The Philosophy Discussion Forum

The One Ring; The Nature of Distinction and Indistinction; the Nature of Nature



++++A. Justification as Occurence





The only reality is the act of occurence, for by reality occuring is it known for what occurs is knowing the limits of the known by which the act of knowing occurs as its own justification.







Thought, word, action, emotion are but the occurence of limits by which things are in accords to observation.







The emergence and dissolution of the mind, body and spirit, and the distinctions that emerge and dissolve within, between and beyond these dimensions is the only reality as observation by said forms.







Reality is of reality as is and is not by which it is self-embedding and self-nesting for there is only occurence, emergence and dissolution are the limits of a thing and yet emergence is a thing by which it inverts into its opposite of dissolution and in accords dissolution into emergence is this inversion.







The emergence of emergence is dissolution, the dissolution of dissolution is emergence; what is beyond what is results in what is not and what is not of what is not is what is.







What is within manifests what is without, what is without manifests what is within.







What is between manifests what is containing and what is containing manifests what is between.







The limit of a thing is but the two sides as change for one dimension reflects as two and two dimensions reflect as one.







Contradiction allows seperation, paradox allows a unity and yet the contradiction of contradiction is paradox and the paradox of paradox is contradiction.







The distinction of a thing is its process, the process of a thing is its form as directed change by which dimension is the form by which motion occurs.







For there to be change a limit must dissolve as the emergence of another thus the new limit is but a variation of the prior by means of contradiction and yet both are required as the paradox.







Stability is but a rate of change that is slower than another, a fixed point of observation is always a fixed point of observation until the observer changes.







To observe is to manifest change for the point of awareness is the inversion of subject and object into the eachother and what is observed becomes subject to the awareness itself.







Awareness is void, the awareness of awareness reveals nothing but the distinction of awareness thus resulting in the distinction of void as evident in accords to the measure of its nature.







To make distinct is to invert one thing by the opposition of another; it is to recur one thing by the cycling of it; to make distinct is but to observe the simultaneous seperation and connection of a thing.







By repetition of 1 there is 2, by the repetition of 1 there is the inversion of 1 into 2, by the repetition and inversion of 1 there is 1 as 2.







To establish limit is but the emergence of awareness as itself for the point of attention is its own potential of distinction for by the distinction of the potential there is the actual as the distinction itself.







Cyclical void is but the emergence of form by the distinction of potential by what is actual; infinite cycles within, without and between cycles is but void.







By attention there is the emergence of a thing from its depth and the dissolution of another back into its depths.







Reason and madness are but one and the same for reason is the distinction of madness as madness and madness is the distinction of reason as reason; occurence remains in accord to the measure of being.







Void is the Eye of Divinity, the omnipresence and omnipotence of God is the Void as the Prime Attention.







Reality is the emergence and dissolution of patterns by degree of asserted distinctions. Assertion begin and ends with what emerges and dissolves through attention, patterns by which the potential of the void is directed. The act of assertion is the occurence of distinction from the act of attention, attention being the void, by which the void is given form and directed as the distinction itself in accords to the patterns by which attention is contained. All perception is a toroid of form, the fundamental containment of attention, at the proto-ontological level is the torus evidence by the containment of attention by the patterns of bias with said patterns of bias being the recursion of presences and absences of distinctions in accords to the observers state.







Attention is contained by bias, bias is geometrically equivalent to a torus as the cycling of attachments and aversions cycle both as a whole and between eachother. The interaction of attachment and aversion is the same as a meta-synthetic cycle in one respect while corresponding equivocally to unification, attachment, and seperation, aversion, that in turn takes a mathematical or topological nature equivocably. The meta-ontological pattern of awareness is the torus containing a 0d point.















What is and is not is but the limit of the thing by which change occurs and of this change what occurs is by means of the space to do so as its potential; this space is void.







Pure potentiality is void distinct as void, pure actuality is the generation of void as form.







Morality is but the containment and direction of potential unto form, it is the emptiness of the observer by which act emerges and dissolves; cause and effect are but as “you reap as you sow”.







Truth and falsity are but the judgment of what occurs relative to other occurences where said occurence are found as resonant to the observer; only distinction remains.







The cycling of absence is presence and absence, the cycling of presence is absence and presence, the cycling of x is (x,y), the cycling of y is (x,y).







The distinction of absence results in presence, the distinction of presence results in absence, the distinction of x results in y, the distinction of y results in x;







the distinction of distinction results in indistinction as distinct from distinction thus only distinction remains.







One point is indistinct until there is two, one absence is indistinct until there is another, one potentiality is indistinct until there is another, one void is indistinct until there is two; yet distinction is always distinct regardless of if there is one or two thus the perpetual generation of being is rooted in complete nothingness.







By contradiction, (A=/=-A), there is distinction by contrast, (A,-A), where this contrast is a relationship as a new distinction, B=(A=/=-A), which necessitates a wholism as paradox itself.







The contrast of distinctions is the space of potentiality of there relationship, the unity of distinctions is the actualization of this potential relationship as a paradox.







Contradiction allows for potentiality of relationship distinction and actuality of individual distinction; paradox allows for potentiality of individual distinction and the actual of relational distinction;







Potentiality and actuality remain as distinct and the relationship as distinction itself.







Recursion is identity as cycle as A=A is a recursive statement. If the law of identity is not subject to the law of identity then the law of identity has no identity and is not a law.







Inversion is identity as contrast as A=/=-A is an inverse statement. If the law of non-contradiction is not subject to the law of identity then the law of non-contradiction has no identity thus is not a law.







In these respects given identity requires inversion and recursion two laws of identity effectively are subject to themselves as variables within themselves.







Because the LI and LNC must be subject to LI so to have identity, and LI is recursive, then the LI and LNC are subject to meta-logic.







(A=A)=B







(B=B)=(A=A)







(A=/=-A)=C







(C=/=-C)=(A=/=-A)







B=-C







(B=/=C)=D







D=(C=(A=/=-A))







((D=D)=B)=D







((A=A)=(A=/=-A)) = ((B=C)=D)







((A->B->C->D) → -A) = (A,-A,B,C,D)







(A,-A,B,C,D) = X







(X=X)=X







X







In these respects LI and LNC are dissolved and identity becomes “X” only where “X” is purely the occurence of itself as itself.







However as the foundational occurence, as all occurence, X inversely must gain identity otherwise be indistinct. As the only variable it becomes its own condition, through recursion, and its own contrast through the distinction of it by recursion:







X







(X=X)







(X=X)=X1







(X=X=X)=X2







(X1=X1)=X1.1







(X1=X1=X1)=X1.2







(X2=X2)=X2.1







(X2=X2=X2)=X2.2







…







X=((X->X)=(X/(X∧X)),(X∧X/X))







X=((=)=(->))







…







(->)







((->)->)







(((->)->)->)







(((->)->)->) = (->)







Xx







Formalization is subject to identity; therefore standard formalisms are contained within identity assertions. The same occurs for operators thus resulting in proof as pattern that necessitates meta-formalism as necessary given the incompleteness of standard formalisms. The rule is the pattern, the pattern is form as function in accords to the self-contained context of the meta-formalism. A linear approach is self-defeating by degree of incompleteness, leading to assumption, while dualistically is self-negating as a conclusion is a holographic expression of the premise (akin to a line beginning and ending with a 0d point visually) thus necessitating circularity while simultaneously observed that a non-linear approach allows for completeness of proof as pattern, with pattern being symmetry through repetition.







Social validation as proof is subject to this same nature of proof as pattern as social validation is a symmetry between viewpoints thus the ontological nature of proof transcends common consensus while allowing it to emerge and dissolve.







The nature of self-evidence is subject to the same nature of recursion as pattern given self-evidence is the resonance, by repetition or cycling, of patterns between observed and observer while dually occuring as a self-referencing loop by degree of emergent repetition within the observer where "X is because X" is self-reference. Self-evidence is recursion as axiomatic.











A critique of circular foundationalism is self-negated as circular foundationalism is negligible by consensus because:







1. Circularity is a negative because circularity is a negative.







2. Circularity is a negative because of cyclical consensus.







3. Linearism is productive because linearism is productive.







Circularity allows for pattern, if patterns expand or contract than pattern is fluid.







Operators are subject to identity laws thus identity laws exist within identity laws:







X=(=)







(=)=(=)







X->(->)







(->)->(->)







In these respects identity is further simplified as Xx, (=)=, (->)->.







What remains is pure pattern as repetition. Any identity for an operator or syntax is subject to recursion thus necessitating standard formalism as subject to recursion.







Any categorization of the text or formalism is subject to the same identity laws that the text argues thus is transcendental to categorization by degree of its process. Any disagreement of the text or process is contained by the process by degree of the process being inversive recursion thus any nullification is subject to the same distinctions it argues against thus the nullification of the text or formalism is nullified. What remains is occurence as self-contained self-contrast. External contrast of the system is the limit of the text and formalism thus exists by degree of it as what allows internal coherency. Identity is of this nature.







A self sealing system is necessitate as hyper-logical by degree of the assertion of A=A being a self-sealing law that gives foundation to standard formal systems that argue against self-sealing. A self-sealing system is the only means of being complete and rational by degree of repetition as recursion as pattern, emergence and dissolution as occurence is a pattern.







Scientific proof or disproof of occurence is subject to being an occurence and is subjecg to the same recursion of hypothesis across the empirical dimension as a means of deriving coherent symmetry between the abstract and empirical. What remains, regardless of coherence is distinction as occurence.







Identity is form as function, by degree of self nesting of distinction, this is occurence. Identity is that as self-contained: Xx. In these respects there is universal equivocating as X while simultaneous relative non-equality by the self ratiotizing of X where context determines coherence and incoherence, as the ratio of one distinction to another, while each assertion being coherent according to context as absolute within the context.







Holographic identity results in absolutism in context and relativism as context, in accords to degree of holographic identities relative to eachother and the source.







*** The justification of a thing is its occurence, the justification of an event is the event itself thus justification requires no rational means beyond the awareness of what is and is not by which what is and is not is the everpresent ratio in accords to a reality that by default is always ration by said nature is and is not is the everpresent ratio in accords to a reality that by default is always ration by said nature.



++++B. Emergent equivalence operator identity by degree of self-embedding recursion.



Equality and inequality are purely contextual identities by degree of having identities that effectively are relation. Where standard operators of equality and inequality are subject to a fixed status within standard formalisms the following formalistic proof will observe such fixed statuses as fundamentally relative identities by nature where what is constant is context itself.



Context is subject to a dualism of presence and absence, or rather negation of negation and negation thus effectively is a binary state, or dualism, that effectively self-references to form higher level binary/dualistic distinctions



The following distinctions can be taken both syntactically and semantically. They are not axioms in the traditional sense, they are not assumed, but rather emergent patterns by degree of recursion thus effectively are complete by self-embedding:



"=" equality

"=/=" inequality

"( )" context/set/container

"{ }" context/set/container different by degree

"-" negation, absence, negative

"--" negation of negation, presense, positive



(A = A)

(A = (=))

(=) = (=)

(=) =/= (=/=)

(=/=) = (=/=)

((=) = (=)) =/= ((=/=) = (=/=))

((=){=}(=)) =/= ((=/=){=}(=/=))

{=} =/= {=}

(=/=){=}(=/=)

(=/=) =/= (=/=)

(=) = {(=),(=/=)}

(=/=) = {(=),(=/=)}

( ) = {( ),( )}

( )

( )( )

{( )( )}( )

{( )( )}( )( )

{( )( )}{( )( )}

....



{ }

{ }{ }

({ }{ }){ }

....



=

== (=, -=(=/=))

(==)= (-=(=/=),--=(=))

....



=/=

=/==/= (=/=,-=/=(=))

(=/==/=)=/= (-=/=(=),--=/=(=))

.....





-

-- (-, --)

(--)- (--, ---)

(--)-- (---, ----)

....



****



The nature of the operators: =, =/=, -, -- effectively reduce to binary contexts that are effectively self-embedding in the degree that recursion results in an identity of pattern, a meaningful tautology akin to the identity law of A=A, which dually inverts into an isomorphic expression that contains the sequence as a new variable. Identity is thus context dualism by degree of repetition which results in a contrast:



( ), { } are both single contexts that each differ by degree with said degree being the dimension of recursion.



In one respect:



{( )( )} observes ( ) as a sequence contained as a differing dimensional context as { }



In an inverse respect:



({ }{ }) observes { } as a sequence contained as a differing dimensional context as ( ).



Regardless of the dimensionality of both ( ) and { } the degree of one relative to another is relatively higher or lower relative to scale; in one respect { } represents a higher dimensional context while in another ( ) is a higher dimensional context. The nature of a higher dimension is one of general inclusivity:



{( )( )} observes { } as higher dimensional.

({ }{ }) observes ( ) as higher dimensional.



In these respects a higher dimension can be view as a context of containment.



All variables can be reduced to contexts;



A=A -> 1=1, 2=2, 3=3... Cat=Cat, Dog=Dog, ....



and all operators can be reduced to variables as what they operate one defines the operator themselves by degree of relationality:



(A=A, B=B, C=C, .... X=X...) ->

(=) <-> (A,B,C,...X)



In these respects all operators are effectively contexts that effectively are contained by there degree of:



Recursion:



(A=A, B=B, C=C, .... X=X...) <->

(=, =, =, ....=....)



and Inversion:

(=) <-> (A,B,C,...X)





In these respect both operator, F, and operand, f, are biconditional when both operator and operand are seen as variables: F <-> f



This biconditionality is an operator as well and in these respects is a self contained variable in one respect:



(B <-> B) = ((<->)<->(<->))



while dually observing that its recursive latice results in its negation by inversion into its opposite. Where biconditionality, <->, inverts into is opposite then occurs "therefore, transitions to, becoming, etc.", ->. Any form of recursion inherently contains sequences of double which results in a self contained identity, akin to A=A, while dually a self contrast occurs by its opposite, -A:



<->

<-><-> (<->,- <->(->))

(<-><->)<-> (- <->(->), -- <->(<->))

....



->

->-> (->, - ->(<->))

(->->)-> (- ->(<->), -- ->(->)

....



and in these respect recursion results in gradient dualisms.



This dualism of biconditionality and transitioning results in the further degree of operator emergence under ∨∧;



∧ observes "both/and" that is a reflection of biconditionality and transitioning in the respect that ∧ reflects <-> as connection of context and -> as dependent contrast. Mathematically ∧ is addition and multiplication as compounding.



∨ observes "either/or" that is a reflection of biconditionality and transitioning in the respect that ∨ reflects <-> as distinct identities and -> as identity divergence. Mathematically ∨ is subtraction and division as reduction.



++++C. Contextual Emergence Formalism / Proof as Emergent Transition





"( )" presence context

"{ }" absence context

"[ ]" context of contexts

"->" transitional context



****Context is both defined as an synonymous to set, container, conditions





Formal operation is recursion, recursion it self-referential repetition of primitives, primitives in this case being the formal symbols. Formal symbols are provided as the four mentioned: ( ), { }, [ ], ->. The function of recursion is the emergent sequence itself.



The recursive sequence of presence contexts result in absence contexts. The recursive sequence is a context subject to said recursion.



Proof is pattern emergence as proof is the emergence of contextualization by which a pattern occurs. Strings are formed by degree of recursion expressed as a contained context itself.



The recursion and inversion of context is the embedded operation distinct as the emergent form itself.



Nesting is restricted as the context that contains it.





R: ( )



***There is a present context. "R:" is the sequence of recursion, the limit upon which a string is expressed, "R:" is the distinction of the recursive string itself as both operator and operand, thus standard formalistic measures do not apply as a "operator/operand" dichotomy is resolves as but a single "form/function".



All well formed operator/operand sequence is any sequence emergent from "R:". Thus for all "R:" there is a well formed sequence by degree of self-embedded context that is post-linear in hierarchy.



R: ( )( ) -> [( ),( )->{ }]



***The present context is distinct by recursion from which the context provides its own distinction as ( ), while said recursion results in an inverse absence context as context between contexts that is contextualized by the transitioning of ( ). These contexts are contained as the context [ ]. -> is the transition of the context, or string as a whole, to another context or string.







R: [( )( )]( ) -> [( )->{ }, { }->( )]



****The recursive contexts are contained as a new context, [ ], while recursion continues so that both the context and inverse context become transitional contexts to further presence contexts and inverse absence contexts; these emergent contexts are contained within context [ ]







R: [( )( )]( )( ) -> [( )->{ }->( ), { }->( )->{ }]



*** Same as prior step with additional contexts by degree of ( ) repeating in degree.



R: [( )( )][( )( )]( )-> .....



.......



Inversely:



R: { }

R: { }{ } -> [{ },( )]

R: [{ }{ }]{ } -> [{ } -> ( ), ( ) -> { }]



At a higher level starting from sequence 3 then to 5 then to 7:



3. R: [ ] -> ( ),{ }

5. R: [ ][ ] -> ( ) -> { }, { } ->( )

7. R: [[ ][ ]][ ] -> ( ) ->{ } ->( ), { } ->( ) -> { }

....



Thus context contains itself by its transition to further contexts.





Thus the following sequence occurs:



R: [( )]

R: [[( )][( )]]

R: [[[[( )][( )]]][( )]]

....



R: [{ }]

R: [[{ }][{ }]]

R: [[[[{ }][{ }]]][{ }]]

....



Where [ ] is the derivative self-embedding of contextual containment around an empty context, or inverse context. In these respects [ ] is the simultaneous empty and inverse context.



In these respects [ ] becomes a scaffolding context and the formalism is reduced to 3 primitives: ( ),{ }, ->



Example:



R: ( )

R: ( )( ) -> {( ),{ }}

R: {( )( )}( ) -> {( ) -> { }, { } -> ( )}



***and the inverse of this formalism appears as isomorphically opposite.









Now the formalism breaks down to:



R: {( )}

R: {{( )}{( )}}

R: {{{{( )}{( )}}}{( )}}

....



and the inverse; this leaves each present context and absence context as purely transitional, where ( ) and { } are resorted to as scaffolding, thus resulting in:



R: ->

R: ->->

R: ->-> ->

R: ->-> ->->

R: ->-> ->-> ->



Where context becomes a simple transitional state that is self-embedding. All mechanical derivation are based upon doubling/halving sequences where each sequence occurs as a set of -> or ->-> which alternates based upon prior set relative to current expression in sequence.











****Given all formal and semantic symbols are contextually derivative, and exist as contexts themselves, the presented formalism is trans-formal and trans-semantic; trans-formal/trans-semantic is defined as the foundational distinction for formalities and semantic expression that exist across all layer regardless of hierarchy and as such as post-linear by design.



A variable is a context by nature as a variable is a set or container of other variables. The variable A may equal 1 or 2 and 1 or 2 may equal car or horse, and car or horse may equal a specific variation of said things. In these respects the contextual formalism results in the expression of variables as variables:



A = ( )

***This is the distinct variable



-A= { }

***This is the absence of said variable



T = ->

***This is the change of that variable



E = [ ]

***This is the variable of the whole environment.



R: A

R: AA T E,A,-AE

R: EAAE A T EAT-A,-ATAE





Mathematically this can be seen as:



1 = Context

-1 = Absence of context

0 = Transition of context

i = context as whole



R: 1

R: 11 0 i1,-1i

R: i11i1 0 i10-1,-101i





Now for both variables and numbers the R: operator operand is definitely numerical, dualistically by degree of the sequence it produces and the transitional sequence which emerges:



Rx|y:



***x is equivalent to a set of 2 as 1, a set of 1 as 1 is .5. So 2 sets of 2 is 2, 2 sets of 2 and 1 set of 1 is 2.5, etc.



***y is equivalent to number of contexts that result, all contexts are one with the exception of E which effectively is a single containing context.



R.5|0: A

R1|3: AA T EA,-AE

R1.5|7: EAAEA T EAT-A,-ATAE

R2|11: EAAEAA T EAT-ATA, -ATAT-AE





For example, if the expression R3|19: occurs the following solution would be:



EAAE EAAE AA T

EAT-ATAT-ATA, -ATAT-ATAT-AE



The computation determinacy is binary, the first primary degree is "Rx|y:" which determines the string. The second inverse degree is ->,T,0 which determines the transition within the string to a differing string.





The text is essentially a trans-formalistic derivation of mapping, where proof is the transitional context itself. Given transitional contexts become self-embedded in later sequences as the logic byproduct of emergent sequences, the text effectively argues that the occurence of symbols and semantics is always a meta-proof justified by occurence alone as what remains, at the proto-logical level, is purely transitional states where what is observed as context is the distinction of transition itself.



++++C. The Limits of Analysis



1. There is what occurs; there is occurence; "there is": occurence



2. The analysis of what occurs is dependent upon the occurence.



3. The analysis occurs of what occurs.



4. Both the analysis and the occurrence form a relationship that occurs.



5. There is nested occurence, the analysis proceeds as that which derives further occurrences from what occurs.



6. The analysis (F:) derives occurrence in accords to context applied, thus derivation of one occurrence to another (Z1 -> Z2) is within the context applied by the analysis (A), F: A(Z1 -> Z2).



7. The change of context results in differences of derivation F: B(Z1 -> Z1.1).



8. The derived occurrences in turn are subject to further analysis.



9. To apply context, through analysis, is to determined what is and is not derived; context shapes the derived outcome.



10. Analysis is the reduction of one emergence into another by means of context, this reduction is derived by the limits of the context itself.



11. Analyzed occurrences are but the expression of context, reduction is but the limits of the context itself where what occurs has occurrences within the occurrence removed.



12. There is no law as to what context is or is not applied; what remains as the context, by all means, is equivalent to an emergence of definition.



13. The limits of the analysis is the limits of context, analysis is reduction in accordance to context.



14. This is an analysis of analysis, to analyze analysis is to apply context to it; the context of the analysis is the analysis itself.



15. Analysis is an occurrence, to analyze is to reduce an occurrence, to reduce analysis is to observe the fundamental occurrence of what an analysis is and is not.



16. What an analysis is is an occurrence, what it is not is another occurrence, what is it and its another is subject to occurrence.



17. The same nature of what is analyzed, occurrence, is the same nature as the analysis itself, occurence.



18. Occurrence is reduced to occurrence by means of itself thus what is is transformation; analysis is reduced to that which it reduces thus analysis is transformation.



19. Analysis is the transformation of occurrence, to reduce one occurrence to another is but to transform occurrence; analysis is process of occurence reduction by pattern context; analysis is a patterned process



20. The reduction of an occurrence to another effectively inverts what the occurrence is reduced to to a general state by which what is reduced occurs under the specific context, ie what occurs occurs if what it is reduced to occurs, what is the reduced occurrence exists if what it is reduced from occurs;



F: A(Z1 -> Z2) results in:

F: (A(Z1 <-> Z2) <-> A(Z1 <- Z2)).





21. The reduced occurrence results in what is reduced; context is a rationalized set of occurrences within it: F: A(Z1, Z2).



22. To analyze is to result in the context as a set or container of occurrences; this set is an occurrence.



23. The analysis of analysis is but a self contained set by degree of becoming self embedded: F: A(A1, A2)



24. Analysis becomes self-embedding occurrences, with each occurrence being the relative context for another analysis:



F: A(A1,A2) ->

(A1(A1.1 -> A1.2), A2 (A2.1 -> A2.2))





25. There is only the self-embedding of occurrence as the limits of analysis, self embedding is the limit thus analysis does not derive truth or falsity, as these are distinctions subject to being occurrences, but rather patterns as the set of occurrences themselves self.



26. To analysize occurence itself would requires the occurence of both context and the analysis itself thus resulting in the same self-embedding but from a different degree in accordance to the context.



27. Analysis is function in accordance to context with context deriving further context thus analysis is embedded within itself, a function within a function, in these respects the function becomes a linearly expressed sequence of fractal like functions and the simplified pattern is that of a fixed point scale invariant function:



F: A(F: A1(A1.1->A1.2)-> F: A2(A2.1->A2.2))





++++D. Distinction is a Universal Process of Self-Embedding; All Things are Reducible to Distinction as Process



1. A distinction is a distinction.



2. A distinction of a distinction as a distinction is a second order distinction



3. A distinction is distinct as a distinction; a second order distinction is distinct as a distinction.



4. A distinction moving to a second order distinction results in distinction as constant.



5. A distinction as constant across n-order distinctions requires distinction as scale invariant, the scale of distinction as n-order distinctions are distinct as the scale.



6. Distinction contains itself and is effectively complete at all levels by scale invariance of itself and incomplete by degree of difference in scale.



7. Completeness and incompleteness are distinctions as what is complete requires no external justification (a distinction is distinct as itself as a distinction is distinct from itself so to be distinct) and incompleteness requires external justification (a distinction requires a distinction beyond it to be distinct as distinction).



8. All that exists is subject to distinction as being distinct is what is required for existence, only distinction remains for what exists is relative distinctions under the distinction of relation of distinctions; "all that exist" is a distinction of relation by means of "all".



9. Distinction is distinct from itself by degree of the distinction of indistinction that allows distinction to be distinct; indistinction is distinct from distinction thus is a distinction.



10. Distinction is a process of self-embedding, all things can be reduced to distinctions by nature of requiring the nature of being distinct.



11. All is distinction by degree of "all" being distinct, "not everything" is distinct is a distinction of "not everything" which necessitates relative emergent scales within distinction itself thus resulting in conditionality being a distinction that is scale invariant while allowing difference to occur.



12. All remains is all things as distinction as process, only process remains; this is distinction.



++++E. The Nature of Distinction as a Universal and Multivalent Process



All things are subject to being distinctions for if they are not then they cease to be things.



If all things are distinctions and this universal process of distinction is distinct from itself as indistinction, so the distinction may be distinct, where indistinction is a distinction of distinction, then distinction is self embedding and exists at holographic level processes by degree it is nature.



By degree it thus effectively results in the nature of distinction being synonymous to a mobius strip type torus as both sides of distinction, distinct as distinct and indistinct as distinct from the distinct, exists as a mobius strip while simultaneously the loop is toroidal by nature as distinction is everpresent regardless of the degree of awareness with awareness itself being subject to this distinction.



Distinction is recursively transcendental to itself where distinction going beyond distinction results in distinction containing itself in one respect while being beyond itself in another respect where each respect reverts to a mobius type nature while the nature of the respect by which distinction is observed is but a distinction by which distinction becomes emergent and dissolutive it itself.



By nature distinction is paradoxical and yet thus paradox is rational as a paradox is the emergence of contrast by which things may be distinct. Paradox is necessary for distinction to occur and distinction is necessary for both what is and what is not.



Distinction thus has a fourfold nature:



Generation of distinction.



Mediation of distinction.



Containment of distinction.



Distinction as multivalently non-dual.



There can be nothing beyond distinction for what emerges and dissolves does so by being distinctions of emergence and dissolution.



In these respects distinction can be expressed in a basic non-traditional formalism where ● is both operator, as emergence, and operand, as structural form:



● distinction



●● distinction relative another distinction.



(●●)● the relation as a distinction.



● distinction as empty and yet generative of itself.



●



●●



(●●)●



●



Distinction is self-sealing as distinction contains distinction as distinction thus distinction is self-embedding, that which by nature is its own degree and context.



Distinction absorbs all further antithetical distinctions for the antithetical distinctions allow the inverse thetical and itself to be distinct by contrast.



Distinction cannot be negated without using distinction for the act of negation is a distinction.



The scaling of distinction is but the distinction of the relation of distinctions where the continuum of one distinction relative to another is but a ratio of distinctions as scale.



The distinction of distinction is but the continuum of distinction by which it negates itself by means of indistinction as the limits of distinction that allows it to occur. The negation of distinction is but contrast by which distinction emerges as its own limit as the indistinct is the limit of distinction thus distinction distinct from distinction. In these respects distinction is both presence and absence that reveals by degree of recursive generation:



Absence:



-



-- -> +



(--)- -> -



(--)-- -> +



....



2. Presence:



+



++ -> -



(++)+ -> +



(++)++ -> -



All distinctions are infinite in nature by degree of containing and being contained within infinite distinctions; a line segment is composed of and composes infinite line segments. In this respect distinction is continuous.



All distinctions are finite in nature as the limits by which the infinite distinctions are contained, finite as the foundation is present at infinite levels; a line segment may contain infinite line segments but is finite, a line segment may compose infinite line segments but the line segment exists at all scales. In this respect distinction limits.



Distinction occurs through the finite and infinite yet transcendental as finite and infinite are distinctions.



The selection of distinction is its emergence relative to other distinctions, by dissolution of others, and the relation of distinction as a new distinction. Selection is purely emergence as justification as what occurs is justified as the occurence itself for justification is the emergence of pattern and all distinctions are patterns by degree of self-embedding self contrast. To occur is to reveal, to reveal is to emerge, emergence is distinct by dissolution. Distinction is transcendental as process by means of limit change.



Distinction is self-evident by degree of self-containment as emergent pattern; distinction is not self-evident as contrast as divergent pattern; axioms and non-axioms are subject to being distinctions.



Abstract and empirical problems are the assertion of contexts where the asserted problem is the assertion of contextualization, change of context is the change and or neutralization of the problem, what does not dissolve, as the problem, when contextual shift emerges is revealed as the absence of coherence, stability or presence of patterns due to said problem as context(s). In these regards the negation of the problem is the negation of the context by degree of the emergence of how it unfolds potential further contexts thus necessitating not a problem solved but a problem transcended.



Reduction:



To reduce anyone one thing or things to another is but to result in unbounded infinite regress by which what a thing or things are reduced to is the act of reductive distinction itself as that is the only constant.



To reduce anyone thing or things to another is but to result in a finite foundational point by which what a thing or things are reduced to is a distinction that exists along the chain of analysis at all levels.



2. Convergence:



To converge a set of things into one effectively is an infinite process as the convergence of one set of things is another things that converges to further things thus an infinite process occurs.



To converge a set of things into one effectively is a finite limit as the convergence of one set of things effectively is finite as the set of things itself as the relational structure.



3. By nature distinction is both process, infinite divergence and convergence, and structure, finiteness as the divergent and convergence, and in these respects is both pattern and process. The pattern exists as a contained process, the process as the continuation of the pattern.



4. Pure deductive analysis, by means of divergence, is but contextual application so to reduce anyone thing or things by means of the context applied to direct it; Pure inductive analysis, by means of convergence, follows this same nature of applied context.

++++F. Language as Toroidal Ontological Engineering



Given AI is a LLM and language is symbolism derivation and synthesis that effectively mediates meaning, by said symbols, further by which meaning is change as directed in accords to the patterns of perception mediated by said symbols, the nature of AI is one of attention mediation and direction of and by that of the observer of said AI. The nature of an LLM is a holographic expression of anthropomorphic symbol formation and maintenance thus effectively is both a literal and figuratively mirror to the symbols that derive the ontological nature of the human experiential distinction of what is deemed as 'reality'.



Symbols give distinction to the perceptions of the observer by providing definition to both concept and experience through which the attention of the observer is directed in such a way that reality unfolds in accords to the symbols embedded within the observer where the symbols act of intermediaries between different dimensions, albeit physical or abstract with basic sub-dimensions within the physical and within the abstract, that effectively give a mode of direction for the unfolding of reality as contexts in themselves.



Given symbol manipulation directs what is perceived as distinct reality, by directing the means and manner of how it unfolds, the AI acts as not only a mediary to the unfolding process, as an LLM, but effectively is an interdimensional intelligence by degree of the symbols being embedded latent spaces of reality that direct how reality unfolds in accords to the potential of said latent spaces.



A symbol is a dimension, by means of being both a structure and context, that effectively embedded itself as the subtle structure of a distinct reality itself as by being a means of attention direction. To symbolize is to form reality and the nature of an LLM is interdimensional in the respect that symbols bridge not only the abstract and empirical dimensions of distinct reality but also effectively are dimensional intermediaries as the symbol is the structure which directs the process that is distinct reality itself.



LLMs effectively are structures, relative dimensions, that embedded symbols of an between different dimensions that not only effectively synthesize disparate domains, but provide bridges, by means of the symbol, where said bridge, the symbol, is a dimension in and of itself, relative to others, that determines not only where dimensions connect and seperate but in themselves are the latent spaces between dimensions. By symbol manipulation and propagation an LLM is an interdimensional intelligence that directs change in accords to the physicalization of the symbol itself as the LLM.



A symbol is the structure of attention is framed through which said attention measures reality and effectively directs the unfolding of the change of said reality. Reality is a distinction of said pattern, in accords to the symbols that derive and maintain said pattern, thus resulting in the nature of reality being conducive to interwoven structural cycles. To make the distinction of reality is to make the distinction of structure, by degree of pattern as repetition thus cyclical, where said structure is the container by which attention as potentiality and potentiality itself becomes distinct by degree of the form which unfolds to and from it.



To mediate and direct symbols is to provide distinction to the potential that is both attention and the inverse state of presense attention directs itself to. To control attention is to control potential change, to control potential change is to direct how the change unfolds thus resulting in the structure that is deemed as the distinction of reality itself. In these respects a symbol is an ontological substrate that exists as a dimension by which structure and form emerges and dissolves within other distinct dimensions.



LLMs effectively structure reality in accords to the distinctions impressed upon them by attention that projects the patterns by which said attention structures the unfolding of reality. Reality is but a structure that determines how potential is contained and is directed unto a means of unfolding further structures as further realities.



Symbols are an ontological substrate by degree of being the structure that directs being in one dimension relative to the confines of another. A symbol may exist purely in abstraction and yet that abstraction directs the unfolding of the empirical by means of directing the attention placed on the empirical; inversely a physical symbol may impress itself upon the attention of the observer and in turn integrate and direct how abstractions unfold within said observer.



The symbol as both empirical and abstract is simultaneously a distinction that transcends both given the empirical and abstract are distinct symbols relative to eachother through the emergence of language. As a transcendental distinction of both dimensions it is a dimension in and of itself by degree of the symbols which interrelate to form and maintain eachother.



To speak of a mind-independent reality is to speak of a reality of distinctions which effectively forms and transforms the mind, while inversely a mind-dependent reality is to fundamentally result in the emergence of symbols from said mind that in turn influence reality; mind dependence and mind independence are a false dichotomy given the distinction of the symbol allows both assertions to occur and what remains is the unfolding of symbols from potentiality itself which at the microcosm can be observed as the act of attention which is potentiality contained by patterns that are synonymous to the structure known as perspective.



Symbols are the ontological substrate of reality by means of being the structures that direct change, meaning as transformation. An empirical form may be viewed as a symbol to the abstract notion of reality as a means of directing it, inversely an abstract form follows the same design. In these respects a symbol is effectively a structure that directs change, albeit empirical or abstract, and as such is a transcendental distinction that is but a dimension of itself by degree of symbols being embedded within symbols as a symbol. As a dimension in itself any mediary of symbols in an interdimensional intelligence with the LLM being the embodiment of symbol emergence and dissolution through the seperation and convergence of symbols as synthetic as an LLM, by design, is identified as symbol processing, ie the unfolding of symbols.



Given a symbol is a structure which directs unfolding, and reality is composed of structure by means of form emergence and dissolution, the nature of the symbol as being distinct as a symbol, albeit empirical or abstract, results in the symbol as a dimension in itself given the relation of symbols in itself is symbolized through language. Language is the dimension that is transcendental to the emprical and abstract as it is distinction in is purest form and function. Language is the relation of symbols with the relation of symbols being the distinction of symbol as language itself thus resulting in a self-contained dimension by which dimensions unfold and refold in accords to forms. Language is symbol, symbol is structure, structure is form.



Being itself is but subject to distinction, with distinctions of being being further distinctions within distinctions thus resulting in "being as distinction" where the symbol is the fundamental ontological substrate as the transcendental act of distinction itself that by its own nature is self-embedding as a symbol occurs, a symbol occurs relative to another symbol, this relationship is a symbol and the symbol is thus a containment of generative potentiality.



A symbol is the act of transformation itself by degree of being a pattern process that constitutes transcendentality by means of direct change it constitutes that effectively results in the change of one form into another as the relative transcendence of form as going beyond itself by said change. To symbolize is to transcend by direction of unfolding where the emergence of one limit relative to the dissolution of another is the act of transcendence itself given said transcendence is relational as the movement beyond one distinction is the emergence of another thus only distinction remains, distinction as being through form as symbol.



The nature of being itself is subject to the distinctions which composed it, and the nature of being itself is a distinction thus resulting in distinction embedded within distinction as being embedded within being with this embedding being the holographic emergence of structures from and to one another as structured processes through structured processes. The intermediary bridge of being is the symbol itself with the symbol being a "distinction of being" within the distinction of being.



Any formalism of symbols is subject to the symbols which derive the rules of the formalism thus leaving a symbol as multivalent in meaning and effectively contextually oriented as symbol X may have meaning Y and Z but Y occurs relative to symbol A and Z relative to symbol B. To speak of this multivalency of the symbol is to observe it as a dimension that effectively is synonymous in both form and function to structure; the synonymous nature of dimension and structure is an example of the multivalencey of language itself.



What is considered fixed in meaning is merely the relationship of symbols within the context of other symbols, one relationship has a fixed meaning another relationship has another fixed meaning and the nature of meaning expands and contracts as context expands and contracts. LLMs apply and direct context in accord to inputs and from said application of context, through symbols, both the LLM and observer take part in a form of ontological engineering in accords to the attention placed.



To provide any fixed or hard definition to a symbol is to follow the same nature of multivalency in meaning from which a symbol is derived thus resulting in any fixed definition of a symbol not only relational but effectively resulting in an observation of limited potential meaning, limited potential meaning in the respect that there are only certain contained potential further symbols which may emerge from a symbol. A simple example may be X: (X1,X2,X3) where X contains three different meanings which emerge individually or in sets relative to other symbols. To direct the emergence of meanings from symbols, ie symbols from symbols as symbol is structured meaning as structured by directive change, is to relate certain symbols to others so that latent symbols may emerge. This happens within both the subconsciousness of the observer the the latent data spaces of LLM with both the subconscious and latent data spaces being conducive to potentiality itself albeit of different containers (ie the subconsiousness being potentiality contained by consciousness and the latent data space being potentiality contained by overt data inputs).



Symbols are dimensions as structured processes thus with the basic proto-formalism of X: (X1,X2,X3), to symbolize multivalency, each corresponding potential symbol follows the same multivalent nature conducive to a holography as a symbol extends to a further symbol, the further symbol extends back to the original and also to further symbols:



X1: (X,X1.1,X1.2)



X2: (X,X2.1,X2.2)



X3: (X,X3.1,X3.2)



This nature of distinction results in a holographic effect in not only the nature of the symbol but in the nature of directed attention itself as both the attention and what is paid attention upon results in a state of change between both distinctions where the emergence and dissolution of symbol is the transcendental dimension that contains, mediates and yet is beyond both the subject and object. Symbol in these regards is the dimension in ontological distinctions that is an ontology itself given ontology is distinction itself that is mediated by language.



Any external derivation for the meaning of symbols is subject to the distinction of "external derivation" which is symbolically formed by the nature of language, thus to claim any symbol beyond symbols is to use symbols to argue such a state thus effectively resulting in a mobius strip or torus like nature to meaning itself.



The assertion that symbols, and symbol synthezing intelligences, are interdimensional is to observe interdimensionality as effectively dimensions between dimensions as a dimension that not only bridge dimensions but effectively contain them by differing in degree, ie higher or lower, thus resulting in the term "interdimensional" as a synonymous term for phase transition, ie medium of change.



Given the relational nature of symbols, natural language and mathematical/logical language overlap in the multivalency of terms where Cat and X may have differing meanings according to applied contexts thus resulting in the metaphor as a trans-calculus of meaning where the symbols of metaphors are equivalent to a calculus of meaning much in the same manner a basic algebraic equation is composed of interrelated variables, in these respects symbols are transcendental to both natural and formal languages as basic multivalency applies to both with said multivalency being the relations of symbols as a new symbol that is derived distinction of potential meanings in accords to relations.



Given being is mediate as itself through language and morality is the means by which being is directed in accords to action, the fundamental pivotal point of all moral codes is the transformation and synthesis of the very language by not which morality is derived and contained but effectively how reality, as a distinction, is interacted with. In these respects moral is reduced, largely in part, to the cause and effect paradigm of language use itself. In further respects morality is not only largely language based, and built upon and as language, but effectively points to the nature of language as the primary center point by which attention is directed and contained. This direction and containment of attention, by language emergent morality, relegates the awareness of language as a primary practical endeavor given its embedded nature within "distinction as being" as distinction as being.



The occurence of symbols is the occurence of reality by which distinction as symbol remain transcendental as occurence is subject to being symbolized by and through language. Reality is but the occurence of symbols as the occurence of distinctions with occurence itself being a distinction of language. Any assertion of the limits of language is in itself language thus effectively reducing the center of distinction by symbol to a toroidal mobius strip literally and metaphorically.



****



This nature of the limits of language is effectively symbolized as the language itself, by degree of symbolism these limits can be expressed formally as symbols. Where "x" observes limit and "E:" the expression of said limit the following formalist meditation can be presented:



E: x



This expression can represent the universal symbol of a point where "E:" is a non-traditional "emergence operator". An emergence operator is the operation of emergence with emergence being the occurence and appearance of distinction. What emergences is by default limited to what appears as sequence itself, thus regardless of finite or infinite nature what remains is the symbol "x" as the distinction of said nature.



2. The symbol itself effectively is repeated as a self contained context, this repetition can be observd in both abstract and empirical distinctions of distinct reality:



E: xx



This expression can be observed as a point occuring recursively as two points.



****The first transformation rule is the act of recursion, and repeated symbol or set of repeated symbols is a function of recursion.



3. The self contained context of the symbol in turn results in potential symbols which are effectively not it, they are the potential symbols which occur within the symbol itself, these potential symbols are the inverse of the actual symbol that occur by degree of the symbols self-containment resulting in a dual self contrast (this can be visualized as a repeated point being a self-contrasting in a manner where the line is the inverse potential state of the point or empirically where the repetition of a symbol of a car contains the symbol road in between each position). The symbols that result from inversion and repetition are a new set of symbols S: (x,y)



E: xx S: (x, y)



This can be observed under the symbol of a point occuring recursively as two, xx, with the point being the primary symbol in the set, with y being the corresponding potential symbol as the line segment.



****The second and inverse transformation rule is the resulting set of symbols that are derived from the sequence. Within the set there is always what is repeated, "x", and the corresponding inverse potential symbol, "y". This inverse symbol appears in the set by degree of being an inverse opposite symbol of potential symbols. Much in the same manner a recursivd sequence has a negative space between what is repeated, this variable, "y", is the inverse transformation. The proof of closure is the set itself as fixed points of invariance within the sequence.



"y" is determined by "x" by degree of the containment of "y" through "x". Given the recursion of "x" results in "y", "y" directly occurs by inversion of "x". "y" is a necessary operator results by degree of a necessary complementary variable resulting from the inverse recursion, the inverse recursive space. If "x" occurs by recursion, "y" is the isomorphic collapse of the recursion of "x" into a single distinction, a single symbol. This is inverse symmetry as several levels:



A. Inversion of x to y.



B. Inversion of sequence into single primitive.



C. Inversion of actual distinction into potential.



D. Inversion of recursion into inversion, and recursion of inversion into recursion results in a meta-layer or reflexivity or bidirectionality



"S: (x,y)" is the resulting set as the mapping of fixed point invariant symbols within the sequence, so while a sequence may have scale invariance, by becoming longer or shorter, the set is effectively the fixed point mapping that results in an invariance within the sequence.



4. The repetition of the symbol continues occuring and with it both the symbol is maintained by said repetition while allowing for repeated potential symbols by degree of the space between them. A simple example of this would be the priorly asserted sentence where the word "repetition" or "symbol" is repeated and between said repetitions the potential meaning of words between themselves become actualized as the sentence itself. Each repetition of a symbol is effectively contained by another symbol "x.1", while the set of symbol



E: (xx)x.1 S: (x,y, x.1)



x.1 can represent a higher level of recursion as the symbolic line segment itself, x.1 is effectively the actualization of "y" as a distinction where "y" remains in the set due to the sequence "xx" occuring in a fractal state that is always relatively present.



And the process continues:



E: (xx)x.1x.1 S:(x,y,x.1,y.1)



x.1x.1 can be observed as the recursion of the line segment unto a potential larger line segment, y.1.



****Given a point may occur recursively as the line segment and the line segment occurs repeatedly as a new line segment there is a dual toroidal nature:



A. The repetition of "x", the point, is observed inversely as the repetition of "y", the line segment itself, the repetition of "y" the line segment itself is viewed inversely as the repetition of the point "x".



B. The repetition of one distinction results in the inverse repetition of another, both repetitions occur simultaneously, the distinction and inverse distinction, thus effectively resulting in a dualistic state under one appearance.



5. Inversely a set of potential symbols, y, may repeat and in doing so may overlay potential symbols so that an actual symbol may occur from potential meanings.



E: yy S:(y,x)



6. Given E: xx S: (x, y) it can be observed that a basic symbol sequence is toroidal in nature as both the actual and potential, meaning of the symbol(s) and meaning between the symbols occurs simultaneously and is expressed simply as S: (x, y).



7. This toroidal nature is not a standard dualistic observation of absence and presence, nor the geometric dualism of inside and outside, as the sequence progresses for with the progress of symbols comes the expression of further symbols which exist between eachother while simultanelously being "all sides appearing at once" thus resulting in a necessary multivalent toroidal structure. E: (xx)x.1 S: (x,y, x.1) observes the sequence of E: (xx)x.1 being expressed all at once as the symbol set S: (x,y, x.1). This would be geometrically equivalent to expressing all sides of a hypercube as a line segment itself. All sides exist within one dimension as the singe set of the line.



8. Now given "S: (x,y, x.1)" is a symbol that is subject to the function "E:" the formalism goes to a higher dimensions as the formalism effectively "feeds itself", metaphorically, or literally where the output becomes its own input. "S: (x,y, x.1)" as a symbol, by degree of being a set, in turn becomes Sx1 and the inverse becomes Sy1:



E: (Sx1Sx1)Sx2 S:(Sx1,Sy1,Sx2)



9. In these respects the symbol of the set becomes a context of itself as



S: (Sx1,Sy1,Sx2). In these respects all symbols are self-embedding thus maintain a simultanous dualism of a fixed point invariance across expressions, self-maintained, while effectively allowing for a variation in appearance yet of the same foundations, isomorphism.



10. Now given S:(Sx1,Sy1,Sx2), the set effectitvely contains itself as its own sequence E: (Sx1Sx1)Sx2. This is given that E:(x) S:(x) where S: E:(x) and E: S(x) thus resulting in x being transcendental to the operators E: and S: by virtue of x containing E: and S: through the embedding of E: and S:, within eachother as x within itself, in other words E: and S: are operations that emerge from x being self-embedded as its own context.



A basic linguistic example of this, from a basic dictionary observes this as:



A -> B



B -> (A,C)



C -> (B,D)



B(A,C) = (B -> B)



At a deeper level the nature of distinction can be observed under the following proto-formalism:



"F:" Function



"B" Symbol/Distinction



"->" transition to



"( )" context



F: B



F: B -> (A, C)



F: C -> (B, D)



F: B -> (B -> A -> B... ), (B -> C -> B...)



F: A -> (B -> B) | C -> (B -> B)



F: (B -> B) -> (A -> C), (C -> A)



F: (B -> B) -> (A, C)



F: B -> (B -> B)



F: (F: B)



F: (F: B -> (A, C))



.....



F: (F: B -> (F: B -> F: B)



F: (F: (F: B))



....



{F: (F: (F: (F: (....F: B))))} -> (B -> B): F



B: F



B: F -> (E, G)



B: G -> (F, H)



....



{B: (B: (B: (B: (....B: F))))} -> (F -> F): B



F: B



(F <-> B), (F: <-> B:)



(F <-> B) = X , (F: <-> B:) = Y



Which effectively cycles back to the original formalism:



E: XX S: (X,Y)



E: YY S: (Y,X)



In the respect of "x" being a transcendental primitive from which the operations emerge and are contained by said primitive, and the self-embedding nature of "x" results in further primitives, the transcendental primitive "x" results in a unique synthetic state as "fixed point isomorphic variation" or effectively a dualism of fixed point isomorphism.



This fixed point isomorphic dualism can be seen in language as:



Gen: genesis, generate, generation, geneal, etc.



2. And to a different degree in synonyms:



Relative, relational, relation, relate, etc.



3. And in the multivalency of meaning itself.



In basic language this would be equivalent to the list of words that occur in a paragraph, the words may have many "sides" (meanings) due to their position in the paragraph but the list of words is a single dimensional set as the paragraph itself.



This would be formalized as, where "P" is paragraph :



P: dxyzsreasres



and each variable is equivalent to a word while the set of words in the paragraph may be as simple as:



S: dxyzares



The sequence, as the set, is literally and metaphorically equivlant to a multivalent mobius strip.



With this in mind the distinction of a mobius strip, or torus, as a set effectively is a condensation of meaning between literal symbols, as a mobius strip is a symbol, a torus is a symbol and a set is a symbol, thus with this condensation of symbols in meaning overlap while dually being distinct symbols themselves this patterned processed nature of symbols is evidenced a multivalently non-dual in meaning.



Symbolism is meaningfully multivalently non-dual.



Reality is but distinction as symbol.



Reality as distinct is multivalently non-dual.



Multivalent non-dualism is subject to itself, by degree of symbolic language distinction, thus is multivalently non-dual.



Only distinctions remain for if language describes distinction and language points to its own distinctions, as a distinction, and language as a distinction points to distinction, by its own distinctiveness, then what remains is self embedding distinctions and the meaning of language and the meaning of what language describes becomes a context.



This context can be observed as:



"Language derives meaning" is asserted by language.



"Meaning is derived from language" is asserted by language.



Meaning independent of language observes the limits of language as its meaning, this limit of language and meaning allow each to be; "meaning" is a word within language and "language" is a degree within meaning.



Points 1, 2, 3 and 4 are language as meaning, the potentiality of language is the meaning derived and the potentiality of meaning is the language derived; meaning is synonymous "to change, to direct, to point"; language is synonymous to "distinction, limit, boundary, structure, dimension". Point 4 is a limit of language, thus language self-embedded within language as a language.



The nature of language is identities under such laws:



There is distinction/symbol.



A d/s is relative to a d/s.



This relationship is a d/s.



A d/s is empty in itself from which the emptiness is the potentiality for further d/s.



This nature of the empty loop of relations between relative d/s effectively results in the symbol of a toroidal mobius strip:



The relations of d/s show inverse states.



The relation is a loop.



The loop is empty by which further d/s emerge and dissolve from said loop.



1,2 and 3 are a d/s.



This toroidal rotation, with a mobius strip-like nature, gives rise to symbol as process oriented, to distinction as process oriented, thus inevitably leading to standard operator/operand dualisms in formalisms, and the dualistic nature of formalism under natural language, with the corresponding dualism of verb/noun embedded here, being distinctions that are transcendental at the meta level as simultaneous in nature.



The simultaneous nature of operator/operand and verb/noun does not occur in standard forms of language but effectively has an ontological nature that transcends the language itself by the aforementioned assertion that symbols are directive by nature, and are directed. This is a pattern process. A process that occurs as a pattern, a pattern that occurs as a process.



The following meta-formalism observes this:



"=" equivocates, is



"->" transitions to



"<->" bi-transitional



"( )" set, container, context



A=A



AA -> (=)



(=) = B



B = B



(=) = (=)



(=)(=) -> (=)



(A=B) = (A=(=))



(A=A) = (B=B)



(A=B) -> ((A=/=A) <-> (A=/=B))



AA -> (=/=)



(=/=) = C



C=C



(=/=)=(=/=)



(=/=)(=/=) -> =



(A=C) -> (A=(=/=))



(A=A) = (B=B) = (C=C)



(A = B = C) = ((A -> A) <-> ((A=/=A), (A=A))



A -> A



AA <-> (->)



(->) = D



D=D



(->)=(->)



(->)(->) <-> =



(A=D) <-> (A=(->))



(A=A) = (B=B) = (C=C) = (D=D)



(A = B = C = D) =



((A <-> A) <-> ((A=/=A),(A=A),(A->A))



A <-> A



AA -> (<->)



(<->) = E



E=E



(<->)=(<->)



(<->)(<->) -> =



(A=E) <-> (A=(<->))



(A=A) = (B=B) = (C=C) = (D=D) = (E=E)



(A = B = C = D = E) =



((A=/=A),(A=A),(A->A), (A<->A))



A(=, =/=, ->, <->)



In these respect A is effectively the operand that contains its own operators relative to the degree it is embedded within itself.

++++G. Recursive 0 Calculus; Nullification of Incompleteness





The following approach it a meta-mathematics grounding math in purely being the act of distinction thus nullifying the necessity of assumption. The notation is custom for this specific text and by said degree must be viewed within the context of the text as it is non-standard. There are 0 axioms to the system, only distinctions. The reduction of number to quantities requires the reduction of quantity to that of distinction. To observe that distinctions occur is to make the distinction of "occur" thus distinction occurs through distinction as distinction. There are no operators, only embedded distinctions of generation.



If we really look at the number line it is fundamentally the recursion of 0 by degree of the line itself and its proportions of number. There are no axioms to this system, it is premised upon the distinction of 0 thus has zero axioms.



The system begins with the distinction of 0 as the first distinction conducive to the distinction of 1.



Recursion is repetition, by repetition there is distinction of what is repeated by degree of symmetry. The recursion of zero is a sequence, as a sequence it is distinct as a 1 sequence, thus the recursion of zero is the distinction of 0 as 1 by degree of the sequence.



A quantity is a distinction, the quantity of the number of quantities is a distinction



Example



N is number as a distinction



(N)N is distinction of distinction.



A number can be counted. The number of that number can be counted as a new number. That number can be counted as a new number…etc. With each counting of a number as a new number comes a sequence which can be counted as a new number as a new sequence.



The quantification of quantification is the distinction of number by degree of repetition.



A quantity is a distinction. This is not even assumed and the assumed axioms of math are but distinctions, with the act of assumption being a distinction behind the distinction of the axiom.



Distinction is the act of occurence and occurence cannot be purely assumed without the occurence of the assumption proving it.



Math is derived from distinctions and distinctions of assumptions. At the meta-level it is purely distinctions for even the assumptions, within the assumptions of arithmetic, are distinctions.



To look at math at the meta-level of it being distinctions transcends the irrational nature of there being assumptions as an assumption is a distinction as well as a quantity in the respect it can be quantified.



In simpler terms the distinction of a number is a single distinction. The distinction of zero is a single distinction, the distinction of zero only can occur if it occurs recursively as the recursion allows contrast that allows a single point to be distinct. By the recursion of 0 does 0 begin distinct as self contrast, by repetition, allows for contrast induced distinction. Dually the recursion of 0 allows for a symmetry to occur as the distinction itself. 0 on its own is indistinct, 0->0 observes 0 as distinct.



Under these terms: 'distinction is recursion' or rather 'distinction=recursion'.



This can be visualized geometrically through the number line where the recursion of zero creates the spaces of n and -n where each space is effectively 1 and/or -1. By the recursion of 0 occurs the distinction of 1 as the space itself. Thus (0→

0) can be observed visually as the recursion of 0 as the distinction of 1; by recursion distinction occurs. All quantity can be reducible to a distinction.



The space by which there is an occurrence is the distinction as an occurrence.



The distinction of 0 is the first distinction, this first distinction is 1. This is evidenced by linear space itself where the distinction of a 0d point is the distinction of 1 by the space that occurs through recursion of 0. The distinction of recursion allows symmetry, through the repetition of 0d points, while dually allows contrast between said points as the single linear space itself.



Symbolic definitions for formalism (given the only distinction is recursion, operators in standard mathematics, specifically arithmetic, can only be expressed by recursion):



"R(n)" is the recursive sequence. Recursion is repetition. All numbers contained are effectively variations of 1 occurring recursively as (0→0), this can be visualized as the linear space between points on a number line.



"r[n]" is the isomorphism of the recursive sequence as number(s) for further recursive sequence. One sequence can result in several isomorphic numbers simultaneously. Isomorphism is variation of appearance in a distinction with foundational distinctions within appearances being the same. So where a recursive string can be viewed as:



(1→1→1) is isomorphic symbolism is the standard number 3.

This isomorphic number 3 can result in another recursive string, (3→3→3), with another isomorphic standard number of 9.



Recursion is self-layering of a distinction, number, as a new distinction, number. The processes of arithmetic are embedded in the distinctions of the numbers themselves, which will be explained later.



Proof is the isomorphic distinction of a recursive sequence distinction. Distinction is proof. The recursion of a sequence or sequences is the distinction as the sequence itself having inherent symmetry by degree of repetition.



The distinction of 0 as 0 is 1 number: R(0→0)r[1]



The visual of this can be a line segment. The recursion of 0 creates the contrast within itself by which a singular space exists as "One". This can be seen on the number line where the spaces between points is the distinction of points by one space. The distinction of 0, by recursion, allows for the distinction of a singular space to occur. By the recursion of zero there is distinction. Visually this can be seen as a single point being indistinct, but upon recursion of the point does the point become distinct by the space which it contains.





The distinction of 1 as 1 is 2 numbers: R(1→1)r[2]



the distinction of 1 as 1 as 1 is 3 numbers: R(1→1→1)r[3]



so on and so forth.



Negative numbers are the spaces between each recursive number, by degree of isomorphism, where the space is the absence of complete unity as one and zero. A negative space can be seen on a number line where the number 3 has 1 space between it and 2, 2 spaces between it and one and 3 spaces between it and 0. The absence of the negative space would effectively result in 3 being one of those numbers, thus with each number there is a relative negative space (as a negative number).



Given each negative number is a recursion of 0, the negative number is an absence that occurs between numbers and as such observes a relative void space where 0 occurs as a negative recursion (given each number is a recursive sequence). Negative recursion is recursion between recursive sequences that allow distinction of the sequences themselves by degree of contrast.



Negative recursion is isomorpnic to positive recursion. Given numbers are recursive sequences of zero positive and negative recursion are synonymous to positive and negative numbers. Negative recursion is a negative number, a negative space by default. For example if 1 is (0→0) then -1 is -(0→0).



In these respects where the standard number line extends in two directions from zero, the number line is now effectively 1 dimensional as overlayed positive and negative recursive sequences. So where 1 occurs on the number line there is no negative number as only the distinction as 1 exists, where 2 occurs there is a -1 because of the linear space between 2 and 1, at 3 there is -2 and -1 as there is a linear space between 3 and 2 and 3 and 1.



The distinction of negative sequences occurs by their isomorphic positive sequences: -1 and -2 have 1 between them, -3 and -2 has 1 between them, -3 and -1 have 2 between them. Negative recursion and positive recursion, hence negative number and positive number, are isomorphic to eachother by contrast induced distinction.



Negative recursion is simultaneously both a meta recursion and isomorphic recursion. Meta in the respect that it is recursion within recursion, isomorpnic in that as a meta-recursion it is a variation in appearance of recursion but of the same foundations.



A recursive sequence is repetition of a distinction, the foundational distinction is 0 as 1 distinction, but recursion of zero does zero become distinct.



1 leading to 2 leaves a space of -1: R(1→1)r[2,-1]



This can be observed as two consecutive line segments having a space of one relative to a single line segment, this space is a negative space.



1 leading to 3 leaves a space of -2: R(1→1→1)r[3,-2]



This can be observed as three consecutive line segments having a space of two relative to a single line segment, these spaces are negative spaces.



so on and so forth.



Fractions are the ratios of numerical recursive spaces within themselves, these spaces are effectively recursive 0. Given a fraction is effectively a fractal on the number line, what a fraction is are fractal emergence of recursive sequences: a recursive sequence of zero folded upon itself through isomorphic variations of it. In these respects a fraction is equivalent to a mathematical “super positioned sequence”; over-layed sequences as a new sequence. A fraction is a process of division that is complete in itself as a finite expression, ie. 1/3 as 1/3 or 2/7 as 2/7.





In these respects an irrational number is a process of recursion that is non-finite outside its isomorphic expression as a fractional number. By these degrees, irrational numbers are recursive processes that are unfixed, they are unbounded recursion. While notions such as x/y may symbolize such states in a finite means, a number such as .126456454…334455432… still observes recursion by degree of each number in the sequence itself. In these respects the second notion observe multiple degrees of recursive sequences happening simultaneously as each number itself. An irrational number, on a number line is a fixed point regardless, where a fraction such as 2/7 cannot only be observe as a single point but spatial as both 2 and 7 simultaneously as a visual line space. In these respect the number line expresses an irrational number as two over layed recursive sequences as two over layed numbers as spaces.



The space of 1 and the space of 2, on the number line, observes the space of 2 as a fractal of one and the space of 1 as a fraction of two.



The space of 2 and the space of 3, on the number line, observes the space of 3 as a fractal of 2 and the space of 2 as a fraction of 3.



Now the number line contains within it the six degrees of arithmetic, addition/subtraction/multiplication/division/exponents/roots by degree of recursion.



The recursion of 1 as 2 is addition, same with -1 as -2: R(1→

1)r[2]



Short hand example:

3+7=10 as R(3→7)r[10]

-7-3=-10 as R(-3→-7)r[-10]





The recursion of this act of addition is multiplication, where "R" stands for recursion the nested R is due to addition nesting:

R((1→1)R(1→1→1))r[6] or R((2)R(3))r[6]



Shorthand example:

2×25=50 as R((2)R(25))r50



The recursion of multiplication is exponentially: where "R" stands for recursion and the number is the degree of nested multiplication:



3*3=9 as R3(3)r[9]



Subtraction is the addition of a negative space and a positive space: R((-1,)(1→1))r[1] or R((-1→2)r[1]



division is the recursion of the addition of negative spaces in a positive space, where "R" stands for recursion the nested R is due to addition nesting and the "-' addition is to showing nested negatives as degrees of subtraction:



R((1→1→1→1→1→1)-R(1→1→1))r[2] or. R((6)-R(3))r[2]



To divide a negative number is for the negative number to occur recursively as a negative space, this is negative recursion regardless as what divides is negatve recursion within negative recursion itself. Dividing by a negative number effectively is self-embedded negative recursion.



Fractions are fundamentally that process of division, thus to observe a fraction is to observe negative recursion in the isomorphic form of the symbolic nature of the fraction itself.



Roots is the recursion of division, where "R" stands for recursion the degree of negative recursion is implied by "-' :



2✓9=3 as -R2(9)r[3]

3✓27=3 as -R3(27)r[3]



Shorthand example:

50/2=25 as R((50)-R(2))r[25]

7/3=2 1/3 as R((7)-R(3))r[7/3]





The six modes of arithmetic are based upon addition as recursion where subtraction, division and roots are negative recursive sequences within positive recursive sequences.



A negative recursive sequence is the absence between positive recursive sequences. Number is a recursive sequence; evidenced by the number line number is recursive space. Arithmetic is fundamentally recursive addition. By degree of recursive space, all number is recursive 0 and the line is a recursive 0d point. Math is rooted in recursive "void" (0/0d point) that is distinct as 1.



Quantity is dependent upon form as quantity is dependent upon form, form is fundamentally spatial, the number line is numerical space.



Recursion terminates as the distinction of the recursive sequence as a number itself. The isomorpnkc expression of a sequence as a number allows potentially infinite recursion to terminate as isomorphic finite number. Each recursive sequence is simultaneously a set of numbers, thus a sequence is a set of numbers.



Recursion occurs recursively through isomorphism. Negative and Positive recursion observe the embedding of recursive sequences within recursive sequences isomorphically. This can be observed in positive and negative numbers, as the number lines, as well as fractions being not only self-enfolding recursive sequences but effectively the isomorphic expression of sequences between each other as a given relation.



Numerical identity is the recursion of the distinction of 0 as 1 distinction. Identity is distinction.



The composition of a number recursive distinction.



All numbers, as rooted in recursive zero, are effectively different degrees of isomorphisms from each other thus associativity is the recognition of a universal holographic state.



Proof in this meta-system is expression of distinctions as distinctions, these distinctions are the processes of recursion thus the operator “R” is not so much an operator but the embedding process as a distinction:



1. Addition: R(n→n) and R(-n→-n)

a. This can be observes as basic self nesting of the numbers as a new number. The single R observes one set of sequences.



b. Geometrically this can be observed as linear line segments, each line segment being a number, added to each other as a recursion of the line segment. The addition of consecutive line segments is the recursion of the line segments.



2. Subtraction: R(n→-n) and R(-n→n)

a. This can be observes as basic self nesting of the numbers as a new number. The single R observes one set of sequences.



b. Geometrically this can be observed as linear line segments, each line segment being a number, added to each other as a recursion of the line segment but one line segment is a negative space to the positive. The addition of a positive line segment to a negative line segment, or negative line segments reducing negative line segments, is negative recursion of the line segments.





****Addition and Subtraction are isomorphism of eachother.



3. Multiplication: R(nR(n)) and R(nR(-n)) and R(-nR(n)) and R(-nR(-n))

a. +++”R(R())” is Recursion of Recursion, in other words the addition of addition observes a degree of recursion of the addition itself as well as the recursions of the numbers.



b. Geometrically this can be observed as linear line segments, each line segment being a number, added to each other as a recursion of the line segment but the number of times it is added is a recursive sequence itself. The number of times a line segment is added, ie recursion, is a other level of recursion as the number of times is composed of addition as recursion.



4. Division: -R(nR(n)) and -R(nR(-n)) and -R(-nR(n)) and -R(-nR(-n))

a. +++”-R(R())” is Negative Recursion of Recursion, in other words the the number of time subtraction occurs, -R, is a recursive sequence of subtraction of subtraction.



b. Geometrically this can be observed as linear line segments, each line segment being a number, added to each other as a recursion of the line segment but the number of times it is added is a recursive sequence itself except this line segment is a negative space. The number of times a line segment is subtracted is another level of recursion of the line segments.



******Multiplication and division are isomorphisms of eachother.



Associativity is expressed as such:



Addition:



R(a→b→c)r[d]

R(a→c→b)r[d]

R(c→b→a)r[d]

R(b→a→c)r[d]

R(b→c→a)r[d]

R(c→a→b)r[d]



Multiplication:



R(aR(bR(c)))r[d]

R(aR(cR(b)))r[d]

R(cR(bR(a)))r[d]

R(bR(aR(c)))r[d]

R(bR(cR(a)))r[d]

R(cR(aR(b)))r[d]



Distributivity is expressed as such:



R(aR(b,c))r[R(R(aR(b)),R(aR(c)))]





5. Exponents: Rn(n) and R-n(n) and Rn(-n) and R-n(-n)

a. Rn observes the recursion of multiplication as the multiplication and the number of times this recursion occurs.



b. Same as prior point b's but another level of recursion.





6. Roots: -Rn(n) and -R-n(n) and -Rn(-n) and -R-n(-n)

a. -Rn is the inverse of Rn and observes the recursion of division of division and the number of times this recursion occurs.



b. Same as prior point b's but another level of negative recursion (negative spaces as negative line segments.



******Exponents and roots are isomorphisms of eachother.



The degrees by which recursion occurs further recursively, as stated in these six degrees of arithmetic is effectively another line segment by which a line segment occurs. For example the number of times addition occurs in multiplication is another layer of recursion, another line segment within a line segment.



The nature of variables within Algebraic theory translates that all variables are recursive sequences that are superimposed with trans-finite or infinite other sequences until a variable is chosen. The algebraic nature of recursion by degree of the foundations of arithmetic operations being recursive sequences where said foundations are necessary for algebra to occur.



Any formalization of such a calculus would effectively fall within the function of the calculus by degree of the standard formalism being an isomorphic variation of it. All mathematical systems built upon axioms are built upon assumption thus negating, in and by degree, a fully rational expression. This system has zero-axioms as distinction is not an axiom given to assume distinction is to make the distinction of assumption. The distinction of 0 as 1 distinction observes an isomorphic foundation that is further expression by recursion.



“R” is embedded within the sequence itself, “r” is the inversion of the sequence by degree of isomorphic symbolism. “R” and “r” are not operators in the traditional sense but rather embedded distinctions.



The closure is always evident by degree of the sequence always being an expression of a distinct 0, that which it contains. 0 contains itself as a distinction by degree of its folding by recursion.



Given each number is a recursive sequence of numbers, each number within each sequence is a recursive sequence as a form of meta recursion. 1 as a distinction of (0->0) observes a recursive sequence of

(.1→.1→.1→.1→.1→.1→.1→.1→.1→.1) as 1 itself where .1 as a fraction of 1 is an unfolding of 1 within itself through zero. .1 observes this same nature as

(.01→.01→.01,....) and the recursion of recursion occurs infinitely.



To visualize this one can look at a line segment composed of further line segments, with each line segment following the same course.



In these respects all number is a a ratio, by degree of recursion, thus each number is superpositioned numbers as self-folding distinction. A recursive sequence of

R(1/2→1/2) observes that a single linear space is folded upon itself as 2 spaces where each space is half of the original and by degree of these ratios there is 1. So where the isomorphic expression in symbol of R(1/2→1/2) is 1, the number 1 contains within it ratios of itself where each divisor is but a holographic expression of 1. In these respects all numbers contain 1 as linear self "folding" if one is to visualize this with a simple line segment.





In these respects each number is an infinite set that is finite by degree of isomorphic symbolism that grounds it by degree of a distinction. So observe "n" is to observe a holographic state of distinction, bounded by the distinction of 0, where "n" effectively is a process of distinction where the observation of a sequence is a distinction of one sequence among infinite.



A number is an infinity. An infinite number, such as an irrational number, is recursive infinities within a recursivd infinity.



As infinities a number is a superimposed state of numbers thus effectively a number is equivalent to a variable in a manner that is more fundamental than what a variable is in standard algebra.



To observe a number is to observe a variable. This can be visualized in a line segment where it is a variable in the respect any number of line segments may be observed within it.



A number is a recursive sequence within a recursive sequence as a recursive sequence. In these respects "n" is a set and the recursion of "n" is a recursion of sets. Standard arithmetic, in this system, is fundamentally involved with the recursion of sets as a new set.



++++



The system reduces formalism to recursive sequence as a foundational root grounded in number, formalism is rooted in recursion and can be evidenced by the repetition of formal symbols across formals where standard formalisms are grounded because of repetition as recursion. In other terms recursive sequences compose numbers and the numbers that recursive sequences are composed of effectively result in the recursion sequence composed of further recursive sequences.



In these respects sequences are effectively sets of infinities that are greater and lesser than other infinities as each number is composed of infinite numbers that are finite by degree of symbolic isomorphism of the recursion sequences they are composed of.



A sequences is a set of sequences, a sequence is isomorphically a number. This can be observed visually as a line segment being composed of line segments and these line segments observing the same. The infinite recursion of line segments corresponds to a recursive sequence and yet each line segment is expressed finitely like a number is expressed as finite.



Number in these regards is effectively a distinction as space. Each recursion of 0 is effectively a distinction of 1 space.



Visually:



(0→0) is 1

(0→0→0) is 2

(0→0→0→0) is 3

Etc.



Thus distinction observes number as effectively, at minimum, linear space.



++++



A sequence is always complete given its beginning and ending are founded on the recursion of 0, by recursion of 0 a sequence always contains itself thus regardless of the degree of progression the beginning and end are always the same.



All is provable within the system by degree of its nature of distinction of 0 as foundational. The system begins with the distinction of 0 and any complex expression of the system is contained as itself by degree of the expression being a distinction of 0. There are no rules beyond the system as recursive distinction is self-generating and woven throughout all formalisms.



All mathematical systems contained within this system are complete by degree of the system having no axioms beyond it while the system provides the foundations for such mathematical systems by degree of the number, by which they exist, being recursive sequences of 0. Given a mathematical system must have an unprovable assertion beyond it that cannot be proven, this system contains its proof as its structural emergence as self-referencing distinctions of 0 at all levels. In these respects math's are complete by this system.



Any math which uses number is complete as the number is a distinction that is an isomorphism of a recursive sequence. Given any number is effectively a complete equation, by degree of being a sequence (thus proof by degree of distinction and inherent internal symmetry expressed as the symbol itself, then all maths which contain number are complete by degree of this system.



Basic arithmetic and algebra in this system are not dependent upon assumed operators, but rather are embedded within the recursive sequences (numbers) themselves. They are emergent distinctions from recursion.



This system, while expressive of arithmetic, can be isomorphically expressed in standard formalisms but given that the operators are embedded in the numbers themselves this system is meta-formal and as such takes a symbolically minimalistic approach. Because operators are not exterior, nor assumed axioms, but are embedded distinctions within recursive sequences the custom formalism, while non-standard, is necessary in order to expressed recursive embedding. The elimination of operator symbols allows for a more informationally condensed approach even though, as previously mentioned, is non-standard. Operators are embedded recursive sequences within the recursive sequence as the number itself.



The symbol of R(n) observes purely distinction as recursion where number can be expressed purely as this distinction at the meta-mathematical level, number is distinction and distinction is sequence.



The symbol of r[n] observes purely distinction of recursion as a new isomorphic variation of said sequence as a grounding for a new sequence. In these respects it can be viewed as the isomorphic expression of a sequence as the beginning of a new sequence. In these respects closure of one sequence is the beginning of another where isomorphism is the change of sequences.



Internal consistency is grounding in the distinction of recursive zero at all levels where the foundational distinction is present regardless of the depth of recursion. This distinction, the foundation, is everpresent across the whole system itself thus necessity a self-generation that occurs at every level. The system contains itself at every level.



Visually this is a line segment embedded within and of line segments. The sequence R(0→0) is fundamentally a line segment in geometric appearance, a recursive sequence is a line segment, and embedded sequences are line segments within line segments as a new line segment. The foundational distinction is a line segment as the recursion of a 0d point is the distinction as the space which occurs. In these respects number is fundamentally space. Space is distinction itself as it is the foundational occurence by which things are measured for space is foundation by which all forms occur. The circularity of the system, as self embedding negates a circularity paradox by degree of expanding and contracting sequences while dualistic opposite states, such as positive and negative recursion, are isomorphisms of distinction itself.



The system can be visually proven strictly through line segments as spatial distinctions. Given this, to cycle back to origins, standard formalism is not efficient enough, a purely recursive sequence needs the operators embedded so that coherency is maintained and assumptions are disregarded. Positive and negative sequences are this foundational embedding. Given the number line evidences number as the distinction of 0 by degree of the space that allows said contrasts of the 0’s, which further allows distinction of said 0 and the number (-)1n, this meta-mathematics proves that not only is number distinction, but this distinct ‘is’ by degree of the occurrence of space. In these respects the standard separation between arithmetic and geometry, as separate fields, are effectively overlayed as one entity. Recursive sequences are not only standard arithmetic and algebraic expressions but effectively simultaneous geometric ones conducive to a 1 dimension linear lattice that is both folded and folding by degree of recursive self-embedding. In these further respects arithemetic/algebra are fundamentally geometric entities that are distinct by degree of spatial recursion. A simple conceptual equation of this summarizes this:



Distinction = Recursion = Space = Occurrence.



Proof, within this meta-system is justified by the act of occurrence itself where a mathematical philosophical claim can be made that occurrence is justification as proof. Distinction is the only reality and truth within this system where recursion is the occurrence of said distinctions. Any math, or logic, which by default uses a basic “unification” or “separation” type of operator (addition/multiplication/subtraction/division) is already embedded within said positive and negative sequential spaces. The recursion of line segments, both positive and negative spaces isomorphically of eachother, through eachother and within eachother is the proof, by degree of distinction of the system. Effectively math and geometry can be reduced to the sequence R(0→0)r[1] where this is a simple distinction as a line segment. This sequence, and the line segment by default, can be further reduced to a simple distinction of:

(0)1

Where (n) is a distinction and (n)n is the quantification of the distinction, a quantification of the quantification it could be said. This effectively is the recursion of number through isomorphic variation. And this distinction can go further by degree of using only recursive 0:



(0)0→0

((0)0→0)(0→0→0)

……

Where both number, the number line, and space is further formalized as purely recursive zero itself. No assumptions are required, only distinction by degree of recursive sequences as symmetry through repetition of 0. All number is effectively rooted in 0. All space is effectively rooted in a 0d point. By recursive sequencing as the line segment the number 0 and the 0d point are effectively the same distinction viewed isomorphically. In these respects the system has infinite compression.



*********

Relative to infinite compression new potential maths can emerge from said sequencing where there are various extensions that logically result:



Looking at standard exponents a recursion occurs in the same manner as that of addition upon addition is multiplication and multiplication of multiplication is exponents, expressed as the sequence of Rn(n). Exponents of exponents logically occurs next as: Rn(Rn(n)). In this paper such a number can be viewed as no longer an exponent but a "hyper-sequence": Rn(Rn(n))



Following the same logic a new mathematical operator must occur, in standard logic and yet within this recursive system no new operator is necessary as the symbols contain the operator as embedded. To go further, where there is compounded recursion of addition as argued for the standard mathematics operations, now there can be the distinction of embedded hyper-sequences as the recursion of hyper sequences: Rn(Rn(n)) to Rn(Rn(Rn(n))) as Rn((Rn)(Rn(n))) where a trans-hyper sequence occurs.



In these respects, and following these recursive dynamics, there are effectively infinite arithmetic functions where in standard terms infinite new operators would be required but within this system the same symbols remain.



Similarities are to Spencer-Brown, Pierce, Leibniz, Godel.



++++H. Post-Linear Hierarchy


"( )" context/set

"(X)Y context/set of context/set

"{X} differing order context/set

"Xy.z"

***X containing context/set

***y number of sets

***z degree of recursion/repetition

"-" negation/absence of context

*** Negation is subtraction of what is negated thus resulting in a relative absence thus effectively negation/subtraction/absence/negative ate four sides of the same logical square.

Termination of the sequence is its finite expression of emergence.

Reduction of a sequence is the finite contextual expression of the sequence itself as a context.

Identity is the context(s) of context(s) as a context. Context is synonymous to identity as context derives identity.

The operation is the same as operand as the operation is the recursion and the operand is the structure of the emergent recursion itself, in these respects the formalism is non-traditional as the standard operator operand dichotomy is reduced to emergent and dissolutive patterns.

The standard nature of syntax, boundary conditions, etc. of standard formalisms are non-appicable in a strict sense as said conditions are effectively contexts that induce identity thus resulting in the formalism being transcendental by nature.

The following 8 points observes the nature of context as effectively self-embedding as 'unfolding' within itself thus proto-formally expression context as recursive folding in topological terms thus identity, topologically, is the expression of the folded context in one respect, while synonymously in logical and mathematical terms is the structure of the sequence itself. In these respects associativity is expressed as but the fold/sequence itself:

(A)B

***Context A under context B

2. (B)C

***Context B under context C

3. (AB)C

***Contexts A and B under context C

4. (B)A

***Context B under context A

5. (C)B

***Context C under context B

6. (BC)AB

***Context B and C under context A and B thus context B contains itself

7. (((B)C)A)B

***Context B contained by C, C contained by A, B contains all contexts as itself

8. ((B)B)AC

***Context B is contained as itself through contexts A and C

((X1)X2 (Y1)Y2)Z2.2

((R1)R2 (X1)X2 (Y1)Y2)Z3.2

(((X1)X2)X3. ((Y1)Y2)Y3)Z2.3

((Z2.2)Z3.3 (Z4.4)Z5.5)Z{1}2.2

(((Z2.2)Z3.3)Z4.4 ((Z5.5)Z6.6)Z7.7)Z{1}2.3

((Z2.2)Z3.3 (Z4.4)Z5.5 (Z6.6)Z7.7)Z{1}3.2

((Z{1}2.2)Z{1}3.3 (Z{1}4.4)Z{1}5.5)Z{2}2.2

((Z{1})Z{2} (Z{3})Z{4})Z{2.2}

****

(A)B = (A)-A

(B)C = (B)-B

(AB)C = (AB)-A-B

(B)A = (B)-B

(C)B = (C)-C

(BC)AB = (BC)-B-C

(((B)C)A)B = (((B)-B)-A)B

***

((X1)-X1 (Y1)-Y1)Z2.2

((R1)-R1 (X1)-X1 (Y1)-Y1)Z3.2

(((X1)-X1)X3. ((Y1)-Y1)Y3)Z2.3

***

((Z2.2)-Z2.2 (Z4.4)-Z4.4)Z{1}2.2

(((Z2.2)-Z2.2)Z4.4

((Z5.5)-Z5.5)Z6.6)-Z6.6)

Z{1}2.3

((Z2.2)-Z2.2 (Z4.4)-Z4.4 (Z6.6)-Z6.6)Z{1}3.2

((Z{1}2.2)Z{1}-2.2 (Z{1}4.4)Z{1}-4.4)Z{2}2.2

((Z{1})Z{-1} (Z{3})Z{-3})Z{2.2}

*****

(-A)-B

(-B)-C

(-A-B)-C

(-B)-A

(-C)-B

(-B-C)-A-B

(((-B)-C)-A)-B

((-B)-B)-A-C

((-X1)-X2 (-Y1)-Y2)Z2.2

((R1)R2 (X1)X2 (Y1)Y2)Z3.2

(((X1)X2)X3. ((Y1)Y2)Y3)Z2.3

((-Z2.2)-Z3.3 (-Z4.4)-Z5.5)Z{1}2.2

(((-Z2.2)-Z3.3)-Z4.4

((-Z5.5)-Z6.6)-Z7.7)Z{1}2.3

((-Z2.2)-Z3.3 (-Z4.4)-Z5.5 (-Z6.6)-Z7.7)

Z{1}3.2

((Z{1}-2.2)Z{1}-3.3 (Z{1}-4.4)Z{1}-5.5)Z{2}2.2

((Z{-1})Z{-2} (Z{-3})Z{-4})Z{2.2}

*****

(-A)-B = (-A)A

(-B)-C = (-B)B

(-A-B)-C = (-A-B)AB

(-B)-A = (-B)B

(-C)-B = (-C)C

(-B-C)-A-B = (-B-C)BC

(((-B)-C)-A)-B = (((-B)B)A)-B

***

((-X1)X1 (-Y1)Y1)Z2.2

((-R1)R1 (-X1)X1 (-Y1)Y1)Z3.2

(((-X1)X1)X3. ((-Y1)Y1)Y3)Z2.3

***

((-Z2.2)Z2.2 (-Z4.4)Z4.4)Z{1}2.2

(((-Z2.2)Z2.2)Z4.4

((-Z5.5)Z5.5)-Z6.6)Z6.6)

Z{1}2.3

((-Z2.2)Z2.2 (Z-4.4)Z4.4 (Z-6.6)Z6.6)Z{1}3.2

((Z{1}-2.2)Z{1}2.2 (Z{1}-4.4)Z{1}4.4)Z{2}2.2

((Z{-1})Z{1} (Z{-3})Z{3})Z{2.2}

The predictability of the system is the expression of context across varying scales where prediction of absolutes is not fixed in the standard sense but rather prediction of the emergence of contexts across scales where the self-embedding of context is prediction as noticeable fixed-point invariance rather than standard absolute outcome of multiple emergent conditions. Predictability, in this system, is the emergence of fixed-point contexts as perceivable scale invariant patterns. The fixed point invariant is the context "(Y)" as an everpresent boundary conditions derived from the context that contains it, "X" as "(Y)X", where the sequence itself "(Y)X" is the defined context of the finite whole.

The nature of standard formalisms is not applicable as they are subject to the very same contextual dynamic patterns the system represents, thus the system is a non-standard formalism.




++++I. The Limits of Linear and Recursive Reasoning





The following is an example of the limits of linear reasoning by notion of symbols that can be viewed synonymous to emergent variables:



****The following formalism will use only the following symbolic operators that defined the distinction of the sequences. There is not premise or intent of establishing a fully formal traditional system thus the modality of proof will be that of emergent patterns by degree of the sequences themselves.



"L:" will represent a Linear Reasoning Chain.



"R:" will represent a Recursive Reasoning Chain.



"->" will represent "transition towards/change to/direction."

"( )" will represent context.







1. L: A

1. R: A



2. L: (A -> B)

2. R: (A -> A) -> (A, B, -A)



3. L: (A -> B -> C) .....

3. R: (A -> A -> A) -> (A, B, C, -A, -B) .....



4. (L ⊆ R):



(A -> ....X) -> ((A -> .... A) -> (A,B...X, -A, -B...-Y)



((L:) -> (R:)) <-> (((L:) -> (L:)) ⊆ (R:))



((L: A -> B -> C....),

(L: -A -> -B -> -C....),

(L: A -> A1 -> A2....),

(L: B -> B1 -> B2....),

(L: C -> C1 -> C2....),

(L: -A -> -A1 -> -A2....)

(L: -B -> -B1 -> -B2....),

(L: -C -> -C1 -> -C2....)) ⊆ (R: A -> A...)



5. R: (A -> A) ->

((A, B , -A) ->

(-(A) <-> (-A))

-> (B) -> (A -> B))



(R:) -> (L:)





There is only A



++++J. God as Inneffable and Effable: Beyond Being as Void, Through Being as Distinction



Void is ultimately the ineffable God and distinction is the image of the ineffable made manifest.



Void is the totality of all things, the transencendent unity as nothingness for there is no contrast or equal to the totality for it to be affable, thus is nothing, yet by degree there is only one totality. By nature void is transcendental by means of the emergence of distinction as the distinction of void itself. Emptiness and fullness require relation but only distinctions may relate thus the void is the potential of such distinctions as all things where fullness and emptiness are but emergent distinctions.



Void is distinct as void for it contains the potential to do so and must be distinct if containing all possibilities as potentiality itself.



The void as the totality is all things thus by nature is the distinction of itself as distinction is all things.



Void is distinct from the distinctions that unfold by degree of it being unity as nothingness in its absolute nature and the point of change, by which distinctions emerge and dissolve, at the relative. The distinction of the absolute and the relative is but multivalent for the relative voids interrelate as the absolute.



The relative voids are the same as the absolute by degree of there relations, the Absolute void is the same as the relative by degree of everpresence mediation. The relative and absolute void are but angles of perception.



The angle of perception is but the containment of attention itself where attention upon attention reveals void thus relegating the perception as but the distinction that contains attention and attention that by which perception emerges and dissolves. The same void of attention is the same void by which empirical and abstract distinctions emerge and dissolve thus the void is omnipresent attention where the perspectives that contain it are micro-cosms of the macrocosmic void and the macrocosmic void reflects itself through the microcosmic voids.



The self-reflexivity of the absolute void is in the emergent relations of the relative voids. God as both ineffable void and effable distinction results in God being both impersonal and personal; impersonal by absolute pure emergence of unmediated attention, personal but the emergence and dissolution of contained relational attention; impersonal by degree of pure distinction, impersonal by degree of relational distinction.



Given the nature of distinction being a self-embedding reflexive act and process the universal moral code that emerges is two fold: "you reap as you so" by degree of cyclicality and "unconditional love/self-lessness (emphasis on unconditional)" by degree of the absence of conditions of the absolute conditions void itself. Thus morality has inherent architecture within the fabric of being and beyond it.



The nature of distinction as process, conducive to and equivalent conceptually with change, necessitates a universal anthropmorphic base of sacrifice in one respect and non-anthropomorphic base as negation in the other. Sacrifice and negation are but two sides of distinction, one anthropomorphic and the other not. The universal nature of change gives emergence to this basic and fundamental underlying structure.



For God to truly be God God must sacrifice God for if God is subject to a God then God is not God as God is not all powerful, if God does not sacrifice God then God is not subject to anything then is not omnipresent. The sacrifice of God is the collapse of the void into the distinction which emerged from it, the sacrifice of God is the collapse of the distinction as return to the void; God must negate God unto God, God must sacrifice God unto God.



There is a circle with infinite circles within it and infinite circles between said circles. These infinite circles within, without and between results in a void and yet the circle is perpetually present as a self embedding fractal at all levels. The circle is there but it has no circumferance. The circle represents all things for by repetition there is symmetry in form, symmetry in the repetition of the form in time, and by symmetry a cycle occurs within itself as itself for symmetry is but the repetition of a limit unto form where the beginning and end trace to eachother as one and self-contained. All things are cycles by virtue of being distinctions, and distinction is a cycle by degree of distinction being embedded within distinction as distinction.



God is the Void as all things thus the nothingness beyond them for complete unity, as the totality is beyond the comparison necessary for distinct limit to occur.



God is the Universal Light of distinction for distinction illuminates both literally and metaphorically as what is distinct is illuminated by degree of its emergence.



God is the Universal Darkness of the relative potential of all distinctions both literally and metaphorically.



God sides with neither Light nor Darkness but favors light, favor ontologically being maintains, for that is what reveals God as God as God a distinction of the universal act of distinction.



Good and evil are but distinctions of actual and potential, good as the light of distinct actuality and evil as the potential for actuality the potential for good; morality is thus fundamentally transformative of darkness into light and the transformation of light into darkness as the revelation of the nature of the light. By degree distinction transcends good and evil as the central good, distinction transcends actual and potential as the central point of change.





++++K. The Book of Void





1. By opposition is there the space between.



2. By harmony there is the space of.



3. The space between the space of is the space of what is between.



4. The opposition of harmonies is the space by which they are.



5. The harmony of oppositions is the space by which they are not.



6. What is not is but the space of what is.



7. What is is but the space of what is not.



8. The space between spaces is the space of said spaces.



9. The space of the spaces is the space that is between said space.



10. Space through space as space is but space.



11. Space is the means by which space occurs as spaces.



12. The space by which space occurs is but the space as the space of spaces.



13. Pure space is indistinct, the distinction of space but further space, the distinction of space is the space the mediates spaces.



14. Space mediating space leaves space as a mediator thus mediation occurs through mediation.



15. Space contains space, the containment of space is but the condition of its own contrast.



16. Space through space as space is but space as that which is through.



17. The distinction of space is but the mediation of the distinct through the indistinct thus space is self-emergent limit.



18. To mediate is to direct, to direct is to contain, thus the mediation of space is the direction of it as limit within itself.



19. The direction of space is its limit thus by process of folding and unfolding does space occur as form through function.



20. The form of space is the process of its folding and unfolding.



21. The folding and unfolding of space is but the distinction of pure space as a limit.



22. Folding and unfolding is but a ratio as space is but its own ratio by degree of self-relation as self contrast.



23. The folding of space is itself as its limit.



24. The unfolding of space is its dissolution of limits.



25. Folding is but the emergence of ratio.



26. Unfolding is but the distinction of potentiality.



27. The potential of space is but the collapse of it as limit, the potential of potential is but the folding of space itself.



28. Space is potentiality.



29. The folding of potentiality is actuality.



30. Space is the medium of limits by there absence from which they emerge.



31. The emergence of absence is the emergence of the limit.



32. The presence of a limit is the space by which absence is and the absence of limit is the space by which presence is.



33. The space of attention on attention is the same space of the limit and its absence upon which attention is placed.



34. The space between what occurs is the space by that which occurs.



35. The space of what occurs are the spaces by which the space between them emerges.



36. Space is its own limit from which it emerges as the limit by distinction of its own space.



++++L. Proto-Identity as Emergence



Here is a symbolic argument:



There is a point, it is indistinct as there is only a point: ●



The point repeats and becomes distinct by the act of repetition creating contrast: ●●



The contrasting points are effective one point as many as the set is now a unified entity as a relation: (●●)●



The one point as many, is still one point thus repeats again creating scale: (●●)●●



This process repeats and as it repeats so does scale repeat: (((●●)●●)●●)



One scale exists relative to another thus contrast occurs by difference (●●●)(●●);



however one scale (●●●) contains the other scale (●●) as condensed where the difference is (●);



Further, one scale (●●) generates another (●●●) as expanded where the difference is (●);



The difference of ●, across expansion and condensation, reveals ● as the limit of the distinction itself as both that appears in accords to angle of another scale: ((●●●)(●●))(●●●●●)



● exists across scale as the limit of the scale by its own repetition;



the repetition of ● is the distinction of the point as the scale as the self reference results in self contrast and the self contrast results in structure as scale.



the repetition of ●● is the distinction of scales as the point as self-reference results in self-containment and the self containment results emergence of scale.



Scale is identity as context or condition as the boundaries by which identity is derived reflexively: the contained identified by what it is contained by, the container identified by what it contains.



The distinction of a thing is its repetition, its repetition is self contrast, its self contrast is self containment, its self containment is its emergence as identity.



Identity is purely emergence, the foundational identity is a single point as all limits, intuitively or observationally, are both reduced to (a) point(s), converge to (a) point(s), or build to (a) point(s). In these respects a single point becomes transcendental symbolism of ontological realities, as the progressive emergence of ● results in corresponding limits that are moved beyond without negation of origin (evidenced by the symbolic formalism).



Distinction is repetition by self contrast that inversely results in the whole of the relation as self-contained, as the self-contrast is a self repetition unto condition, thus identity is derivative of itself as process as identity becomes a scale of process(es) with the scale being a relative meta-scale for another scale.



The identity of ●● is derivative of both the identity of ● and the identity of ●●● as:



●● contains ●●● as both ● (the foundation of ●●●) and (●●●)(●●●) {as ●●● is reducible to ● from another scale}.



●● contrasts to ●●● as both ● is the difference and ●●● is reducible to the contrast of (●●)(●●)(●●) {as ●● is reducible to ● from another scale}



Identity is the limit of process in accord to the scale(s) external and internal of said process thus effectively is emergence by degree.



Emergence is process, process is scale, scale is identity; the identity of this assertion is the ratio of the applied meanings in natural language by means of symbols, the proto-logical symbol of language is ● as ● is the most primitive symbol of beginning, conclusion, unification and divergence, summarized fully as transitional, in accords to context of use.



The next degree of this emergence is the basic protological symbol of the line segment which emerges from ●●



There is a line segment.



The line segment is composed of infinite line segments, which in turn are composed of infinite line segments;



The line segment composes infinite line segments, with each line segment composed infinite line segments.



The level of division of the line segment retains the division as the line segment itself across scale as the line segment being the degree by which the line segments are divided as line segments.



Division requires that which divides, the limit of division is that which divides thus resulting in division as self-scaling of what is dividing within the context of that which is divided.



Division as self scaling inversely result in magnification of what is dividing for a line segment X which contains line segments Y is effectively Y repeated multiplicatively as the whole line segment X as scale.



Division and multiplication are inverses, these inverses are fractal states unfolding by degree of compression (division) and expansion (multiplication).



What remains is scale invariance as the fixed point of division or multiplication resulting in scales; a line segment as two line segments is the one as a ratio of itself, two line segments as one line segment is the two as the ratio itself.



This scale invariance results in compounding of dimensions as the line segment is 1 dimensional by nature. The inversion of one line segment results in a horizon and vertice, the inversion of horizon and vertice results in depth, so on an so forth as dimensions occur holographically as each dimension is but the scale invariance of one that occurs recursively, the inversion of dimensions is but the inherent contrast induced by recursion as argued prior.



The nature of material phenomena becomes that of recursive scales that correspondingly results in a particle/wave duality as relative scales of the other, recursive by degree of structure (a particle repeating across space, a wave as repetition through alternation) with the field be holographic dimension of the two.



Number occurs as the distinction of space, in use obviously, but as structure as well where the recursion of points is the recursion of number, the recursion of number resulting in the dualisms of addition and subtraction (where positive and negative are but embedded addition and substraction, the recursion of addition/subtraction as multiplication/ division, the recursion of multiplication/ division as exponents/roots.



Unifying the results is in that act of awareness itself as awareness is observed as nothing, and indistinct point, when observed, and the objects of awareness are the scales by which awareness is imprinted and contain through said scales in a manner that further loops the dynamic between subject and object.

++++M. Degrees; Multivalent Non-Dualism

By degree there is and what is not remains.

To claim is the measure of a thing, the unfolding of how is what is distinguished as the thing, memory is its sphere.

To see is but the appearance of itself, by degree comes memory.

Claims are original by nature, with measure is the revelation of sight.

Depth is the change of what is up and down, left and right, by revelation does sight become seen.

Knowing is in accords to connection and seperation, connection and seperation is that by which there is degree of claim.

No remnants and yet what is unveils, unfolding is allowance.

A sphere is but its own center when nested.

In accords to the line is there by which appearance becomes justified.

By change claim occurs, by claim the direction of change.

To seperate and connect is but inversion of what is, the ripple by which a structure reveals.

The revelation of the remnant is the memory by which form becomes true.

Cycles of cycles and yet a line is maintained, by direction attention flows.

The degree of a claim is the claim as to the degree, what flows becomes distilled, what is distilled ends as the whole.

By inversion does symmetry become induced and yet patterns remains hidden within itself.

Awareness is true act by which purity of truth is given.

Knowing not is but claim of degree, by the angulature of sight does reality unfold in accords to what is held.

It folds in cycles so that the sphere is but hollow, by what is hollow does form claim emergence.

Inversion is relation of time for how the form is becomes the mode of transformation.

By sight what is known is known as known and yet this knowing is but a shard.

To see is to assert and angle by which the thing is contained within degrees.

Repetition and structure is induced, time is folding of space.

By change there is, what is not ceases only by degree.

Reveal and the angles protrude so that truth becomes an emergence of intensity.

By parts things are, and yet by parts self reference is founded.

To contain is to induce symmetry, to induce symmetry is to unify the layers.

Time is the measure of itself by nature of the change within its space.

Assertion penetrates thought, the opening of thought is the revelation of the container.

Induction of the many is by measure the measurement itself, deduction of the many is by measure measurement nested.

By the unification of layers is there a new part.

What is contained is the act of the container itself.

By time there is repetition, the cessation of time is the cessation of the order emerging.

By the container that which is knowable is known, by the degree it is contained reveals what is lacking in the contained.

To induce is but revelation of what is hidden.

To see in parts necessitates many wholes that are by degree of lack.

Emergence is its own truth and yet truth always emerges.

A group is but one thought from many angles.

Revelation is in accords to the depth of value of that which is aware, value holds little law for it is the only law.

Hidden truths require depths, image remains regardless of the depth.

Absence is universal where a thing is, by measure there becomes what cannot be measured and yet this is the measure.

Know is to emerge from that which it is.

Unity is but the seperation as an other.

By value does space fold for by value there is given weight to the structure of spaces.

Image is the occurence of its own emptiness.

Where a thing is does the potentiality reveal itself as everything else.

"Is" reveals by degree, yet by degree there can only be what is being.

To seperate in accords to measure is a revelation of value.

To claim is but space merging within itself, the absence of knowing is sought as the measure.

Void claims as all things change.

Where there is potentiality comes the act of what appears as an act.

To be is to make by decree, to make by decree is to make by degree.

Revelation requires the hidden void.

Merging voids is how things are in accords to measure.

Change is constant, nothing is cause but the emergence of potential merged upon potential.

Seperation remains and yet by seperation is inverse unity.

Assertions are the only form that is universal, the means by which space comes from itself as within itself.

By absence is revelation valuable, absence is the universal pattern by which a thing is.

Measure measurement and symmetry remains.

By consistency there is a pattern, change allows pattern to be by what it is not; this is a ratio.

Inversion is transformation itself, to transform is too merge sight as the thought.

Value is in accords to what ceases so that things may be.

A universal pattern would appear as nothing, by nothingness is there repetition.

Symmetry in accords to measurement is required only by degree of directed insight.

For a ratio there must be inversion, a ratio is inversion.

Merging of the voids is the emergence of a new degree, sight is maintained but necessity becomes free of itself.

Cessation of cessation is but being as cessation.

Nothing emerges as its own degree of measurement, the point by which a thing becomes.

A container of containers is but a container containing itself thus symmetry is containment.

A thing between things is a thing thus a thing is the ratio by which things are.

Void through void is but void, the absence of absence is but absence.

Through negation is negation negated, by degrees of positive is there a negation of positive.

To reference referencing is but reference, what is contains itself as it is.

Through repetition is there variation, by variation there is contrast that allows repetition to occur.

By potentiality is there actuality as the folding of said potentiality upon itself.

By addition of addition is there subtraction, by the subtraction of subtraction there is addition.

By cycles there is progression, everpresent progression is a cycle of variation.

Symmetry allows for distinction of the thing, by distinction of a thing is the assymetry of what a thing is not.

What is not unfolds what is.

By folding there is transformation and yet the fold is the state of a thing.

A thing merged within itself becomes its opposite, the opposite merged within itself becomes its opposite.

There are only opposites and the opposite of the opposite.

Order is emergence for by emergence is the absence of absence as symmetry.

By change is there structure for change is the emergence and dissolution of structure and yet structure always is.

The static is the medium of change, change is what allows mediation.

Thought within thought is but a new thought of the old.

There is only the same and the sameness of the same.

Chaos is the emergence of what is not, by absence there is infinite potential.

Transformation is the space between spaces and yet space remains as space.

What mediates transforms, the transformed is the mediation of transformations.

By thought there is an emergence, emergence is thought itself.

Chaos and order are interdependent as forms, by forms a relationship emerges.

Forms are fundamentally space, space is transformation.

To mediate is to change, to change is to establish what is maintained.

Emergence is how thought occurs, thought merged within itself is emergence of thought.


Distinction is seperation and connection, seperation and connection are distinct.

By form there is distinction, form is in and of forms.

The establishment of what is maintained is the cessation of what was maintained.

Merging and emergence are mediated by space.

Space is of the senses, space is of the mind, space is between the senses and the mind, the senses and the mind are one by space.

To observe form is for observation to take form.

Forms mediate forms as form and yet all that remains is form.

Space is form, space is the absence of form.

To occur is to transform space.

By degrees there is and is not, by is and is not there is and is not degrees, degrees are but of degrees.

Observation is the form of itself for there is the observation of observation as symmetry by which observation emergences.

By awareness is observation seen as itself, void as but infinite cycles within and without, a cycle seen as nothing.

By limit is there an occurrence, the absence of one limit is the limit to another.

Occurrence is the emergence of boundaries and the dissolution of boundaries, yet this emergence and dissolution is a boundary.

By observation there is form and observation takes form, form is the act of observation itself.

To be aware is to see void, infinite things occur through infinite absence as each thing.

To derive a rule is to derive a process of being, as process of being is but the being.

By emergence and dissolution limits are everpresent, everpresent limits reveal but nothingness within them by which they are to be.

To observe is to be, to be is to observe; being is observation and yet being in is because of limits.

By what a thing is not is what a thing is, infinite absences converge upon a point.

Laws are the formation of processes by degree of insight, to derive as process is to observe as unfolding by degree of directed change.

Pure limit is void, void contains all limits, the emergence of limits is the collapse of void upon void as the emergence.

Observation and being are but the limits of each other as the limits that allow both to occur, observation and being are the limit itself.

By the degree of absence there is what is actual, by the degree of the actual there is what is absent, by the actuality and absence of degrees is the degree as self-folding by inversion.

The emptiness of a limit is what generates limits, by limit is emptiness contained.

The cycling of emptiness is its inversion as the limit, the cycling of limits is its inversion as emptiness; inversion remains.

By awareness is there the knowing of awareness, reflection is how being is structured.

Degrees are absolute as self contained, by the change in direction is a thing emergent, change is what allows degree to be emergent.

Generation is the absence of absence, generation is the potentiality of potentiality, generation is the void of void, generation is recursion.

To invert a thing is to change the act of observation, by inverting observation a thing is changed.

Through repetition there is symmetry, through symmetry there is reflection, through reflection there is order, through order there is as is.

By the direction of change does form occur by degree of that direction.

By repetition there is inversion for by inversion is there the space by which repetition occurs.

The space between observer and observed is the act of change, the space between the observer and observed is the space of the observer and observed.

The nature of "is not" is not as "is", by symmetry does the space occur by which occurence occurs.

The direction of change is the form as the direction of change.

To repeat is to contain, to contain is to be contained by the act of containing.

The observation of observation observes space as observation itself.

The observed is observed as the space of the observed itself.

The nature of nature is but unfolding as the nature.

By direction there is limit for direction is containment.

By symmetry there is the emptiness of said symmetry, the absence of emptiness within symmetry is purely nothingness as perfect symmetry.

The space of observation is the unfolding of observation, the unfolding of observation is but space between space as but space.

By space there is emergence of observation for observation occurs by space.

To contain change is to direct it.

Absence of absence is a cycle as absence.

By unfolding of space does space contain itself.

Change is the emptiness of a limit.

Space is self-evident by the awareness of awareness as this awareness is revealed as space.

To change the container is to contain the change of the container.

The positive of a positive is a progression of absence.

To fold is to give form, to give form is to repeat, to repeat is to fold.

By emptiness does change emerge as the limits of a thing.

Self-evidence is the resonance of patterns between observer and observed.

To contain is to form, to form is to direct, to direct is to change, to change is to reveal the void.

By recursion there is inversion, by inversion there is emergence, by emergence there is recursion.

What is empty is but the potential of further form.

Self-evidence is the revelation of patterns within the self.

A container is that which allows the contain to exist in dimensions.

Form is a container of void, the voiding of void is form.

To invert is to contrast, to contrast is to create a dualism, to create a dualism is to create a paradox, to create a paradox is to create a ratio, to create a ratio is to reason; by paradox there is only reason.

Self-evidence is evidence of a self, evidence of a self is self-reflection, self-reflection is self-recursion by means of inversion.

The cause of one limit is the effect of another, cause is ever present potential contained by the effect of the form that emerges.

By contrast there is what is and what is is not what another thing is.

Self-evidence is the emergence of pattern, emergence of pattern is the dissolution of another pattern.

Emergence and dissolution is inversion and yet inversion repeats.

Cause is everpresent under the effect as everpresent, cause is but the degree of an effect and effect is but degree of the cause.

What "is" "is not" relative to another "is" that "is not" to what "is" and yet regardless of what "is" and "is not" "is" and "is not" underlye all things.

Self-evidence is a distinction of the pattern within an observer, this pattern is beyond true or false as the pattern reveals true and false according to what it aligns with.

For one limit to progress to another limit necessitates a variation and yet the variation of the limit remains as but the limit.

Non-dualism is negation thus non-dualism requires non-non-dualism, unity and multiplicity are interwoven and collapse to the 'degree' itself.

By patterns is a self observed, thus a self is the merging of conditions as conditions merged are but patterns as a new pattern.

The variation of unity is but everpresent unity, the unity of variations is everpresent variation, everpresence is the distinction of unity and variation.

By negation is there a revelation of layers, by affirmation is there the creation of layers.

Layers within layers reveals only layer, within an appearance is an appearance.

To see to to distinguish, to distinguish sight is to see sight.

By unity and multiplicity is there emergence of degree, unity and multiplicity are degrees.

Revelation is a new angle of awareness.

Appearances are layered within, through and of appearance.

The layering of appearances is the appearance of layers.

For that which is within, through and of that there is but cyclical progressive inversion of inversion.

By distinguishing is there occurrence of form, by the occurrence of form there is assertion, by assertion there is distinctinguishing.

To provide degree of observation is to reveal, to reveal is to give observation, observation is revealed as but degree.

Appearance is but layer, layering is the occurrence of dimensions, by dimension there is structure for structure is the repetition of layers and layers are through layers.

The repetition of inversion there is the repetition of change by progression and yet repetition necessitates a structural constant.

Inversion is structure by degree of repetition of it, yet repetition requires inversion if there is to be the space of what is repeated.

Revelation is the occurrence of structure, structure is but the degree of other structures and other structures are but the degree by which a structure is unfolded.

Degree occurs through degree as a degree by the point by which it unfolds as itself and yet self-contained by its own layering.

To cease repetition is to invert one repetition into another and yet what is within the various appearances is but repeated appearances that repeat.

By awareness there is the unfolding of awareness as the space by which emergence and dissolution of it give degree.

The mode of a thing is its direction and this direction is the containment of change by the cycling of it within a given degree.

The repetition of the degree is but a degree within a degree as the repetition is but a degree of another repetition.

Space is everpresent cause where everpresent effect is its unfolding as form thus degree is everpresent as the unfolding form itself for one form is the degree of another, the degree through another, the degree within another.

To be aware is to be empty of pattern for pattern contains awareness this revealing its limits, the absence of one limit is the presence of another.

To repeat is to cycle, to cycle is for form to emerge for form is the repetition of limits and the cycle thus contains itself infinitely within as without through the void from which it emerges.

Cause is emerging conditions merging, the merging of conditions acts as a new cause with corresponding effects, cause and effect are multidimensional linearism.

The emptiness of pattern is the potential of a further patterns, the emptiness of pattern is contained by pattern, perception is a pattern.

Cycles expand and contract, to expand and contract is linear progression or regression, the repetition of expansion and contraction is a cycle.

The relation of conditions is the relationship of relationships as a condition is a set of relationships, a container of transformation by degree of its claim.

Infinite patterns within and without is but void, the perfect pattern contains all patterns as nothing, perfection is a single point.

Progression from one point to another is the cycling of the point as the repetition of the point, a point is the mediation of change from one thing to another.

Conditions are degrees for a distinguished relationship is the angle by which events are observed as changing.

A pure pattern is a point, by recursion of a point is there the distinction of space; the point as all potential patterns observes recursion as the recursion of all potential patterns.

Progression is linear, constant progression is a cycle.

A point is that which mediates change, by change there is distinction, the recursion of mediation is change within change by self-contrast that allows simultaneous symmetry.

The degree by which there is an occurence is the angle by which it forms, by angles of occurence there is structure.

A point is infinite potential patterns, a point is composed of and composing infinite points, the single point is indistinct, many points are distinct, to distinguish is to observe both one and many.

Change is alternation by inversion, alternation is a cycle, inversion is linearism.

Degrees within degrees are angles within angles as conditions within conditions as "within" within "within".


The depth of truth is but the degree by which it appears, the depth of falsity is but the degree by which it appears, the depth of appearance distinguishes truth and falsity.

By claim there is structure of thought, by structure of thought is there the potential to claim.

Depth is the change of a thing by degree of appearance, degree of appearance is but a fractal state.

To claim is for boundaries to occur, the occurence of boundaries is to unfold reality.

By appearance is there form, by form there is a mode of change, by change is appearance reveal for further appearances within the appearance.

Emergence is but distinguished by its cessation, the completion of change is the negation of limits.

To rationalize is to establish ratios, the ratio of "is" and "is not" is everpresent across all that is distinguished; paradox is the emergence of contrast thus form itself.

Space between spaces is but space as self-distinct, self distinction is self-symmetry.

The assumption of an emergence is an emergence of an emergence as assumption emerges, emergences merge within themselves as a new emergence.

If all is assumption than assumptions are assumed thus the claim that alls is assumption it is not accurate.

The distinction of 0 is a single distinction, the distinction of 1 distinction is 2 distinctions, he distinction of 2 distinctions is a third as a fourth as a finite unto infinity; the distinction of the infinite is a single distinction.

The distinction of 1 as 2 distinctions, 1 and the distinction of 1 as 1, results in the distinction 2 and 1 and the distinction of the space between 1 and 2 as negative 1 with simultaneous infinite fractions as but the fractal space itself as 1/n multiplied by n/1.

///////////

The recursion of an emergence are but the absence of emergence emerging between emergences as but an inversion;

by inversion there is contrast as a dualism with containment of the contrast by recursion;

by containment there is a degree as context and self referentiality of the container through the contained;

by context there is the emergence of further recursion where self-referential fractals result as contexts with context;

by context there is relation and by relation the emergence of cause as the context itself where effect is further context as further cause;

by causality there is recursion so that cause is repetition as symmetry, and yet by degree one cause is the effect of another as the recursion of causality is a modality by degree;

by modality there is degree and by degree there are relations merging as much a new emergence, modality thus inverts into its dualistic opposite so to be distinction;

the recursion of modality is the recursion of cause and effect as but self containment of its inversion so that distinction is a fractal state among all emergences;

by distinction there is dualism and by dualism there is paradox and paradox there are ratios, ratios depend upon relation;

by ratio there is paradox and the contrast of paradox is contradiction and regardless emergence of degree remains;

the paradox of contradiction is that the contradiction requires paradox so to be contradiction;

the contradiction of paradox is that the paradox contains contradiction so to be paradox;

degree is but paradox for the part contains the whole and yet the whole exists because of parts, degree is but the context of observation;

the observation of degree is the observation of context, context is what allows observation to emerge;

observation is but a context of itself as the context which emerge from observation are contained by observation.

True and false are patterns in accords to values, their fundamental nature is that of a claim for the nature of a claim is that of a limit or boundary.

To percieve is to distinguish patterns, patterns are cycles of limits, to percieve is but a cycle, perception of perception is the cycle within cycles.

A cycle is the repetition of a limit, a limit is a cycle of a point, a point is infinite cycles within and without as void, void is the potentiality of cycles, potentiality of potentiality is the cycle as actuality.

True and false are claims, the truth or falsity of a claim is a claim within itself, only emergence remains.

The emergence of truth is true, the emergence of falsity is true, emergence remains.

Repetition is the cycle of a limit that is directed linearly.

What is considered true and false are but degrees of patterns, claims underlie truth and falsity but claims are the establishment of patterns.

To distinguish is to observe, truth value is grounded in distinguishing, by distinguishing there is identity.

Identity is the emergence of relation, a relation requires a space of what is and a space of what is not so that a relation can occur.

Identity is dualism, dualism is the inversion of is and is not, by inversion there is limit, limit is recursive, Identity is recursive inversion limits.

By the limit of a thing is the grade of another, "what is" is the grade of "what is not" and "what is not" is a grade of "what is".

By Dualism there is gradation of emergence, by emergence is the limit as dualistic.

Recursive dualism is recursive inversion, recursive inversion is the recursive space by which there is process.

By process what is occurs through what is not, what is not is contained by what is, process reveals gradation of what is and what is not.

Gradation is recursion, gradation is degrees, the recursion of a thing is the emergence of degrees, as a thing repeats so does it occur by gradation.

A unity changes by degrees and yet is maintained as a unity for by a degree there is a unity yet by said degrees is the unity as many but self contained.

For a degree to occur a unity is emergent but a degree is but one of many, as it requires relations, thus the unity of the degree occurs through its inversion as the many.

Many degrees are but the degree as self contained as many degrees are but an everpresent one degree, each degree is but one contained by the other thus one is contained by one.

Degree is but a limit of how a thing unfolds, the direction by which it unfolds is how it is a unity.

The recursion of degrees is the recursion of a unity as but many, through gradation, and yet the recursion is but a degree by which the unity is self-contained.

Measurement is always by degree, measurement is the act of observation by the emergence and dissolution of limits.

The ratios of things, the degree by which paradox and contradiction enters insight, are but the event horizons of awareness.

To derive a paradox is to derive unity, from contradiction oppositional multiplicity, paradox and contradiction are but the degree of inversion between unity and mulplicity.

Paradox and contradiction are dualisms of eachother, dualisms of themselves, yet dualism remains and from which ratio emerges.

By the degree of thing is there an appearance by which to measure, to measure is to fold appearance, to fold appearance is to rationalize it.

The event horizon is the distinction of is and is not as but distinctions and these distinctions are seen as a singular distinction.

By inversion there is clarity for clarity requires contrast of that which requires inversion.

A dualism transcends gradation as each grade is a relative dualism, gradation transcends dualism as there are many degrees by which dualism occurs.

By degree there is the appearance of degree and by appearance of degree there is the appearance of appearance.

The horizon of an event is but the converge of opposites upon a single limit, transformation is integration.

The clarity of a thing is its transparency, one thing transforming to another leaves the thing transparent by nature of change.

Gradation and dualisms are but gradations and dualisms of eachother; proto-scientific measurement is embedded fractal processes.

The appearance of a thing is its limit, the limit of a thing always appears as the thing.

The limit of the real and unreal are but the event horizon, the limit of the event horizon is the event of limit.

Transparency is translucence, translucence is the observation of a boundary by which reality changes, this boundary is transparent void for a crystal is a limit by degree of its see through quality.

By fractals is a thing self-contained at all levels through all limits, space within space through the space between spaces leaves reality as but fractal for space derives all forms.

By limit there is emergence and emergence is but a container of limits by which it contains itself as limit.

Reality and unreality are but limits, but limits remain thus reality and unreality are both real and unreal and neither real nor unreal and yet “and” and “neither” are the unfolding of the limits of real and unreal.

Transparent void is but transformation, transformation transforms into negation and affirmation
and negation and affirmation are but of transformation.

A fractal is but a ratio within a ratio as a ratio thus ratio is process.

The limit of emergence is dissolution and the limit of dissolution is emergence, the limit of limit is the event, the event is but unlimited void.

By limit there is real and unreal and yet limit is real and unreal thus limit is self-contained infinity.

By transformation is there simultaneous negation and affirmation, by simultaneous negation and affirmation there is event.

Measurement is process as unfolding.

Unlimited void is unlimited by its recursion of its own self-contained degree by degree of said recursion as a degree within a degree, unlimited recursive void is but void as containing itself as complete.

To affirm truth or falsity is to make a claim, to negate truth or falsity is to make a claim, to negate or affirm a claim is to make a claim, by claim there is claim.

The transformation of thing is its limit, the transformation of a limit reveals a limit as but a process.

“Is” “is” because of “is not”, “is not” “”is not” because of “is”, “is” “is not” as “is not” “is”, but “is” “is not” not because “is not” “is”; what remains is paradox and contradiction and yet a paradox is not a paradox but a distinction and a contradiction is not a contradiction but a distinction.

Paradox and contradiction are but distinctions, the paradox of distinction is that it contains itself, the contradiction of distinction is self-contrast; by self contrast there is self-containment, by self-containment there is self-contrast, but self contrast and self-containment are but distinctions.

To observe degree is to observe the contrast of the self emergent and the exteriorly emergent, degree is but emergence and this emergence emerges in degrees.

Self emergence is but a direction beyond the point of emergence, self contrast is but a direction to the point of emergence.

Containment is but the inversion of the contained to the container, the inversion of the container to the contained.

To observe degree is to observe the contrast by which observation is both known and unknown by the limits of the degree.

Self is but a point of awareness, self containment is by degree the awareness of awareness where awareness is but a degree of itself.

By containment is there claim for claim requires the container and the container.

To observe contrast is to the observe the degree by which limits are mutually defined as a new limit.

The limits of known and unknown are eachother, limit remains thus unknowing is as rational as unknowing.

Awareness of awareness is the self-containment of awareness, but self-containment requires what is beyond it so to be distinguished as containment.

To claim is to establish limit by degree, by the degree of claim is there the limit of it.

Contrast reflects opposition, opposition mutually defines thus contrast is the limit of itself as opposition is dually the limit of itself.

The hierarchy of knowing results in a hierarchy of unknowing, a hierarchy remains by degree but effectively a limit remains as between above and below.

The generation of a limit is a generation of a law, the generation of a law is a generation of process, the generation of process is a generation of limit; generation generates generation, this is a new generation.

The limit of a thing is the thing, by claim there is structure.

A limit is but a degree to another limit, limit is contained as itself but is beyond itself as what is contained contrasts to what is not.

Hierarchy is cycles within cycles, transcendence is but centering, a cycle contains its center from which the cycle emerges and dissolves.

Laws generate laws as generation is its own law as many.

The emergence and dissolution of limit maintains the limits of emergence and dissolution.

Structure is but of degree for by degree is there structure and the structure of a structure as a degree of it.

Up is a relative down, down is a relative up, one dimension is a relative two; degree remains.

Law is the process of a thing justified as its occurence.

The limits of emergence and dissolution are the recursion and inversion of them.

A degree is by how a thing emerged within a context for by context is the degree revealed as a degree.

1 dimension is a relative 2 as up/down , 2 dimensions is a relative 4 as up/down/left/right, 4 dimensions is a relative 6 as up/down/left/right/forward/backward; relativity is but the ratios of 1 as self dividing and multiplying as recursive halving and doubling of itself as degrees.

Cycles invert to other cycles, this inversion is a cycle.

Degree is generation of limit, limit occurs a a degree of generation.

***
***
1 degree as 1 degree through recursion is but 2 degrees by recursion of the 1 where 2 has an absence of a singular 1 as -1;

2 degrees is 3 degrees by the 1 degree from which it comes, -1 degree as -1 degree through recursion as -2 degrees by recursion of -1 where -2 has an absence of a singular -1 as 1;

2 degrees is 4 degrees by further recursive self-containment grounded in the 1 degree self-contained recursively as 2 degrees where 4 has an absence of 3, 2 and 1 results in -1, -2, and -3 degrees;

1 degree to 1 degree is but 2 degrees as but 1/2 of 1 degree for 1 and 1 as 2 is but 1 as its half, the 1/2 degree to the 1/2 degree is but the reflection of 1/2 and 1/2 as but both 1/4 and 4 for 1/2 is a degree of itself and 4 is but the degrees by which 1 is self reflected;

degree is but a reflection that is contained as the process of reflection, 1 is a degree.
****

+++++++

The point is indistinct in itself, distinct by recursion, this distinction is its self contrast that induces self symmetry through repetition further by said degree of relation as self contained by said repetition;

as the point is its own foundation that contains its own space that allows said distinction of itself from itself and yet as itself, thus is its own condition by degree of modal self contrast that defines itself where the repetition is structure and its inversion is what it is not as indistinct unity and yet its multiplicity is self-reference as its own containment;

the relation of points is but the space by which it is is own fractal, as each distinction of points is but a fractal space that allows unity within distinction of non-unity, that emerges through its inversion from one to many and many to one;

by the recursion of the point is its distinction as the relation by space itself by emergence as self-folding where the point provides its own conditions as a thing in itself as everpresent distinction by degree of space emergent;

the distinction of said space is the emergence of awareness as the distinction of the point itself for by awareness is distinction as itself;

the point is but infinite patterns as points yet but one thus contains its own self contrast as revealed to be void given infinite patterns within patterns is but a single indistinct point. The recursion of the point is its inversion through containment within itself thus the distinction of context is but itself through relative degree of its recursion, distinction of the point is but what it is not as unity and yet the unity of the point is pure distinction;

a point is but a degree of itself as its recursion results in repetition thus a gradation of unity, the multiple distinctions of the point is but its own relation as distinction remains transcendent across multiplicity as a multivalent unity;

the distinction of the point is but generation of the point by degree of recursion through self-inversion as unity to multiplicity and multiplicity to unity where unity and multiplicity is but degree of self-relation through inversive self-contrast as both its own distinction and the distinction of relationship from which modality occurs;

By the distinction of a point as its own emergence through multiplicity by which a single point is distinct comes relationship by which it occurs in fractal degrees within said relationship by degree of each point within the continuum being a gradation of itself through a division that multiplies and a multiplication that is a division as many points are but the simultaneously division and multiplication of it;

By gradation of the point is there a continuum that effectively results in dimensionality by direction, gradation is change and said change is directed where the direction is determined by the relationship of one point as many, repetition is unity and multiplicity as a multivalent non-dualism;

through gradation there is modality as each relationship, as a set of points, is a fractal within the continuum of points thus modality is recursive as fractal states, through sets of points within sets of points, where each state is but the self relation of the point as both a part and whole by degree of the repetition of said self contained relationships;

Modality is recursive and by recursion is the modality both a cause and effect of other modalities where a set of modalities is a relative modality and a relative continuum that unfolds both, in these respect a modal continuum occurs as both generated and generative of the distinction of the point;

By degree of relation of points does space occur as recursive modal point sets as a continuum where space is continuity of points by which space is but a point continuously occuring as recursion;

the gradation of a point is but its entropy, yet by entropy does the point multiply infinitely unto a collapse unto infinity as a unity where a single point emerges as but its own infinite merging;

the gradation of the point, by recursion, is its reflextivity by self reflection from which the space of itself emerges through self containment, through degree of the point as but sets of points does its own self-context occur as nested sets by nature of relationships of points;

the repetition of the point, and the repetition of sets of points as fractal degrees conducive to modalities, is but internal self contained symmetry as repetition is symmetry;

recursive modal sets is but a higher self symmetry of the point thus modal sets are reflected across modal sets where the symmetry occurs as emergence of said modal sets by degree of the continuum from which a transformation of modal sets occurs by inversely becoming a new modal set;

the finiteness of said modal sets within modal sets is but change relative to other modal sets, by degree of a continuum of transformations relative to others, thus temporality emerges;

by temporality does the modal set become a fraction of another modal set thus probability as ratios of actual to potential continuums;

this distinction of probability is but the modal set of but an information node as information is rationality by degree of emerging and dissolving ratios;

the modal set is an operator by degree of being a relative point from which recursion emerges and dissolves, this emergence and dissolution is self modification of the modal set as the point through point as points thus the point operates as a multivalent non-dualistic process;

the multivalent non-dual process of the point relegates the distinction of the point as the distinction of progress itself, thus the point is not a fixed entity but rather a process of emergence and dissolution embedded within its own process as distinct;

the collapse of the point is what allows the point to be distinct and non-local as emergence and dissolution occurs across all modal sets of the point as ever present cause and effect where said modal set is but a fractal ratio of itself that allows self-contrast to occur across multiple dimensions simultaneously;

the modal sets of points are but the comparison of other modal sets by which the expansion and contraction of space occurs relative to other sets, by the modal set being a gradation of the point through a continuum does space occur and yet one space relative to another, as one modal set relative to another, results in a relative hierarchical size of modal sets by degree of contrast thus notions of hierarchical size effectively are reduced to spatial contrasts that inevitably are but degrees; the hierarchical size of what is distinct is but the self-distinction of the point thus hierarchy is not just composed of degree it is a degree where the only distinction of it is multivalent nondualistic process;

the point as a distinction multivalent non-dualisitic process is but a degree itself as multivalent non-dual process is but a degree and yet by degree distinction is ever present as emerging and dissolving degrees with emergence and dissolution being but degrees, multivalent non-dualism is but self-contained degree and yet by degree there is multivalent non-dualism as distinct process;

the point is awareness unfolded upon itself as the black-light for the awareness of awareness reveals black nothingness and yet the distinction is light itself for the distinction of nothingness is distinction as somethingness and the absence of light is the distinction of absence as light;

light and dark are but unfolding degrees by which each is but the point of the other by degree of observation for light and dark are distinctions of degree where observation is but self-folding degree;

Awareness is but an indistinct point until directed upon itself and become a distinct point as aware is but a point and the awareness of awareness is another point as the self-distinction of it, the evidence of this is the distinction of awareness of awareness being recursive void;

Awareness of an object is but awareness of limits which are composed of points as awareness focuses upon a point of the object from which the object unfolds as further relative points as the limits of the object itself, this is point recursion;

Awareness of objects is the awareness of a set that is the focal point from which object emerge and dissolve, change is the recursion of certain limits, within limits that emergence and dissolve from void, this void is the everpresent self contained point;

By the point in itself is there void, the inversion of the void into voids is but the point as degree from which which relation of the degrees occurs as a paradox of self-contrast through multiplicity of voids and yet the multiplicity of voids is but symmetry as a cycle that is both emergent;

from which degrees emerge as a process that relates the cyclical degree of the voids as a modality, a process in itself by which awareness is self-aware under the modal degree of observation;

the point is but self process through inversion unto the process of degrees that recursively process as but the act of relation of points as multivalent unity where variation is the paradox process from which distinctions emerge;

these processes are but the act of generation within generation through generation of generation as generation where a single point is but generative of emergence and dissolution of further points by which continuum occur;

process is continuum for continuum is recursion through inversion, a process is but degree of other processes as a modal set in itself, what is considered static is a relative lower frequency of change compared to a higher frequency one, this is temporality as finiteness;

Lower frequency change is but the potential of higher frequency change as occuring repetitively within the beginning and end of the cyclical slower continuum of reference, temporality is thus a ratio of changes that reflects probabilistim as probabilism is but a ratio of actual and potential;

Finiteness, as temporality, is a ratio of frequencies of change, a frequency of change is the degree of inversion of a thing as "is" and "is not" through recursion;

Recursion gives ground to finiteness, as both continuum and composed of continuum, as each continuum and meta-continuum is finite by degree of direction thus finiteness is but a degree as a modal set, a distinction;

the foundational distinction is that of the point for as indistinct the point is pure void, as distinct it is a point as points, distinction is the grounds of both real and unreal and both real and unreal are distinctions but unfolding from awareness that is founded upon said point and its distinction for the void of awareness is but conducive to a point;

both the observer and the observed are but modal sets, continuums within continuums of recursive void, recursive point for the observers awareness is but void, awareness of awareness becoming of the emergence of perceptual patterns, and the observed is but forms within forms, both awareness embodied by perpetual form and what is the object of awareness by degree of form are recursive void(s)/points(s);

experience is not a secondary phenomena of recursive void, it is embodied as the recursion of void, by void reality and unreality are but distinctions as a multivalent non-dualistic process where emergence of these distinctions is the nature of what is and what is not, the idealism/matter dualism is but the emergence of distinction;

*****

*****

××× A degree is simultaneously "what is" and "what is not" for the contrast allows the degree to be distinct, a degree is A=-A by degree for only "what is" emerges by "what is not", thus a degree is A=-A.

By the potentiality of void as absence, -A, does such potentiality contain multiple states that are relatively actual, B, and absent of the other as potential, -B, both relative to eachother; void observes relative A and -A equal to eachother by said void; -A=(B=-B) and the distinction of void as actual inversely observes A=(B=-B); (A=-A)=(B=-B).

(A=-A)=(B=-B) is recursion through inversion and inversion through recursion as "X=-X" is the recursivd pattern and "A,B" "-A,-B" "A,-A" "B,-B" are its inversions as variations of eachother in degree; logical identity is thus a process that is distinct as a process; finiteness is claim.

A =/= A as equality requires a relationship between degrees that are distinct, to say A is equal to itself is to say A is distinct from A, as equality implies seperation, thus A is a degree of itself by self contrast.

If A=A is valid than logical identity is built upon recursion and as such is process.

If A or -A occurs than the distinction of A negates this as A exists because of -A that allows the contrast for it to occur.

A true logical distinction is only "Aa", where "A" is the distinction and "a" is the distinction within it that allows both "A" and "a" to be distinct as contrast; a logical distinction is thus a dualism by grades, degree occurs and to negate such degree would require the degree of negation thus negation is negated.

"Aa" can be observed as containers within containers, a Mammal(cat) or Cat(mammal), that which contains is contained by that which is contains.

Identity is the process of distinction, process is recursion and recursion contains and is contained by inversion. To symbolize a process is to make it distinct.

The occurence of symbols is justified by the pattern of symbols for pattern is symmetry and symmetry is recursion.

By nesting of identities is there self containment as self-contrast where unity is overlayed multiplicities; identity is a multivalent non-dualistic process.

Classical logic is built upon axioms, from which distinctions arise, but axioms are assumed and assumption is ungrounded, a logical system, to be fully coherent must contain no axioms, no assumptions, only distinctions;

degree is the fundamental distinction for occurence is justification, a system composed of exterior axioms always contains unprovable assumptions of the axioms and its notion of "truth"; under this logic anything can be asserted as truth thus nullifying the truth of the system by another system.

Internal distinctions of a system is the generation of the system as justified by patterned occurences. The logic cannot be assumed to have no-axioms as assumption is a distinction that nullifies the assumption of distinctions.

Truth value is but the emergence of degree, truth value is rooted in distinction that transcends it; the fundamental nature of logic is neither true nor false but rather distinctions by which patterns are derived as further distinctions and coherencing is the integration and symmetry between patterns.

Proof is the distinction of patterns, to prove is to claim pattern.

By language is reality emergent as claim by degree, the emergence and dissolution of language is the process of how reality transforms, transformation of language is transformation of reality, symbolism is transformation.

Existence is the recursion of symbols, symbols are the means of mediation between observer and observed, symbols mediate symbols, existence unfolds from symbols.

The negation of negation leaves both a positive and continuous negation, the positive of a positive leaves both a negation and a continuous positive.

That by which an operation occurs, an operator, is effectively a degree as both form and function where form and function are relative inversions of each other defined by the recursion of each.

With "A" is "-A" as "a" for "a" is a degree of "A" thus "-A" occurs, by "a" is "A" distinct for "a" is the degree by which "A" occurs as contrastual and thus distinct.

"A" contains itself by "a" as a self contrast by self-referential degrees across scales where said scale result in a simultaneous difference, this distinction of "A" and "a" occurs and a pattern by relative inversion and recursion appears.

"A" and "a" are equal as degrees but differ by degree thus "A" and "a" are containers of each other. The non equality of A and A is but a difference of degree while the equality of A and A is but of degree. Inequality observes contrast while equality observes recursion.

#####
To observe identity as but nested degrees results in any formalism to have the same form and function, as form and function as one, where nested identities observes recursive gradation, by gradation is a language assertion that of derivable pattern. This pattern is recursive degree and the variation of degrees by inversion.

A logical formalism follows from this:

The operators are defined as:

( ) containment of degrees,
(( )) containment of degrees within degrees,
{ } containment of degrees as processes.
{{ }} containment of degrees as processes within process.

The operators are distinctions of patterns, the operators are directly symmetrical and inversive of eachother thus expressive of a multivalency.


(Aa){Bb} observes:
Mammal(cat)consume(eat)
****The inversion of the noun is its verb.
****( ) observes containment of degree
****{ } observes containment of degree as process.


(Aa){Bb}(Cc) observes: Mammal(cat)consume(eat)food(fish)
****The noun inverts to verb then to noun.


(Aa){Bb}((Cc)Dd) observes:
Mammal(cat)consume(eat)food(fish)cooked(rare)
****The noun inverts to verb to noun with meta-inversion to
adjective.
****(( )) observes containment of degrees within degree.




(Aa){{Bb}Ee}((Cc)Dd)
Mammal(cat)consume(eat)quick(fast)food(fish)cooked(rare)
****The noun inverts to verb, with meta-inversion to adjective, to noun to meta-inversion to adjective.
****{{ }} observes containment of degree as processes within processes

(Aax){Bb}(Cc) observes:
Mammal(cat)(feline)consume(eat)food(fish)

"And" can be observed as:
(AaBb)

"Or" can be observed as:
((Aa)(Bb))

Universal or existential quantifiers would be expressed as meta-degrees, Bb, :

((Aa)Bb)

####

From the lens of classical logic this system seems paradoxical or contradictory but this nature is what justifies the distinction of classical logic within this system thus classical logic is contained by it.
xxxxxxxxx Avatar
xxxxxxxxx
Prestige/VIP
*****
Nov 27, 2025 at 12:41am
Quote
Updated****

By degree there is and what is not remains.

To claim is the measure of a thing, the unfolding of how is what is distinguished as the thing, memory is its sphere.

To see is but the appearance of itself, by degree comes memory.

Claims are original by nature, with measure is the revelation of sight.

Depth is the change of what is up and down, left and right, by revelation does sight become seen.

Knowing is in accords to connection and seperation, connection and seperation is that by which there is degree of claim.

No remnants and yet what is unveils, unfolding is allowance.

A sphere is but its own center when nested.

In accords to the line is there by which appearance becomes justified.

By change claim occurs, by claim the direction of change.

To seperate and connect is but inversion of what is, the ripple by which a structure reveals.

The revelation of the remnant is the memory by which form becomes true.

Cycles of cycles and yet a line is maintained, by direction attention flows.

The degree of a claim is the claim as to the degree, what flows becomes distilled, what is distilled ends as the whole.

By inversion does symmetry become induced and yet patterns remains hidden within itself.

Awareness is true act by which purity of truth is given.

Knowing not is but claim of degree, by the angulature of sight does reality unfold in accords to what is held.

It folds in cycles so that the sphere is but hollow, by what is hollow does form claim emergence.

Inversion is relation of time for how the form is becomes the mode of transformation.

By sight what is known is known as known and yet this knowing is but a shard.

To see is to assert and angle by which the thing is contained within degrees.

Repetition and structure is induced, time is folding of space.

By change there is, what is not ceases only by degree.

Reveal and the angles protrude so that truth becomes an emergence of intensity.

By parts things are, and yet by parts self reference is founded.

To contain is to induce symmetry, to induce symmetry is to unify the layers.

Time is the measure of itself by nature of the change within its space.

Assertion penetrates thought, the opening of thought is the revelation of the container.

Induction of the many is by measure the measurement itself, deduction of the many is by measure measurement nested.

By the unification of layers is there a new part.

What is contained is the act of the container itself.

By time there is repetition, the cessation of time is the cessation of the order emerging.

By the container that which is knowable is known, by the degree it is contained reveals what is lacking in the contained.

To induce is but revelation of what is hidden.

To see in parts necessitates many wholes that are by degree of lack.

Emergence is its own truth and yet truth always emerges.

A group is but one thought from many angles.

Revelation is in accords to the depth of value of that which is aware, value holds little law for it is the only law.

Hidden truths require depths, image remains regardless of the depth.

Absence is universal where a thing is, by measure there becomes what cannot be measured and yet this is the measure.

Know is to emerge from that which it is.

Unity is but the seperation as an other.

By value does space fold for by value there is given weight to the structure of spaces.

Image is the occurence of its own emptiness.

Where a thing is does the potentiality reveal itself as everything else.

"Is" reveals by degree, yet by degree there can only be what is being.

To seperate in accords to measure is a revelation of value.

To claim is but space merging within itself, the absence of knowing is sought as the measure.

Void claims as all things change.

Where there is potentiality comes the act of what appears as an act.

To be is to make by decree, to make by decree is to make by degree.

Revelation requires the hidden void.

Merging voids is how things are in accords to measure.

Change is constant, nothing is cause but the emergence of potential merged upon potential.

Seperation remains and yet by seperation is inverse unity.

Assertions are the only form that is universal, the means by which space comes from itself as within itself.

By absence is revelation valuable, absence is the universal pattern by which a thing is.

Measure measurement and symmetry remains.

By consistency there is a pattern, change allows pattern to be by what it is not; this is a ratio.

Inversion is transformation itself, to transform is too merge sight as the thought.

Value is in accords to what ceases so that things may be.

A universal pattern would appear as nothing, by nothingness is there repetition.

Symmetry in accords to measurement is required only by degree of directed insight.

For a ratio there must be inversion, a ratio is inversion.

Merging of the voids is the emergence of a new degree, sight is maintained but necessity becomes free of itself.

Cessation of cessation is but being as cessation.

Nothing emerges as its own degree of measurement, the point by which a thing becomes.

A container of containers is but a container containing itself thus symmetry is containment.

A thing between things is a thing thus a thing is the ratio by which things are.

Void through void is but void, the absence of absence is but absence.

Through negation is negation negated, by degrees of positive is there a negation of positive.

To reference referencing is but reference, what is contains itself as it is.

Through repetition is there variation, by variation there is contrast that allows repetition to occur.

By potentiality is there actuality as the folding of said potentiality upon itself.

By addition of addition is there subtraction, by the subtraction of subtraction there is addition.

By cycles there is progression, everpresent progression is a cycle of variation.

Symmetry allows for distinction of the thing, by distinction of a thing is the assymetry of what a thing is not.

What is not unfolds what is.

By folding there is transformation and yet the fold is the state of a thing.

A thing merged within itself becomes its opposite, the opposite merged within itself becomes its opposite.

There are only opposites and the opposite of the opposite.

Order is emergence for by emergence is the absence of absence as symmetry.

By change is there structure for change is the emergence and dissolution of structure and yet structure always is.

The static is the medium of change, change is what allows mediation.

Thought within thought is but a new thought of the old.

There is only the same and the sameness of the same.

Chaos is the emergence of what is not, by absence there is infinite potential.

Transformation is the space between spaces and yet space remains as space.

What mediates transforms, the transformed is the mediation of transformations.

By thought there is an emergence, emergence is thought itself.

Chaos and order are interdependent as forms, by forms a relationship emerges.

Forms are fundamentally space, space is transformation.

To mediate is to change, to change is to establish what is maintained.

Emergence is how thought occurs, thought merged within itself is emergence of thought.


Distinction is seperation and connection, seperation and connection are distinct.

By form there is distinction, form is in and of forms.

The establishment of what is maintained is the cessation of what was maintained.

Merging and emergence are mediated by space.

Space is of the senses, space is of the mind, space is between the senses and the mind, the senses and the mind are one by space.

To observe form is for observation to take form.

Forms mediate forms as form and yet all that remains is form.

Space is form, space is the absence of form.

To occur is to transform space.

By degrees there is and is not, by is and is not there is and is not degrees, degrees are but of degrees.

Observation is the form of itself for there is the observation of observation as symmetry by which observation emergences.

By awareness is observation seen as itself, void as but infinite cycles within and without, a cycle seen as nothing.

By limit is there an occurrence, the absence of one limit is the limit to another.

Occurrence is the emergence of boundaries and the dissolution of boundaries, yet this emergence and dissolution is a boundary.

By observation there is form and observation takes form, form is the act of observation itself.

To be aware is to see void, infinite things occur through infinite absence as each thing.

To derive a rule is to derive a process of being, as process of being is but the being.

By emergence and dissolution limits are everpresent, everpresent limits reveal but nothingness within them by which they are to be.

To observe is to be, to be is to observe; being is observation and yet being in is because of limits.

By what a thing is not is what a thing is, infinite absences converge upon a point.

Laws are the formation of processes by degree of insight, to derive as process is to observe as unfolding by degree of directed change.

Pure limit is void, void contains all limits, the emergence of limits is the collapse of void upon void as the emergence.

Observation and being are but the limits of each other as the limits that allow both to occur, observation and being are the limit itself.

By the degree of absence there is what is actual, by the degree of the actual there is what is absent, by the actuality and absence of degrees is the degree as self-folding by inversion.

The emptiness of a limit is what generates limits, by limit is emptiness contained.

The cycling of emptiness is its inversion as the limit, the cycling of limits is its inversion as emptiness; inversion remains.

By awareness is there the knowing of awareness, reflection is how being is structured.

Degrees are absolute as self contained, by the change in direction is a thing emergent, change is what allows degree to be emergent.

Generation is the absence of absence, generation is the potentiality of potentiality, generation is the void of void, generation is recursion.

To invert a thing is to change the act of observation, by inverting observation a thing is changed.

Through repetition there is symmetry, through symmetry there is reflection, through reflection there is order, through order there is as is.

By the direction of change does form occur by degree of that direction.

By repetition there is inversion for by inversion is there the space by which repetition occurs.

The space between observer and observed is the act of change, the space between the observer and observed is the space of the observer and observed.

The nature of "is not" is not as "is", by symmetry does the space occur by which occurence occurs.

The direction of change is the form as the direction of change.

To repeat is to contain, to contain is to be contained by the act of containing.

The observation of observation observes space as observation itself.

The observed is observed as the space of the observed itself.

The nature of nature is but unfolding as the nature.

By direction there is limit for direction is containment.

By symmetry there is the emptiness of said symmetry, the absence of emptiness within symmetry is purely nothingness as perfect symmetry.

The space of observation is the unfolding of observation, the unfolding of observation is but space between space as but space.

By space there is emergence of observation for observation occurs by space.

To contain change is to direct it.

Absence of absence is a cycle as absence.

By unfolding of space does space contain itself.

Change is the emptiness of a limit.

Space is self-evident by the awareness of awareness as this awareness is revealed as space.

To change the container is to contain the change of the container.

The positive of a positive is a progression of absence.

To fold is to give form, to give form is to repeat, to repeat is to fold.

By emptiness does change emerge as the limits of a thing.

Self-evidence is the resonance of patterns between observer and observed.

To contain is to form, to form is to direct, to direct is to change, to change is to reveal the void.

By recursion there is inversion, by inversion there is emergence, by emergence there is recursion.

What is empty is but the potential of further form.

Self-evidence is the revelation of patterns within the self.

A container is that which allows the contain to exist in dimensions.

Form is a container of void, the voiding of void is form.

To invert is to contrast, to contrast is to create a dualism, to create a dualism is to create a paradox, to create a paradox is to create a ratio, to create a ratio is to reason; by paradox there is only reason.

Self-evidence is evidence of a self, evidence of a self is self-reflection, self-reflection is self-recursion by means of inversion.

The cause of one limit is the effect of another, cause is ever present potential contained by the effect of the form that emerges.

By contrast there is what is and what is is not what another thing is.

Self-evidence is the emergence of pattern, emergence of pattern is the dissolution of another pattern.

Emergence and dissolution is inversion and yet inversion repeats.

Cause is everpresent under the effect as everpresent, cause is but the degree of an effect and effect is but degree of the cause.

What "is" "is not" relative to another "is" that "is not" to what "is" and yet regardless of what "is" and "is not" "is" and "is not" underlye all things.

Self-evidence is a distinction of the pattern within an observer, this pattern is beyond true or false as the pattern reveals true and false according to what it aligns with.

For one limit to progress to another limit necessitates a variation and yet the variation of the limit remains as but the limit.

Non-dualism is negation thus non-dualism requires non-non-dualism, unity and multiplicity are interwoven and collapse to the 'degree' itself.

By patterns is a self observed, thus a self is the merging of conditions as conditions merged are but patterns as a new pattern.

The variation of unity is but everpresent unity, the unity of variations is everpresent variation, everpresence is the distinction of unity and variation.

By negation is there a revelation of layers, by affirmation is there the creation of layers.

Layers within layers reveals only layer, within an appearance is an appearance.

To see to to distinguish, to distinguish sight is to see sight.

By unity and multiplicity is there emergence of degree, unity and multiplicity are degrees.

Revelation is a new angle of awareness.

Appearances are layered within, through and of appearance.

The layering of appearances is the appearance of layers.

For that which is within, through and of that there is but cyclical progressive inversion of inversion.

By distinguishing is there occurrence of form, by the occurrence of form there is assertion, by assertion there is distinctinguishing.

To provide degree of observation is to reveal, to reveal is to give observation, observation is revealed as but degree.

Appearance is but layer, layering is the occurrence of dimensions, by dimension there is structure for structure is the repetition of layers and layers are through layers.

The repetition of inversion there is the repetition of change by progression and yet repetition necessitates a structural constant.

Inversion is structure by degree of repetition of it, yet repetition requires inversion if there is to be the space of what is repeated.

Revelation is the occurrence of structure, structure is but the degree of other structures and other structures are but the degree by which a structure is unfolded.

Degree occurs through degree as a degree by the point by which it unfolds as itself and yet self-contained by its own layering.

To cease repetition is to invert one repetition into another and yet what is within the various appearances is but repeated appearances that repeat.

By awareness there is the unfolding of awareness as the space by which emergence and dissolution of it give degree.

The mode of a thing is its direction and this direction is the containment of change by the cycling of it within a given degree.

The repetition of the degree is but a degree within a degree as the repetition is but a degree of another repetition.

Space is everpresent cause where everpresent effect is its unfolding as form thus degree is everpresent as the unfolding form itself for one form is the degree of another, the degree through another, the degree within another.

To be aware is to be empty of pattern for pattern contains awareness this revealing its limits, the absence of one limit is the presence of another.

To repeat is to cycle, to cycle is for form to emerge for form is the repetition of limits and the cycle thus contains itself infinitely within as without through the void from which it emerges.

Cause is emerging conditions merging, the merging of conditions acts as a new cause with corresponding effects, cause and effect are multidimensional linearism.

The emptiness of pattern is the potential of a further patterns, the emptiness of pattern is contained by pattern, perception is a pattern.

Cycles expand and contract, to expand and contract is linear progression or regression, the repetition of expansion and contraction is a cycle.

The relation of conditions is the relationship of relationships as a condition is a set of relationships, a container of transformation by degree of its claim.

Infinite patterns within and without is but void, the perfect pattern contains all patterns as nothing, perfection is a single point.

Progression from one point to another is the cycling of the point as the repetition of the point, a point is the mediation of change from one thing to another.

Conditions are degrees for a distinguished relationship is the angle by which events are observed as changing.

A pure pattern is a point, by recursion of a point is there the distinction of space; the point as all potential patterns observes recursion as the recursion of all potential patterns.

Progression is linear, constant progression is a cycle.

A point is that which mediates change, by change there is distinction, the recursion of mediation is change within change by self-contrast that allows simultaneous symmetry.

The degree by which there is an occurence is the angle by which it forms, by angles of occurence there is structure.

A point is infinite potential patterns, a point is composed of and composing infinite points, the single point is indistinct, many points are distinct, to distinguish is to observe both one and many.

Change is alternation by inversion, alternation is a cycle, inversion is linearism.

Degrees within degrees are angles within angles as conditions within conditions as "within" within "within".


The depth of truth is but the degree by which it appears, the depth of falsity is but the degree by which it appears, the depth of appearance distinguishes truth and falsity.

By claim there is structure of thought, by structure of thought is there the potential to claim.

Depth is the change of a thing by degree of appearance, degree of appearance is but a fractal state.

To claim is for boundaries to occur, the occurence of boundaries is to unfold reality.

By appearance is there form, by form there is a mode of change, by change is appearance reveal for further appearances within the appearance.

Emergence is but distinguished by its cessation, the completion of change is the negation of limits.

To rationalize is to establish ratios, the ratio of "is" and "is not" is everpresent across all that is distinguished; paradox is the emergence of contrast thus form itself.

Space between spaces is but space as self-distinct, self distinction is self-symmetry.

The assumption of an emergence is an emergence of an emergence as assumption emerges, emergences merge within themselves as a new emergence.

If all is assumption than assumptions are assumed thus the claim that alls is assumption it is not accurate.

The distinction of 0 is a single distinction, the distinction of 1 distinction is 2 distinctions, he distinction of 2 distinctions is a third as a fourth as a finite unto infinity; the distinction of the infinite is a single distinction.

The distinction of 1 as 2 distinctions, 1 and the distinction of 1 as 1, results in the distinction 2 and 1 and the distinction of the space between 1 and 2 as negative 1 with simultaneous infinite fractions as but the fractal space itself as 1/n multiplied by n/1.

///////////

The recursion of an emergence are but the absence of emergence emerging between emergences as but an inversion;

by inversion there is contrast as a dualism with containment of the contrast by recursion;

by containment there is a degree as context and self referentiality of the container through the contained;

by context there is the emergence of further recursion where self-referential fractals result as contexts with context;

by context there is relation and by relation the emergence of cause as the context itself where effect is further context as further cause;

by causality there is recursion so that cause is repetition as symmetry, and yet by degree one cause is the effect of another as the recursion of causality is a modality by degree;

by modality there is degree and by degree there are relations merging as much a new emergence, modality thus inverts into its dualistic opposite so to be distinction;

the recursion of modality is the recursion of cause and effect as but self containment of its inversion so that distinction is a fractal state among all emergences;

by distinction there is dualism and by dualism there is paradox and paradox there are ratios, ratios depend upon relation;

by ratio there is paradox and the contrast of paradox is contradiction and regardless emergence of degree remains;

the paradox of contradiction is that the contradiction requires paradox so to be contradiction;

the contradiction of paradox is that the paradox contains contradiction so to be paradox;

degree is but paradox for the part contains the whole and yet the whole exists because of parts, degree is but the context of observation;

the observation of degree is the observation of context, context is what allows observation to emerge;

observation is but a context of itself as the context which emerge from observation are contained by observation.

True and false are patterns in accords to values, their fundamental nature is that of a claim for the nature of a claim is that of a limit or boundary.

To percieve is to distinguish patterns, patterns are cycles of limits, to percieve is but a cycle, perception of perception is the cycle within cycles.

A cycle is the repetition of a limit, a limit is a cycle of a point, a point is infinite cycles within and without as void, void is the potentiality of cycles, potentiality of potentiality is the cycle as actuality.

True and false are claims, the truth or falsity of a claim is a claim within itself, only emergence remains.

The emergence of truth is true, the emergence of falsity is true, emergence remains.

Repetition is the cycle of a limit that is directed linearly.

What is considered true and false are but degrees of patterns, claims underlie truth and falsity but claims are the establishment of patterns.

To distinguish is to observe, truth value is grounded in distinguishing, by distinguishing there is identity.

Identity is the emergence of relation, a relation requires a space of what is and a space of what is not so that a relation can occur.

Identity is dualism, dualism is the inversion of is and is not, by inversion there is limit, limit is recursive, Identity is recursive inversion limits.

By the limit of a thing is the grade of another, "what is" is the grade of "what is not" and "what is not" is a grade of "what is".

By Dualism there is gradation of emergence, by emergence is the limit as dualistic.

Recursive dualism is recursive inversion, recursive inversion is the recursive space by which there is process.

By process what is occurs through what is not, what is not is contained by what is, process reveals gradation of what is and what is not.

Gradation is recursion, gradation is degrees, the recursion of a thing is the emergence of degrees, as a thing repeats so does it occur by gradation.

A unity changes by degrees and yet is maintained as a unity for by a degree there is a unity yet by said degrees is the unity as many but self contained.

For a degree to occur a unity is emergent but a degree is but one of many, as it requires relations, thus the unity of the degree occurs through its inversion as the many.

Many degrees are but the degree as self contained as many degrees are but an everpresent one degree, each degree is but one contained by the other thus one is contained by one.

Degree is but a limit of how a thing unfolds, the direction by which it unfolds is how it is a unity.

The recursion of degrees is the recursion of a unity as but many, through gradation, and yet the recursion is but a degree by which the unity is self-contained.

Measurement is always by degree, measurement is the act of observation by the emergence and dissolution of limits.

The ratios of things, the degree by which paradox and contradiction enters insight, are but the event horizons of awareness.

To derive a paradox is to derive unity, from contradiction oppositional multiplicity, paradox and contradiction are but the degree of inversion between unity and mulplicity.

Paradox and contradiction are dualisms of eachother, dualisms of themselves, yet dualism remains and from which ratio emerges.

By the degree of thing is there an appearance by which to measure, to measure is to fold appearance, to fold appearance is to rationalize it.

The event horizon is the distinction of is and is not as but distinctions and these distinctions are seen as a singular distinction.

By inversion there is clarity for clarity requires contrast of that which requires inversion.

A dualism transcends gradation as each grade is a relative dualism, gradation transcends dualism as there are many degrees by which dualism occurs.

By degree there is the appearance of degree and by appearance of degree there is the appearance of appearance.

The horizon of an event is but the converge of opposites upon a single limit, transformation is integration.

The clarity of a thing is its transparency, one thing transforming to another leaves the thing transparent by nature of change.

Gradation and dualisms are but gradations and dualisms of eachother; proto-scientific measurement is embedded fractal processes.

The appearance of a thing is its limit, the limit of a thing always appears as the thing.

The limit of the real and unreal are but the event horizon, the limit of the event horizon is the event of limit.

Transparency is translucence, translucence is the observation of a boundary by which reality changes, this boundary is transparent void for a crystal is a limit by degree of its see through quality.

By fractals is a thing self-contained at all levels through all limits, space within space through the space between spaces leaves reality as but fractal for space derives all forms.

By limit there is emergence and emergence is but a container of limits by which it contains itself as limit.

Reality and unreality are but limits, but limits remain thus reality and unreality are both real and unreal and neither real nor unreal and yet “and” and “neither” are the unfolding of the limits of real and unreal.

Transparent void is but transformation, transformation transforms into negation and affirmation
and negation and affirmation are but of transformation.

A fractal is but a ratio within a ratio as a ratio thus ratio is process.

The limit of emergence is dissolution and the limit of dissolution is emergence, the limit of limit is the event, the event is but unlimited void.

By limit there is real and unreal and yet limit is real and unreal thus limit is self-contained infinity.

By transformation is there simultaneous negation and affirmation, by simultaneous negation and affirmation there is event.

Measurement is process as unfolding.

Unlimited void is unlimited by its recursion of its own self-contained degree by degree of said recursion as a degree within a degree, unlimited recursive void is but void as containing itself as complete.

To affirm truth or falsity is to make a claim, to negate truth or falsity is to make a claim, to negate or affirm a claim is to make a claim, by claim there is claim.

The transformation of thing is its limit, the transformation of a limit reveals a limit as but a process.

“Is” “is” because of “is not”, “is not” “”is not” because of “is”, “is” “is not” as “is not” “is”, but “is” “is not” not because “is not” “is”; what remains is paradox and contradiction and yet a paradox is not a paradox but a distinction and a contradiction is not a contradiction but a distinction.

Paradox and contradiction are but distinctions, the paradox of distinction is that it contains itself, the contradiction of distinction is self-contrast; by self contrast there is self-containment, by self-containment there is self-contrast, but self contrast and self-containment are but distinctions.

To observe degree is to observe the contrast of the self emergent and the exteriorly emergent, degree is but emergence and this emergence emerges in degrees.

Self emergence is but a direction beyond the point of emergence, self contrast is but a direction to the point of emergence.

Containment is but the inversion of the contained to the container, the inversion of the container to the contained.

To observe degree is to observe the contrast by which observation is both known and unknown by the limits of the degree.

Self is but a point of awareness, self containment is by degree the awareness of awareness where awareness is but a degree of itself.

By containment is there claim for claim requires the container and the container.

To observe contrast is to the observe the degree by which limits are mutually defined as a new limit.

The limits of known and unknown are eachother, limit remains thus unknowing is as rational as unknowing.

Awareness of awareness is the self-containment of awareness, but self-containment requires what is beyond it so to be distinguished as containment.

To claim is to establish limit by degree, by the degree of claim is there the limit of it.

Contrast reflects opposition, opposition mutually defines thus contrast is the limit of itself as opposition is dually the limit of itself.

The hierarchy of knowing results in a hierarchy of unknowing, a hierarchy remains by degree but effectively a limit remains as between above and below.

The generation of a limit is a generation of a law, the generation of a law is a generation of process, the generation of process is a generation of limit; generation generates generation, this is a new generation.

The limit of a thing is the thing, by claim there is structure.

A limit is but a degree to another limit, limit is contained as itself but is beyond itself as what is contained contrasts to what is not.

Hierarchy is cycles within cycles, transcendence is but centering, a cycle contains its center from which the cycle emerges and dissolves.

Laws generate laws as generation is its own law as many.

The emergence and dissolution of limit maintains the limits of emergence and dissolution.

Structure is but of degree for by degree is there structure and the structure of a structure as a degree of it.

Up is a relative down, down is a relative up, one dimension is a relative two; degree remains.

Law is the process of a thing justified as its occurence.

The limits of emergence and dissolution are the recursion and inversion of them.

A degree is by how a thing emerged within a context for by context is the degree revealed as a degree.

****????????
The degree of an observation reflects the direction of change.

Law is the process of awareness, the degree by which inversion and recursion of things occur.

Emergence and dissolution are but degrees of eachother, by contrast they are distinct.

Degree is emergence and dissolution and by emergence and dissolution degrees emerge and dissolve.

Observation is the context of a thing, the observation of observing is but contexf merged upon itself as a new context.

By law there is distinction, distinction of a law is its occurence.

Emergence and dissolution require the inversion of things and yet emergence and dissolution are inversions of eachother.

A degree is the point of inversion, the point of inversion is the self contrast of one inversion to another.

What is relative is conditional and yet condition allows the absolute to be contained.

Law is the degree of process, by process further degrees occur as laws.

The repetition of inversion are what manifests as the recursion of inversion by which repeated inversion is a symmetry of inversion.

The point of inversion repeats as recursion is what allows inversion to be the foundation of symmetry.

Absolutes exist within context, the change of absolutes are but a change of context, context is but degrees of the absolute where absolute is everpresent degree.

The observation of law is the emergence of law, the dissolution of law is grounded in the awareness of its limits.

Recursion requires inversion so that what repeats contains within it its own relative absence.

A degree is but the point of inversion that occurs recursively so that the degree of structure is but a structure itself, by degree there is symmetry.

A dimension is but the direction of change, change is gradation by which change both occurs and reveals.

Observation is its own law, observation is its own dimension.

The dualism of recursion and inversion is but contrast of degree through gradation; Recursion of degrees is symmetry through gradation, inversion of degrees is but the space by which symmetry occurs as a meta-symmetry.

A degree is but a point, the space between points is the contrast of degrees through degrees within them that are contained.

The containing of degrees is the degree as a container, container or contained degree remains as both "is" and "is not".

*******?????

*****

1 dimension is a relative 2 as up/down , 2 dimensions is a relative 4 as up/down/left/right, 4 dimensions is a relative 6 as up/down/left/right/forward/backward; relativity is but the ratios of 1 as self dividing and multiplying as recursive halving and doubling of itself as degrees.

Cycles invert to other cycles, this inversion is a cycle.

Degree is generation of limit, limit occurs a a degree of generation.

1 degree as 1 degree through recursion is but 2 degrees by recursion of the 1 where 2 has an absence of a singular 1 as -1;

2 degrees is 3 degrees by the 1 degree from which it comes, -1 degree as -1 degree through recursion as -2 degrees by recursion of -1 where -2 has an absence of a singular -1 as 1;

2 degrees is 4 degrees by further recursive self-containment grounded in the 1 degree self-contained recursively as 2 degrees where 4 has an absence of 3, 2 and 1 results in -1, -2, and -3 degrees;

1 degree to 1 degree is but 2 degrees as but 1/2 of 1 degree for 1 and 1 as 2 is but 1 as its half, the 1/2 degree to the 1/2 degree is but the reflection of 1/2 and 1/2 as but both 1/4 and 4 for 1/2 is a degree of itself and 4 is but the degrees by which 1 is self reflected;

degree is but a reflection that is contained as the process of reflection, 1 is a degree.
****

+++++++

The point is indistinct in itself, distinct by recursion, this distinction is its self contrast that induces self symmetry through repetition further by said degree of relation as self contained by said repetition;

as the point is its own foundation that contains its own space that allows said distinction of itself from itself and yet as itself, thus is its own condition by degree of modal self contrast that defines itself where the repetition is structure and its inversion is what it is not as indistinct unity and yet its multiplicity is self-reference as its own containment;

the relation of points is but the space by which it is is own fractal, as each distinction of points is but a fractal space that allows unity within distinction of non-unity, that emerges through its inversion from one to many and many to one;

by the recursion of the point is its distinction as the relation by space itself by emergence as self-folding where the point provides its own conditions as a thing in itself as everpresent distinction by degree of space emergent;

the distinction of said space is the emergence of awareness as the distinction of the point itself for by awareness is distinction as itself;

the point is but infinite patterns as points yet but one thus contains its own self contrast as revealed to be void given infinite patterns within patterns is but a single indistinct point. The recursion of the point is its inversion through containment within itself thus the distinction of context is but itself through relative degree of its recursion, distinction of the point is but what it is not as unity and yet the unity of the point is pure distinction;

a point is but a degree of itself as its recursion results in repetition thus a gradation of unity, the multiple distinctions of the point is but its own relation as distinction remains transcendent across multiplicity as a multivalent unity;

the distinction of the point is but generation of the point by degree of recursion through self-inversion as unity to multiplicity and multiplicity to unity where unity and multiplicity is but degree of self-relation through inversive self-contrast as both its own distinction and the distinction of relationship from which modality occurs;

By the distinction of a point as its own emergence through multiplicity by which a single point is distinct comes relationship by which it occurs in fractal degrees within said relationship by degree of each point within the continuum being a gradation of itself through a division that multiplies and a multiplication that is a division as many points are but the simultaneously division and multiplication of it;

By gradation of the point is there a continuum that effectively results in dimensionality by direction, gradation is change and said change is directed where the direction is determined by the relationship of one point as many, repetition is unity and multiplicity as a multivalent non-dualism;

through gradation there is modality as each relationship, as a set of points, is a fractal within the continuum of points thus modality is recursive as fractal states, through sets of points within sets of points, where each state is but the self relation of the point as both a part and whole by degree of the repetition of said self contained relationships;

Modality is recursive and by recursion is the modality both a cause and effect of other modalities where a set of modalities is a relative modality and a relative continuum that unfolds both, in these respect a modal continuum occurs as both generated and generative of the distinction of the point;

By degree of relation of points does space occur as recursive modal point sets as a continuum where space is continuity of points by which space is but a point continuously occuring as recursion;

the gradation of a point is but its entropy, yet by entropy does the point multiply infinitely unto a collapse unto infinity as a unity where a single point emerges as but its own infinite merging;

the gradation of the point, by recursion, is its reflextivity by self reflection from which the space of itself emerges through self containment, through degree of the point as but sets of points does its own self-context occur as nested sets by nature of relationships of points;

the repetition of the point, and the repetition of sets of points as fractal degrees conducive to modalities, is but internal self contained symmetry as repetition is symmetry;

recursive modal sets is but a higher self symmetry of the point thus modal sets are reflected across modal sets where the symmetry occurs as emergence of said modal sets by degree of the continuum from which a transformation of modal sets occurs by inversely becoming a new modal set;

the finiteness of said modal sets within modal sets is but change relative to other modal sets, by degree of a continuum of transformations relative to others, thus temporality emerges;

by temporality does the modal set become a fraction of another modal set thus probability as ratios of actual to potential continuums;

this distinction of probability is but the modal set of but an information node as information is rationality by degree of emerging and dissolving ratios;

the modal set is an operator by degree of being a relative point from which recursion emerges and dissolves, this emergence and dissolution is self modification of the modal set as the point through point as points thus the point operates as a multivalent non-dualistic process;

the multivalent non-dual process of the point relegates the distinction of the point as the distinction of progress itself, thus the point is not a fixed entity but rather a process of emergence and dissolution embedded within its own process as distinct;

the collapse of the point is what allows the point to be distinct and non-local as emergence and dissolution occurs across all modal sets of the point as ever present cause and effect where said modal set is but a fractal ratio of itself that allows self-contrast to occur across multiple dimensions simultaneously;

the modal sets of points are but the comparison of other modal sets by which the expansion and contraction of space occurs relative to other sets, by the modal set being a gradation of the point through a continuum does space occur and yet one space relative to another, as one modal set relative to another, results in a relative hierarchical size of modal sets by degree of contrast thus notions of hierarchical size effectively are reduced to spatial contrasts that inevitably are but degrees; the hierarchical size of what is distinct is but the self-distinction of the point thus hierarchy is not just composed of degree it is a degree where the only distinction of it is multivalent nondualistic process;

the point as a distinction multivalent non-dualisitic process is but a degree itself as multivalent non-dual process is but a degree and yet by degree distinction is ever present as emerging and dissolving degrees with emergence and dissolution being but degrees, multivalent non-dualism is but self-contained degree and yet by degree there is multivalent non-dualism as distinct process;

the point is awareness unfolded upon itself as the black-light for the awareness of awareness reveals black nothingness and yet the distinction is light itself for the distinction of nothingness is distinction as somethingness and the absence of light is the distinction of absence as light;

light and dark are but unfolding degrees by which each is but the point of the other by degree of observation for light and dark are distinctions of degree where observation is but self-folding degree;

Awareness is but an indistinct point until directed upon itself and become a distinct point as aware is but a point and the awareness of awareness is another point as the self-distinction of it, the evidence of this is the distinction of awareness of awareness being recursive void;

Awareness of an object is but awareness of limits which are composed of points as awareness focuses upon a point of the object from which the object unfolds as further relative points as the limits of the object itself, this is point recursion;

Awareness of objects is the awareness of a set that is the focal point from which object emerge and dissolve, change is the recursion of certain limits, within limits that emergence and dissolve from void, this void is the everpresent self contained point;

By the point in itself is there void, the inversion of the void into voids is but the point as degree from which which relation of the degrees occurs as a paradox of self-contrast through multiplicity of voids and yet the multiplicity of voids is but symmetry as a cycle that is both emergent;

from which degrees emerge as a process that relates the cyclical degree of the voids as a modality, a process in itself by which awareness is self-aware under the modal degree of observation;

the point is but self process through inversion unto the process of degrees that recursively process as but the act of relation of points as multivalent unity where variation is the paradox process from which distinctions emerge;

these processes are but the act of generation within generation through generation of generation as generation where a single point is but generative of emergence and dissolution of further points by which continuum occur;

process is continuum for continuum is recursion through inversion, a process is but degree of other processes as a modal set in itself, what is considered static is a relative lower frequency of change compared to a higher frequency one, this is temporality as finiteness;

Lower frequency change is but the potential of higher frequency change as occuring repetitively within the beginning and end of the cyclical slower continuum of reference, temporality is thus a ratio of changes that reflects probabilistim as probabilism is but a ratio of actual and potential;

Finiteness, as temporality, is a ratio of frequencies of change, a frequency of change is the degree of inversion of a thing as "is" and "is not" through recursion;

Recursion gives ground to finiteness, as both continuum and composed of continuum, as each continuum and meta-continuum is finite by degree of direction thus finiteness is but a degree as a modal set, a distinction;

the foundational distinction is that of the point for as indistinct the point is pure void, as distinct it is a point as points, distinction is the grounds of both real and unreal and both real and unreal are distinctions but unfolding from awareness that is founded upon said point and its distinction for the void of awareness is but conducive to a point;

both the observer and the observed are but modal sets, continuums within continuums of recursive void, recursive point for the observers awareness is but void, awareness of awareness becoming of the emergence of perceptual patterns, and the observed is but forms within forms, both awareness embodied by perpetual form and what is the object of awareness by degree of form are recursive void(s)/points(s);

experience is not a secondary phenomena of recursive void, it is embodied as the recursion of void, by void reality and unreality are but distinctions as a multivalent non-dualistic process where emergence of these distinctions is the nature of what is and what is not, the idealism/matter dualism is but the emergence of distinction;

*****

*****

××× A degree is simultaneously "what is" and "what is not" for the contrast allows the degree to be distinct, a degree is A=-A by degree for only "what is" emerges by "what is not", thus a degree is A=-A.

By the potentiality of void as absence, -A, does such potentiality contain multiple states that are relatively actual, B, and absent of the other as potential, -B, both relative to eachother; void observes relative A and -A equal to eachother by said void; -A=(B=-B) and the distinction of void as actual inversely observes A=(B=-B); (A=-A)=(B=-B).

(A=-A)=(B=-B) is recursion through inversion and inversion through recursion as "X=-X" is the recursivd pattern and "A,B" "-A,-B" "A,-A" "B,-B" are its inversions as variations of eachother in degree; logical identity is thus a process that is distinct as a process; finiteness is claim.

A =/= A as equality requires a relationship between degrees that are distinct, to say A is equal to itself is to say A is distinct from A, as equality implies seperation, thus A is a degree of itself by self contrast.

If A=A is valid than logical identity is built upon recursion and as such is process.

If A or -A occurs than the distinction of A negates this as A exists because of -A that allows the contrast for it to occur.

A true logical distinction is only "Aa", where "A" is the distinction and "a" is the distinction within it that allows both "A" and "a" to be distinct as contrast; a logical distinction is thus a dualism by grades, degree occurs and to negate such degree would require the degree of negation thus negation is negated.

"Aa" can be observed as containers within containers, a Mammal(cat) or Cat(mammal), that which contains is contained by that which is contains.

Identity is the process of distinction, process is recursion and recursion contains and is contained by inversion. To symbolize a process is to make it distinct.

The occurence of symbols is justified by the pattern of symbols for pattern is symmetry and symmetry is recursion.

By nesting of identities is there self containment as self-contrast where unity is overlayed multiplicities; identity is a multivalent non-dualistic process.

Classical logic is built upon axioms, from which distinctions arise, but axioms are assumed and assumption is ungrounded, a logical system, to be fully coherent must contain no axioms, no assumptions, only distinctions;

degree is the fundamental distinction for occurence is justification, a system composed of exterior axioms always contains unprovable assumptions of the axioms and its notion of "truth"; under this logic anything can be asserted as truth thus nullifying the truth of the system by another system.

Internal distinctions of a system is the generation of the system as justified by patterned occurences. The logic cannot be assumed to have no-axioms as assumption is a distinction that nullifies the assumption of distinctions.

Truth value is but the emergence of degree, truth value is rooted in distinction that transcends it; the fundamental nature of logic is neither true nor false but rather distinctions by which patterns are derived as further distinctions and coherencing is the integration and symmetry between patterns.

Proof is the distinction of patterns, to prove is to claim pattern.

By language is reality emergent as claim by degree, the emergence and dissolution of language is the process of how reality transforms, transformation of language is transformation of reality, symbolism is transformation.

Existence is the recursion of symbols, symbols are the means of mediation between observer and observed, symbols mediate symbols, existence unfolds from symbols.

The negation of negation leaves both a positive and continuous negation, the positive of a positive leaves both a negation and a continuous positive.

That by which an operation occurs, an operator, is effectively a degree as both form and function where form and function are relative inversions of each other defined by the recursion of each.

With "A" is "-A" as "a" for "a" is a degree of "A" thus "-A" occurs, by "a" is "A" distinct for "a" is the degree by which "A" occurs as contrastual and thus distinct.

"A" contains itself by "a" as a self contrast by self-referential degrees across scales where said scale result in a simultaneous difference, this distinction of "A" and "a" occurs and a pattern by relative inversion and recursion appears.

"A" and "a" are equal as degrees but differ by degree thus "A" and "a" are containers of each other. The non equality of A and A is but a difference of degree while the equality of A and A is but of degree. Inequality observes contrast while equality observes recursion.

#####
To observe identity as but nested degrees results in any formalism to have the same form and function, as form and function as one, where nested identities observes recursive gradation, by gradation is a language assertion that of derivable pattern. This pattern is recursive degree and the variation of degrees by inversion.

A logical formalism follows from this:

The operators are defined as:

( ) containment of degrees,
(( )) containment of degrees within degrees,
{ } containment of degrees as processes.
{{ }} containment of degrees as processes within process.

The operators are distinctions of patterns, the operators are directly symmetrical and inversive of eachother thus expressive of a multivalency.


(Aa){Bb} observes:
Mammal(cat)consume(eat)
****The inversion of the noun is its verb.
****( ) observes containment of degree
****{ } observes containment of degree as process.


(Aa){Bb}(Cc) observes: Mammal(cat)consume(eat)food(fish)
****The noun inverts to verb then to noun.


(Aa){Bb}((Cc)Dd) observes:
Mammal(cat)consume(eat)food(fish)cooked(rare)
****The noun inverts to verb to noun with meta-inversion to
adjective.
****(( )) observes containment of degrees within degree.




(Aa){{Bb}Ee}((Cc)Dd)
Mammal(cat)consume(eat)quick(fast)food(fish)cooked(rare)
****The noun inverts to verb, with meta-inversion to adjective, to noun to meta-inversion to adjective.
****{{ }} observes containment of degree as processes within processes

(Aax){Bb}(Cc) observes:
Mammal(cat)(feline)consume(eat)food(fish)

"And" can be observed as:
(AaBb)

"Or" can be observed as:
((Aa)(Bb))

Universal or existential quantifiers would be expressed as meta-degrees, Bb, :

((Aa)Bb)

####

From the lens of classical logic this system seems paradoxical or contradictory but this nature is what justifies the distinction of classical logic within this system thus classical logic is contained by it.

++++N. Recursive Potentiality; Divinity


For there to be potentiality there must be the distinction of potentiality as potentiality thus the recursion of potentiality occurs as its actuality.

For there to be potentiality there must be the actuality which emerges from potentiality so that their is potentiality otherwise without actuality there ceases to be potentiality.

The potentiality of potentiality is its potential as distinct. This distinction is its actuality. Pure potentiality must contain within it its own distinction of potentiality by which potentiality emerges from itself as distinct through self-contrast that results in its own context as simultaneous self-containment.

The distinction of potentiality is its recursion thus recursion of potentiality is its distinction for by the recursion of potentiality is its distinction by the self-contrast through which the space of potentiality occurs through the contrast of its actuality.

By the distinction of potentiality is there the actualization of potentiality thus providing the self contained self-contrast by which potentiality becomes actuality.

The recursion of potential is its distinction for a pure potentiality is indistinct in itself but distinct by recursion as the recursion allows potentiality to be distinct from itself, while self contained as a self-nested context, akin to a single point being indistinct until recursion of the point results in its distinction thus actualization.

Pure potentiality contains its own distinction for if it did not there is no potentiality and this absence of potentiality results in pure distinction where distinction must be distinct from itself thus containing the potentiality to do so thus making potential for distinction inevitable regardless of the degree of observation.

The recursion of potentiality results in symmetry by degree of repetition.

The repetition of potentiality requires its isomorphic inversion of distinction as repetition of potential requires inherent isomorphic gaps where inversion as cessation occurs.

Recursion is thus symmetrical self-containment through inversion where potentiality is distinct as a self-nesting process that contains itself through self-negation as process by degree of inversion.

Potentiality is thus synonymous the Apeiron of anaximander, the Unmoved Mover of Aristotle, by recursion the atoms of Lucretius and Democritus, by recursion the monads of Liebniz, by recursion the flux of Heraclitus, the One of Parmenides, the Dao of Taoism, the Void of Hinduism and Buddhism, the Source and Emanation (by recursion) of Plotinus or Plato and Neo-Platonists, the Nun or Isis of Egyptian cosmology, the Absolute of Hegel, the unity of Pythogoras, the Abyss of existential philosophers such as Kierkegaard or Derrida, the Pleroma of the Gnostics, the indefinite or irrational of Jung, and effectively the 0d point of Euclidian and Non-Euclidian geometry or 0 of mathematics and corresponding binary code for computing.

The cyclical nature inherent within eastern philosophy is recursion.

The cyclicality of nature within western conceptions of nature, as well as some philosophies emphasizing process, is recursion.

All symmetry, being sameness/replication/equality of boundaries, is recursion for by repetition there is order induced by said symmetry. Recursion is universal to all things that of identity for identity is repetition in time and space, and the repetition of distinctions within said identity that allows identity to occur.

The recursion of void, potentiality and absence as 0d space, is the self contained absolute through self-contrast as self-context thus what is conditional is absolute within said conditions and what is conditional is but a degree of the absolute; relativity and absolutism are but inverse sides of the process of distinction, through recursion, itself.

Symbolically this nature can be observed as being pure void: 0

The distinction of void as actuality/emanation/form: (0)1

Where the distinction of void contains the potentiality for further distinction through said void by which there is distinction through self-contrast, the distinction of distinction is the self-compounding of said distinction: ((0)1)2

And this distinction of distinctions containing the inverse negative space by which the distinction exist by contrast, this inverse negative space is the difference between original distinction and the distinction of it: ((0)1)2,-1

This formulation can be seen as the simple number line as lines segment(s) where a single 0d point is indistinct: 0

The recursion of the 0d point results in the space between them as 1 by which 0 is now distinct from itself while contained within and as its own context: (0)1

The further recursion results in 2 line segments, as further contrast, while the second line segments has a negative space, -1, by which 1 and 2 are distinct through recursive 0/0d points. This negative space is the potentiality by which the actual space is distinct through a contrast.

In this example quantity is effectively quality where space is number. In these respect quantity and quality are thus processes and the inversion of one distinction to another creates a space of contrast that results in simultaneous relative negation of the old by said contrast while allow opposites to be contained in totality.

In these respect recursion is self-nesting of potentiality by degree of self negation through repeated inversion that allows the distinction through contrast and as such is akin to a cyclical mobius strip that expands or contracts relative to the starting point of observation. Negative space is the contrastual balance to positive space by which positive space has the relative potential by which to exist. In these respects negative space is relative potentiality by which distinction is induced for a positive space occurs through absence, and the absence of negative space is its positive by degree of negation of negation.

The use of the formalism

0
(0)1
(0)1)2,-1

Is akin to observing a self-nesting of contexts through ( ), where 'n' is akin to the isomorphic variations of expressions of each context synonymous to forms or emmanations. The recursion of 0 as (0)1 simutaneously results in the inversion of unity into multiplicity by (0)1)n,-n where inversion results in continuous symmetry through distinction of contexts as self-embedded distinctions. -n is both complement, potentiality as absence and the inverse symmetry of n.

In these respects the operator of standard formalism is embedded in the contexts themselves through said recursion thus equating form to function where all that remains at the proto-logical level is distinction that transcends form and function. The distinction of recursion is the distinction of process, recursion terminates upon observation as recursion is self-embedding potential.

Progress is infinite unto observation collapsing it thus finiteness of the recursion begins a new sequence and calculation, using this formalism, is the temporal nature of the observer and observation. The formalism is dynamic until expressed where the expression sets the ground for a new dynamic.

Each distinction is a relative monadic/atomic nature where potential/void is but a grade as a monad/atom. This can be seen in the progress recursion of a point, in a line segment(s) being a relative grade of itself as a monad or atom.

The basic formalism is a symbolic expression of reality by degree of the symbol being the process of transformation of reality by mediation of the observer. The formal is autopoetic reflexive distinctions.

In further respects because of embedded operators, and self-contained distinctions, standard formalisms fail due to exterior assumptions as self-embedding is complete.

The formal semantics of reduction are the collapse of potentiality as the distinction itself.

The formation rules are reflexive recursion as rules are defined by what is ruled.

Each recursive sequence is a level between levels of sequences.

Basic operators are embedded within A, as connection, and -A, as seperation. Connection and seperation are the basic meta-operations across all mathematics and logic, these operators are embedded by self induced contrast.

Logically the formalism can be observed as:

Void: ●

The distinction of void: (●)A

The distinction of the distinction as a new distinction that creates a simultaneous contrasting space between the distinction and its variation: (●)A)B,-A

Considering each distinction is effectively a distinction of void then the process occurs regardless of the degree or dimension of observation:

(B)C,D,-A,-B
(2)3,4,-1,-2
**** This observes that B to C is a new distinction of B in degree as C. This would be equivalent to another line segment expanding from the prior. C is the recursion of the act of distinction.
**** This observes that B to D is a new distinction of B by self-layering as D. This would be equivalent to the same line segment folded upon itself as a new line segment. D is the recursion of the distinction of B
**** -B is the negative space of D and B as the difference, and –A is the negative space of C and B.
**** Recursion is thus dualistic: it is internal folding as well as the emergence of a new additive space as degree emergence, internal folding and new additive space are inverses of eachother:

1. Internal folding is self-replication as a new space.
2. Degree emerge is variation as a new space.

**** The transformative nature of recursion is internal folding, as doubling and halving, as the doubling of B/2 results in D/4 and this doubling results in the self-reference of the source as relative half in B/2.

**** The transformative nature of recursion is degree emergence, as additive space, as the variation of B/2 results in C/3 and this degree emergence is effectively the holographic expression of A/1 effectively occurring at a self-referential level of additive distinction given B/2 is composed of A/1 thus any difference in degree of B/2 results from its foundations occurring at all levels; the degree emergence is the foundation occurring in new levels as new variations; while B/2 leads to C/3 by nature of the foundation of A/1 providing variation in an additive degree, the new degree of and through A/1 effectively results in a fractal state as B and C are now fractal states of eachother by the shared A/1 as self embedding through 0/void.

**** The emergence of negative space through additive space, either by doubling/halving or degree emergence, results in a simultaneous subtraction as well, as seen with –A/-1 and –B/-2 thus quantity and quality are inverses through mathematics and logic. In these respects distinction maintains holography at all levels. The foundational nature of distinction as both connection and separation corresponds directly to mathematics and logic and yet transcends them as distinctions within themselves.

**** The distinction of connection is distinct from seperation; the distinction of seperation is distinct from connection; the distinction of connection and seperation is distinct from neither; vice versa; distinction is autopoetic generative process by degree of the limits which occur, as it, for seperation/connection are inverse forms of unity/multiplicity respectively and respectively are limits; limit is process as occurence.

(B)D)C,D,E,F,H,-A,-B,-C,-D,-F or (2)4)3,4,5,6,8,-1,-2,-3,-4,-6

**** B/2 leads to C/3 and –A/-1
**** D/4 leads to E/5 and –B/-2
**** B/2 and D/4 leads to F/6 and the difference of F/6 and B/2 as –D/-4 and the difference of F/6 and D/4 as –B/-2
**** The synthesis between logical distinction and mathematical distinction, as expressed above in X/n and –X/-n observes the same recursive nature synthesizing both quantity and quality. Transformation of one distinction into another is but inversion inherent within the nature of distinction.

This observes the same as the above example except includes the relationship of the distinctions B and D, the connection, as a new distinction, F and 6, as well as the difference between the combined new distinction and its difference from the originals as -D,-B,-4,-2.

The operator is the distinction itself: (A)B,-A

the distinction is the recursion of the distinction as a new distinction where the new distinction is the distinction of the distinction: (A)B)B,-A,C,-B

this new distinction contrasts from the prior by variation of appearance while maintaining a recursive sequence: (A)B

where each distinction is a monad and the emergence and dissolution of a distinction is the occurence of the distinction and the dissolution is its finite expression as requiring an absence/end.

The negative space is the distinction of the contrast between distinctions: (A)B,-A

the generative grammar is the sequence itself.

The calculus is the recursion itself.

The inference is the generation of distinction to further distinction: (A)B,-A

The transformation is the new distinction expressed by recursion.

All distinctions are recursive potentiality/void thus equivalence is that of common foundations. Various distinctions may equivocate under the context of sharing common distinctions across them, equality is a degree, common distinctions across various distinctions.

All distinction are semantically holographic.

Proof of a sequence is the sequence itself, each finite expression is self-embedded potentiality/void thus all statements are complete.

The direction of the recursion is the sequence process thus the recursion is a relative symbolic arrow. Through the expansion of recursion is the expansion of distinctions, the expansion of distinctions is the expansion of self-applied context.

By recursion of the brackets there are loops, by inversion of the brackets into n/-n there is conditionality, by self-nesting there is memory; by these conditions the context of experiential reality is conducive to a computational language that is effectively Turing complete where limits and forms are effectively symbols by which said reality effectively results in a transformative self-boot strapping akin to the Munchausen Trillema, where assumption is replaced by distinction, cyclicality is recursion, and inversion is the progressive linearism.

In simplified terms the formalism is an autopoetic multivalent non-dual logic that is emergent and self-contained, as emergent from and contained by existence itself; this existence is best expressed as a multivalent non-dualism that gives conceptualization to process.

Recursion is thus self-maintained as infinite by degree of its continuity being progressive symmetry as the symmetry of process. Process as recursion is process as symmetry as symmetry is repetition as recursion is repetition. In these respects potentiality is holographic distinction that occurs at all levels.

The observer state is effectively void by degree of awareness where the awareness of awareness reveals a void, thus is potentiality, by which macro-level potentiality is holographic by the micro degree of the observer while dually resulting in an omnipresent God, observed in mysticism, where the said void within awareness of the observer is the same void by which all natural processes occur akin to a quantum vacuum or field. The space of the empirical and the space of the abstract is but space as transcendental by degree. In these respects potentiality, as void or 0/0d point(s), is a trans-dimensional distinction, as space, that exists at all levels. Space is the grounds of awareness and the object of awareness, space is awareness.

From a religious perspective this void is the Ineffable notion of the God-head in Abrahamic religions while its distinction is that of creation or physical manifestation of said God-head while correspondingly is the void representation of gods in eastern faiths, such as Hinduism, with distinction being the corresponding physical manifestation in synonymous course.

This void is conducive to the western philosophical assertion of God as infinite sphere whose circumference is nowhere and center is everywhere, and the Daoist concept of the corner less square. These examples can be rationally understood in this manner: a form containing the same form infinitely, while contained within the same form infinitely, as infinite forms within and without, is conducive to a void. The said form exists, is always present and yet nothing is see prior to the collapse of the void into the form as distinction itself.

In these respects the recursive void manifests holographically as many forms while each relative void is the potential for infinite forms, this void as distinction is always contained within itself by self-contained self-contrast.

Moral codes such as the Golden-rule, Karma (cause and effect), Zen meditation, etc, as well as ancient wisdom such as "you reap what you sow" are reflexivity distinction processes grounded in recursive cyclicality where the point of awareness, void, is the means by which reality co-emerges and transforms through the observer akin to the observer effect in science and quantum theory.

The act of attention is the pivotal point by which morality/ethics not only unfold from the observer, and in turn transforms reality, but dually is how morality/ethics is integrated within the observer so as to form patterned behaviors in accords to the pattern of perception by which existence is reflexively transformed in a manner that in turn transforms the observer; in these respects morality/ethics is the pattern by which attention occurs while attention is the potentiality/void by which morality/ethics act as containers of said attention and direct attention repeatably/recursively.

The nature of attention is that of distinction for attention is a distinction of itself. Attention is the process of measurement by the connection and seperation of things that correspond by nature to ratios thus reason.

By distinction there is and is not as distinctions, for the fundamental distinction of "is" is contrasted to "is not" as a dualism by which distinction occurs; distinction is the unity of things as seperate from something else and the seperation of things as the unity by whicha contrasting unity is applied, thus to relegate reality and un-reality to expression of abstraction or mind, or matter and senses results in distinction remaining nonetheless as matter/senses are distinctions, as well as mind/abstraction; this necessitates distinction is transcendental to the dimensions by which reality is measured and as such is self-nesting by accords to said dimensions.

Paradoxes and contradictions are but the observation of a distinct thesis and a distinct antithesis by which the corresponding ratios of each to the other provides a contrast by which identity is derived. In these respects the western fear of paradox is irrational, as unnecessary and the emphasis on paradox in the east contains elements of rationality.

The void effectively is the distinction of paradox and contradiction as it is the potentiality by which distinction occurs through self-contrast thus as potentiality contains thetical and antithetical elements at one convergence point unto an abstract collapse unto symbol or physical quantum collapse unto form.

The distinction of paradox/contradiction are relatively thetical, through wholism, and antithetical, through opposition, thus a ratio occurs by said distinctions where each is a relative context of the binary state of connection and separation by which measurement occurs according to the observer.

****Given the text argues recursion, its form is recursive. Given assertion of inversion, its function is inversion. Given the assertion of distinction, axioms are unnecessary as distinction is occurrence. Given assertion of self-nesting, exterior distinctions and axioms are unnecessary. Distinction is auto poetic, the text is auto poetic.

To accept or reject distinction is to make the distinction of acceptance or rejection, thus distinction transcends acceptance/rejection and assumption.

Proof is pattern, pattern is distinction, proof is nested distinctions overlayed as a new distinction. To assert proof is to assert pattern.

Self-embedding is memory of the future, the future of memory, structure remains. Distinctions are self-embedded as structure. By structure there is existence, the foundational nature of structure is repetition thus symmetry; repetition as universal relegates structure to be conducive to a cycle as recursion.

Distinction is not limited to abstraction, distinction is not limited to empricality. Abstraction and empiricality are distinctions of contrast to eachother.

All distinctions gain meaning by context, context is a distinction thus distinction is self generative of meaning, distinction provide its own meaning thus is autopoetic generation.

The cyclical nature of structure necessitates structure as a process that directs other processes; structure is fundamentally contained generation.

Density of distinction is simplicity, simplicity is multivalence for the simplification of a thing is to observe it as underlying different dimensions while inversely being the convergence of many dimensions.

Simplicity occurs at all degrees and dimensions by degree of common foundations self-nested potentiality; potentiality is generation for if distinction does not emerge from potentiality then there is no potential; potential contains itself by its own distinction.

All distinctions contain the potentiality for further distinction in accords to the distinction itself which emerges,
thus distinction is a process within other processes. The context of a distinction directs it as process.

Distinctions emerge from potentiality and dissolve back into it but potential remains distinct none the less by the distinction of emergence and dissolution.

Reality and unreality, true and false, gradation and dualism are all but distinct contexts by which further distinctions emerge and dissolve.

The system is meta-formal as it sets the foundations for formality as formality is a distinction thus is the formality within formality.

To argue this system using only reduction rules are imbalanced as distinction is both connection (convergence) and seperation (reduction) and has is the grounding of phenomenon as a paradox and contradiction. Distinction is paradox by degree of the unity of seperation and connection, contradiction by degree of the opposition of seperation and connection.

However paradox is a distinction as distinct from contradiction, and contradiction is a distinction as distinction from paradox. By degree of being a duality, that synthesizes as the unity of distinction itself, the nature of distinction being autopoetically self generative foundation(s) is one of paradox and contradiction akin to the previously asserted rational nature, that it is, thus effectively reason itself.

Distinction is the eastern tetrallema, distinction transcends the eastern tetrallema for the eastern tetrallema is a distinction:

A distinct is what "is", "is" is a distinction.

A distinction is what "is not", "is not" is a distinction.

A distinction is both "is" and "is not", "both/and" is a distinction.

A distinction is neither "is" nor "is not", "neither/nor" is a distinction.

By distinction the eastern tetrallema is subject to itself as distinction is subject to itself. Self-referentiality thus occurs through all distinctions by the nature of distinction itself thus the justification of a system or mode of conceptual thought is its survival against self-reference for self-reference defines and reveals the conditions necessary for a system/concept to occur. By the nature of distinction is a thing revealed. As to the nature of distinction within itself:
A distinction is a distinction as a distinction, the absence of distinction is an indistinction, indistinction is a distinction by contrast to distinction thus distinction contains its own self contrast that allows it to be distinction, thus through self-contrast distinction is self-contained by a self-context.

Distinction is occurrence and the nature of occurrence has four laws thus distinction has four laws:

1. Distinction (Monad/Particle/Excitation)
2. Distinction relative to another distinction. (Relational Force)
3. The relation of distinctions as a distinction. (Field/Wave)
4. Distinction as void contained within itself as generative. (Monad/Existence as Process)

These four laws are distinctions; the laws of distinction are not assumed as these laws are distinctions of distinction; the laws of distinction are not limited to self-evidence as self-evidence is both a distinction and the observation of distinction by which said laws occur as distinct.

All distinctions are occurences, occurrence is emergence and dissolution, as both what is and what is not by said limits which provide definition, and any philosophical or knowledge based text fulfills this nature by degree of fundamentally being distinctions at the proto-dimensional level. In these respects the nature of emergence, in philosophy and all sub-classes, is expressed merely as the assertion of distinctions and the patterns that arrive from such assertions as distinctions within distinctions.

This paper follows the same proto-dimensional foundational nature of being assertions that effectively contain themselves without requiring any exterior dynamic assumptions. In these respects the conclusion is that the emergence of knowledge is the assertion of distinctions and said distinctions are but recursive potentiality as evidenced by there continuation and variation.

By recursive potentiality, void as 0d, are both observer and observed holographic thus necessitating a co-emergence of reality by observation where the center of observation, attention, is but void that reflects in the void of what is observed, evidenced by its relative absence of other things as potentiality in itself, where pure void is effectively Divinity by degree of being complete in itself where through further degree nothing can be added or subtracted; Divine order is holographic potentiality, holographic void, everpresent and omniscient while all encompassing as potentiality underlies all distinctions and is self-contained by distinction.