Why is explaining low-probability events a problem?

If explanation required making an event highly probable, rare-but-genuine outcomes (like a particular radioactive decay) could never be explained. The statistical-relevance model addresses this by counting an explanation good when it cites factors that raise or lower the event's probability, regardless of the absolute value.

Statistical and Probabilistic Explanation

Statistical and probabilistic explanation asks how science can explain events that follow from probabilistic laws rather than deterministic ones.

Definition

A statistical explanation accounts for an event by citing statistical laws and conditions that confer a probability on it; on the inductive-statistical reading the explanation makes the event highly expectable, while on the statistical-relevance reading it cites factors that change the event's probability.

Scope

This topic covers Hempel's inductive-statistical (IS) model, the problem of explaining low-probability outcomes, the ambiguity of statistical explanation and the requirement of maximal specificity, and Salmon's statistical-relevance (SR) model that recasts explanation in terms of probabilistic relevance rather than high probability.

Core questions

Can an event be explained if the relevant statistical law gives it only a low probability?
What is the problem of the ambiguity of inductive-statistical explanation?
Why does Salmon replace high probability with statistical relevance?
How do statistical explanations relate to underlying causal processes?

Key concepts

statistical law
reference class
requirement of maximal specificity
statistical relevance
high-probability requirement
ambiguity of IS explanation

Key theories

Inductive-statistical (IS) model: Hempel models statistical explanation as an inductive argument conferring high probability on the explanandum, subject to a requirement of maximal specificity to avoid ambiguity.
Statistical-relevance (SR) model: Salmon argues that what explains is citing factors statistically relevant to the outcome, partitioning a reference class by relevance rather than seeking high probability.

History

Hempel introduced the inductive-statistical model in 1965 alongside the deductive-nomological model. Recognizing that high probability is neither necessary nor sufficient for explanation, Salmon and collaborators developed the statistical-relevance model in 1971, later embedding it within his causal-mechanical theory in 1984.

Debates

High probability versus relevance: Hempel ties statistical explanation to making the event expectable, while Salmon objects that improbable events (such as rare recoveries) can be explained when the right relevance relations are cited.

Key figures

Carl Hempel
Wesley Salmon
Richard Jeffrey

Seminal works

hempel1965
salmon1971
salmon1984

Frequently asked questions

Why is explaining low-probability events a problem?: If explanation required making an event highly probable, rare-but-genuine outcomes (like a particular radioactive decay) could never be explained. The statistical-relevance model addresses this by counting an explanation good when it cites factors that raise or lower the event's probability, regardless of the absolute value.