I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this causal entropy cannot decrease from a robust cause to its effect. Due to its analogy with the second laws of thermodynamics and statistical physics, I call the latter conclusion the causal second law. In this paper, I clarify the key assumptions, prove the causal second law, give sufficient conditions for causal entropy increase, relate the causal second law to statistical mechanics and thermodynamics, and argue that the reversibility objection does not threaten it. In addition, I claim that the causal second law is compatible with a non-metaphysical understanding of supervenience and the open systems view, argue that it does not imply a causal time arrow, reflect on relaxing the robustness condition, question whether it is necessary to invoke thermodynamics to show that special sciences' time arrows exist, and discuss a transition-relative-frequency-based, special-science-internal characterization of causal regularities.
Causal regularities have an associated notion of entropy which cannot decrease from a robust cause to its effect, assuming that certain key assumptions, familiar from physicalist accounts of the special sciences and from physics, hold. In the limiting case where, as Hume (1739, 173) puts it, "the same cause always produces the same effect," an argument for this claim can be succinctly formulated as follows. If the same cause always produces the same effect, then any physical instantiation of the cause, following the laws of physics, must evolve to a physical instantiation of the effect. But then, if the number of distinct physical instantiations of the cause cannot decrease during their time evolution, there must be at least as many physical instantiations of the effect as physical instantiations of the cause. By defining the causal entropy of the effect and the cause as the number of their physical instantiations, it follows that the causal entropy of the effect must be at least as large as that of the cause.
The paper clarifies and motivates the key assumptions-primarily, state-supervenience and measure-preservation-behind a physically more plausible version of this argument and extends the argument to robust causal regularities of any special science (which term I understand here broadly to include folk physics and folk psychology, along with chemistry, biology, psychology, economics, and so on) for which these assumptions hold. With this terminology, the main claim can be restated as follows: if a special science has robust causal regularities, and if it satisfies state-supervenience and measure-preservation, then the special science has an entropy principle tied to its own domain. Due to its analogy with the second laws of thermodynamics and statistical physics, I call this entropy principle the causal second law. 1 Section 2 details the assumptions and proves the causal second law for robust causal regularities on their basis. In Section 3, I argue that when an effect has multiple possible causes, a case that is typical in special sciences, causal entropy from an actual robust cause to its effect strictly increases. I also show why causal entropy must generally increase due to the mismatch between the descriptive capabilities of a given special science and physics.
In Section 4, I turn to the relationship between the causal second law and the second laws of thermodynamics and statistical mechanics. I reconstruct an explication of the second law by Jaynes (1965), arguing that it provides a perspective in which thermodynamic entropy can be understood as causal entropy applied to the special science of thermodynamics. This justifies introducing the term entropy outside thermodynamics and statistical mechanics, associating it generally with causes and effects, and illustrates that, under certain circumstances, practically useful expressions can be derived from the causal second law. I also address time reversal invariance, showing that the reversibility objection does not threaten the exceptionless character of the causal second law for robust causal regularities of special sciences that satisfy the key assumptions.
In Section 5, I return to the background assumptions; in particular, I argue that the approach can be extended to multiply realized robust causation, that we can relax the metaphysical reading of state-supervenience, and that the relevant sense in which measure-preservation is invoked is compatible with the open systems view. Although the main claims of this paper remain conditional upon the so-relaxed assumptions, the section briefly motivates their general plausibility. I also argue that the reasons for the strict increase of causal entropy for robust causes allow robustness to be relaxed to portionality.
Finally, Section 6 is devoted to the framework of the discussion, the dynamical systems approach to causation. I point towards a number of open problems and directions for further development. I argue that the approach provides a clear distinction between entropyfrom-cause-to-effect and entropy-in-time (6.1); emphasize the description-relativity of the results (6.2); address the viability of philosophical projects that aim to infer that causes precede their effects from an entropy increase in thermodynamics (6.3); ask whether, in the light of the results of this paper, it is necessary to invoke thermodynamics to show that special sciences’ time arrows exist (6.4); show that strengthening state-supervenience to history-supervenience permits a special-science-internal characterization of robust regularities (6.5); and address the practical usefulness of the causal second law (6.6).
The main text keeps the discussion informal; formal definitions and proofs are in the Appendix.
Even though David Hume’s attempt to define the causal relation from regularities has been frequently criticized (Andreas & Guenther, 2021), the property that a cause is regularly followed by its effect is one of th
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