---
title: Probabilistic Causation
type: concept
tags: [philosophy-of-science, causation, probability, frequentism, propensity, bayesian]
sources: ["[[sources/2023-anjum-rocca-phi403-causation-in-science]]", "[[sources/2023-anjum-rocca-phi403-lecture-15-credence]]", "[[sources/2023-anjum-rocca-phi403-lecture-16-probabilistic-causation]]", "[[sources/2023-anjum-rocca-phi403-lecture-17-conditional-probability]]"]
created: 2026-04-20
updated: 2026-04-20
---

# Probabilistic Causation

The view that **causes raise the probability of their effects**. Probabilities can enter the analysis in one of three philosophically distinct ways:

## 1. Credence (epistemic probability)
Probability as **degree of belief** under uncertainty. The world is causally determinate (probability 0 or 1), but our knowledge is limited; a 0.7 forecast expresses credence, not a worldly chance ([[sources/2023-anjum-rocca-phi403-lecture-15-credence]]). Bayesian reasoning operates in this register: update prior credence in a hypothesis *T* in light of evidence.

## 2. Frequentism (ontological, Humean)
Probability = **the long-run frequency** of outcomes over a sequence of trials. Fits a regularity theory of causation: a 60 % chance of E given C *just is* the fact that E follows C 60 % of the time ([[sources/2023-anjum-rocca-phi403-lecture-16-probabilistic-causation]]). The standard interpretation of probabilities in RCTs and evidence-based decision making.

**Danger: the ecological fallacy.** Applying a population-average probability directly to an individual case assumes each individual is the statistical average. This is an invalid inference.

## 3. Propensity (dispositionalist, ontological)
Probability = an **intrinsic tendency** of a property or situation to produce an outcome. Propensities are strengths of [[concepts/dispositionalism|dispositions]]; they *produce* frequencies, they are not defined by them. Propensity theory can be singularist (each case has its own propensity) or long-run (Donald Gillies: propensities reveal themselves through frequencies).

Propensities allow **overdisposing**: a power can exceed probability 1 in strength while still not guaranteeing the effect, because interferers may be present. A mathematical probability cannot exceed 1 — so propensities are not reducible to probabilities.

## Conditional probability and the ratio formula

P(A|B) = P(A ∩ B) / P(B) when P(B) > 0. The course ([[sources/2023-anjum-rocca-phi403-lecture-17-conditional-probability]]) warns: the formula is *a mathematical definition*, not a guarantee that it captures the natural-language conditional "the probability of A given B". Well-known pathologies:
- If P(A) = 1 then P(A|B) = 1 for any B ("humans are mortal given that God is good").
- If A and B are probabilistically independent, P(A|B) = P(A).
- The material conditional p → q is true whenever p is false — so verificationist inferences are trivial.

Cartwright (1989): "if we don't put causation into our calculations, we won't get any out."

## Relevance to BPM
PPM outputs are probabilities — but *which* interpretation? A transformer's softmax is arguably a frequentist output trained on sample frequencies, but is often consumed as credence (operator belief) or propensity (case-level tendency). The chosen interpretation determines what a prediction *means* and how it should drive interventions. See [[concepts/aleatoric-vs-epistemic-uncertainty]] for the ML-flavoured cousin of the credence/chance distinction.

## Related
[[concepts/causation]] · [[concepts/dispositionalism]] · [[concepts/regularity-theory-of-causation]] · [[concepts/aleatoric-vs-epistemic-uncertainty]] · [[concepts/rct-limitations]]