---
title: "PHI403 Lecture 15 — Credence: Probability from Uncertainty"
type: source
tags: [philosophy-of-science, probability, credence, bayesian, chaos-theory]
authors: [Anjum, Rani Lill; Rocca, Elena]
year: 2023
venue: "PHI403 Causation in Science, NMBU"
kind: handout
raw_path: "raw/Philosophy of Science/PHI302 15 Credence Probability From Uncertainty.pdf"
created: 2026-04-20
updated: 2026-04-20
key_claims:
  - Probability can be ontological (worldly chance) or epistemological (degree of belief / credence).
  - On causal determinism, ontological probabilities are 0 or 1; all genuine probability talk is credence about limited knowledge.
  - Chaos theory is deterministic but epistemically unpredictable — hypersensitive to initial conditions we cannot specify to full accuracy.
  - Bayesian reasoning updates credence (on [0,1]) in a hypothesis in light of new evidence; stubbornly held priors can block updating.
---

# PHI403 Lecture 15 — Credence: Probability from Uncertainty

The first of three lectures on probability in causal reasoning. The key distinction:

- **Ontological probability (chance)** — there are probabilistic causes in the world; drunk driving genuinely raises the probability of an accident.
- **Epistemological probability (credence)** — causes are absolute (yes or no), but our knowledge is limited; probability is a degree of belief.

For a **causal determinist**, once the initial conditions are fixed (coin tossed, Big Bang happened), the outcome is determined — Laplace's demon would know it. All probability talk is then credence.

**Chaos theory** complicates the picture: the world is deterministic, but outcomes are unpredictable *in principle* because the system is hypersensitive to initial conditions no finite specification can fix (weather forecasting).

**Bayesian reasoning** operates in the credence register: priors get updated by evidence; the maximum degree of belief is 1. The lecture closes with three reflective questions: can a hypothesis be held so strongly that no counter-evidence would lower one's credence? Can it be held so weakly that no evidence would raise it? Does prior confidence affect what counts as relevant evidence?

## Connections
Back-link: [[sources/2023-anjum-rocca-phi403-causation-in-science]]. Concepts: [[concepts/probabilistic-causation]] · [[concepts/aleatoric-vs-epistemic-uncertainty]] · [[concepts/causation]].