The Inference Framework

TL;DR

This paper presents a comprehensive framework for inference, covering deductive reasoning, inductive inference, and probabilistic updating, based on a collection of historical sources and foundational principles.

Contribution

It constructs a theory of entropic inference from first principles, integrating deductive, inductive, and probabilistic reasoning methods.

Findings

Develops a unified theory of inference based on entropy principles

Provides a systematic approach to updating probabilities with new information

Synthesizes historical and foundational perspectives on inference

Abstract

The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The majority of these chapters are not original, but are a collection of various sources through the history of the subject. The first section deals with deductive reasoning, which is inference in the presence of complete information. The second section expands on the deductive system by constructing a theory of inductive inference, a theory of probabilities, which is inference in the presence of incomplete information. Finally, section three develops a means of updating these probabilities in the presence of new information that comes in the form of constraints.