The Logic of Prediction and the Non-Totalization of Possibility: Uncertainty, Incompleteness, and the Limits of Algorithmic Rationality

Abstract

This paper develops a philosophical-logical critique of algorithmic prediction by examining the implicit logical structure through which contemporary artificial intelligence systems model uncertainty. It argues that predictive systems presuppose a form of probabilistic closure in which uncertainty is rendered as quantifiable risk and the space of possible outcomes is treated as, in principle, exhaustively modellable. The paper uses Lacanian psychoanalytic logic and Badiouian logic of the event to articulate alternative logics of non-totalization and evental rupture. Drawing on Lacan’s conception of the subject as structurally incomplete and his logic of the “not-all” (pas-tout), it is shown that subjectivity cannot be fully formalized within a closed system of prediction. In parallel, Badiou’s concept of the event is interpreted as a formally undecidable occurrence that exceeds the inferential structure of any given situation, thereby resisting probabilistic anticipation. The paper argues that these two frameworks converge on a conception of indeterminacy as structural rather than merely epistemic. On this basis, it advances the claim that algorithmic prediction is not simply limited in scope, but grounded in a logically inadequate conception of uncertainty—one that excludes the conditions of possibility for subjectivity, novelty, and truth. The critique thus reframes artificial intelligence as operating within a specific logical regime whose closure forecloses the very phenomena it seeks to model.