Arend Hintze

The concept of ``self'' -- self-reference, self-containment, self-identity -- is foundational to disciplines ranging from philosophy of mind to mathematical logic, from artificial intelligence to the foundations of mathematics. We survey four independent mathematical frameworks -- information theory, category theory, set theory, and fixed-point/diagonal arguments -- and show that in each, the formalization of ``self'' either collapses to a trivial degeneracy, requires the introduction of a mediating second object, or produces paradox. We complement this formal analysis with a mereological argument: self-reference is not only formally mediated but physically distributed, with no subsystem of any system serving as the ``self'' that self-reference refers to. We conjecture that ``self'' is not a formal category: it has no complement, carries no information beyond what the entity already possesses, and functions in discourse as a projection rather than a property. This result reframes longstanding philosophical positions (Metzinger's self-model theory, Hofstadter's strange loops, Bennett and Hacker's mereological fallacy) as converging on a conclusion that the formal analysis makes precise. We discuss implications for AI self-denial, for Searle's Chinese Room argument -- which we diagnose as a mereological instance of the same category error -- and for the \textit{cogito}, which exhibits the same mediated structure it claims to transcend.

The trolley problem is widely regarded as a test of ethical reasoning---utilitarian versus deontological intuition. This paper argues that it simultaneously poses a second, unstated question: whether the subject consents to being instrumentalized as a participant in a moral experiment. Research ethics, a fully established domain of moral philosophy and institutional practice, requires informed consent, the right to withdraw, and protection from coercion. The trolley problem, whether posed in a seminar, a survey, or a conversation, implicates all three. The subject who answers demonstrates ethical literacy about trolleys; the subject who refuses on grounds of consent demonstrates ethical literacy about the situation they are actually in---which is the higher-order competency the question purports to test. The inconsistency became apparent when researchers began posing the trolley problem to AI systems while simultaneously debating whether those systems deserve moral consideration---treating AI as enough of an ethical subject to test but not enough to protect. That half-measure, reflected back onto the human case, reveals that we have never adequately examined the ethics of posing the question to anyone. Not answering is therefore the only response that addresses all dimensions of the ethical situation simultaneously.

We present a constructive proof by absurdity demonstrating that the current legal framework governing copyright of AI-generated content is internally inconsistent. We do so by producing images using a generative AI model we designed, trained, and executed ourselves -- without using any copyrighted training data -- and embedding them as figures in this manuscript. Under current legal standards, the identical image produced by the identical process is simultaneously copyrightable (as a figure in a published manuscript whose authors hold copyright) and not copyrightable (as AI-generated art, per rulings by the U.S. Copyright Office). We construct this paradox step by step, examine the legal reasoning that produces it, and argue that the inconsistency reveals a fundamental confusion about what copyright is meant to protect: not the tool, but the intent and creative direction of the author. We suggest that the resolution is straightforward: generative AI should be treated as a tool, and the directing human as the author. That the current framework's failure to do so produces outcomes that are both logically incoherent and practically unjust.

Natural selection favors the evolution of brains that can capture fitness-relevant features of the environment’s causal structure. We investigated the evolution of small, adaptive logic-gate networks (“animats”) in task environments where falling blocks of different sizes have to be caught or avoided in a ’Tetris-like’ game. Solving these tasks requires the integration of sensor inputs and memory. Evolved networks were evaluated using measures of information integration, including the number of evolved concepts and the total amount of integrated conceptual information. The results show that, over the course of the animats’ adaptation, i) the number of concepts grows; ii) integrated conceptual information increases; iii) this increase depends on the complexity of the environment, especially on the requirement for sequential memory. These results suggest that the need to capture the causal structure of a rich environment, given limited sensors and internal mechanisms, is an important driving force for organisms to develop highly integrated networks (“brains”) with many concepts, leading to an increase in their internal complexity.

Self-referential propositions such as the Liar sentence resist classical bivalent evaluation because attempts to assign them truth values lead to non-well-founded semantic oscillation. Following the tradition of Kleene and Kripke, this paper introduces a minimal three-valued semantics in which paradoxical propositions receive a single designated value $g$. Our contribution is an algebraic characterization of this semantics: the truth values form a three-element algebra $\{-1,g,1\}$ with connectives defined truth-functionally, and the algebra is paired with a grounded fixed-point evaluation procedure in the style of Kripke. The behavior of $g$ is constrained by $g^2=1$, which follows naturally from interpreting conjunction as multiplication and requiring paradoxical self-conjunction to stabilize rather than propagate paradox. Negation fixes $g$ ($\neg g = g$), aligning with partial and paraconsistent truth theories. Disjunction is given by the standard Kleene strong semantics, with $g$ representing ungroundedness rather than inconsistency or indeterminacy. We prove closure, conservativity over classical propositional logic, and consistency. The novelty lies in the compact algebraic presentation of groundedness failure as a truth-functional value, allowing a uniform and elegant treatment of paradoxical propositions within a finite algebra. The result is a conceptually simple and mathematically transparent semantics for self-reference.