Subjectivity of Priors
A foundational critique of bayesian-apologetics: the “garbage in, garbage out” problem. 1
The Problem
Bayes’ Theorem requires:
- P(H): The prior probability of the hypothesis
- P(E|H): The likelihood of the evidence given the hypothesis
When H involves a supernatural entity (God), assigning numerical values to these variables is entirely speculative. One cannot statistically model the psychology, intentions, or behaviors of a divine being.
Example: Swinburne’s Priors
richard-swinburne assigns a high prior probability to the idea that if God exists, He would want to become incarnate, suffer, and provide atonement. This is a theological assumption about divine psychology — not an empirical claim that can be assigned a probability. 1
Consequence
No matter how rigorous the subsequent mathematics, if the inputs are based on subjective theological assumptions rather than empirical data, the output is ultimately meaningless. This is why the same Bayesian framework can be used to “prove” diametrically opposed conclusions — the math simply reflects the priors chosen.
See Also
- bayesian-apologetics
- dwindling-probabilities
- humes-argument-against-miracles
- agrippas-trilemma — The regress problem explains why priors must be chosen somewhere: justification cannot be infinite
- fine-tuning-argument — Priors over possible universes: the “measure problem” in physical guise