The Fixed-Point Paradox and the Incoherence of Counterfactual Freedom
Year: 2025
Type: article
Abstract: This paper presents a formal theorem proving the structural incoherence of Counterfactual Freedom (CFF)—the ability to have done otherwise—within any causally and temporally consistent epistemic framework. Building upon established work in prediction and self-reference paradoxes (e.g., Newcomb's Problem), we introduce the Fixed-Point Paradox (FPP): an embedded agent cannot possess both epistemic access (\Box_k E) to a future action and the modal power of CFF (\Diamond_m \neg E) to alter it without generating a deductive logical contradiction. Importantly, the argument grounds the FPP in fundamental limits of computability theory and informational closure, demonstrating CFF to be a formally uncomputable property for any self-referential system. This structural constraint leads to the Axiomatic Opacity Constraint, eliminating all theories that require CFF. By proving that CFF is either unverifiable or contradictory, the paper uses a Closure Theorem to reduce the free will debate to a single, coherent descriptive model: the compatibilist framework of measurable, computable reason-responsiveness (\rho-metric). This clarifies that the remaining philosophical disagreement is solely a semantic dispute over the labeling of this coherent model as 'freedom'. The result vindicates Aristotle's ancient intuition with the formal rigor of modern modal logic and theoretical physics.
Author: Toupin, Daniel
Language: English
Topic: Free Will and Agency
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7079478126
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