Ceteris Paribus Laws: A Naturalistic Account

Abstract

An otherwise lawlike generalisation hedged by a ceteris paribus (CP) clause qualifies as a law of nature, if the CP clause can be substituted with a set of conditions derived from the multivariate regression model used to interpret the empirical data in support of the generalisation. Three studies in human biology that use regression analysis are surveyed, showing that standard objections to cashing out CP clauses in this way—based on alleged vagueness, vacuity, or lack of testability—do not apply. CP laws also cannot be said to be simply false due to the indefinitely many conditions not explicitly stated in their associated model: scientific CP clauses imply that these are, given the evidence, not nomically relevant.

Acknowledgements

I thank three anonymous referees of this journal for helpful comments on an earlier version of this paper.

Notes

[1] These were: infant age, sex, infant weight, infant length, respiratory rate, mode of delivery, ethnic background, socio-economic group, maternal smoking history, smoking habits of household members other than the mother, family history of asthma (in a first-degree relative), hypertension before or during pregnancy, mother participated in the intensive or the usual care arm of the relevant cohort study (Stick et al. 1996, 1061).

[2] No multicollinearity is a key modelling assumption in multivariate linear regression (other important assumptions are uncorrelated errors, homoskedasticity, and no model specification error). In practice, two or more independent variables are often correlated with each other, which can threaten to render the model's coefficient estimates unstable. But this is not always the case, and tests for robustness are available and are frequently used.

[3] I thus disagree with Hausman, who claims that, generally, scientific context can at best vaguely determine what the ‘other things’ are and what it is for them to be ‘equal’ (Hausman 1989, 309–310; cf. Hausman 1992)—quite on the contrary, I take Stick et al. (1996), Lødrup Carlsen et al. (1997), and Hoo et al. (1998) to have precisely determined what qualifies as such (for more on this, see sections 4 and 5 infra). I also take a different approach from those of Earman and Roberts (1999) and Schurz (2001b, 2002), who propose that putative CP laws in the special sciences are a species of non-strict statistical generalisation (see also infra).

[4] I shall not be concerned here with the general definition of ‘lawlikeness’, or the logical form of law-statements. I take the term ‘lawlike’ to apply, roughly, to any true generalisation that is universal, supported by empirical evidence, testable, and explanatory, and that has the form ‘(F → G)’ (where the quantifier is dropped, schematic letters ‘F’ and ‘G’ denote whatever the correct relata of laws of nature are—events, states, properties, capacities, etc.—and ‘→’ stands for a connective that expresses the type of nomological necessity, if any, appropriate for law statements). My focus will be exclusively on the specific contribution of the CP clause to lawlike statements (cf. Fodor 1991, 22; Lange 2002, 407).

[5] Completer accounts of CP laws have in one form or another been proposed by Hausman (1989, 1992), Fodor (1991), Pietroski and Rey (1995), and, perhaps, Hempel (1988).

[6] Further examples of spurious ‘CP laws’ in the literature are: ‘CP, if you're thirsty you will eat salt’ (Mott 1992, 340); ‘CP, all charged objects accelerate at 10 m/s²’ (Woodward 2000, 310); ‘all compounds containing hydrogen are safe for human consumption’ (Earman, Roberts, and Smith 2002, 294), and ‘CP, nuts consumption is lethal’ (Kowalenko 2011, 448).

[7] The counterexamples work as expected against Fodor (1991), Hausman (1992), and Pietroski and Rey (1995); see Mott (1992), Woodward (2000, 250ff), and Schurz (2001a), respectively.

[8] This does not mean that the naturalistic account of CP laws equates ‘CP (F → G)’ with ‘most F are G’ or even with ‘normally, F → G’ (if ‘normally’ is read in a statistical frequency sense). It can easily account for the concept of biological normality or typicality, which is independent of statistical frequency: it may be the case, for example, that ‘ceteris paribus, sea turtles have long life spans' or ‘ceteris paribus, lions have manes' are genuine CP laws of biology, despite the fact that the vast majority of sea turtles do not survive the first hour of their lives, and that many lions do not have manes—so long as the multivariate model applied to the observational evidence in support of these generalisations controls for the appropriate interferers, such as e.g. predation, environmental factors, etc., supported by independent evidence or background knowledge (see also Kowalenko 2011, 451–452).

[9] See, e.g. Scriven (1961), Cartwright (1980a, 1980b), Giere (1988, 1999), and, perhaps, Hempel (1988; for divergent interpretations of Hempel, see Giere 1988; Earman and Roberts 1999; Eliot 2011); cf. also Lange (1993, 234; 2000).

[10] Earman, Roberts, and Smith acknowledge that their position on Newton's law requires a realism about component forces that Cartwright does not share. For criticism of Cartwright's anti-realism about component forces see, e.g. Creary (1981) and Spurrett (2001); for a defence, see, e.g. Lange (2002, 421).

[11] The contemporary Cartwright has come around to the view that the laws of nature are strictly true, after all (see, e.g. Cartwright 2002), because she now believes that they quantify over capacities or dispositions, and their relations (thus ‘capturing the essence’ of reality). I take the examples in the text to illustrate that one can justifiably believe in true laws that ‘capture the essence’ of what we observe—in the sense of capturing those elements of the system that produce the phenomena we observe—without such an ontological commitment.

[12] As the Surgeon General's report puts it, ‘Standard analyses implicitly assume an absence of confounding from all unmeasured factors’ (USDHHS 2004, 20; my emphasis); i.e. they implicitly assume that indeterminately many other factors take null value.

[13] The manner in which the CP clause ‘implies’ this is not unrelated to a mode of semantic implication identified by Wittgenstein in his famous ‘colour exclusion problem’ (Wittgenstein 1929, 1977). The use of the colour predicate ‘red’ in the description ‘A is red’ says that A is red, and ipso facto implies that A is not one of indefinitely many other possible colours; e.g. one among the semantic implications of ‘A is red’ is that ‘A is not blue’. Similarly, the use of variables {X₁ … X_n} in the description of C_F in ‘F & C_F → G’ says that {X₁ … X_n} are relevant to the truth of putative law ‘F → G’ (‘nomically relevant’), and it ipso facto implies that indefinitely many other variables {X_n+1 X_n+2, …} are nomically irrelevant. The difference between this case and Wittgenstein's is that {X₁ … X_n} and {X_n+1 X_n+2, …}, rather than colour predicates in a ‘colour space’ linked by a set of internal relations associated with that space, are disjoint sets of conditions in what we might call a ‘condition space’ linked by the relevant class of CP laws associated with that space.

[14] I do not assume a particular semantic theory of implicit meaning, content, or reference here; but I take it as uncontroversial that propositional content is (at least sometimes) underspecified by linguistic meaning, and suggest that sentences containing scientific CP clauses provide a further example of such underspecification.

[15] Most researchers would of course be justifiably suspicious of any putative evidence for ‘angelic influence’ (Hempel's example) as an interferer with the known forces governing binary star systems, simply because the theoretical disruption its inclusion in the completer of the relevant CP law would cause might not be a price worth paying for saving the law (‘angelic force’ as a fifth fundamental force of nature?). Lakatos noted that the successful falsification of a CP hypothesis depends on the degree of corroboration of its CP clause; when that degree is not very high, i.e. when the explicit content of the CP clause is still the subject of active investigation and uncertainty, then scientists must rely on their ‘instinct’ or a ‘hunch’ (Lakatos 1970, 114n5)—though the latter may be guided by the heuristics of their research programme. This is still true, except that on the present account the instinct must be brought to bear on the selection of the model from which CP laws are derived.