Question

In Bayesianism, the assignment of prior probabilities to different theories is indeed a subjective task, and your anticipation that there is no correct answer aligns with the inherent subjectivity of this process. The challenge of assigning priors is especially pronounced when dealing with untested theories that are differentiated by their perceived plausibility.

Your example of comparing two god hypotheses—one involving random draws and another based on rewarding good deeds—illustrates the difficulty in assigning priors to untested and unverifiable theories. The question of whether one should be given a higher or lower prior probability based on the ease with which it is imagined is an interesting one.

In Bayesian probability, the idea of coherence, as you mentioned, suggests that a superset cannot have a smaller probability than a subset. This principle is rooted in logical consistency. However, when it comes to the specific situation of comparing imaginative and untested theories, Bayesian probability acknowledges the irreducible subjectivity of such judgments.

Probability subjectivists, following the ideas of statisticians like de Finetti and Ramsey, would indeed argue that subjective choices play a crucial role in these situations. While coherence is a guiding principle, the absence of verifiable or testable evidence for these theories leaves room for individual judgment and personal inclinations.

In summary, your intuition that the answer to this question is irreducibly subjective aligns with the Bayesian perspective on the subjectivity inherent in assigning prior probabilities, particularly in cases where there is no empirical evidence to guide the assignment. The process involves a combination of logical considerations, coherence principles, and individual subjective judgments.

Answer 1

The question concerns Bayesianism and the subjectivity involved in assigning prior probabilities to theories without empirical evidence. It encompasses statistical methods and philosophical concepts, where subjective judgment plays a critical role in interpreting probabilistic data and comparing scientific hypotheses.

Step-by-step explanation:

The topic at hand deals with Bayesianism and the challenges in assigning prior probabilities to theories, particularly when empirical evidence is lacking.

Bayesianism incorporates subjective judgments into the probabilistic framework, a process that is influenced by philosophical concepts such as coherence, a priori knowledge, and principles of parsimony.

The Bayesian perspective not only involves rigorous statistical analysis but also philosophical underpinnings, such as coherentism and contextualism, to guide the assignment of priors and interpretation of theories.

This methodology allows for a blend of empirical data, logical deductions, and personal inclinations in determining the credibility of scientific hypotheses.

In summary, the assignment of priors in Bayesianism is a subjective endeavor that requires weighing various factors, including empirical evidence, logical coherence, and intuitive plausibility.

It highlights the intersecting paths of epistemology and statistics, where philosophy provides a framework for understanding the principles that guide Bayesian analysis.