Abstract
An influential argument against Reichenbach’s Principle of the Common Cause (RPCC), first proposed by Elliott Sober (1987, 2001), consists on an example which involves correlations between bread prices in Britain and sea levels in Venice. The following quotation summarises the spirit of the whole argument:
Because both quantities have increased steadily with time, it is true that higher than average sea levels tend to be associated with higher than average bread prices. […] we do not feel driven to explain this correlation by postulating a common cause. Rather, we regard Venetian sea levels and British bread prices as both increasing for endogenous reasons. […] Here, postulating a common cause is simply not very plausible, given the rest of what we believe. (Sober 2001, 332)
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- 1.
Cf. (Reichenbach 1956, 157).
- 2.
I follow here the work by Hofer-Szabó et al. in the late 1990s and early 2000. See Hofer-Szabó et al. (1999, 2000a, b) and Rédei (2002) for the main results of the program. We need to be aware that this ‘formalisation’ will only approximately capture some of the subtleties in Reichenbach’s original intuitions. The whole program hinges however on the assumption that it is possible for the formal results achieved to be translated back into claims about the actual physical systems involved, and in particular into causal claims.
- 3.
This definition is of positive correlation. A completely symmetrical definition may be given for negative correlations. Distinguishing between positive and negative correlations will not be important in what follows and positive correlations will thus be assumed.
- 4.
- 5.
Cf. Reichenbach (1956, 159).
- 6.
- 7.
Reichenbachian common cause incomplete probability spaces are very common and, in fact, most examples aimed to rule out screening-off as a necessary condition for common causes exploit such incompleteness.
- 8.
Cf. Hofer-Szabó et al. (2000a).
- 9.
Definition 4 ensures that the extension operation be consistent with the old event structure \((\mathcal S,p)\). In particular, the embedding h is defined such that correlations stay invariant under the extension operation, that is \(Corr(A,B) \equiv Corr_p(A,B) \equiv Corr_{p'}(A,B)\). See Hofer-Szabó et al. (2000a) for details.
- 10.
Cf. Hofer-Szabó et al. (1999, 384).
- 11.
I point the reader to San Pedro and Suárez (2009) for a recent assessment of the significance of common cause completability, possible criticisms to it and possible strategies to avoid these.
- 12.
Cf. Sober (2001, 334). The appeal to ‘higher than average values’ rather than just ‘values’ is mainly motivated by criticism to an earlier version of the counterexample (Sober 1987). There is no need to review such arguments here since they will not play any important role in the foregoing discussion. The important point is that Sober’s later formulation stands. Sober also refers to ‘higher than average values’ as ‘absolute values’ and I shall use these two expressions indistinctly.
- 13.
- 14.
This is explicitly required in the formal definition of correlation (Definition 1).
- 15.
Cf. Hoover (2003).
- 16.
Cf. Steel (2003).
- 17.
See Steel (2003) and references therein for further details.
References
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San Pedro, I. (2012). Venetian Sea Levels, British Bread Prices and the Principle of the Common Cause: A Reassessment. In: de Regt, H., Hartmann, S., Okasha, S. (eds) EPSA Philosophy of Science: Amsterdam 2009. The European Philosophy of Science Association Proceedings, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2404-4_29
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