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 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.

concepts/causation · concepts/dispositionalism · concepts/regularity-theory-of-causation · concepts/aleatoric-vs-epistemic-uncertainty · concepts/rct-limitations