Notes on E. T Jayne's Probability Theory: The Logic of Science

1. Plausible Reasoning

This section lays down some arguments on constructing probability theory as an extension of logic. Warning: it gets very hand-wavy and philosophical, but is compelling.

Deduction vs Plausibility

Boolean Algebra

Desiderata on Plausible Reasoning

2. The Quantitative Rules

TLDR: Jaynes’ desiderata for plausible reasoning is isomorphic to probability theory

This section is devoted to deducing the quantitative rules for inference which are a consequence on desiderata described in chapter 1 (i.e. consistent reasoning).

• Roughly follows the same structure as the boolean algebra section
• i.e. Deriving probabilistic analogues to the rules of boolean algebra

Bigger picture: plausible reasoning under our desiderata is isomorphic to probability theory

The Product Rule

The Sum Rule

Sources

Probability Theory: The Logic of Science Reading Course Introduction - YouTube

https://bayes.wustl.edu/