Bayesian Argumentation

What is a good argument? From a logical point of view, a good argument is logically sound. But in the real-world people rarely argue with pure logic. From a rhetorical point of view, a good argument is one that is persuasive. But how can this be measured? In this series of essays, I consider this question from a Bayesian point of view.

Argument and Information In the previous essay in this series, we introduced the idea of relevance, and said that a premise is relevant to the conclusion iff $P(A \vert B) > P(A \vert \bar{B})$. Consider the argument (𝐴) this is a good candidate for the job because (𝐵) he has a pulse. Having a pulse may not be a very persuasive reason to hire somebody, but it is probably quite relevant, because if the candidate did not have a pulse, the subject would probably be much less likely to want to hire him.

Why Accept the Premise? In the previous essay in this series, we defined the ideas of necessity and sufficiency from the perspective of a Bayesian rational agent. If an argument is necessary, then if the subject were to reject the premise, they would decrease their acceptance of the conclusion. And if an argument is sufficient, then if the subject were to accept the premise, they would increase their acceptance of the conclusion.

This is the final article in my series on Bayesian Argumentation. To understand this essay, read the introductory article for definition of key concepts and terminology. Relevance is Not Absolute Relevance exists in the context of the subject’s other prior beliefs. For example, if the subject believes that ($\bar{𝐶}$) the car is out of gas, and also ($\bar{B}$) the battery is dead, then both of these are good reasons to believe ($\bar{A}$) the car won’t start.

Bayesian Argumentation: Summary of Definitions Below is a summary of all the terms and equations defined in the essays in this series, followed by a detailed example. Claim: A statement that one can agree or disagree with Premise: A claim intended to support or oppose some conclusion Conclusion: The claim supported or opposed by the premise Argument: A premise asserted in support of or opposition to some conclusion For an argument with premise 𝐵 and conclusion 𝐴, and a subject whose beliefs are represented by probability measure P…