Justifying the principle of indifference.

Area of Science:

• Epistemology
• Decision Theory
• Bayesian Reasoning

Background:

• The Principle of Indifference is a fundamental concept in probability and statistics.
• It is used to assign equal probabilities to mutually exclusive and collectively exhaustive events when there is no information to suggest otherwise.
• The principle has been subject to various interpretations and justifications, including pragmatic and epistemic ones.

Purpose of the Study:

• To present a novel argument for the Principle of Indifference.
• To explore two interpretations of this argument: pragmatic and epistemic.
• To determine the preferable interpretation and its implications for Bayesian epistemology.

Main Methods:

• The paper frames the argument for the Principle of Indifference in two ways: minimizing worst-case expected loss (pragmatic) and minimizing worst-case expected inaccuracy (epistemic).
• It analyzes the compatibility of the epistemic argument with Evidentialism, a prominent theory in epistemology.
• The relative plausibility of Evidentialism is used to evaluate the preference between the pragmatic and epistemic interpretations.

Main Results:

• The epistemic argument for the Principle of Indifference is shown to contradict Evidentialism.
• The relative plausibility of Evidentialism provides a reason to prefer the pragmatic interpretation of the argument.
• This preference extends to a broader endorsement of pragmatic arguments for norms in Bayesian epistemology.

Conclusions:

• The pragmatic interpretation of the argument for the Principle of Indifference is favored over the epistemic one.
• The findings suggest a general preference for pragmatic justifications in Bayesian epistemology.
• This work contributes to the ongoing debate on the foundations and justifications of probabilistic reasoning.