The law of identity is grounded under assertions thus assumptions. All assumptions are that which is assumed. This shows the isomorphism of one identity into another, ie one assumption to many, as well as the recursion of one identity across multiple states, ie "assumption" ranging across all assumptions. This results in a triad of identity properties:
1. All assertions contain underlying assertions from which they are derived, thus necessitating an underlying assertion which forms it. This results in all assertions, as deduced from another assertion, as being an inherent middle assertion.
2. All assertions invert from one assertion into another, thus necessitating an inherent emptiness to each individual assertion. This results in all assertions, as directing from one assertion to another, as being an inherently void assertion.
3. All assertions as repeating through other assertions and inherently empty, mandate the assertion as a contextual loop. All assertions, as both repetitive and empty, are a loop where each variable is an inherent contextual assertion.
To delve deeper into this:
1. Assumption of Inherent Middle ( • )
All assumptions as recursive necessitate a necessary common bond amidst assumptions through the underlying assumption which repeats. All assumptions exist as variations of eachother through a recursive state, thus all assumptions exist as a center point to further assumptions within the continuum of assumptions. All assumptions as having common underlying assumption necessitates an inherent middle assumption. All assumptions, as recursive, are inherently circular and act as a middle term: (P-->P)
2. Assumption of Inherent Void {( )}
All assumptions as inverting to another assumption necessitate an inherent emptiness of the assumption. All assumptions as intrinsically empty necessitate an inherent isomorphism where one assumption inverts to many tautological assumptions. All assumptions are void in themselves unless they continue to further assumption, thus each assumption as void voids itself into another assumption. An assumption as void negates to an assumption as existing, one axiom inverts to many.
Everytime a assumption progresses to another assumption, the new assumption contains elements of the old (through recursion) but the new assumption is not the old context and contains what the prior assumption is not. Thus the new assumption always contains an absence of the old assumption in one respect, due to newness of the assumption, while it contains elements of the old assumption at the same time. This isomorphism of isomorphism breaks down to three different degrees as a triad of dualisms.
1. Nothing into Being: (• --> P)
2. Thetical Being into Antithetical Being: (P --> -P)
3. "Nothing into Being" into "Thetical Being into Antithetical Being":
(• --> P) --> (P --> -P)
All assumptions, as inversive, are inherently linear and progressive:
{P --> (Q <--> -P)}
3. Assumption of Inherent Context {( • )}
All assumptions as recursive and void necessitates all assumptions as contexts that have both one and many meanings: one meaning as underlying many assumptions, many meanings as inverting from one assumption to another.
Assumptions as inherent middles necessitate a symmetry where each assumption as a center point observes each assumption as circular through recursion. The assumption as a centerpoint is that which is repeated, through a cycling, across further assumptions.
Assumptions as inherently void necessitates all assumptions as progressive linear functions where a function, as that which changes one form to another, is fundamentally formless. A phenomenon changes from one form into another through that which is without form.
All assumptions are generalized state of things that are composed of particulars that are not being observed, each assumption is thus a variable. Each variable as a generality, is composed of particular which are empty of definition, thus each variable is strictly empty in and of itself as a context. In simpler terms each generality is composed of particulars, which as undefined, leave the general context as empty. This emptiness allows a change, as progression, from one form into another.
All assumptions as variables are therefore contexts. All assumptions, as contexts, are inherently empty self referential loops inverting to other empty self-referential loops, existing through the point of view of the observer:
{{(P-->P) --> (Q --> -P)} --> {(P-->P) --> (Q --> -P)}}
The 3 laws of Inherent Middle (Recursion), Inherent Void (Isomorphism) and Inherent Context (Loops) exist as intertwined and One and the Same. This oneness occurs through a spiral:
1) The voiding of void results in One supreme context where void, as Nothingness, is negated through the act of "being".
2) This context is voided into multiple contexts as the inversion of one context into many.
2a) This single context still exists through the voiding of void which is synonymous to the negation of negation. The single context is thus continually voided into many contexts as void is not subject to being.
3) The inversion from void into being is grounded in inversion of one symmetrical state into another as isomorphism. Being, through context, is the opposite symmetrical state of being.
4) The multiplication of contexts, through the voiding of contexts is recursion. One context is repeated through many.
5) The repetition of contexts is a cycling of contexts. All contexts as repeated necessitates a containing of void through being. What is not is contained by what is.
5a) Each context as containing void necessitates each context as intrinsically empty.
5b) Each context as inverting from one context to another necessitates each context as progressively containing further contexts.
5c) Contexts as both empty and containing further contexts necessitate context repeat through context where all context is looped through further contexts. This looping of contexts is the containment of void through being alone.
6) The repetition of context is the inversion of Nothingness into being with this being inverted from one being into another.
6a) Isomorphism is two fold: It is the inversion of Nothingness into Being as symmetrical, and the inversion of one being into many as symmetrical.
6b) All contexts are variations of the One Context as the repitition of this isomorphism. All contexts as variations of the One Context are variations of the other contexts. The Many are variations of the One, the One is the summation of the Many as a variation of the Many.
7. The isomorphism of isomorphism, void into being and being into many being, is recursive as isomorphism is repeated.
8. The repetition of being, from one state into another, is isomorphism. Isomorphism and recursion are thetical and antithetical respectively and exist as one phenomenon through context. The recursion of context, as further contexts, is itself a context. The isomorphism of one context into many is the emptiness of context where one context contains the potential, ie "void", of another context.
9. Contexts as self contained loops, through the one context, are actual contexts. The emptiness of the contexts, as void, is the potential contexts. Contexts as actual contain contexts as potential, this actuality and potentiality exist as the context itself. The joining of the actual, to that of the potential, as in context voided from one state into many, is the context as the synthesis between symmetrical opposites.
10. All contexts as both being and inherently empty, actuality containing potentiality, isomorphism occurring through recursion, actuality through potentiality, are synthetic in nature. All contexts thus maintain simultaneous truth and false values reflecting both "being" and "nonbeing".
11. Isomorphism, recursion and the context are three different principles of being which each exist through the other.
11a) Isomorphism exists through recursion where one is repeated by its inversion into many.
11b) This containment of void, or potentiality through being, necessitates isomorphism existing through context as "being".
11c) Recursion exists through isomorphism, where the repition of being is the inversion of one state into a symmetrical opposite as a variation of the original.
11d) This repitition of void, within the context as potential context, necessitates recursion existing through context as being.
11e) Context contains further contexts and context contains potential contexts.
11f) Context is self referential through the One context.
12) Context exists through Context as Context.