Dwindling Probabilities
A principle in probability calculus identified by alvin-plantinga as a fundamental problem for bayesian-apologetics.
The Principle
When you multiply the probabilities of multiple independent or conditional events together, the overall probability of the entire chain being true drastically drops. This is mathematically unavoidable. 1
Application to Theological Claims
Complex historical-theological claims (like the resurrection) require a chain of connected hypotheses:
God exists → God wanted incarnation → Jesus was incarnation → tomb was empty → appearances were physical → …
Each link’s probability is ≤ 1.0, and typically << 1.0. Multiplying them together yields a posterior far lower than intuition might suggest.
Implication
Plantinga’s critique is internal to Christian philosophy — he doesn’t reject the resurrection, but argues that the Bayesian-mathematical approach to proving it is self-defeating. The very formalism that richard-swinburne uses to argue for a 97% probability is mathematically incapable of supporting that conclusion once the full chain of necessary hypotheses is accounted for. 1
See Also
- alvin-plantinga
- bayesian-apologetics
- subjectivity-of-priors
- humes-argument-against-miracles
- agrippas-trilemma — Chained justifications face the regress problem; the trilemma formalizes why chains must terminate