Dual Lattice Transcendental Logic
“=” equivalence
“->” therefore, transitioning to
“>” greater than
“=/=” inequality
“-” negation, absence
“<->” if and only if
“( )” context, set
“…” continuum, regress/progress
(A=A)
*** A is A, A equals A. The nature of the identity law is identity by degree of self-symmetry, a tautological loop, by which the law of identity itself is emergent recursion as the distinction of said emergence.
(A=A)=B
****The law of identity is subject to being a variable.
(B=B) = (C, (A=A))
**** The law of identity, as a variable, is both ruther subject to the law of identity as recursive and is the law of identity; the law of identity holds at different scales.
((B=B) = (A=A)) = ((A=A)=(A=A))
(C=C) = (D, (B=B))
->…
(X=X) = (X2, (X1=X1))
****Scale invariance occurs for the law of identity.
(A=B=C=…X) = (A=A) = (B=B) = (C=C) =… (X=X)
A= (A → …X…)
**** The law of identity contains itself and by said self-embedding results in a continuum. This continuum is both composed of further continuums and effectively is a process of continuity. Each relative finite continuum is the law of identity, by recursion, and is the process of identity.
A = ((A → A) → …A)
****A variable is a self-referential process.
(A → A) = (A > A)
****A variable as a process necessitates its identity as change where it becomes relatively greater than itself.
(A =/= A) = -(A = A)
***A variable greater than itself is not equal to itself and as not equal to itself is the negation of identity.
(-A =/= A) = (-(A=A) =/= (A=A))
*** Identity as a variable; the negation of the variable is the negation of identity, the presense of the variable is the presence of the identity.
(-A=-A) = ((A=/=A)=(A=/=A))
***The absence of identity is equivalent to the absence of identity, absence of identity is a relative identity.
((-A=-A)=(-A=-A)) = (A=A)
***The absence of identity is an identity at a higher order, identity is identity.
(A=-A) = ((A=A)=(-A=-A))
***Identity and absence of identity are both identities at a higher order thus are equivalent in this context of higher order.
((A=A) ↔ (A=/=A) ↔
(-A=/=-A) ↔ (A=-A)) = (A ↔ -A)
****Equality and inequality are conditional on eachother by degree of necessary contrast that allows each to be distinct.
(=) ↔ (=/=)
***Equality and inequality are bi-conditional.
(<->) → (<->)
***Bicondtionality is a variable that transitions to further biconditionality.
(->) → (->)
****Transition transitions to further transitions.
(((->)->)->)
****Transition is self-embedding as the distinction itself.
( )
( )( )
(( )( ))( )
(( )( ))( )( )
***There is context, context exists relative to another context, this relation is a context, context is empty and yet generative to further context.
(A = ( )) = ((=),(=/=),(->),(<->),(>),(-)(…))
****A variable is a context, all operators are variables.
A
AA = (A,-A)
(AA)A = (-A,–A)
(AA)AA = (–A,—A)
…
***There is a variable, this variable self references so that is it self contained in one respect and self-contrasting to its own negation in another. The self-referencing of the variable is a new variable that follows the same nature.
=
== = (=,-=(=/=))
(==)= = (-=(=/=),–=(=))
…
=/=
=/==/= = (=/=,-=/=(=))
(=/==/=)=/= = (-=/=(=),–=/=(=))
…
->
->-> = (->, - ->(<->))
(->->)-> = (- ->(<->),-- → (->))
…
↔
<-><-> = (<->, - <->(->))
(<-><->)<-> = (- ↔ (->), – <->(->)
…
>
>> = (>, -)
(>>)> (- >(-), --(>))
…
-
-- = (-, >)
(–)- = (-- (>), - > (-))
…
…
… … = (… , -… ( ))
(… …) … = (-…(( )), --…(…))
…
A
AA
(AA)A
(AA)AA
(AA)(AA)A
…
((AA)(AA)…A) = B
…
B
BB
(BB)B
(BB)BB
…
((BB)(BB)…B) = C
…
C
CC
(CC)C
…
****Each self-reference of a variable is a new variable as a sequence. An infinite sequence is a variable as a process.