The Manchester hooters

Every working day at five o'clock the factory hooters sound in Manchester. At the same time in London the workers down tools and go home. The one follows the other with perfect regularity, day after day.

No one takes the Manchester hooters to be the cause of knocking-off time in London. If they were silenced, no Londoner would stay at work any longer. And yet the connection is as regular as a regularity theory of causation could possibly require.

In The Cement of the Universe John L. Mackie himself pointed out that on his analysis the hooters count as a cause (Mackie 1974, pp. 81–84, after Andreas and Günther, SEP, §1.3; Graßhoff and May cite the 1980 edition, p. 81). According to Andreas and Günther, the example is modelled on one of Russell's (1921). Graßhoff and May call the case a counter-example “formulated by Mackie himself”, which his INUS condition could not resolve (Graßhoff and May 2001, p. 85).

Intuition knows the explanation. Both events go back to the same convention: at five o'clock it is knocking-off time. In Manchester the time of day sets off the hooters; in London it sets off the workers going home. The hooters and the London workers going home are two effects of a common cause.

Graßhoff and May put this into a definition: an epiphenomenon is present when two events have a common causal factor without being causally relevant to each other (Graßhoff and May 2001, p. 101).

Two further factors complete the picture. The hooters can also sound outside that time, for instance through an off-schedule trigger, and the Londoners can also go home on some other occasion. The two regularities are:

Mackie's theory explains causes as INUS conditions (Mackie 1965): as an insufficient but non-redundant part of a condition that is unnecessary but sufficient for the effect. A cause is accordingly an indispensable part of a cluster that is not necessary for the effect (Vol. III, §2.5).

Let us test the cluster made up of the hooters and the absence of an off-schedule trigger, written M * ¬D. The box with the sign ¬ on the arrow from D marks the absence.

The cluster is sufficient for the London workers going home. The hooters sound only at five o'clock or in the event of an off-schedule trigger. If they sound and there is no off-schedule trigger, then it is five o'clock, and at five o'clock the Londoners go home. In the table these are cases 5 and 6 (Vol. III, §2.5).

None of its conjuncts is redundant. The hooters alone are not sufficient: in case 3 they sound because of an off-schedule trigger, and in London people stay at work (Vol. III, §2.5).

Nor is the absence of an off-schedule trigger alone sufficient: in case 1 there is no off-schedule trigger, but also no hooters and no knocking-off time. The cluster is therefore minimally sufficient. The hooters are an indispensable part of it and pass Mackie's test: they are an INUS condition of the London workers going home (Vol. III, §2.5).

The table records all eight combinations of time of day, off-schedule trigger and other occasion, with the values that the two regularities fix for the hooters and for the London workers going home. The time of day alone is sufficient for their going home: in every case with five o'clock (5 to 8) the Londoners go home (Vol. III, §2.5).

Likewise the other occasion: in every case with it (2, 4, 6, 8) they go home (Vol. III, §2.5).

Together with the hooters cluster there are three minimally sufficient conditions, and their disjunction is necessary: every case in which the Londoners go home satisfies at least one of them.

Here the INUS analysis stops. It minimises the sufficient conditions, but not their disjunction. According to it, the hooters are a cause of the London workers going home.

Mackie concluded from this that a pure regularity theory could not be the whole story of causation (Mackie 1980, p. 86, after Graßhoff and May 2001, p. 103). Baumgartner calls the hooters “the most famous concrete example” of this kind of structure, the example “based on which Mackie (1974) ultimately abandoned the attempt to provide a genuine regularity theoretic analysis of causation” (Baumgartner 2008, section “Spurious Regularities”).

Mackie minimised only one half of his analysis. He strikes redundant conjuncts from sufficient conditions, but does not check whether the list of sufficient conditions itself contains anything redundant. That is exactly what minimal necessity requires, introduced by May (1999) and by Graßhoff and May (2001): a necessary condition is minimally necessary if it contains no proper part that is also necessary (Vol. III, §2.5).

In the cases in which the hooters cluster is satisfied, 5 and 6, it is always also five o'clock. Where the cluster is present, the common cause is present as well (Vol. III, §2.5).

Let us strike the hooters cluster and check what remains: the disjunction of time of day and other occasion covers every case in which the Londoners go home. It is a necessary proper part of the disjunction from chapter 4. That disjunction was therefore not minimally necessary, and the hooters cluster drops out. It is a free rider of the common cause.

Nothing further can be struck. Without the other occasion case 2 would remain uncovered, without the time of day case 5. The minimal theory of the London workers going home is (Vol. III, §2.5)

The Manchester hooters do not occur in it. They are not causally relevant to the London workers going home.

After minimisation there remains the structure that intuition saw from the start. The time of day is a cause of the hooters and, separately from that, a cause of the London workers going home. No arrow leads from the hooters to their going home.

The perfect regularity between the two is thereby not denied but explained: where the common cause is present, both effects occur. The dotted line shows the correlation; it is not a causal claim.

On an ordinary Monday at five o'clock the time of day, the hooters and the London workers going home are present, the off-schedule trigger and the other occasion are not. The clusters of the time of day are fired: the one for the hooters and the one for the going home. Their arrowheads are filled, for they show the instantiated regularity of this case. The hooters sound on this Monday, but they belong to no fired cluster of the London workers going home.

In 2001 Graßhoff and May formulate the case with seven factors (§4.1, pp. 101–104). The hooters and the time of day are together sufficient for the workers in Manchester going home, and so is some other occasion in Manchester. In London the same holds with the London hooters:

From (13) and (14) a further sufficient condition (15) follows: no other occasion in Manchester, the Manchester workers go home, and the London hooters sound. Then it must be 5 p.m., and the Londoners go home. No part of it is sufficient. In Graßhoff and May the spurious candidate is therefore the Manchester workers going home, not the hooters themselves; the pattern is the same as in chapter 3. With this condition, the Manchester workers going home is a partial cause of the London workers going home, if causes are identified with minimally sufficient conditions. At this point, Graßhoff and May write, Mackie concludes that a pure regularity theory cannot be the whole story of causation (Graßhoff and May 2001, pp. 101–104).

The solution: a minimally sufficient condition is a cause only if it is part of a minimal theory. If (15) is appended to (14), the result is the disjunction (16). It is not minimal (Graßhoff and May 2001, pp. 101–104):

“But we can leave out the first disjunct and still have a necessary disjunction (this shorter disjunction is (14); it is ex hypothesi necessary). The spurious minimal sufficient condition is not, according to our definition, a causal regularity.” (Graßhoff and May 2001, p. 103)

They also show that the spurious condition finds no place in another minimal theory: if it replaces a disjunct of (14), the theory becomes false (17). “The only minimal theory of L_L is (14), which is the intuitively correct set of causal regularities” (p. 104). And they state that the solution is general: it depends neither on the number of alternative causes nor on the complexity of the conjunctions, as long as these factors are logically independent of one another.

In 1965 Mackie had proposed the INUS condition, an analysis of the cause by means of regularities between kinds of events. In 1974, in The Cement of the Universe, he turned the case of the hooters against it and gave up a pure regularity analysis (Baumgartner 2008, §7 and n. 21).

Michael May, in his Hamburg dissertation Kausales Schliessen (1999), and Graßhoff and May, in Causal Regularities (2001), introduced the minimisation of the necessary conditions. With it the hooters objection is resolved within regularity theory; the definition of causal relevance as part of a minimally necessary disjunction of minimally sufficient conditions is stated in the abstract of the 2001 paper (Baumgartner 2008, §7 and n. 21).

Baumgartner and Graßhoff treat the case in 2004 “in all detail” (thus Baumgartner 2008, n. 21) in Kausalität und kausales Schliessen, pp. 99–103. Baumgartner (2008) presents the solution in his reassessment of regularity theories. Baumgartner and Falk (2023) write: “To render this principle precise, Graßhoff and May ([2001]) determined that only minimally necessary disjunctions of minimally sufficient conditions of scrutinized effects are amenable to a causal interpretation.” (Baumgartner 2008, §7 and n. 21)

References. 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. Eine Untersuchung über kausale Erklärungen und Theorienbildung. Dissertation, University of Hamburg. — Mackie, J. L. (1965): Causes and Conditions. American Philosophical Quarterly 2, pp. 245–264. — Mackie, J. L. (1974): The Cement of the Universe. Oxford: Oxford University Press; Graßhoff and May cite the 1980 edition. — Baumgartner, M. and G. Graßhoff (2004): Kausalität und kausales Schliessen. Bern: Bern Studies in the History and Philosophy of Science. — Baumgartner, M. (2008): Regularity Theories Reassessed. Philosophia 36, pp. 327–354. — Andreas, H. and M. Günther (2026): Regularity and Inferential Theories of Causation. In: E. N. Zalta and U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy, revision of 5 January 2026, §1.3. — Russell, B. (1921): The Analysis of Mind. London: George Allen & Unwin (cited after Andreas and Günther). — Baumgartner, M. and C. Falk (2023): Boolean Difference-Making: A Modern Regularity Theory of Causation. British Journal for the Philosophy of Science 74. The formalisation of chapters 2 to 6 is that of Volume III, case A-FH.