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The Inference Framework

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.