Direction and Description
Introduction
Thermodynamics and statistical mechanics, unlike other branches of physics, seek to explain directionality. One of the major problems of statistical mechanics, a problem addressed in several papers in this issue, is whether this goal has in fact been fully achieved.1 Let me emphasise at the outset that I do not provide an answer to this much-discussed question. Rather, I undertake a general examination of explanations of directionality, and their relation to causal explanations, focusing on how modes of description affect some kinds of explanations of directionality. I argue that ascription of directionality is sensitive to standards of similarity and schemes of description, individuation and classification in ways ascription of causality is not. Interestingly, these rather general considerations about the differences between various types of explanation lead to quite specific conclusions about the feasibility and desirability of reduction. Reduction of one explanatory level to another frequently comes up in the context of statistical mechanics; but other areas in which directionality is at issue, for instance, evolutionary theory, can also benefit from the analysis offered here.
I begin by introducing notions of necessity and contingency that differ both from their counterparts in modal logic, and from the notions of causality and chance (Section 2). These notions are closely related to the notions of stability and instability. Expanding on an idea of Davidson's, I show that assessments of necessity and contingency (stability and instability) depend crucially on modes of representation and individuation. This observation provides a different reading of Jaynes's position, which is usually construed as subjectivist (Section 3). Necessity and contingency are then related to the explanation of directionality in general, and statistical mechanics in particular (Section 4). Turning to reduction, I argue that reduction of directionality to the fundamental causal level is, as a rule, unnecessary, and in many cases, unwarranted (Section 5). Finally, I apply the insights arrived at in 2 Necessity and Contingency as Degrees of Stability, 3 Description, 4 Directionality, 5 Reduction to the Gould–Dennett debate about natural selection.
Section snippets
Necessity and Contingency as Degrees of Stability
Some states are more stable than others: a tennis ball inside a (not too large) sphere is in stable equilibrium, whereas a ball on top of the same sphere is in a far less stable state. Stability is characterised in terms of effects of small changes, a stable state being one to which the system returns if subjected to a small change. Note, however, that in our example both balls, the stable and the unstable, move in accordance with the same laws of Newtonian mechanics, indicating that causality
Description
In his celebrated ‘Causal Relations’, Davidson draws a distinction between causal and explanatory contexts: whereas the truth of singular causal statements is independent of the description of the events in question, explanatory contexts, much like other intensional contexts, are description-sensitive. Thus, compare:
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Lord Kelvin made significant contributions to thermodynamics.
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Sharon knows that Lord Kelvin made significant contributions to thermodynamics.
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The reaction caused the explosion.
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The
Directionality
On the basis of the distinction between causality and chance on the one hand, and necessity and contingency on the other, we are now ready to draw a parallel distinction between types of directionality. Directionality can appear at the basic level of (causal or random) events, manifested by processes that unfold in one direction rather than the other, or unfold more frequently in one direction than in the other. Whether there are in fact such processes is, of course, an empirical question.18
Reduction
Since there are, on the analysis of the previous section, different kinds of directionality, the question of how they are related naturally arises. In principle, different combinations of the two types are possible. Consider, for example, a biological change in a certain population of organisms. It can arise from a change at the basic level of the genome, as a result of mutation, crossing over, transposition and so on (as when radiation induces mutation), or from natural selection feeding on
The Gould-Dennett Debate on Natural Selection
To conclude, I would like to see what bearing the above considerations have on a current debate about Darwinism. We can note at the outset that there are important analogies between the second law in its statistical formulation and evolution through natural selection.25 Both theories eliminate earlier teleological explanations, proffering
Acknowledgements
I am grateful to Orly Shenker and Itamar Pitowsky for their comments on an earlier version of this paper, and for many stimulating conversations. I have also benefited from reading Shenker (1997), and from questions and suggestions made by David Albert, Meir Hemmo, Barry Loewer, John Norton and Hilary Putnam.
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