Abstract
The paper argues against the widely accepted assumption that the causal laws of (completed) physics, in contrast to those of the special sciences, are essentially strict. This claim played an important role already in debates about the anomalousness of the mental, and it currently experiences a renaissance in various discussions about mental causation, projectability of special science laws, and the nature of physical laws. By illustrating the distinction with some paradigmatic physical laws, the paper demonstrates that only law schemata are strict whereas causal laws are generally non-strict. Several potential replies to this argument are discussed and rejected as unsound.
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Notes
If there is such a thing as instantaneous causation as some claim to have located it in quantum systems (cf. Esfeld 2010b), it should we viewed as a very different kind of causation incomparable to the one we encounter in the special sciences and in physics outside quantum theory.
If one rejects deterministic causation in favor of physical causal laws as irreducibly probabilistic, the conditional takes the form “\(\forall x(\phi x \rightarrow _{[P(\psi |\phi )]} \exists y(\psi y \wedge Rxy))\)”. In words: “For all individuals x, if x instantiates the property \(\phi \), then to probability \(P(\psi |\phi )\) there is an individual y which instantiates property \(\psi \) and to which x stands in the relation R.” \(P(\psi |\phi )\) is the probability of y instantiating \(\psi \) conditional upon x’s instantiation of \(\phi \). Of course, if one thinks of physical causal laws as irreducibly probabilistic, Davidson’s “perfect predictability under the terms of the system” (2001/1970, 218) does not hold in any case, and the falsity of PSL is immediately accepted. This is the reason why we restrict our discussion to the existence of deterministic and reducibly probabilistic physical causal laws.
A system that is coupled to a heat bath is a system that is in good thermal contact with a much larger system (the heat bath) with a given temperature. The system and the heat bath can exchange heat and energy freely and since the heat bath is (ideally, infinitely) larger then the system, the temperature of the heat bath stays constant at all times. If the system and the heat bath are both in equilibrium the temperature of the system equals the temperature of the heat bath.
A reversible change to the system is a slow change in time through which the system remains in equilibrium (or very close to it).
It would have to use a formula such as: “\(\forall x(Gnx \wedge Vx \wedge Px \wedge F_{V'}x \rightarrow \exists y(Gny \wedge P'y \wedge (P'=\frac {nRT}{V^{\prime }}) \wedge Rxy))\)”. In words: “For all spacetime regions x, if they host n moles of gas in a container of volume V, such that the gas the gas acts onto the walls of the container with pressure P and such that a particular force \(F_{V'}x\) is applied to the container eventually altering it to volume \(V'\), then there is a second spacetime region y that is distinct from, but proximate to, x that hosts n moles of gas in a container such that the pressure of the gas equals \(\frac {nRT}{V^{\prime }}\)”. The length of this expression makes clear why using the compact string of symbols of Eq. 1 is very useful to state certain causal laws in physics.
Note that the term “law schema” is foreign to the language of physics, which accesses the distinction from context or by describing Eq. 1 as an “idealization”. Obviously, the terminology used to capture the distinctions is of secondary importance to the capturing of the distinctions itself.
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Harbecke, J. On the Distinction Between Law Schemata and Causal Laws. Acta Anal 28, 423–434 (2013). https://doi.org/10.1007/s12136-013-0185-5
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DOI: https://doi.org/10.1007/s12136-013-0185-5