On the Metabolic Identity

On the Metabolic Identity is a short philosophical statement, in numbered propositions, on the recognition that contradiction is constitutive of identity. The piece states a single formal result: given an involutive negation N on a domain Φ and the axiom that the metabolism of any element with its own negation returns the element — M(x, N(x)) = x — the operation M is necessarily non-commutative. The proof is three lines. From this forced asymmetry the piece argues that direction in the fold of identity is what time, causation, and the observer/observed asymmetry are; and that classical identity, x = x, is what metabolic identity looks like once it has stabilized. The piece engages, in passing, Heraclitus, Parmenides, Plato, Aristotle, Hegel, Nāgārjuna, Wittgenstein, Saussure, and the canonical paraconsistent positions (Priest, Deleuze, Bhaskar, Derrida); it differentiates from each in a single line and passes. Substantive engagement with these traditions, with the algebraic neighborhood (symmetric quandles, De Morgan algebras, MV-algebras), with the empirical instantiation question for x = x, and with the philosophy-of-mind implications of the consciousness corollary, is given in The Palintrope: Recursive Dialectical Realism and the Generative Structure of Reality (ISBN 9798231943791), of which this piece is an overview distillation.