The General Law of Identity

While the conventional Law of Identity (A = A) is based on self-reference, it can be valid only within a field of the abstract (such as in mathematical definitions. It can be argued also that the essence of A = A is reference to the uniqueness of A; if an object is unique, then it can be identical only with itself.

Undeniably, the factor of "Uniqueness" is essential in identifying things - however, it is not the full or complete description of identity.

A generalised Law of Identity encompasses all aspects of formation of identity. First, based on the truth of Interconnectedness, nothing exists in isolation. An observed object must relate to a reference. It must be part of a general group of belonging.

Obviously, all objects belonging to the same group exhibit differences among each other. This is the truth of uniqueness of the object, an essential part of identity.

Finally, while identity preserves itself over the passage of time, then its potential for future development must be taken as an essential part of its existence.

The General Law of Identity:

Identity of object (A) is defined by its three properties:

its origin, its uniqueness and its potentials

The three aspects necessary to identify an object (A) are:

- Reference:

Belonging to a general group is an important property of object (A), necessary to describe its coordinates or background of existence. What distinguishes (A) among other objects belonging together to their common class - is what gives (A) its unique identity. Therefore, the reference to the general group {G} to which object (A) belongs - is necessary to identify the object. Properties of {G} describe the field in which (A) exists. It describes the functions and relationships are common between (A) with other objects.

- Uniqueness:

The second aspect of identity of object (A) is its individual list of specific properties { S } which are not shared with any other object. For any object, to be itself - a unique existence - there must be properties characteristic of that object alone, unshared by any other in the general set of origin. In the extreme situation, when all visible attributes of (A) are shared with the other objects in the general group of its belonging – still, at least one difference must exist to differentiate (A) from other similar objects. The element of difference can be for example its unique genes, fingerprint, or the 'time and space' coordinates, being the 'event' of its emergence in reality, specific to its existence.

- Potentiality:

The third aspect of identity is a set {P} which contains informational account of possible states of development of (A) changes which still do not alter its identity. The set of potentials {P} presents a field of possibilities, which the actual state of (A) can develop into. Possibilities can be in form of scenarios motivated by inner tendencies, or possibilities of environmental events affecting (A). The actual state of (A) can be regarded as a manifestation of a previous potential, or what previously was considered as a possibility for the object to develop (such as - for example - the state of adulthood, being a potential in a prior state of being a child). Similarly, the current state of (A) possesses the ability to develop into a future potential state.

Accordingly:

A = { G , S , P }

As time progresses, changes (such as growth or decline) may develop in object (A). Despite occurring changes, however, (A) remains consistent with its identity over the passage of time.

For simplicity in presentation, all elements of sets { G } and { S } - related to object ( A ) - can be referred to as properties (a1, a2, a3,….), or also collectively by (la) - representing the actual state of (A).

Furthermore, the set of potentials {P} can be referred to by a list of possible scenarios (p) containing the spectrum of potentiality of future states of (A).

This presentation offers a simple form for the General Law of Identity:

A = {a, p}

where,

{a} - signifies the actual - current - state of (A),

{p} - signifies the potential - future - state of (A).

The abovementioned description of The General Law of Identity seamlessly dissolves the perceived dichotomy between actuality (a) and potentiality (p), integrating both within the entity of (A).

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How does the General Law of Identity

A = {G, S, P}

differ from the Conventional Law of Identity

(A = A)

Obviously, (A = A) yields zero information about A. The Conventional Law of Identity gives no knowledge about the identified object. In contrast, the General Law: A = {G, S, P} - provides information about the general aspect of belonging (or the set of {G} ), and the specific aspect of uniqueness {S} - as well as predictions for future potential development {P}.

Obviously, items, which are time-unrelated (such as mathematical concepts of triangle, circle, etc…) have their potentiality {P} of future change equals to zero. An object, which has zero-potentiality of change (such as mathematical objects) - is useful in explaining the difference between the Conventional Law of Identity (A = A) and its General form, mentioned above A = {G, S, P} :

Let's take a case of defining a unique number, for example number 10. According to the General Law of Identity,

number 10, belongs to the group {G} of positive whole numbers, and its uniqueness {S} is strictly defined as being the

only integer between 9 and 11. In cases related to mathematical entities, the General Law of Identity is almost the

same as the Conventional Law of Identity (identifying the general nature of the considered number and its specific value) and having potentials of future change = 0. This reduces A to its own uniqueness A = A. Apart from abstract and fixed mathematical concepts, the conventional Law of A = A becomes a useless circularity.

Conclusion:

The abovementioned description of The General Law of Identity:

- seamlessly dissolves the dichotomy between actuality of the observed object - and its future potentiality, integrating both within the current entity of the identified object. The General Law of Identity explains the dynamism of identity over time through the power of inner potentials and external possibilities,

- validates the uniqueness of the observed object by making it 'stand out' in the reference of the general category, to which the identified object belongs.

- Includes both Physical ({G}, {S}) properties as well as nonPhysical properties {P} within the components of Identity. The factor of "potentiality" - has a nonPhysical nature, being mere information of scenarios and possibilities, which do not have a physical existence at the current actual state of Identity. Nonetheless, the nonPhysical factor of potentiality remains considered as an essential part of the inward make up of the identity.

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Author: Darshams