Researcher ORCID Identifier
0009-0001-0946-0770
Graduation Year
2025
Date of Submission
4-2025
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Second Department
Philosophy
Reader 1
Sam Nelson
Rights Information
© 2025 Jackson T. Salumbides
Abstract
This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, this thesis develops a mathematical perspective on how determinism can coexist with unpredictability, uncertainty, and epistemic boundaries.
Recommended Citation
Salumbides, Jackson T., "Mathematics and Determinism: Chaos, Quantum Mechanics, and the Limits of Predictive Structure" (2025). CMC Senior Theses. 3935.
https://scholarship.claremont.edu/cmc_theses/3935
Included in
Dynamical Systems Commons, Logic and Foundations Commons, Logic and Foundations of Mathematics Commons, Other Mathematics Commons, Philosophy of Science Commons, Quantum Physics Commons
