A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochen’s freewill theorem  and strong free will theorem , we discuss the plausibility of a third axiomatic option – geometric language; the code-theoretic axiom. We suggest freewill choices at the syntactically free steps of a geometric language of spacetime form the code theoretic substrate upon which particle and gravitational physics emerge.
The Code-Theoretic Axiom: The Third Ontology
Quantum Gravity Research
Los Angeles, CA 90290, USA
Received 12 August 2019
Accepted 14 October 2019
Published 7 November 2019
A logical physical ontology is code theory, wherein reality is neither deterministic nor random.
In light of Conway and Kochen's free will theorem [The free will theorem, Found. Phys. 36(10)
(2006) 1441–1473] and strong free will theorem [The strong free will theorem, Not. Am. Math.
Soc. 56(2) (2009) 226–232], we discuss the plausibility of a third axiomatic option geometric
language; the code-theoretic axiom. We suggest that freewill choices at the syntactically-free
steps of a geometric language of spacetime form the code-theoretic substrate upon which par-
ticle and gravitational physics emerge.
Keywords: Physics; number theory; code theoretic.
1.1. The code-theoretic axiom
Reality is neither deterministic nor random. Instead, it is code-theoretic, wherein
spacetime and particles are discrete and built of a Planck-scale geometric code a
¯nite set of shape symbols, ordering rules and non-deterministic syntactical freedom.
Broadly speaking, there are three axioms for a physical ontology one can assume.
One is the idea that the universe is a deterministic causal chain or algorithm playing
itself out. An example of this is the model of the Newtonian clockwork universe,3
which postulates that if one knew the starting conditions, a powerful computer could
predict every event.4 A second option is the axiom of pure randomness, where a
particle can appear anywhere in space and time according to probabilities dictated
by quantum mechanics.5 The third possibility is what we will henceforth refer to as
code theory, where, e.g., the Planck-scale fabric of reality operates according to a
geometric language with syntactical freedom creating order and preventing the
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