One of the most seemingly unimportant yet nonplussing conundrums of metaphysics is that of identity. It is clear the brain has been written with a system which evaluates identity; we recognize objects to be the same through time, as they exit our perceptions, and as they are removed from the mental stack. As we consciously evaluate and probe this system, however, we notice its inability to make apodictic judgements, visible in cases such as Theseus’ ship and cloning.

In the case of humanity, however, there appears to be a particular element of identity for any non-materialist: the soul. This element is the source of free will, and is commonly conceived to have some “personality,” or general uniqueness. This soul is also regarded as the true identity—the soul is absolutely immaterial and may even be immortal.

Despite this critical nature of the soul in an individual’s identity, however, we also conceive objects related to them in the determination of their identity, or “who they are.” Among these are an individual’s cognition, morality, body, social existence, and history.

In this sense, the observable identity is something like a multilinear form—with a particular set of vector spaces and their duals to mapping to identities representing the effect of continuity despite change for an identity:

$\text{An } \textit{identity} \text{, denoted } \iota \text{, is a map between lists of a cognitive system,}$$\text{moral system, physical system, social system, and historicity, }$$\text{which may be expressed as the tensor of the duals of cognitive }$ $\text{systems, moral systems, physical systems, social systems, and }$$\text{historicity.}$

$\Theta^{\prime}\otimes\Eta^{\prime}\otimes\Rho^{\prime}\otimes\Sigma^{\prime}\otimes\Pi^{\prime} = \Iota$

$\text{Where }\Theta \text{ is the vector space of cognitive systems, }\Eta\text{ is the vector }$$\text{space of moral systems, } \Rho \text{ is the vector space of physical systems, }$$\Sigma \text{ is the vector space of social systems, } \Pi \text{ is the vector space of }$$\text{historicities, and } \Iota \text{ is the set of all identities, a ring. The dual}$ $\text{operator, } ^{\prime} \text{, is here defined as}\operatorname{Hom}(\Chi, \Iota) \text{ where } \Chi$ $\text{is the set specified.}$

But these objects are transitory. And though this fact suggests that we ultimately look toward the putative soul as the chief source of identity, this idea breaks down in the consideration of mental illnesses and cerebral thought experiments: are people really the same if they lose their memories, or have their personalities altered? The theoretical soul would remain, but intuition would recognize the individual as a different person.

Our idea of the soul, however, is further used in our descriptions of altered realities: what one might do or believe if he were born in a different country, or in a different era. A soul is necessary for this statement to have any literal meaning, because spatiotemporally, genetically, in terms of personality, and in terms of memory no element would be shared. This lack of shared features again appeals to a different identity, according to our intuition.

Instead, perhaps we should reason that these sorts of statements are not about an identity, but rather what one imagines the current personality (though formed by the conditions which might be changed by this new theoretical origin) to do if it were in whatever time or location.

As a result of this observation, we may take notice to the fact that our arguments or beliefs which rely on some form of reasoning similar to

If I were born X, I would Y.

are fallacious if the desire or knowledge requisite for W behooves the conditions of “I”’s existence in the current reality and not the one broached.

Beyond venial fallacies, the notion of human identity is critical in Morality. Specifically, the ideas of Justice, since the maxims of Desert and the notion of volition are contingent on specific individuals, whose identities are liable to change, as discovered.

Justice contained an explicit identification of critical morality as the true determinative variable of Desert. While the consequences of this fact were briefly discussed with expiation, another explanation, viz. that the identity possessing a critical morality deserving of a particular punishment or reward no longer exists, may be used to explain how a person may have performed some act with moral implications without consequence (positive or negative) justly.

Volition, however, is challenging. If an individual has a desire for a specified amount of time, and allows a particular action by another party, and receives positive feeling before, during, and after the event, yet much later experiences negative feeling because of it, has he consented to this suffering?

This question may appear merely cavil—an individual consents to an action because he believes it is of positive feeling (generally), so he has not consented to suffering, only positive feeling which comes as a result of a particular event.

But let us allow a ridiculous hypothetical. Suppose there is a man who has the subconscious and conscious desire to be punched for a duration of three seconds, in five-minute intervals. In the times where he does not desire to be punched, he desires subconsciously and consciously not to be punched at the same magnitude of the previous inverse pair.

If during the time of positive desire the man is unable to fathom his inevitable suffering (by the inability to actualize knowledge because of a brain state, Aristotelianistically), such future suffering is a violation of emotional freedom since he as an agent is drawn away from the truth concerning his future reality.

The same conclusion is reached if we are perspicuous with identities—there are two here, where one desires to be punched but another does not. The punching of the former results in the involuntary suffering of the other, thus causing material immorality.

The most challenging notion related to identity and Justice, however, is the temporally disjunct responsibility. This moral conception relies on the contiguity of the self for a responsibility, ideally which exists eternally. Once we recognize identity as the combination of multiple elements, however, how can we reconcile this notion of contiguity in responsibility despite change in identity?

This may depend on the intent of the responsibility. If it is merely to correct an error, or generally, a motion of Utility, a relevant match of historicity is the only element necessary (e.g., even if a person spills a drink and before cleaning it loses his memories, personality, and transmutes into a different physical form, he must clean his mess).

If it is a motion of Justice (e.g., the making of a promise by a person was contingent on whether he was interrupted or not) only the moral system in the respect of critical morality is relevant. In parallel with previous observations, this is a result of the fact that retribution appeals to actions which represent an agent (i.e., accidents do not necessarily have critically moral ramifications)—thus a contiguity of immoral ideas or intents for which the pure agent is the author are incumbent.

Though the common intuition of human identity throughout time is sufficient for the vast majority of moral considerations encountered by humanity, this perspicuity on identity is necessary for the maintenance of morality in extreme contexts.

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