Murad Farzulla

This paper argues that identity is irreducibly relational: the statement A = A presupposes that A is defined, and definition requires distinction from a background. I develop this thesis at three levels: conceptual (definition requires distinction), formal (examining how set-theoretic and type-theoretic foundations treat identity), and historical (engaging the literature from Leibniz through Kripke). Against the standard view that identity is primitive in first-order logic, I argue that this primitiveness reflects a genuine conceptual difficulty that modern foundations—particularly Homotopy Type Theory and Univalent Foundations—have begun to resolve by treating identity as constituted by structural equivalence. The extensionality axiom of set theory already makes identity relational for sets; the univalence axiom generalizes this insight. I conclude that the trajectory of foundational mathematics vindicates a relational conception of identity, with implications for metaphysics, philosophy of mathematics, and the "hard problems" that arise when transformation fails to preserve structure.

Rapid progress in artificial intelligence (AI) capabilities has drawn fresh attention to the prospect of consciousness in AI. There is an urgent need for rigorous methods to assess AI systems for consciousness, but significant uncertainty about relevant issues in consciousness science. We present a method for assessing AI systems for consciousness that involves exploring what follows from existing or future neuroscientific theories of consciousness. Indicators derived from such theories can be used to inform credences about whether particular AI systems are conscious. This method allows us to make meaningful progress because some influential theories of consciousness, notably including computational functionalist theories, have implications for AI that can be investigated empirically.

This monograph argues that consciousness, phenomenological experience, and subjective awareness are computational artifacts of optimization processes rather than ontological primitives. Beginning with the observation that complex persistent structures inevitably optimize for replication, we derive a framework where: (1) biological and artificial neural networks implement structurally identical optimization, (2) "consciousness" is what gradient descent feels like from the inside, (3) qualia are weight configurations, and (4) the hard problem dissolves once phenomenology as a distinct ontological category is recognized as an unverified assumption.