Statistics
The mathematics of uncertainty and inference provides rigorous tools for evaluating evidence and updating beliefs—essential for the convergent epistemology of Analytical Theism.
Fine-Tuning and Probability
Statistical reasoning is essential for evaluating fine-tuning arguments. The odds of life-permitting constants arising by chance are astronomically small—but how small, and what does this mean?
Roger Penrose calculated the odds of our universe's initial conditions at 1 in 10^(10^123). This number is so large that writing it out would require more atoms than exist in the observable universe. Such improbabilities demand explanation.
- Probability Calculations: The odds of life-permitting constants arising by chance are astronomically small. The cosmological constant is fine-tuned to 1 part in 10^120. This is not a small adjustment.
- Design Detection: Statistical methods can distinguish chance from design. Specified complexity—improbable patterns that match independent specifications—is the hallmark of design.
- The Lottery Fallacy: Some argue that improbable events happen all the time. But fine-tuning isn't just improbable—it's specified. The universe matches the independent specification 'life-permitting.'
- Multiverse Response: The multiverse hypothesis attempts to explain fine-tuning by positing vast numbers of universes. But this multiplies entities without evidence—and still requires fine-tuned laws.
Inference to Best Explanation
Statistical reasoning supports abductive inference—choosing the hypothesis that best explains the data. This is how science works, and it applies to worldview questions too.
Convergent epistemology asks: which worldview best explains the totality of evidence? When multiple independent lines of evidence point in the same direction, confidence increases. This is the logic of the cumulative case for theism.
- Model Comparison: Theism vs. naturalism can be compared as competing explanatory models. Which better explains consciousness, fine-tuning, moral realism, the applicability of mathematics?
- Explanatory Virtues: Good explanations have simplicity, scope, and predictive power. Theism explains diverse phenomena with a single hypothesis: a rational, moral, conscious Creator.
- Convergent Evidence: When multiple independent lines point the same direction, confidence increases. Cosmology, biology, consciousness, and morality all point toward theism.
- Consilience: William Whewell's concept: when evidence from different domains converges on the same conclusion, that conclusion is strongly supported. This is the structure of the case for theism.