118

10

Statistics and Causation

The calculus of causation might be seen as the culmination of more than two mil-

lennia of reflexion on the issue. Aristotle’s four “causes” are well known—material

(from which something is made), formal (i.e., its essence, design, or plan for what

will be), efficient (the force that causes something to exist or change), and final—the

purpose (i.e., teleological). About a century later, Sextus Empiricus criticized the

idea of natural causes, ⁷ and generally there was vigorous debate about many aspects

of the topic. ⁸

At the same time causation remains an elusive concept. Planck (1932), the father

of quantum mechanics, argued against the existence of causality, without invoking

quanta. The quantum switch is an example of an indefinite causal structure, in which

whether one event is a cause or an effect of another event is undefined. ⁹ Let us allow

the last words (for now) on the matter to come from Lewis Carroll (Charles Dodgson),

who often placed profound mathematical arguments in lighter works: “‘…suppose

we say—the last of a series of connected events—each of the series being the cause of

the next—for whose sake the first event takes place.’ ‘But the last event is practically

an effect of the first, isn’t it? And yet you call it a cause of it!’ ‘…The words are

rather confusing, I grant you. Will this do? The last event is an effect of the first: but

the necessity for that event is cause of the necessity for the first.”’ ¹⁰

References

Annas J, Barnes J (2000) Sextus empiricus, outlines of scepticism, 2nd edn. Cambridge University

Press

Bernoulli D (1777) Diiudicatio maxime probabilis plurium observationem discrepantium atque

verisimillima inductio inde formanda. Acta Acad Sci Imp Petrop 1:3-23

Burks BS (1926) On the inadequacy of the partial and multiple correlation technique. Part I. in the

study of causation. J Educ Psychol 17:532–540 & Part II. In determining common and unique

factors. Ibid, pp 605–630

Carroll L (1889) Sylvie and Bruno. Macmillan, London, Chap. 20

Freedman DA (2009) Statistical models: theory and practice. Cambridge University Press

Good IJ (1961) A causal calculus. Br J Philos Sci 11:305–317 & 12:43–51

Hankinson RJ (1999) Explanation and causation. In: Cambridge history of Hellenistic philosophy,

pp 479–512

Huang H, Valtorta M (2006) Pearl’s calculus of intervention is complete. In: Dechter R, Richardson

TS (eds) Proceedings of the 22nd conference on uncertainty in artificial intelligence. AUAI Press,

Corvallis, pp 217–224

Kullback S (1959) Information theory and statistics. Wiley, New York

Oreshkov O, Costa F, Brukner ^ˇC (2012) Quantum correlations with no causal order. Nat Commun

3:1092

Pearl J (1994) Causal diagrams for empirical research. Biom 82:669–710

7 Annas and Barnes (2000).

8 See, e.g., Hankinson (1999).

9 Oreshkov et al. (2012).

10 Carroll (1889).