Abstract
Special sciences (such as biology, psychology, economics) describe various regularities holding at some high macroscopic level. One of the central questions concerning these macroscopic regularities is how they are related to the laws of physics governing the underlying microscopic physical reality. In this paper we show how a macroscopic regularity may emerge from an underlying microscopic structure, and how the appearance of multiple realizability of the special sciences by physics comes about in a reductionist-physicalist framework. On this basis we explain how complexity at the high level can arise due to a sort of harmony between the microscopic dynamics and observer-dependent macroscopic properties. We show that observer-dependent properties, which underlie the emergence of macroscopic properties and of macroscopic complexity, are objective physical facts. We argue that such physical properties remove the mystery from the multiple realizability of special sciences’ kinds, since the latter are grounded in shared physical properties. Finally we explain how and in what sense in our reductive physicalist approach the special sciences are still autonomous after all.
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Notes
It is by no means general that the recipe generates output states that are as complete as the input states, and can therefore be used as input states. For example, in classical mechanics if the input is a complete description of the mechanical state then so is the output. But whether or not this is also the case in quantum mechanics depends on interpretation (by the way, the notion of completeness we use here is unrelated to the notion addressed in the context of quantum mechanics, for example by Einstein et al. 1935).
Roughly speaking, entropy describes the amount of a system’s energy that cannot be harvested as work. In statistical mechanics it is often associated with degree of order or amount of information. We shall not go into these technical details here; they can be found in introductory textbooks on thermodynamics and statistical mechanics.
Classical and quantum, as well as the other theories of physics.
Given their masses and perhaps other internal properties.
Actually this becomes a problem that is unsolvable analytically already for very few degrees of freedom: this is known as the three bodies problem.
The kinetic energy of a single particle is half of its mass times its velocity squared: description of this quantity omits the position, and the direction of the velocity. The quantity in question is the average of this magnitude over all the particles, at a point of time; and this quantity omits the details of which kinetic energy does each particle have or even the distribution of the kinetic energy, as long as the average is conserved.
The relation between temperature and average kinetic energy is complex and the term ‘account’ above is meant to include the necessary qualifications in this particular context. Chang (2004 on temperature and elsewhere on other notions) convincingly points out that standard reductive accounts that are meant to be in terms of low level theories unavoidably include notions that are taken from high level theories and even pre theoretic phenomena, so that the result is not purely reductive. We accept this line of thinking. However our point here is not only the epistemological one regarding inter-theoretic reduction, but rather a metaphysical point, namely, we wish to put forward the hypothesis of ontological reductive monism and to show here in outline how such a hypothesis is coherent and how it can account for the special sciences.
Entropy in Boltzmann’s approach is associated with the Lebesgue measure of the set to which the microstate of the system at each time belongs. In Gibbs’s approach, entropy, like other thermodynamic magnitudes, is formally associated with a function over the entire accessible state space. See Hemmo and Shenker (2012, Ch. 11), for an explanation of how Gibbs’s notion of entropy is actually an application of Boltzmann’s notion for some special albeit important circumstances. We show there that Boltzmann’s and Gibbs’s approaches can be accommodated within a single statistical mechanical theory, which is the theory we briefly describe here.
Although they understood these notions in different ways. For literature on the historical origin and foundations of statistical mechanics, see the previous footnote.
One might say that the accessible region is determined by the interactions between O and G, which bring about this correlation. This might be the case and we address this option later, but it is not a priori necessary, and we shall also consider a case where this doesn’t hold in Sect. 6.
The way this correlation is brought about is the subject matter of discussions of the mind–body problem, which we don’t address here. As long as one accepts that the mental is associated with the physical state of affairs, this issue will not affect our approach.
One might make the reasonable conjecture (though by no means conclude!) that (in this case) the microstates of O that are in O 1 share a certain aspect which gives rise to this experience of O. If that conjecture is true, this shared aspect would explain the fact that all of these microstates have the same effect on O’s experience: it is the shared aspect itself that affects O’s experience. And if that shared aspect is describable in terms of the theory T, then we have an explanation, in terms of the theory T, for the origin of the experience of O. But the above conjecture is not logically necessary, since multiple realizability of the mental by the properties of theory T (e.g. physics or biology) is logically possible.
We don’t address here methodological individualism in the social sciences, apart from making some comments on the way it may relate to the conceptual framework that we propose in this paper. See overview in Heath (2015).
The regularities described by, say, classical mechanics, in the domain where they effectively hold, can of course be explained as the outcomes of deeper reality and deeper regularities. For the sake of the present discussion we assume that the micro-mechanical regularities are true about the world. One may replace these with other regularities, and our general schematic ideas will hold equally there as well. For example, with respect to quantum mechanics, see Hemmo and Shenker (2015).
O could then either begin the experiment immediately, or put some constraints on G to keep it in the same macrovariable M 0 and begin the experiment later on. This doesn’t make a difference for our purposes. In both cases we say that G is prepared with the macrovariable M 0, in which the experiment begins.
For possible shortcuts see Hemmo and Shenker (2012).
An important feature of B(t) is that its Lebesgue measure is conserved under the dynamics for all times in accordance with Liouville’s theorem.
For more details about how probabilities are determined in statistical mechanics, and in particular about how to choose the measure relative to which probabilities are distributed uniformly over the state space, see Hemmo and Shenker (2012).
Notice that this “collapse” describes only the experience of O due to the actual trajectory of O + G. The other trajectories, the counterfactual ones, retain their theoretic counterfactual status: no trajectory is erased and there is no branching in or out. The microscopic dynamics and ipso facto the evolution of the entire blob B(t) remain completely deterministic and unitary at all times. In particular, the collapse satisfies Liouville’s theorem at all times without ever violating it.
This expansion may result in an entropy increase or decrease, depending on the structure of the macrostates and the way the blob evolves over the state space. But we do not argue for this here, and nothing in what follows hinges on it. For more about entropy, see Hemmo and Shenker (2012).
Given formally be the Lebesgue measure.
In appropriate orders of magnitudes fluctuations are observed, in accordance with the predictions of statistical mechanics, but not of thermodynamics. See also Callender (2001).
This notion of complexity may prima facie seem different than the one often used by people who are doing complexity modeling in social science. An example here is the emergence of complex patterns of behavior from the interactions of relatively unified components of the system which can be characterized by relatively simple properties and that are governed by relatively simple rules, as in Sawyer (2005, p. 3). Here is the connection between the two notions of complexity. A simple system in Sawyer's terms will also be simple in Kolmogorov's terms, in the sense that a concise algorithm is available to describe the evolution of the macro-variables of the system. A chaotic system is maximally complex since there is no finite algorithm for generating the evolution of its macrovariables. You need to provide an endless and ever growing amount of data that will make no progress. The best one can do is offer broad qualitative and disjunctive predictions, which is not even probabilistic in any non trivial sense. The intermediated case is where you can only generate a probabilistic prediction, but it is still better than mere guessing. Nevertheless, the evolution of the states of complex systems in the sense presupposed in complexity modeling in social science can be described and predicted in mathematical terms of dynamical systems theory. In our terms the way to understand this situation is as follows. With respect to certain macrovariables, which are the initially more transparent ones, an algorithm is unavailable, due to a high degree of complexity. The solution is to look for other non trivial macrovariables for which the construction of an algorithm (usually a probabilistic and approximate one) is possible.
Note that chaos is a special sort of macroscopic (non) regularity in the sense that the divergence of trajectories is independent of the partition to macrostates since the microscopic evolution is highly sensitive to initial conditions up to a fractal structure of the state space.
This starting point is rejected by dualists. Explicit dualism is a position we don’t consider in this paper.
We don’s ask here what ‘physics’ is and don’t address the so-called Hempel’s dilemma in this paper.
We don’t use the term token physicalism since our assumption is compatible with type physicalism, whereas in the literature the term token physicalism is often used to name some sort of non-reductive-physicalism.
Note that the discussion here doesn’t address the question of the multiple realizability of O’s mental states, but rather the multiple realizability of G’s properties, as experienced by O; see also footnotes 12 and 13.
Here we don’t distinguish between directly experiencing kinds and theoretically conceiving of kinds. The difference between these two sorts is immaterial to our present argument. We use the term ‘experience’ to denote all manners of relating to a kind.
As we said (in footnote 30) we don’t address here the question of the multiple realizability of our psychological experience, which is about the multiple realizability of the mental kinds we experience (e.g. intentional, qualia states) by physical kinds. The way to account for such mental kinds is different; see also footnotes 12 and 13.
Another important example is Boltzmann’s H theorem (and forget for a moment that it is not really a theorem). The Maxwell–Boltzmann energy distribution characterizes a macrostate in terms of a highly non trivial macrovariable. And the only reason why this macrovariable is interesting is the very fact that it corresponds to the experienced state of equilibrium of an ideal gas; see Hemmo and Shenker (2014).
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Acknowledgments
We are grateful for the meticulous and extremely valuable comments of Yakir Levin, and for the very helpful suggestions and the critical reading of Itzhak Aharon and two anonymous reviewers. All of these helped us improve this paper substantially. This research is supported by the Israel Academy of Sciences Grant Number 713/10 and by the German-Israel Foundation Grant Number 1054/09.
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Hemmo, M., Shenker, O. The emergence of macroscopic regularity. Mind Soc 14, 221–244 (2015). https://doi.org/10.1007/s11299-015-0176-x
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DOI: https://doi.org/10.1007/s11299-015-0176-x