This is a preview of subscription content, log in via an institution to check access.
Notes
Thanks to Marc Lange for very helpful correspondence and corrections to an earlier draft.
Some terminological regimentation: Many philosophers use “law” to refer to relationships or patterns within nature. By contrast, as I will use the expression, “laws” are representations or descriptions of those relationships or patterns. This fits aspects of ordinary scientific usage, according to which, e.g., Maxwell’s equations are described as laws of nature and also avoids ruling out certain possibilities by terminological fiat—e.g., that laws might have exceptions. (It is unclear what might be meant by the claim that patterns in nature have exceptions.).
This is only a necessary condition. In distinguishing between laws and accidental generalizations, an additional requirement is that laws must be stable/invariant under some initial and background conditions that are produced by “testing interventions” (cf. 2003, 239ff).
This also bears on the general argument Lange gives in support of his claim that there is no non-maximal sub-nomically stable set containing accidents (pp. 32ff.). This has some plausibility if the counterfactuals in the argument are interpreted as “reasons to believe” claims. However, the claim seems less plausible if the relevant counterfactuals are interpreted as having to do with physical dependence. Consider a proposition r that characterizes the magnitude of some physical quantity at some particular space–time point s, where r is accidental. Let T be the set of propositions characterizing the values of all physically relevant variables in the entire backward light cone of s, all the way back to whatever happened at the beginning of the universe. T will not consist of all the accidental truths since, for example, it will not include truths about events at space like separation from s. Is T sub-nomically stable despite being non-maximal? Certainly, the truth of the propositions in T does not physically depend on truths about what happens at spacelike separation from s.
This version is weaker than Lewis’ doctrine of Humean Supervenience (HS) since HS requires that fundamental properties are instantiated by point size entities and that the only fundamental relations are geometrical.
Candidate systems are evaluated in terms of their simplicity, informativeness and perhaps other theoretical virtues prized in science. The Best System of a world is the system that best combines these virtues. The laws of a world are certain propositions entailed by the world’s best system. For defenses and developments of Lewis idea see Loewer (1996).
Dispositionalists can hold (ii) since they think that fundamental properties essentially possess dispositions and so their instantiations do determine which generalizations are lawful.
For example, if “whenever ice is placed in warm water it melts” is lawful, then the corresponding counterfactual “if this ice cube were placed in warm water it would melt” is true.
Given some plausible assumptions (2) is incompatible with any Humean account.
Lange thinks that there are stable sets between the largest non-maximal set and the set of metaphysically necessary truths. For example, there is a set of “meta-laws” that would still hold were first-degree laws false. Whether there are such stable sets of course depends on what counterfactuals are true.
On Lewis’ account both laws and counterfactuals supervene on the totality of categorical propositions, so in a sense neither is ontologically more basic than the other. However, Lewis analyses counterfactuals in terms of world similarity and his account of similarity involves laws; so laws are conceptually more fundamental than counterfactuals.
The truth of (1) is compatible with each of the accounts of laws mentioned above but only Lange’s account requires that it is true. Lewis’ account of counterfactuals violates (1) but that is not a consequence of his Humeanism but a feature of his particular account of counterfactuals.
Lange seems to blame possible world semantics for this result. But it holds in any counterfactual logic that endorses the validity of A □→ L → A □→ A&L, and A □→ A&L and B is entailed by A&L, then A □→ B.
The story will have to be even more complicated since the proposition expressed by a token counterfactual is context dependent.
The idea is that the lawful consequences of very small (and perhaps even counter-legal) departures from actuality are of interest to us in contemplating the consequences of alternative decisions (cf. Loewer 2006).
Lange assumes that sentences necessarily exist complete with their Kaplanian character; add a context, and sentences have everything they need to express a proposition (see p. 192, note 15).
I have condensed Lange’s proof by moving quickly to its strongest version. My presentation is drawn from pp. 71–74.
As always, thanks to John Roberts and Marc Lange for our on-going conversations about lawhood.
Re Woodward’s note 4: T is unstable since Coulomb’s law might have been violated in s’s backward light cone, had it been violated at spacelike separation from s.
That it is an irrelevant antecedent is compatible with propositions about the towns’ locations being relevant (just not as counterfactual antecedents).
Woodward’s “substantial range” of invariance could extend to counterlegal antecedents. Moreover, interventions on C break C’s causal connections and so can violate laws (2003, §3.5).
References
Armstrong, David. 1983. What is a law of nature? Cambridge: Cambridge University Press.
Bird, Alexander. 2007. Nature’s metaphysics: Laws and properties. Oxford: Oxford University Press.
Carroll, J. 1994. Laws of nature. Cambridge: Cambridge University Press.
Dummett, Michael. 1993. The seas of language. Oxford: Oxford University Press.
Herschel, William. 1830. A preliminary discourse on the study of natural philosophy. London: Longman, Rees, Orme, Brown, and Green.
Kratzer, A. 1991. Modality. In Semantics: An international handbook of contemporary research, ed. A. Von Stechow, and D. Wunderlich. Berlin: de Gruyter.
Lane, Anthony. 2009. The current cinema: Highly Illogical. The New Yorker 85 (no. 14-May 18): 80–1.
Lange, Marc. 2002. Who’s afraid of ceteris-paribus laws? (or: how I learned to stop worrying and love them). Erkenntnis 57: 407–423.
Lange, Marc. 2009. A tale of two vectors. Dialectica 63: 397–431.
Lange, Marc. (forthcoming). How to explain the Lorentz transformations.
Lévy-Leblond, Jean-Marc. 1976. One more derivation of the Lorentz transformations. American Journal of Physics 44: 271–277.
Lewis, David. 1973. Counterfactuals. Cambridge Mass.: Harvard University Press.
Lewis, D. 1976. The paradoxes of time travel. American Philosophical Quarterly 13: 45–152.
Lewis, David. 1979. Counterfactual dependence and time’s arrow. Nous 13: 455–476.
Loewer, Barry. 1996. Humean supervenience. Philosophical Topics 24: 101–127.
Loewer, Barry. 2006. Counterfactuals and the second law. In Causal republicanism, ed. Huw Price. Oxford: Oxford University Press.
Loewer, Barry. 2011. Laws and time. In Toby Handfield (ed.) On the Neglected Problems of Time.
Maudlin, Tim. 2007. The metaphysics within physics. Oxford: Oxford University Press.
Stalnaker, R. 1998. On the representation of context. Journal of Logic, Language, and Information 7: 3–19.
von Fintel, K. 2001. Counterfactuals in a dynamic context. In Ken Hale: A life in language, ed. M. Kenstowicz. Cambridge: MIT Press.
von Fintel, K. 2006. Modality and language. Encyclopedia of philosophy, 2nd edn, ed. D. Borchert. Detroit: MacMillan.
Warmbrōd, K. 1981. An indexical theory of conditionals. Dialogue 20: 644–664.
Whewell, William. 1837. History of the inductive sciences, vol. 1. London: John W. Parker.
Woodward, J. 2003. Making things happen: A theory of causal explanation. New York: Oxford University Press.
Woodward, J., and Christopher Hitchcock. 2003. Explanatory generalizations, part II: Plumbing explanatory depth. Nous 37: 181–199.
Acknowledgments
Thanks to Jim Woodward, Barry Loewer, and John Carroll for their patient and generous criticism, and to John Roberts for reviewing an earlier draft.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Woodward, J., Loewer, B., Carroll, J.W. et al. Counterfactuals all the way down?. Metascience 20, 27–52 (2011). https://doi.org/10.1007/s11016-010-9437-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11016-010-9437-9