### Identity and Division

*What is the relation between experience and identity?* Clearly, a purely logical account of identity cannot lay claim to our ‘experience’ of identity, only its most formal aspects. Even an ontological account of identity, identity as collection of experiences or even identity as a pure cognitive event, would again demonstrate only the tautological function of identity (for example, agent A is that entity which experiences ‘being-agent-A’.) Like the tangled hierarchies implicit in the cogito, the ontological perspective aims to resolve at a higher position than it began: it seeks to make decisions based on a total comprehension, which is to be accomplished by a rigorous division. We say that logic studies this same schism, but algebraically rather than differentially. Yet a profound question remains silent: why is the subject missing from our experiential space? Where has identity gone?

It is to Alain Badiou’s credit that we now think the relation of a subject to an event as essentially multiple. But this same principle undermines the mathematical principle of continuity upon which we must base any ontological analysis of a ‘system’ of events. Even if we approach identity naively, as meaning a “belonging in a certain way to a certain state of affairs,” we cannot thereby functionally account for its continuity (a subject still maintaining its identity despite, even perhaps because of her transpositions, or non-continuously varying degrees-of-belonging.) We already see that we have need for a more complicated algebraic structure, one which at least allows for division into partial membership classes. The very nature of equivalence depends fundamentally on this division into ‘similar’ sets.

Furthermore, the fact that inclusion itself is already an ontological division demands further explanation. For example, an identity cannot be ‘induced’ from the situation by the simple observation (or negotiation) which decides that such-and-such belongs to the state of affairs, or does not. In reality, we cannot rigorously establish the existence of the void or the multiple from a pure induction. Rather, even induction depends on a rigorous subdivision of the One until this operation approaches its ‘vulgar’ limit (of non-accuracy, of meaning ‘nothing’.) So when we say this ‘limit’ (zero) belongs to every set, even to itself, we mean that induction (the operation-as-limit) has meaning only when the situation its observes is already understood as meaning ‘nothing.’ Hence the infallibility of the inductive process; it is already a “transductive” tautology! So ‘identity’ (as singularity) refers only to the void’s self-belonging (by subdivision into *n* classes of varying degrees of 'belonging'...)

We can of course use induction to demonstrate that the endless process of the self-division of the void will "eventually" produce a pure distinction, a tautological “A is A (and not B)” which, by being so utterly commonplace, completely escapes attention. Distinction masquerades as some sort of absolute truth-event, a pure objective identity. *We claim to the contrary that the void is never self-identical, that it never belongs to itself or anyone else.* In fact, the power of the void is not ‘activated’ by its emptiness but rather the mathematical intuition of the operator, the one who utilizes the void in order to reconstruct a shrinking remainder of the 'original' existential-schematic, again only of this 'layer' of being. Thus, we claim that this operation of division cannot in fact account for the reciprocal yet asymmterical relation between experience and identity.

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