The Impossibility of Laplace's Demon and the Principle of Probabilistic Amplification

This paper presents a logical and mathematical analysis of the reflexive paradox of prediction — the incompatibility between classical determinism and agents capable of accessing their own predicted future.Building on Gödel’s incompleteness theorem, Turing’s halting problem, and related impossibility results (Wolpert, Moore, Earman), we show that any self-referential predictive system inevitably generates internal contradictions, even in a fully classical universe.To resolve this, we introduce a minimal causal principle called probabilistic amplification, where physical evolution is modeled as iterative reinforcement of self-consistent outcomes.This approach preserves causal structure while eliminating logical paradoxes, suggesting that indeterminism is not a failure of knowledge but a requirement of reflexive consistency.The framework follows the intellectual tradition of Gödel, Turing, and Penrose, extending it into a formal dynamical setting that unifies logic, computation, and physical law. Keywords: determinism, reflexivity, diagonalization, incompleteness, halting problem, probabilistic amplification, indeterminism, self-reference, Cantor, Gödel, Turing, Penrose.