Abstract
Standard philosophical accounts attempt to understand physical modality either in terms of special metaphysical entities and relationships (“relations between universals”, “powers”, “dispositions”) or in terms of the organization of non-modal information, as in Best Systems Analysis. This paper defends an alternative to both these approaches in which invariance and various independence conditions play a central role. The methodological importance of separating law-claims from claims about initial and boundary conditions is highlighted
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
I do not mean that our notions of law and physical modality contain some covert reference to or relativization to epistemic factors. Rather the idea is that these notions are engineered for contexts and beings with epistemic and calculational limitations and this is reflected in the character of those concepts. In the same manner, an insect wing might be “designed” for performance in air currents with certain characteristics without its being the case that we need to think of the wing as somehow “relativized” to those currents.
I also acknowledge that what follows is my gloss on Wigner. I’m not concerned with whether it is in every respect an accurate report of his views. Rather I treat Wigner as an inspiration for a certain picture of laws.
If one thinks of the notion of “law” as the sole basic element in understanding of physical modality, then one will presumably think of the independent variability of initial conditions in purely negative terms—it is just a matter of the absence of any law according to which values of \(X_{\textit{1}}\) constrain values of \(X_{\textit{2}}\). An alternative approach might include physical independence as among the basic elements needed to understand physical modality. I regret that I lack the space to explore this idea here.
Note that this is not just a matter of the generalization failing to be false for those variations over which it is invariant; the requirement is rather that the generalization must “apply to” systems exhibiting the variations in question and accurately describe the nomological relationship holding under the variations. For example, although a version of the Newtonian gravitational inverse square law that is explicitly restricted to phenomena near the surface of the earth does not make false claims about celestial phenomena, it does not count as invariant under changes in initial conditions describing celestial phenomena.
See Woodward (2013).
A similar observation holds for so-called backtracking counterfactuals. Suppose that in the actual world the cat is on the mat a time t. Then it is certainly arguable that the counterfactual, “If the cat had not been on the mat at t, something about the past would have been different” has an interpretation under which it is true—either some prior initial condition would have been different or, as Lewis claims, a prior miracle would have occurred. This again is an interpretation of the counterfactual under which we consider whether it is reasonable to infer the truth of the consequent given the supposition of the antecedent. However, although some philosophers seem to dispute this, I take it to be uncontroversial that it is not true that making it the case that that the cat is not on the mat at t, would make the past different. Again it is the latter (interventionist) interpretation that is relevant to the assessment of invariance claims.
Lange (2009, xiii) takes subjunctive facts, expressed by counterfactuals, to be “ontologically primitive and responsible for laws”. My view differs in several important respects. First, I make no claims about what is most primitive or fundamental. My view is that laws and counterfactuals are so entangled that there is no basis for claiming one of these is more fundamental than the other. Second, Lange does not distinguish among kinds of counterfactuals in elucidating laws in the way that I do. Roughly, Lange requires that laws hold under all (allowable) counterfactual suppositions consistent with them. I require that this be true only for a specific subclass of counterfactuals,—those that have an interventionist or at least manipulationist interpretation in the manner described above. As a result, Lange’s account is (I believe) subject to counterexamples along the lines of (S)—that is, on Lange’s account, the truth of a counterfactual like (S) means that SR fails to be invariant or counterfactually stable, which I take to be the wrong result (see Woodward 2011). Finally, my notion of invariance is graded, as explained below, while Lange’s analogous notion is an all or nothing matter.
I suspect that the temptation to think of the gravitational force law as a claim about the total force derives in part from thinking of laws as straightforward descriptions of “Humean” regularities relating properties that do not carry any modal commitments. If we think instead of the law as describing the component of the gravitational force on \(m_{\textit{1}}\) which is due to mass \(m_{\textit{2}}\), we have a much more accurate description of the content of the law. Note, however, that this is no longer a description of a “Humean” regularity characterized in non-modal terms, since “due to” and perhaps “component” are not properly Humean.
This relativization to a domain is not just the triviality that laws hold when they hold; it rather involves the claim that laws would continue to hold if non-actual conditions (and non-actual processes leading to these conditions) within their domain of invariance were to be realized, where (at least often) this domain can be given an independent specification—in physics this is often done by specifying length or energy scales in which the law holds.
Perhaps one might think of the relationship between current effective theories and the deeper theories that underlie them is in terms of a kind of robustness or invariance of the former under variations in the latter, but where the invariance is conceptual or mathematical in nature, having to do with the fact the effective theory continues to hold under variations in some mathematical space of possible deeper theories. This sort of invariance is different from the more “empirical” variety considered in the body of this paper. I lack the space to explore it here. In any case, this sort of grounding is very different from what metaphysicians of science have in mind when they talk about “grounding”.
Note also that effective laws (obviously) can be recognized as having that status (on the basis of features F they possess) in the absence of information about the more fundamental laws that underlie them. So we can ask the question of what those features F are. Relative invariance is my candidate for such a feature.
Contrast this with philosophical accounts of laws that, like the BSA, do not begin with a distinction between laws and initial conditions but instead impose a general simplicity constraint that operates on an undifferentiated Humean mosaic. On such conceptions simplicity in connection with laws and simplicity in connection with initial conditions are treated in the same uniform way. See Woodward (2013) for some difficulties to which this leads. Note also that philosophical accounts of unification that do not begin with a distinction between laws and initial conditions and instead assess degree of unification just by counting the number of independently acceptable premises (or something similar) will fail to capture the different role played by unification considerations with respect to laws and initial conditions.
For example, philosophers who wish to ground laws in dispositions typically retain something very like this picture of laws.
This is a point that is emphasized in Wilson (forthcoming).
Cartwright (1999) has repeatedly observed that (i) a great deal of specific structure (which she calls a nomological machine) must be present in a system before it generates (what I would describe as concrete and specific) regularities. Apparently influenced by the philosophical tradition that associates laws with such regularities, she concludes that laws themselves require such structure in order to hold. Laws thus have a sort of derivative status—derivative on the machines that generate them, whose behavior is due to capacities that are assembled in a particular way. I agree with the initial observation (i) but for exactly that reason would resist the association of laws with highly concrete regularities.
At the conference at which I presented this paper, it was noted that several recent accounts of laws treat the Past Hypothesis (PH) as having nomological status (and as central to an acceptable account of lawhood), despite the fact that PH looks in some respects as a claim about initial conditions. It was suggested that this showed I was wrong to attach any great importance to the contrast between laws and initial conditions. Without commenting on PH, I think this is the wrong moral, for the reasons described above. Assuming for the sake of argument that PH is defensible science, if it blurs the line between lawful and non-lawful in the way described, the conclusion we should draw is that this is a context in which the notion of law no longer fruitfully applies, not one in which we are dealing with something that is both a law (or nomological) and a claim about initial conditions.
An anonymous referee suggests that the use of this example to criticize the BSA assumes that there is a fact of the matter about whether \(L_{\textit{1}}\) or \(L_{\textit{2}}\) (or neither) is a law even if the experiment is never done. I agree. The referee infers from this that, on my view, “the actual pattern of physical facts does not alone fix what the laws are, since nothing about the world without the experiment determines which law is correct” and that, consequently, which law is correct “must depend on some non-Humean fact”. I lack the space to respond in detail, but let me make the following remarks (see Woodward 2013 for more discussion). First, the notion of “fixing” here is metaphysically loaded (and in my opinion unclear). If we instead ask the clearer question of what sorts of information is used to discover or infer to laws, the answer is that in actual practice this involves a mix of claims that may be “Humean” and non-modal and other claims that carry modal or causal or nomological commitments. (I assume for the sake of argument that the contrast between “modal” and “non-modal” is clear, even though I think this is not always the case). The pattern of inference is: Non-modal information N+ modal information \(\hbox {M}_{1}-\)\(\rightarrow \) new modal information \(\hbox {M}_{2}\). As far as inference goes, it is indeed true that the non-modal information N is not sufficient to fix (or as econometricians would say) “identify” \(\hbox {M}_{2}\). But this does not mean that the nomological facts in \(\hbox {M}_{2}\) are independent of “everything” in the world or all “the physical facts”, unless we simply identify the expressions in quotes with N, which seems arbitrary. When I do an experiment and use the result to (reliably and correctly) support a claim about a law, this use of the experiment requires that certain modal (or causal or nomological) claims about the processes generating the experimental result be true—for example, claims about the absence of confounders, that the experimental result has been produced in certain ways and so on. I see no reason to deny that these are “physical facts”, having to do with how matters stand in the world. Nor do I see any reason to suppose it must be possible to fully translate these modal claims into non-modal claims, in the absence of the actual exhibition of such a translation.
The second thing to be said is that the criticism makes assumptions about modal claims needing truth-makers of the sorts postulated by metaphysicians—assumptions that I would reject, for reasons described in Sect. 7.
It is worth underscoring that these sorts of considerations contrast with the metaphysical arguments usually offered for and against a grounding role for dispositions. The argument described above is instead methodological—the law framework is methodologically superior for the reasons described.
The idea that the laws govern is also connected by some to the notion that they have their source in a divine lawmaker who prescribes rules that nature must obey. Contrary to what some have suggested, I don’t think that any such theological connection is really assumed in discussions of law in modern science.
I thus put aside, for reasons of space, any discussion of whether the BSA and similar accounts provide a “metaphysical explanation” of some kind for laws and physical modality, as claimed by, e.g. Loewer (2012). For a variety of reasons I don’t think that they do, but this is a matter for another paper.
A further remark: We should distinguish the idea that claims about physical modality, invariance and so on should be responsible to how matters stand in the world, which I endorse, from the idea that we can illuminate modal claims by postulating special metaphysical entities or relationships to serve as truth-makers for them, which is what the advocate of non-Humean stuff claims. On my view, modal claims can be true because of how matters stand in the world without having the simple discrete truth-makers or correspondents envisioned in talk of relations of necessitation between universals and so on. And one can be a non-Humean about modal claims, in the sense that they are not reducible to claims about Humean regularities, without postulating non-Humean stuff as truth-makers for such claims (It’s the “stuff” part of “non-Humean stuff “ that the invariance-based account rejects). Analogously, claims about the probability of red on spins of a roulette wheel can be true even though there is no metaphysical item, chance, present in the machine to serve as truth-maker.
References
Beebee, H. (2000). The nongoverning conception of laws of nature. Philosophy and Phenomenological Research, 61, 571–594.
Carroll, J. (1994). Laws of nature. Cambridge: Cambridge University Press.
Cartwright, N. (1999). The dappled world. A study of the boundaries of science. Cambridge: Cambridge University Press.
Cartwright, N., & Ward, K. (2016). Rethinking order: After the laws of nature. London: Bloomsberry Academic.
Hicks, M. (Forthcoming). Dynamic humeanism British Journal for the Philosophy of Science.
Lange, M. (2009). Laws and lawmakers. New York: Oxford University Press.
Loewer, B. (2012). Two accounts of laws and time. Philosophical Studies, 160, 115–137.
Maudlin, T. (2007). The metaphysics within physics. Oxford: Oxford University Press.
Mumford, S. (2004). Laws in nature. London: Routledge.
Sklar, L. (1991). How free are initial conditions. In A. Fine, M. Forbes, & L. Wessels (Eds.), PSA 1990 (Vol. 2, pp. 551–564). East Lansing, MI: Philosophy of Science Association.
Wigner, E. (1967). Symmetries and reflections. Bloomington: Indiana University Press.
Wilson, M. (Forthcoming). Physics avoidance. Oxford University Press.
Woodward, J. (2003). Making things happen: A theory of causal explanation. New York: Oxford University Press.
Woodward, J. (2011). Counterfactuals All the way down? (symposium on Marc Lange: Laws and lawmakers: Science, metaphysics, and the laws of nature). Metascience, 20, 27–33.
Woodward, J. (2013). Laws, causes, and invariance. In S. Mumford & M. Tugby (Eds.), Metaphysics and science (pp. 48–72). Oxford: Oxford University Press.
Woodward, J. (Forthcoming). Laws: An invariance-based account. In L. Patton, & W. Ott (Eds.), Laws of nature: Metaphysics and philosophy of science. Oxford: Oxford University Press.
Acknowledgements
A version of this paper was presented at the Conference on New Trends in the Metaphysics of Science, University of Paris/Sorbonne. December, 2015. I am very grateful to the participants for a number of helpful comments and suggestions. I am also grateful to the two anonymous referees for this paper for their suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Woodward, J. Physical modality, laws, and counterfactuals. Synthese 197, 1907–1929 (2020). https://doi.org/10.1007/s11229-017-1400-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-017-1400-5