Foundations of Physics 38 (2):101-150 (2007)
AbstractI explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.
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Everything you always wanted to know about structural realism but were afraid to ask.Roman Frigg & Ioannis Votsis - 2011 - European Journal for Philosophy of Science 1 (2):227-276.
The Applicability of Mathematics to Physical Modality.Nora Berenstain - 2017 - Synthese 194 (9):3361-3377.
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References found in this work
What is structural realism?James Ladyman - 1998 - Studies in History and Philosophy of Science Part A 29 (3):409-424.
The Emperor’s New Mind: Concerning Computers, Minds, andthe Laws of Physics.Roger Penrose - 1989 - Science and Society 54 (4):484-487.
Are We Living in a Computer Simulation?Nick Bostrom - 2003 - Philosophical Quarterly 53 (211):243-255.