Refuting the Metaphysics of Wolfram and Tegmark

TL;DR

This paper critically examines Wolfram's hypergraph physics and Tegmark's Mathematical Universe Hypothesis, arguing that their philosophical assumptions about truth and reality are flawed, despite the potential of combinatorial structures for future physics.

Contribution

The paper challenges the philosophical foundations of Wolfram and Tegmark's theories, emphasizing the importance of clear notions of truth and the role of combinatorial structures in physics.

Findings

Wolfram's theory conflates potential and actual existence of mathematical truths.

Tegmark's MUH relies on gematria, a questionable proof of its claims.

Combinatorial structures like directed acyclic graphs are promising for future physics.

Abstract

Wolfram's hypergraph dynamics should replace outmoded models in physics. This should even more so be the case if experimental evidence for the theory is found (which I believe is probable). However, due to the breadth and depth of the theory, it may be difficult to produce experimental evidence which falsifies it. Some of Wolfram's personal work relating to his physics project is philosophical, and so mechanics of particular phenomena in the natural world can become a triviality or an aside. In other words, the general theory "casts a wide net", and it is the philosophical topics I will challenge. I find that Wolfram must adopt a radical epistemology through his so-called Observer Theory because there is no clear notion of Truth. Tegmark believes in an objective Truth, but I find its relation to the observer untenable, and the proof of his Mathematical Universe Hypothesis (MUH) is gematria. I argue both Wolfram and Tegmark conflate the inherent potential of mathematical truths with their instantiation or actuality in reality, making a similar error to that of the "so-called" Pythagoreans rebuked by Aristotle. Nonetheless, I believe that combinatorial structures of the kind used in the physics project (abstract rewriting, directed acyclic graphs) will be the future of physics as we know it.