Authors: Alexandre Harvey-Tremblay
***DRAFT: Please note that this paper is a draft. It’s purpose is to help me collect my thought and to facilitate informal discussion about the ideas presented herein. This draft remains accessible to facilitate this conversation. For production quality publications, please instead refer to my latest research on a) geometric thermodynamic and b) axiomatic science. *** The aim of this work is, first, to set the basis for a formal model of science, then, it is to show that the laws of physics are its theorems. Necessarily, all formal theories that are the product of science are theorems of our model. As this includes physics, our model is, therefore, its logical foundation. In the first part of the paper we present and investigate a number of desiderata regarding the formal practice of science including definitions and properties previously anticipated in the literature. Then, we present a formal model of science meeting these criteria. We define the domain of the theory of everything in physics as the set of all statements decidable by the practice of science in nature. For each named concept of the previous sentence (theory, physics, statement, decidable, practice of science and nature), we produce a suitable mathematical definition. The central thesis of this work is to show that the laws of physics are a theorem of these definitions; ergo, the laws of physics are formal theorems of science. With this definition, the difficulty of producing a sound axiomatic basis for the domain is reduced to formalizing the practice of science within mathematics and the laws of physics are simply theorems provable in it. Main result: The ideal practice of science consists of constructing a message (in the sense of Shannon's theory of information) of experiments (the elements of the message) constrained by the requirement that its elements are verifiable (provable) within some set of logical resources (the statistical priors of the message). In this context, we define the priors as Nature and we qualify the message as scientific. Nature is thus a general proof checker for experiments, and the World is understood by constructing a maximally informative scientific message. Central thesis: We show that the equation of state regarding the construction of a scientific message bounds nature (the priors) to a cosmology entirely emergent from the entropy of the scientific message. We argue that our model is an axiomatic realization of the (later) participatory universe envisioned by John Archibald Wheeler (the aphorism "it from bit"), in which the "it" and its properties are formally derived from the "bit" which we define as (and only as) the information obtained by practice of science. This derivation of the laws of physics is based only on the practice of science in nature and is thus scientifically irrefutable.
Comments: 89 Pages.
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