distinction as Proto-Ontological Grounding
1. Logical Identity is Foundationless; Logic is Relative Nested Tautologies.
((A=A)=(A=A))=(A=A).....
The identity law has to be subject to itself if it is to have identity, but as being subject to itself it results in the distinction being subject to itself, and infinite regress occurs.
((A=A)=(A=A))=(A=A).....
If the law of identity is not subject to itself than the law of identity ceases:
((A=A) =/= (A=A))= -(A=A).....
Now if infinite regress or absence of the laws, non-law, occurs it is subject to the laws of identity and the same process ensues:
IG = IG
((IG=IG)=(IG=IG))=(IG=IG).....
NL = NL
((NL=NL)=(NL=NL))=(NL=NL).....
But if the infinite regress and non-law is subject to an absence of identity than nothing can be said, but neither can identity be claimed for anything else.
What remains if the identity law is subject to itself is nested tautologies.
These nested tautologies are relative to other nested tautologies if a proposition is present:
((A=A)=(A=A))=(A=A)..... -> ((B=B)=(B=B))=(B=B).....
All logical rules, syntax, formalisms, semantics, etc. are subject to the identity laws if they are to have an identity. Thus to argue standard x-order logic against this meta-formalism is to enact said formalism.
In these respects syntax become a performance of invariant constraint as tautology becomes invariant by nesting, constraint as the form of the tautology and performative by degree of its emergence. What remains of logic and logical identity is empty loops within loops.
If the axiom of identity is left unexamined than the foundations of logic is nested assumption thus logic is not required as assumption remains regardless of its depth.
2. The Law of Non Contradiction Negates itself at the Meta-Level; Recursion Negates LNC
The Application of the LNC on LNC by degree of a recursive hierarchy results in LNC negating itself as the recursive hierarchy itself given LNC exists across the hierarchy resulting in a fixed point scale invariant state, between the identities that compose it thus resulting in the very same identities which compose LNC as not equalling themselves.
"=" identity equivalence
"=/=" identity non-equivalence
"<->" biconditional identity
A =/= -A
B =/= (A=/=-A)
((B=B), (B =/= -B))
((B =/= -B) = (A=/=-A)) = (C=/=-C)
((B = A), (-B = -A)) <-> (B =/= -B) = (A=/=-A)
((B =/= A), (B =/= -A)) <-> (B =/= (A=/=-A))
((B=A), ((B=/=A) = (B =/= B)))
If “=” exists in distinct stages, and each state requires a corresponding identity of the stage as S=S, S1=S1, S2=S2, etc. than equality is divided according to each state as a fixed point of identity division and any application of “=” is a application of division of the distinct heirarchies of equality itself.
****All standard formalism, rules, syntax and semantics are subject to LNC if they are to have identity, thus the meta-formalism is prior to such objects.
3. Identity as Recursive Contextualization
A=A requires A=/=-A as (A=A) =/= (A=/=-A)
and yet (A=/=-A) = (A=/=-A)
so equality is not equal to inequality and inequality is equal to inequality
So.. ((A=A) =/= (A=/=-A))=((A=A) =/= (A=/=-A))
Condensed further:
((=)=/=(=/=)) = ((=)=/=(=/=))
Condensed further:
(=/=)=(=/=)
(A =/= -A) → (=) =/= (-(=/=))
****where equality and inequality are variables given what they represent in identity is variable dependent:
example: (A=A) = (B=B) → (=)A = (=)B
A = (=) and -A = (-(=))=(=/=))
Thus
(-(=/=)) → (=)
↔
A = (=) and -A = (=/= ↔ (-(=))
Thus
(=) =/= (=)
Thus A=/=A
However, at the meta-level A equals an operation: (A = ●)
Thus
(● =/= ●)
resulting in:
(=)=/=(=)
and equality becomes conditional context that effectively results in recursion as the primary identity as
(=)=/=(=)
reduces to:
( )=/=( )
where A=A results in
(=/=)=(=/=)
And
(=)=/=(=)
thus
(=/=)(=)(=/=)
(=)(=/=)(=)
Which reduces at the meta level to contexr recursion:
( )( )( )
With context as the fixed point:
( )
thus only empty context remains as a variable
( )A
Until recursion gives structure:
( )A( )A
(( )A( )A)B
In these respects identity is recursive contextualization. Variable is the only remaining primitive thus identity is:
( )A
****Any law/syntax/semantics/etc. is subject to the identity of A=A if the law/syntax/semantic/etc. is to have identity thus they are subject to this formalism.
4.Russel's Paradox Side Stepped by Recursion
A
(A)B
((A)B)C
(A, C) <-> B
(((A)B)C)D
(A,B,C,D) <-> (B,C)
((A)...n) <-> (B.....n-1)
(B.....n-1) <-> (B.....n-1)
((B.....n-1) <-> (B.....n-1)) <-> ((A)...n)
((A)...n) <-> ((A)...n)
((A)...n)● <-> ((A)...n)●
● <-> ●
5. ++++M Logic; Mobius Logic
1. All distinctions are a dualism of presence and absence, the presence of one as the absence of another, the absence of one as the presence of another.
2. All distinctions are simultaneous presence and absence, as dually both they are a mobius strip.
3. The presence of X contains the absence of X as X.1 as the part,
****A line segment as X.1 and X.2 where X.1 is not X but a part thus X is not present as the part.
the presence of X is part of the absence of X as X.1.1
****A line segment as X where X.1.1 is not X but as X is a part.
4. The absence of X contains the presence of X as X.1,
****X.1 as a segment of X is the presence of X at a different scale but this different scale is not X defined by a seperate scale.
the absence of X as part the presence of X as X.1.1
****The scale where X is a part of X.1.1 is X as X.1.1 at a different scale.
****Containment is both mereological and representational as these distinctions of mereological and representing are effective the operation of M.
5. All distinctions are M; M is the variable of Mobius strip, simultaneous opposites.
6. M follows the logic of points 3 and for as M results through -M by the contrast for M to be distinct as M as M can only be distinct by what it is not; the absence of contrast is the absence of distinction
7. M and -M are contained within and part of another M; M is self-embedding as a fixed point that occurs across scale thus resulting in a recursive fixed point operation.
8. Standard epistemological terms would result in M being a paradox, a contradiction, both a paradox and contradiction as a higher order paradox, and neither paradox or contradiction as a higher order contradiction;
A. M as paradox is the unity of opposites by contained relation
B. M as contradiction is the multiplicity of opposites by contrasting opposition.
C. Both paradox and contradiction are a higher order paradox by degree of point A.
D. Neither paradox nor contradiction are a higher order contradiction by degree of point B.
9. Point 8 contains points A and B as M, points C and D as M, thus point 8 is M as opposite Ms.
10. M is the act of distinction, wherever distinction emerges or dissolves M logic is the foundational operation; by degree it is recursive as the repetition of any distinction allows for a contained presence while the inverse contrast allows said distinct by the very same recursion.
This can be observed with a single point: ●
The recursion of the point as: ●● results in:
A. The containment of ● by ●●.
B. The self contrast of ● by ●●.
C. ●● is the recursive structure.
D. ● is the recursive process.
E. M is distinction as structural process.
F. Standard symbolic languages which results in a process/pattern, form/function, operator/operand dichotomy as effectively contained as M. A symbolic language that removes this dichotomy would be left with a higher dichotomy of M that as a structural process is recursive function finite as emergent form: M, MM, (MM)M
11. The refutation of M logic require M logic thus proving M logic; any logic outside of M logic is but a sub-logic thus resulting in M being transcendental containment.
12. Formalism:
M is a transcendental operator variable. A transcendental operator variable can be defined as such. It is distinction in simple terms. In synonymous terms:
Transcendental is change as limit emergence and dissolution,
Operator is the structure of the change,
Variable is the foundational nature than can vary in appearance in accords to context.
Transcendental operator variable can be defined as the emergence and dissolution of structural change, embedded within itself, that changes appearance in accords to self-scaling.
The syntax and function of the formalism is recursion as distinction.
M
MM
M(+,-)
M(+)M(+) (x)
M(x)M(x) (^)
M(-)M(-) (÷)
M(÷)M(÷) (rts)
M(++) (-)
M(+++) (+)
.....
M(--) (+)
M(---) (-)
....
MM
M (->,<->)
M -> M (M<->M)
M <-> M (M -> M)
MM
M(+,-) M(->,<->)
M(+,-)(->,<->)
M(x●,y●)
***x●, y●: opposite distinction sets
MM
M(x●,y●)
M(x●x●) (y●)
M(y●y●) (x●)
**** In this context
x● = quantity as a distinction
y● = quality as a distinction
MM
M (●,●●)
**** ● = distinct fixed point/geometric point
**** ●● = distinct scale/geometric point scale
M(● ●) (●●)
M(●● ●●) (●)
M
MM
(M)M
((M)M) (M, MM)
(MM)M
(M)MM
M(M)M
(M)M(M)
(MMM)
M
6. Contextual Equivocation; Identity as Relative Tautologies
1. There is identity.
2. Identity as equivocable, A=A, is tautological.
3. Identity as relational, A <-> B, is conditional.
4. Equivocable identity is relational by degree of equivocation contrasting to non-equivocation. (A=A)<->(A=/=-A)
5. Relational Identity is equivocable by degree of relation containing the Identity as itself. (A<->B)=(A<->B)
6. Fundamentally Identity is reducible to operation as
(A=A)<->(A=/=-A) reduces to
(=)<->(=/=)
And
(A<->B)=(A<->B) reduces to (<->)=(<->)
7. As emergent by nature of operation identity, as equivocable, identity contains itself:
A= (A1=A1)
A=A
((A1=A1)=(A1=A1))
A1 = (A1.1 = A1.1)
A1=A1
((A1.1=A1.1)=(A1.1=A1.1))
A1.1 = (A = (A=A))
8. As emergent by nature of operational identity, as relational, identity contains other identity
(A<->B)<->C
A<->B
(C<->D)
D<->(A<->B)
(A<->B)<->(C<->D)
A<->(B,C,D), B<->(A,C,D), C<->(A,B,D),
D<->(A,B,C)
9. The equivocation of relationships is the contrast the the relationship
(A<->B)=(A<->B)
(A<->B) =/= (-A<->-B)
Thus the relationship requires contrasting equivocations
((A<->B)=(A<->B))=/=(-A<->-B)=(-A<->-B)
and the operation of equivocation is not equal to itself
((A<->B)=(A<->B))=/=(-A<->-B)=(-A<->-B)
((<->)=(<->))=/=((<->)=(<->))
(=)x =/= (=)y
10. The relations of the equivocations are the containment of the equivocations:
A<->B
(A=A)<->(B=B)
Thus the equivalence requires contained relationships:
(A<->B)=(A<->B)
((A=A)<->(B=B))=((A=A)<->(B=B))
And the operation of relation is equivalent to itself:
((A=A)<->(B=B))=((A=A)<->(B=B))
((=)<->(=))=((=)<->(=))
(<->)x = (<->)x
11. Identity is process, this process is relative equivocation where equivocation occurs by contexts emergent from relations where said context allows equivocable identity to be emergent while dually allowing contrast of what equates by degree of the relational dynamic necessitating a difference of what equates.
12. Identity is relational tautolologies, the regress of tautological relationships is nullified as the tautological process of equivalence being a fixed point, the circularity of tautological relationships is nullified as the relational process of contrast results in emergent tautologie.
13. The Nature of identity as process results in relation, <->, as the foundational primitive however the equivocation that inversely emerges from relationship is but an inverse side of the same relationship applied to itself for the relation of relations is the equivocation of relations through relation thus only context as variable remains:
((<->)<->(<->)) = ((<->)<->(<->))
(<->)=(<->)
((<->)=(<->))
((<->)=(<->)) <-> ((<->)=(<->))
(=)<->(=)
(=,<->)
( )
2. Context is the foundational nature of relational and equivocable identity as the identity itself results in an empty context.
3. The empty context is indistinct on its own terms and distinct, as an identity, upon relation or equivocation to further contexts
( )a = ( )a
( )a <-> ( )b
However given the nature of equivocation and relation are inverse sides of context itself what remains is context nesting as identity:
( )
( )( )
(( )( ))
( )
This nesting of context is not only the scale invariance of the context but also the recursion and emergence of scale invariances to new scale invariances:
( )
( )( )
(( )( ))
( ) = (( )( ))
(( )( )) =
((( )( ))(( )( )))=
( )( )( )( )( )( )( )=
( )( )( )( )( )( )( )( )( )( )( )( )( )( )=
(( )( )( )( )( )( )( )( )( )( )( )( )( )( ))=
( )= ( )( )( )( )( )( )( )( )( )( )( )( )( )( )
(( )( ))=( )( )( )( )( )( )( )( )( )( )( )( )( )( )
( )=( )
(( )( ))=(( )( ))
( )n = ( )n
(n = n)=(( )=( ))
n = ( )
(( ) = ( )) = (( ) = ( ))
((=)=(=))
(=)
( )
( )<->( )
(( )( ))<->(( )( ))
( )a <-> ( )b
(a<->b)=(( )<->( ))
a,b <-> ( )
(( ) <-> ( )) <-> (a<->b)
((<->)=(<->))
(<->)
( )
( ), ( )( ), ( )( )( ) <-> (( )( ))
( ) <-> ( )( )
( )( ) <-> ( ), ( )( )( )
( )( )( ) <-> ( ), ( )( )
( ) <-> ( )
( )
( )=(=,<->)
( )<->(=,<->)
(=,<->)
( )
( )
( )( ) = {( ),( )}
( )( )( )= {( ),( ),( ), (( )( ),( ))}
( )
(( )( ))
(( )( ))( ), (( )( ))(( )( ))
(( )( ))( )
(( )( ))( )( ), (( )( ))(( )( ))(( )( ))
(( )( ))(( )( ))
(( )( ))(( )( ))( ),
(( )( ))(( )( ))(( )( ))(( )( ))
( )
4. The emergence of context is the emergence of derivation as contextualization is derivation thus the derivation of a context, from a context necessitates the emergence of a new context and the dissolution of another
( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) ->
(( )( )( ))
->
(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))
->
( )( )( )( )( )
->
(( )( )( )( )( ))
->
(( )( )( )( )( )) =
((( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( )))
=
( )
The derivation of context is the contextualization of one context, or contexts, through another context(s) by which context effectively is a self-embedding boundary, transformation is but a shift in observable limits where the change of limits is the maintenance of limits. Context is limit. Limit is distinction.
For a single context to occur results in its indistinction:
( )
For the context to be distinct it must self contrast:
( )( )
and by said self contrast there is a containment of context as a context:
(( )( ))
What remains is context with the indistinct context reverted back to indistinct:
( )
However this indistinct context contains infinite contexts, potentially, while the infinite contexts are a single distinct context
( )<->( )x
or a set of finite simultaneous contexts:
( ) <-> (( )l,( )m,( )n)
Regardless of what is potentially there the nature of the context transforming to another context is relative to the context applied to it:
( )( )n -> ( )y
( )( )m -> ( )z
Thus the derived context is the relation of the prior.
An infinite indistinct context is distinct by recursion:
( )x
( )x( )x
This recursion collapses the infinite context into a finite context of infinite contexts as the infinities maintain being infinite but effectively are finite by relation:
(( )x( )x)y
Thus each context is effectively a scale of infinite contexts:
(( )x( )x)y
(( )x( )x( )x)z
And in these respects a context is a scaling of the context by which it is derived. However each scale is a scale of infinite contexts thus derivation is a continuous process and the application of context is the application of transformation thus equating the context to a process by degree of the continuity it contains.
This continuity is the continuum of contexts made finite by degree of the limits of the infinities being distinct.
What remains is a scale invariant tautology.
As scale increases so do fixed points:
( )( )
(( )( ))(( )( ))....
( )( )( )
(( )( )( ))(( )( )( ))....
Which the fixed point across scales the fixed point context becomes the distinction that allows ratios within the scale, as a sequence, to occur. In these respects contextualization is derivation and the proof of a thing is the unfolding process that reveals as the thing. Context is thus form as process where traditional expression of form as operand, and process, as operator, are collapsed within the limits of the emergence itself.
However the single context contrasts itself across scale thus with dimensional scaling, a dimension being a sequence, the single context self contrasts as both the emergence of scale and the emergence of scales to scales.
What remains is a context embedding itself across scale as a new scale thus resulting in identity being embedding tautologies at multiple levels As the tautologies manifest infinitely so do the fixed points thus resulting in a perpetual state of continuous finiteness.
What remains is a single context that reveals only as recursive embedding within recursive embedding which allows the context to be distinct. In these respect the single context is the limit of contexts as the derivation of them. Derivation, at the meta-level, is recursion as sequence, sequence as pattern, thus what constitutes the existence of a phenomen is the contextualization of it as the limits of it.
What remains is embedded tautologies, as a new tautologies, thus resulting in embedding of tautologies itself being a tautologie and only pattern as context remains.
Empty context, ( ), is the grounds of distinct contexts by degree of recursion where context in and of itself is a tautology and loop as recursion. The emptiness of context is the point of change of one context into another as the empty context is but the potentiality of contexts made distinct by the recursion of said potentiality as the distinction of said potentiality contained within it.
In these respects and empty context results in further contexts which eventually saturate to a single context again with this process itself being the simple recursion of contexts, ( )( ), as a context ( ) thus the context contains itself (( )( )).
Context is thus the process of derivation and derivation it a tautological process of derivation derives further derivation thus resulting in a fixed point being equivalent to a process of change by which scale emerges.
The question of why distinction from indistinction, something from nothing, presence from absence, being from void is answered in the question itself:
Indistinction is distinct as indistinction,
Nothing is something as nothing,
Absence is the presence of absence,
Void 'is' void.
The answer is the tautology of the distinctions themselves as distinct thus the identification of a negation is the presence of identification and "what is not" is but the assertion of "what is" by degree of the claim "what is not" occuring.
Identification of nothing is the identification of identification emerging from nothing as nothing is but the identification of nothing thus the emergence of identification as identification leaving only tautologies.
Given the emergent nature of tautology as a whole, and the corresponding nature of identity as tautological in form and function, what is considered self-evident or axiomatic is but the emergence of an identity, that is not reduced any further, as a foundation to derive a recursive chain of assertions where the base axiom is represented across scale and different degrees as the argument or formulation itself.
What is considered axiomatic identity is but an emergence of one context from many that in turn is used as a pivotal point for further contexts/identities to transform through said axiom. In these respects basic linear reasoning is holographic expressions of axioms through their surrounding contexts as the axiom maintains itself across the assertions themselves.
In these respects and axiom is the derivation of contexts as a recursive fixed point across contexts. By degree of the recursion of a fixed point, as a new scale, resulting in a further fixed point, there are effectively infinite axioms by which to derive conclusions and the axioms of any system are merely the system as a projection of specific context by degree of the system being a holographic expression of the axiom itself.
This can be expressed under the following where "( )" is an axiom and ● is operation as point of change.
( )x
( )x ● ( )y
(( )x ●( )y)( )x.1
( )x ● ( )z
(( )x ● ( )z)( )x.2
( )x ● ( )x.n
(( )x ● ( )x.n)( )x●x
( )x●x
( )x ● ( )x
( )●( )
(( )●( ))
(●)
(●)(●)
((●)(●))
((●)(●))●
(●●)●
(●●)●●
(●●)(●●)●
.....
( ) = ●
( ) <-> ●
(<->,=,●)
( )
●●
●
****Relative to identity being reducible to process the standard nature of formalisms do not apply as the operations are equivalent to variable identities, in this respect the argued formalism is transendentally formal (transcendental by degree of containing and occuring beyond standard formal rules).
7. Distinctions as Self-Contained Self-Contrast; Meta-Formalism
"A" identity, distinction
"=" is or equals
"( )" context, container, set
"○" Scale invariant self referencing context
"<->" biconditional
"-" absence, negation
"+" presence, emergence
1. A
2. A=A
3. ((A=A) <-> (-A=-A)) <->
((A=/=-A) <-> (A = - -A))
4. (A <-> -A) <-> ((A=A) <-> (-A=-A))
5. (A <-> -A) = B
6. B = B
7. (B = B) <-> (-B=-B) <->
((B =/= -B) <-> (B = - -B))
8. (B <-> -B) <-> ((B=B) <-> (-B=-B))
9. (B <-> -B) = C
10. ....D....
11. (A <-> A) = (B <-> -B) = (C <-> -C) =...
12. ● <-> - ●
13 (● <-> - ●) <-> ((● =/= - ●) <-> (● = - -●))
14. ● = (+,-)
15. (+, -)
16. ( )
17. ( ) = ( )
18. (( ) <-> -( )) <->
((( ) =/=( )) <-> (( )=--( )))
19. (( ) <-> -( )) <-> (( ))
20. (( )) = (( ))
21. ...(..(( ))..)...
22. ○
23. A = ( )
A = ○
● = ( )
● = ○
( ) = ○
24. (A <-> ● <-> ( ) <-> ○) = X
X1 = A
X2 = ●
X3 = ( )
X4 = ○
25. (X = (X1, X2, X3, X4)) <->
(((X = X1) <-> Y1),
((X = X2) <-> Y2),
((X = X3) <-> Y3),
((X = X4) <-> Y4))
Y(1,2,3,4) = ( )
****
X <-> Y
27. (A) <-> (●) <-> (( )) <-> (○)
28. ...(..(( ))..)...
29. (( )<->( )) = ((( )=( )),(-( )=-( )))
30. (<->)=(+=+, -=-) <-> (( )<->( ))
31. ((+=+) <-> (-=-)) = ((--=--)<->(++=++))
32. ((=) <-> (=)) = ((=) <-> (=))
33. (<->,=)
34. (<->)<->(<->),
(=)<->(=)
(<->)=(<->)
(=)=(=)
35. ( )=( ), ( )<->( )
36. ( )
8. The Nature of Polarity by Contradiction
1. Pure convergence results in all distinctions unified as indistinct nothingness as there is not distinction to converge.
2. Pure divergence results in all distinctions seperated as indistinct nothingness, as there is no distinction to diverge.
3. Pure convergence and divergence are effectively nothingness; the pure convergence of both processes is effectively nothingness, the pure divergence of both processes is effectively nothingness.
4. What remains is the process of the distinction of "nothingness" thus convergence and divergence is the recursive distinction of "nothingness".
5. The distinction of nothingness is not nothingness but the distinction of nothingness thus there is no nothingness but the distinction of it.
6. Pure convergence is contracting "nothingness", pure divergence is expanding "nothingness".
7. Thus convergence is the distinction of contraction, this contraction is the repetition of multiple distinctions unto a unity.
8. Thus divergence is the distinction of expansion, this expansion is the repetition of a unified distinction unto a multiplicity.
9. Pure unity has no contrast thus is nothing; pure multiplicity is only contrast thus is nothing.
10. Distinct Unity is unity because of contrast to distinct multiplicity, distinct multiplicity is multiplicity as the unity of distinct multiplicity.
11. What remains is distinction, this distinction is the polarity of absolute convergence and absolute divergence, this polarity is the distinction of "nothingness" as a recursive distinction.
12. Only distinction remains, what is indistinct is but a distinction of the distinct.
1. Logical Identity is Foundationless; Logic is Relative Nested Tautologies.
((A=A)=(A=A))=(A=A).....
The identity law has to be subject to itself if it is to have identity, but as being subject to itself it results in the distinction being subject to itself, and infinite regress occurs.
((A=A)=(A=A))=(A=A).....
If the law of identity is not subject to itself than the law of identity ceases:
((A=A) =/= (A=A))= -(A=A).....
Now if infinite regress or absence of the laws, non-law, occurs it is subject to the laws of identity and the same process ensues:
IG = IG
((IG=IG)=(IG=IG))=(IG=IG).....
NL = NL
((NL=NL)=(NL=NL))=(NL=NL).....
But if the infinite regress and non-law is subject to an absence of identity than nothing can be said, but neither can identity be claimed for anything else.
What remains if the identity law is subject to itself is nested tautologies.
These nested tautologies are relative to other nested tautologies if a proposition is present:
((A=A)=(A=A))=(A=A)..... -> ((B=B)=(B=B))=(B=B).....
All logical rules, syntax, formalisms, semantics, etc. are subject to the identity laws if they are to have an identity. Thus to argue standard x-order logic against this meta-formalism is to enact said formalism.
In these respects syntax become a performance of invariant constraint as tautology becomes invariant by nesting, constraint as the form of the tautology and performative by degree of its emergence. What remains of logic and logical identity is empty loops within loops.
If the axiom of identity is left unexamined than the foundations of logic is nested assumption thus logic is not required as assumption remains regardless of its depth.
2. The Law of Non Contradiction Negates itself at the Meta-Level; Recursion Negates LNC
The Application of the LNC on LNC by degree of a recursive hierarchy results in LNC negating itself as the recursive hierarchy itself given LNC exists across the hierarchy resulting in a fixed point scale invariant state, between the identities that compose it thus resulting in the very same identities which compose LNC as not equalling themselves.
"=" identity equivalence
"=/=" identity non-equivalence
"<->" biconditional identity
A =/= -A
B =/= (A=/=-A)
((B=B), (B =/= -B))
((B =/= -B) = (A=/=-A)) = (C=/=-C)
((B = A), (-B = -A)) <-> (B =/= -B) = (A=/=-A)
((B =/= A), (B =/= -A)) <-> (B =/= (A=/=-A))
((B=A), ((B=/=A) = (B =/= B)))
If “=” exists in distinct stages, and each state requires a corresponding identity of the stage as S=S, S1=S1, S2=S2, etc. than equality is divided according to each state as a fixed point of identity division and any application of “=” is a application of division of the distinct heirarchies of equality itself.
****All standard formalism, rules, syntax and semantics are subject to LNC if they are to have identity, thus the meta-formalism is prior to such objects.
3. Identity as Recursive Contextualization
A=A requires A=/=-A as (A=A) =/= (A=/=-A)
and yet (A=/=-A) = (A=/=-A)
so equality is not equal to inequality and inequality is equal to inequality
So.. ((A=A) =/= (A=/=-A))=((A=A) =/= (A=/=-A))
Condensed further:
((=)=/=(=/=)) = ((=)=/=(=/=))
Condensed further:
(=/=)=(=/=)
(A =/= -A) → (=) =/= (-(=/=))
****where equality and inequality are variables given what they represent in identity is variable dependent:
example: (A=A) = (B=B) → (=)A = (=)B
A = (=) and -A = (-(=))=(=/=))
Thus
(-(=/=)) → (=)
↔
A = (=) and -A = (=/= ↔ (-(=))
Thus
(=) =/= (=)
Thus A=/=A
However, at the meta-level A equals an operation: (A = ●)
Thus
(● =/= ●)
resulting in:
(=)=/=(=)
and equality becomes conditional context that effectively results in recursion as the primary identity as
(=)=/=(=)
reduces to:
( )=/=( )
where A=A results in
(=/=)=(=/=)
And
(=)=/=(=)
thus
(=/=)(=)(=/=)
(=)(=/=)(=)
Which reduces at the meta level to contexr recursion:
( )( )( )
With context as the fixed point:
( )
thus only empty context remains as a variable
( )A
Until recursion gives structure:
( )A( )A
(( )A( )A)B
In these respects identity is recursive contextualization. Variable is the only remaining primitive thus identity is:
( )A
****Any law/syntax/semantics/etc. is subject to the identity of A=A if the law/syntax/semantic/etc. is to have identity thus they are subject to this formalism.
4.Russel's Paradox Side Stepped by Recursion
A
(A)B
((A)B)C
(A, C) <-> B
(((A)B)C)D
(A,B,C,D) <-> (B,C)
((A)...n) <-> (B.....n-1)
(B.....n-1) <-> (B.....n-1)
((B.....n-1) <-> (B.....n-1)) <-> ((A)...n)
((A)...n) <-> ((A)...n)
((A)...n)● <-> ((A)...n)●
● <-> ●
5. ++++M Logic; Mobius Logic
1. All distinctions are a dualism of presence and absence, the presence of one as the absence of another, the absence of one as the presence of another.
2. All distinctions are simultaneous presence and absence, as dually both they are a mobius strip.
3. The presence of X contains the absence of X as X.1 as the part,
****A line segment as X.1 and X.2 where X.1 is not X but a part thus X is not present as the part.
the presence of X is part of the absence of X as X.1.1
****A line segment as X where X.1.1 is not X but as X is a part.
4. The absence of X contains the presence of X as X.1,
****X.1 as a segment of X is the presence of X at a different scale but this different scale is not X defined by a seperate scale.
the absence of X as part the presence of X as X.1.1
****The scale where X is a part of X.1.1 is X as X.1.1 at a different scale.
****Containment is both mereological and representational as these distinctions of mereological and representing are effective the operation of M.
5. All distinctions are M; M is the variable of Mobius strip, simultaneous opposites.
6. M follows the logic of points 3 and for as M results through -M by the contrast for M to be distinct as M as M can only be distinct by what it is not; the absence of contrast is the absence of distinction
7. M and -M are contained within and part of another M; M is self-embedding as a fixed point that occurs across scale thus resulting in a recursive fixed point operation.
8. Standard epistemological terms would result in M being a paradox, a contradiction, both a paradox and contradiction as a higher order paradox, and neither paradox or contradiction as a higher order contradiction;
A. M as paradox is the unity of opposites by contained relation
B. M as contradiction is the multiplicity of opposites by contrasting opposition.
C. Both paradox and contradiction are a higher order paradox by degree of point A.
D. Neither paradox nor contradiction are a higher order contradiction by degree of point B.
9. Point 8 contains points A and B as M, points C and D as M, thus point 8 is M as opposite Ms.
10. M is the act of distinction, wherever distinction emerges or dissolves M logic is the foundational operation; by degree it is recursive as the repetition of any distinction allows for a contained presence while the inverse contrast allows said distinct by the very same recursion.
This can be observed with a single point: ●
The recursion of the point as: ●● results in:
A. The containment of ● by ●●.
B. The self contrast of ● by ●●.
C. ●● is the recursive structure.
D. ● is the recursive process.
E. M is distinction as structural process.
F. Standard symbolic languages which results in a process/pattern, form/function, operator/operand dichotomy as effectively contained as M. A symbolic language that removes this dichotomy would be left with a higher dichotomy of M that as a structural process is recursive function finite as emergent form: M, MM, (MM)M
11. The refutation of M logic require M logic thus proving M logic; any logic outside of M logic is but a sub-logic thus resulting in M being transcendental containment.
12. Formalism:
M is a transcendental operator variable. A transcendental operator variable can be defined as such. It is distinction in simple terms. In synonymous terms:
Transcendental is change as limit emergence and dissolution,
Operator is the structure of the change,
Variable is the foundational nature than can vary in appearance in accords to context.
Transcendental operator variable can be defined as the emergence and dissolution of structural change, embedded within itself, that changes appearance in accords to self-scaling.
The syntax and function of the formalism is recursion as distinction.
M
MM
M(+,-)
M(+)M(+) (x)
M(x)M(x) (^)
M(-)M(-) (÷)
M(÷)M(÷) (rts)
M(++) (-)
M(+++) (+)
.....
M(--) (+)
M(---) (-)
....
MM
M (->,<->)
M -> M (M<->M)
M <-> M (M -> M)
MM
M(+,-) M(->,<->)
M(+,-)(->,<->)
M(x●,y●)
***x●, y●: opposite distinction sets
MM
M(x●,y●)
M(x●x●) (y●)
M(y●y●) (x●)
**** In this context
x● = quantity as a distinction
y● = quality as a distinction
MM
M (●,●●)
**** ● = distinct fixed point/geometric point
**** ●● = distinct scale/geometric point scale
M(● ●) (●●)
M(●● ●●) (●)
M
MM
(M)M
((M)M) (M, MM)
(MM)M
(M)MM
M(M)M
(M)M(M)
(MMM)
M
6. Contextual Equivocation; Identity as Relative Tautologies
1. There is identity.
2. Identity as equivocable, A=A, is tautological.
3. Identity as relational, A <-> B, is conditional.
4. Equivocable identity is relational by degree of equivocation contrasting to non-equivocation. (A=A)<->(A=/=-A)
5. Relational Identity is equivocable by degree of relation containing the Identity as itself. (A<->B)=(A<->B)
6. Fundamentally Identity is reducible to operation as
(A=A)<->(A=/=-A) reduces to
(=)<->(=/=)
And
(A<->B)=(A<->B) reduces to (<->)=(<->)
7. As emergent by nature of operation identity, as equivocable, identity contains itself:
A= (A1=A1)
A=A
((A1=A1)=(A1=A1))
A1 = (A1.1 = A1.1)
A1=A1
((A1.1=A1.1)=(A1.1=A1.1))
A1.1 = (A = (A=A))
8. As emergent by nature of operational identity, as relational, identity contains other identity
(A<->B)<->C
A<->B
(C<->D)
D<->(A<->B)
(A<->B)<->(C<->D)
A<->(B,C,D), B<->(A,C,D), C<->(A,B,D),
D<->(A,B,C)
9. The equivocation of relationships is the contrast the the relationship
(A<->B)=(A<->B)
(A<->B) =/= (-A<->-B)
Thus the relationship requires contrasting equivocations
((A<->B)=(A<->B))=/=(-A<->-B)=(-A<->-B)
and the operation of equivocation is not equal to itself
((A<->B)=(A<->B))=/=(-A<->-B)=(-A<->-B)
((<->)=(<->))=/=((<->)=(<->))
(=)x =/= (=)y
10. The relations of the equivocations are the containment of the equivocations:
A<->B
(A=A)<->(B=B)
Thus the equivalence requires contained relationships:
(A<->B)=(A<->B)
((A=A)<->(B=B))=((A=A)<->(B=B))
And the operation of relation is equivalent to itself:
((A=A)<->(B=B))=((A=A)<->(B=B))
((=)<->(=))=((=)<->(=))
(<->)x = (<->)x
11. Identity is process, this process is relative equivocation where equivocation occurs by contexts emergent from relations where said context allows equivocable identity to be emergent while dually allowing contrast of what equates by degree of the relational dynamic necessitating a difference of what equates.
12. Identity is relational tautolologies, the regress of tautological relationships is nullified as the tautological process of equivalence being a fixed point, the circularity of tautological relationships is nullified as the relational process of contrast results in emergent tautologie.
13. The Nature of identity as process results in relation, <->, as the foundational primitive however the equivocation that inversely emerges from relationship is but an inverse side of the same relationship applied to itself for the relation of relations is the equivocation of relations through relation thus only context as variable remains:
((<->)<->(<->)) = ((<->)<->(<->))
(<->)=(<->)
((<->)=(<->))
((<->)=(<->)) <-> ((<->)=(<->))
(=)<->(=)
(=,<->)
( )
2. Context is the foundational nature of relational and equivocable identity as the identity itself results in an empty context.
3. The empty context is indistinct on its own terms and distinct, as an identity, upon relation or equivocation to further contexts
( )a = ( )a
( )a <-> ( )b
However given the nature of equivocation and relation are inverse sides of context itself what remains is context nesting as identity:
( )
( )( )
(( )( ))
( )
This nesting of context is not only the scale invariance of the context but also the recursion and emergence of scale invariances to new scale invariances:
( )
( )( )
(( )( ))
( ) = (( )( ))
(( )( )) =
((( )( ))(( )( )))=
( )( )( )( )( )( )( )=
( )( )( )( )( )( )( )( )( )( )( )( )( )( )=
(( )( )( )( )( )( )( )( )( )( )( )( )( )( ))=
( )= ( )( )( )( )( )( )( )( )( )( )( )( )( )( )
(( )( ))=( )( )( )( )( )( )( )( )( )( )( )( )( )( )
( )=( )
(( )( ))=(( )( ))
( )n = ( )n
(n = n)=(( )=( ))
n = ( )
(( ) = ( )) = (( ) = ( ))
((=)=(=))
(=)
( )
( )<->( )
(( )( ))<->(( )( ))
( )a <-> ( )b
(a<->b)=(( )<->( ))
a,b <-> ( )
(( ) <-> ( )) <-> (a<->b)
((<->)=(<->))
(<->)
( )
( ), ( )( ), ( )( )( ) <-> (( )( ))
( ) <-> ( )( )
( )( ) <-> ( ), ( )( )( )
( )( )( ) <-> ( ), ( )( )
( ) <-> ( )
( )
( )=(=,<->)
( )<->(=,<->)
(=,<->)
( )
( )
( )( ) = {( ),( )}
( )( )( )= {( ),( ),( ), (( )( ),( ))}
( )
(( )( ))
(( )( ))( ), (( )( ))(( )( ))
(( )( ))( )
(( )( ))( )( ), (( )( ))(( )( ))(( )( ))
(( )( ))(( )( ))
(( )( ))(( )( ))( ),
(( )( ))(( )( ))(( )( ))(( )( ))
( )
4. The emergence of context is the emergence of derivation as contextualization is derivation thus the derivation of a context, from a context necessitates the emergence of a new context and the dissolution of another
( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) ->
(( )( )( ))
->
(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))
->
( )( )( )( )( )
->
(( )( )( )( )( ))
->
(( )( )( )( )( )) =
((( )( )( ))(( )( )( ))(( )( )( ))(( )( )( ))(( )( )( )))
=
( )
The derivation of context is the contextualization of one context, or contexts, through another context(s) by which context effectively is a self-embedding boundary, transformation is but a shift in observable limits where the change of limits is the maintenance of limits. Context is limit. Limit is distinction.
For a single context to occur results in its indistinction:
( )
For the context to be distinct it must self contrast:
( )( )
and by said self contrast there is a containment of context as a context:
(( )( ))
What remains is context with the indistinct context reverted back to indistinct:
( )
However this indistinct context contains infinite contexts, potentially, while the infinite contexts are a single distinct context
( )<->( )x
or a set of finite simultaneous contexts:
( ) <-> (( )l,( )m,( )n)
Regardless of what is potentially there the nature of the context transforming to another context is relative to the context applied to it:
( )( )n -> ( )y
( )( )m -> ( )z
Thus the derived context is the relation of the prior.
An infinite indistinct context is distinct by recursion:
( )x
( )x( )x
This recursion collapses the infinite context into a finite context of infinite contexts as the infinities maintain being infinite but effectively are finite by relation:
(( )x( )x)y
Thus each context is effectively a scale of infinite contexts:
(( )x( )x)y
(( )x( )x( )x)z
And in these respects a context is a scaling of the context by which it is derived. However each scale is a scale of infinite contexts thus derivation is a continuous process and the application of context is the application of transformation thus equating the context to a process by degree of the continuity it contains.
This continuity is the continuum of contexts made finite by degree of the limits of the infinities being distinct.
What remains is a scale invariant tautology.
As scale increases so do fixed points:
( )( )
(( )( ))(( )( ))....
( )( )( )
(( )( )( ))(( )( )( ))....
Which the fixed point across scales the fixed point context becomes the distinction that allows ratios within the scale, as a sequence, to occur. In these respects contextualization is derivation and the proof of a thing is the unfolding process that reveals as the thing. Context is thus form as process where traditional expression of form as operand, and process, as operator, are collapsed within the limits of the emergence itself.
However the single context contrasts itself across scale thus with dimensional scaling, a dimension being a sequence, the single context self contrasts as both the emergence of scale and the emergence of scales to scales.
What remains is a context embedding itself across scale as a new scale thus resulting in identity being embedding tautologies at multiple levels As the tautologies manifest infinitely so do the fixed points thus resulting in a perpetual state of continuous finiteness.
What remains is a single context that reveals only as recursive embedding within recursive embedding which allows the context to be distinct. In these respect the single context is the limit of contexts as the derivation of them. Derivation, at the meta-level, is recursion as sequence, sequence as pattern, thus what constitutes the existence of a phenomen is the contextualization of it as the limits of it.
What remains is embedded tautologies, as a new tautologies, thus resulting in embedding of tautologies itself being a tautologie and only pattern as context remains.
Empty context, ( ), is the grounds of distinct contexts by degree of recursion where context in and of itself is a tautology and loop as recursion. The emptiness of context is the point of change of one context into another as the empty context is but the potentiality of contexts made distinct by the recursion of said potentiality as the distinction of said potentiality contained within it.
In these respects and empty context results in further contexts which eventually saturate to a single context again with this process itself being the simple recursion of contexts, ( )( ), as a context ( ) thus the context contains itself (( )( )).
Context is thus the process of derivation and derivation it a tautological process of derivation derives further derivation thus resulting in a fixed point being equivalent to a process of change by which scale emerges.
The question of why distinction from indistinction, something from nothing, presence from absence, being from void is answered in the question itself:
Indistinction is distinct as indistinction,
Nothing is something as nothing,
Absence is the presence of absence,
Void 'is' void.
The answer is the tautology of the distinctions themselves as distinct thus the identification of a negation is the presence of identification and "what is not" is but the assertion of "what is" by degree of the claim "what is not" occuring.
Identification of nothing is the identification of identification emerging from nothing as nothing is but the identification of nothing thus the emergence of identification as identification leaving only tautologies.
Given the emergent nature of tautology as a whole, and the corresponding nature of identity as tautological in form and function, what is considered self-evident or axiomatic is but the emergence of an identity, that is not reduced any further, as a foundation to derive a recursive chain of assertions where the base axiom is represented across scale and different degrees as the argument or formulation itself.
What is considered axiomatic identity is but an emergence of one context from many that in turn is used as a pivotal point for further contexts/identities to transform through said axiom. In these respects basic linear reasoning is holographic expressions of axioms through their surrounding contexts as the axiom maintains itself across the assertions themselves.
In these respects and axiom is the derivation of contexts as a recursive fixed point across contexts. By degree of the recursion of a fixed point, as a new scale, resulting in a further fixed point, there are effectively infinite axioms by which to derive conclusions and the axioms of any system are merely the system as a projection of specific context by degree of the system being a holographic expression of the axiom itself.
This can be expressed under the following where "( )" is an axiom and ● is operation as point of change.
( )x
( )x ● ( )y
(( )x ●( )y)( )x.1
( )x ● ( )z
(( )x ● ( )z)( )x.2
( )x ● ( )x.n
(( )x ● ( )x.n)( )x●x
( )x●x
( )x ● ( )x
( )●( )
(( )●( ))
(●)
(●)(●)
((●)(●))
((●)(●))●
(●●)●
(●●)●●
(●●)(●●)●
.....
( ) = ●
( ) <-> ●
(<->,=,●)
( )
●●
●
****Relative to identity being reducible to process the standard nature of formalisms do not apply as the operations are equivalent to variable identities, in this respect the argued formalism is transendentally formal (transcendental by degree of containing and occuring beyond standard formal rules).
7. Distinctions as Self-Contained Self-Contrast; Meta-Formalism
"A" identity, distinction
"=" is or equals
"( )" context, container, set
"○" Scale invariant self referencing context
"<->" biconditional
"-" absence, negation
"+" presence, emergence
1. A
2. A=A
3. ((A=A) <-> (-A=-A)) <->
((A=/=-A) <-> (A = - -A))
4. (A <-> -A) <-> ((A=A) <-> (-A=-A))
5. (A <-> -A) = B
6. B = B
7. (B = B) <-> (-B=-B) <->
((B =/= -B) <-> (B = - -B))
8. (B <-> -B) <-> ((B=B) <-> (-B=-B))
9. (B <-> -B) = C
10. ....D....
11. (A <-> A) = (B <-> -B) = (C <-> -C) =...
12. ● <-> - ●
13 (● <-> - ●) <-> ((● =/= - ●) <-> (● = - -●))
14. ● = (+,-)
15. (+, -)
16. ( )
17. ( ) = ( )
18. (( ) <-> -( )) <->
((( ) =/=( )) <-> (( )=--( )))
19. (( ) <-> -( )) <-> (( ))
20. (( )) = (( ))
21. ...(..(( ))..)...
22. ○
23. A = ( )
A = ○
● = ( )
● = ○
( ) = ○
24. (A <-> ● <-> ( ) <-> ○) = X
X1 = A
X2 = ●
X3 = ( )
X4 = ○
25. (X = (X1, X2, X3, X4)) <->
(((X = X1) <-> Y1),
((X = X2) <-> Y2),
((X = X3) <-> Y3),
((X = X4) <-> Y4))
Y(1,2,3,4) = ( )
****
X <-> Y
27. (A) <-> (●) <-> (( )) <-> (○)
28. ...(..(( ))..)...
29. (( )<->( )) = ((( )=( )),(-( )=-( )))
30. (<->)=(+=+, -=-) <-> (( )<->( ))
31. ((+=+) <-> (-=-)) = ((--=--)<->(++=++))
32. ((=) <-> (=)) = ((=) <-> (=))
33. (<->,=)
34. (<->)<->(<->),
(=)<->(=)
(<->)=(<->)
(=)=(=)
35. ( )=( ), ( )<->( )
36. ( )
8. The Nature of Polarity by Contradiction
1. Pure convergence results in all distinctions unified as indistinct nothingness as there is not distinction to converge.
2. Pure divergence results in all distinctions seperated as indistinct nothingness, as there is no distinction to diverge.
3. Pure convergence and divergence are effectively nothingness; the pure convergence of both processes is effectively nothingness, the pure divergence of both processes is effectively nothingness.
4. What remains is the process of the distinction of "nothingness" thus convergence and divergence is the recursive distinction of "nothingness".
5. The distinction of nothingness is not nothingness but the distinction of nothingness thus there is no nothingness but the distinction of it.
6. Pure convergence is contracting "nothingness", pure divergence is expanding "nothingness".
7. Thus convergence is the distinction of contraction, this contraction is the repetition of multiple distinctions unto a unity.
8. Thus divergence is the distinction of expansion, this expansion is the repetition of a unified distinction unto a multiplicity.
9. Pure unity has no contrast thus is nothing; pure multiplicity is only contrast thus is nothing.
10. Distinct Unity is unity because of contrast to distinct multiplicity, distinct multiplicity is multiplicity as the unity of distinct multiplicity.
11. What remains is distinction, this distinction is the polarity of absolute convergence and absolute divergence, this polarity is the distinction of "nothingness" as a recursive distinction.
12. Only distinction remains, what is indistinct is but a distinction of the distinct.