Abstract
This paper aims to distinguish two main types of coarse graining, and reveal the relationship between the notions of coarse graining and emergence. In physics, some forms of coarse graining seem to be indispensable to show a physical property, and the other merely changes our descriptions of the system. To clarify the notion of coarse graining, this article investigates the cases of the renormalization group method and irreversibility, both of which have been important topics in philosophy of science, and the case of the rigid body in classical mechanics, which is an elementary case including coarse graining. The case studies reveal the distinction between substantial and mere coarse-graining. This distinction clarifies the relationships between the notions of coarse graining and emergence and further provides some implications for the issues about emergence.
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Notes
The comparison class is classified into two kinds: “Composite” and “Limits” (Butterfield, 2011b, p. 1066). In the case of “Composite”, a system is composite, and its comparison class is its component systems. In the case of “Limits”, a system is a limit of a sequence of systems and its comparison class is a set of its finite systems.
The compatibility between reduction and emergence seems to be at odd with traditional understandings of these notions. However, these definitions are not peculiar, for the definitions are based on the traditional arguments about reduction and emergence in philosophy and applicable to several cases in science.
The notion of explanatory novelty in Franklin and Knox (2018) relies on the novelty explored by Knox (2016). Knox shows that thermodynamics has a novel explanatory value compared with statistical mechanics. Although Boltzmann’s principle establishes a link between statistical mechanics and thermodynamics, the latter has its own explanatory value. Knox considers the differences between diesel and petrol engines. While the petrol engines require spark plugs, the diesel engines do not. Thermodynamics provides an explanation for this difference, and this explanation relies on an abstraction, such that the process is adiabatic. In terms of statistical mechanics, the difference in the engines can be explained based on the Boltzmann’s equation as the bridge law. However, thermodynamics provides a better explanation than statistical mechanics. Thermodynamics is based on the notion of heat and work and explains why a process is assumed to be adiabatic. On the other hand, the thermodynamic notions are reduced to kinetic energy in statistical mechanics, and the roles of the assumption about the adiabatic process cannot be explained within statistical mechanics. Therefore, she concludes that thermodynamics has an explanatory novelty compared with the statistical mechanics.
Batterman and Rice (2014) argue that the RG method is different from other usual ways of reasoning, which they label the minimal model. Lange (2015) and Reutlinger (2017) criticize this view and argue that the minimal model is not different from other usual scientific explanations. Rodriguez (2021) calls this criticism a commonality strategy for explanation. Rodriguez partially admits the validity of the commonality strategy, but he also argues that the RG method demonstrates a qualitative novelty, which the commonality account fails to capture.
Another objection is that the asymmetry “arises from our perspective and so is anthropocentric” (Robertson, 2020, p. 561). The coarse-graining procedure itself does not change the physical systems at all, but merely changes our perception of the system. In this sense, the framework based on this procedure seems to be too anthropocentric. Robertson’s counterargument to this objection is as follows: The choice of cell size for coarse graining is arbitrary. However, the size of cells is not completely arbitrary, but is limited by the purpose of uncovering irreversible dynamics. This strategy has been applied in the field of physics. The choice of physical variables and their definitions (such as mass, energy, and entropy) largely depends on the purpose of the physicists. Therefore, the ZZW framework is not anthropocentric.
Note that this argument cannot be straightforwardly applied to other cases of continuum, such as fluid considered in Batterman (2018) and Wilson (2017). This articles has investigated only the continuum as a description of a rigid body, and other cases like fluid might be ontological emergence unlike the rigid body.
It is true that the cases considered above deal with multiple models, but these are not the instance of the multiple model idealization. The multiple model idealization deals with more varied types of models as examples, such as climate science. Therefore, this idealization is not relevant to our purposes.
Some might consider that the existence of friction seems to be a novel property for the model of a frictionless plane and imply ontological emergence. However, this is not a case of ontological emergence, because the friction is not the aim of this models. The models with and without friction are used to understand or demonstrate a classic mechanical behavior. When a lower-level model of atoms composing a plane does not show friction and a higher-level model of plane, as a continuum, show friction, the friction might be ontological emergence.
The meaning of the ontological emergence in this article is based on De Haro’s argument (De Haro, 2019, p. 2). The ontology in this article does not mean metaphysical ontology that is mind-independent and takes no account of interpretations, but ontology of scientific models. The scientific models in physics are merely mathematical equations and the intentions of scientific agents are required to connect the models with the empirical world as Giere (2010) argues. Therefore, the ontology of scientific models investigated in this article is not completely mind-independent. That is, ontological emergence in this article does not refer to what is completely mind-independent entities or properties, but some properties given by interpretations of models.
The interests or aims of agents determine what is the target property, but not arbitrary. This article assumes that the agents belong to their scientific community. The scientific community deals with particular realms of this world such as the critical phenomena, the behavior of classical rigid body, organisms, or global climate, and in each community the issues or problems are shared by their agents. Based on this assumption, agents in this somewhat old-fashioned scientific community share the same aims and interests about the target system, and there is a consensus about the target property among scientists. In this sense, the target property is, at least partially, objective to imply ontology of scientific models. In contrast, when they do not share the same target property of the model because they have different aims or interests, the distinction about coarse graining explored in this article is not applicable.
While Butterfield (2011a) has pointed out that robustness is a condition of emergence, De Haro suggests that robustness is not a necessary condition of emergence (De Haro, 2019, p. 10). Because coarse graining involves a process of ignoring details, the stability and autonomy of the target properties are ensured.
An anonymous referee has pointed out the existence of these cases related to the RG. The philosophical implications from them also are an important topic about coarse graining.
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Acknowledgements
This research is supported by Grant-in-Aid for JSPS Fellows 20J01142. I thank two anonymous referees for fruitful comments, and Tetsuji Iseda, Yukinori Onishi, Kazuaki Takasan, Kazuhisa Todayama, and Yoshinari Yoshida for valuable discussions.
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Morita, K. A fine-grained distinction of coarse graining. Euro Jnl Phil Sci 13, 12 (2023). https://doi.org/10.1007/s13194-023-00513-0
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DOI: https://doi.org/10.1007/s13194-023-00513-0