Identity in structuralism
The structuralism view of identity resorts to a potentially infinite differential/negative power:
In other words, A obtains/sustains the identity only through its differences from others. The minimal level of subjectivity here should not be neglected. Let us summarize it with a formula: “I’m not this one!”.
There are multiple critiques toward this structuralism stance. A version of Holism is implied: if one’s identity dependends on potentially infinite other ones, then there will be a huge network of “mutual dependency” – indeed, its the Buddhist Pratītyasamutpāda.
This view is obviously more involved than the tautological interpretation of identity in classical formal logic. Also it’s closely related to reflexive determination by Hegel and alienation by Marx (even discursive theories by Lacan).
Identity in dialectics
The potentially infinite self-related negativity is the core of subjectivity. Instead of explicit references to the others, we can move one step forward from structuralsm:
Note the arbitrariness A – there is no need to even explicitly use the letter A, because the identity is the negativity. A dialectical turn happens here: difference is inscribed into the core of identity. Let us modify the formula from “I’m not this one!” to “I am NOT!”.
A more delicate view is to involve the absence of A, rather than (explicit or implicit) difference from others:
The identity of A is the effect or event it would have caused or lead to (in some space/field/cosmology) if A were absent. Note the subjunctive mood. Let us think of the value of a product, a commodity: its identity is related to what will happen if I exchange it for something else, i.e. the effect due to its absence. The slight difference lies in the imaginative intentionality toward either the past-present (would have been) or the future (will be).
(under construction)