Regularity theory of causal relevance · Narratives
Causality.
Eight cases, one definition.
The Manchester hooters sound every day at five, and in London the workers go home; ice-cream sales and drownings rise together; one says a short circuit caused a fire, although short circuits are neither sufficient nor necessary for fires. The regularity theory of causal relevance after Graßhoff and May uses a single definition to distinguish the factors that are causally relevant to an effect from those that merely occur together with it regularly.
The theory goes back to Graßhoff and May (2001) and May (1999). The three volumes are working drafts (as of 29 September 2026) and are provided here for discussion.
One definition
Four terms, each resting on the one before.
- 1
Factor
A kind of circumstance that in each single case is either present or absent. The effect, too, is a factor.
Example "short circuit", "oxygen present", "fire"
- 2
Cluster
An and-combination of conditions ("factor is present" or "factor is absent") that is sufficient for the effect. If one condition is struck out, it no longer is.
Example short circuit and oxygen present, for the fire
- 3
Minimal theory
An or-combination of clusters that is necessary for the effect: in every case with the effect one cluster holds. If one cluster is struck out, a case with the effect remains in which no other cluster holds.
Example short circuit with oxygen, or flammable liquid with spark and oxygen
A factor is causally relevant to an effect if and only if, for every set of factors that contains it and the effect, there is a minimal theory of the effect formed from that set in which its presence or its absence is a condition of a cluster.
A finding about the recorded factors supports the proposition that a factor is causally relevant but does not prove it: further factors can refute it. Causal relevance is not a degree.
How a factor drops out when the set of factors is extended: ice cream and drowning →Narratives
Each card opens a narrative with animated diagrams and tables. The numbers come from the volumes.
Basic terms
The visual language, the definition applied to one example, and the difference between a regularity and a single case.
The visual language
Reading the diagrams
Arrow, arc, alternative, absence, hollow and filled head: six signs with which every diagram can be read.
Read the narrative →Cluster and minimal theory
The warehouse fire
Neither sufficient nor necessary and still causally relevant: the short circuit as a condition of a cluster.
Read the narrative →The single case
Suzie and Billy
Regularity and single case: which throw broke the bottle is shown by the active cluster, the one whose conditions were all met in this case.
Read the narrative →Causally relevant or merely accompanying?
Three cases in which a factor seems causally relevant and is not.
The paradigm case
The Manchester hooters
How a case on which the regularity theory seemed to founder is solved by minimal necessity.
Read the narrative →Common cause
Ice cream and drowning
Regularly together, but not causally connected: hot weather is causally relevant to both effects, ice-cream sales are not causally relevant to drowning.
Read the narrative →No difference to the outcome
The switch
A factor that fixes the track but not the outcome: why the switch is not causally relevant to arrival.
Read the narrative →Data and experiments
When a comparison supports a verdict, when it does not, and what the theory then requires.
Homogeneity
One absent condition is enough
Why an experiment need not hold everything constant: if a single condition of a cluster is absent in all compared cases, the cluster holds in none of them.
Read the narrative →Experimental data
The statin trial
What a randomised trial licenses: the sign of the risk difference decides whether the statin is a condition of a cluster for the event or for its absence.
Read the narrative →Simpson's paradox
Kidney stones
The verdict is suspended: the size of the stone co-determines which treatment a patient receives.
Read the narrative →The volumes
Three volumes with 96 pages in total, in English, as working drafts. Each volume can be read online and is available as a PDF.
Qualitative theory
Minimal theories, homogeneity, the deductive path to the causal hypothesis, causal hypergraphs and fallacies.
Experimental data
The two homogeneity checks Gate A and Gate B, the decomposition of the risk difference by the clusters of the complete theory, experimental designs as instances of one inference.
Casebook
The Manchester hooters, benchmark cases from the literature, qualitative and experimental cases, audits of whole papers.
Sources
The theory
Graßhoff, G. and M. May (2001): Causal Regularities. In: W. Spohn, M. Ledwig and M. Esfeld (eds.), Current Issues in Causation, Münster: Mentis, pp. 85–114. — May, M. (1999): Kausales Schliessen. Dissertation, University of Hamburg. — Baumgartner, M. and G. Graßhoff (2004): Kausalität und kausales Schliessen. Bern.
The cases
Each narrative follows a case from Volume I or Volume III; the tables and formulas are those of the volumes. The diagrams use the visual language of the volumes.