Abstract
I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but also by answering what-questions, that is, by providing what I call scientific descriptions. Based on this distinction, I develop three forms of understanding: understanding-what, understanding-why, and understanding-how. I argue that understanding-how is a particularly deep form of understanding, because it is based on mechanistic explanations, which answer why something happens in virtue of what it is made of. I apply the three forms of understanding to two case studies: first, to the historical development of thermodynamics and, second, to the differences between the Clausius and the Boltzmann entropy in explaining thermodynamic processes.
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Notes
In The Open Society and Its Enemies, Popper (1945/2020, p. 30) criticizes methodological essentialism and defends methodological nominalism, in which what-questions are not important: “The methodological nominalist will never think that a question like ‘What is energy?’ or ‘What is movement?’ or ‘What is an atom?’ is an important question for physics; but he will attach importance to a question like: ‘How can the energy of the sun be made useful?’ or ‘How does a planet move?’ or ’Under what condition does an atom radiate light?’ And to those philosophers who tell him that before having answered the ‘what is’ question he cannot hope to give exact answers to any of the ‘how’ questions, he will reply, if at all, by pointing out that he much prefers that modest degree of exactness which he can achieve by his methods to the pretentious muddle which they have achieved by theirs.” Obviously, I don’t agree with Popper, but he also uses what-questions and how-questions in a more general way than I do.
I can envision a rough taxonomy for scientific descriptions into material, structural, and functional descriptions, but such a project is still undone and would be the subject of another paper.
Fig. 1 
Relation between understanding, explanation, and description. Understanding can be gained in two different ways, by asking a what-question or a why-questions. Answers to what-questions are scientific descriptions, and answers to why-questions lead to a scientific explanations. Whereas scientific explanations occur in two different forms, namely, causal or non-causal, there is not yet a further fine-grained taxonomy of scientific descriptions. The dashed arrow indicates that a scientific description may be used (in different degrees) in scientific explanations
The Greek word that Aristotle uses is αιτια (aitia), which is standardly translated as cause. Since Vlastos (1969) distinguishes between Aristotle’s causes and becauses, there is a debate whether to translate αιτια rather as explanation (see also Annas, 1982, section III for a defense of explanation). We will see in the following that explanation would be more suitable in my scheme.
Probably the first extant discussion of understanding and explanation is Plato’s Phaedo, which Aristotle explicitly criticizes (Annas, 1982).
As Hennig mentions in section VI by citing Avicenna and Aquinas, there have been many attempts to unify the four causes in the history of philosophy.
Hennig (2009, section II) emphasizes that Aristotle has something more general in mind than what something consists of, namely, that which potentially is the result; therefore, there are other examples where the material cause is not only matter or not matter at all.
Cartwright et al. (2020) distinguish two questions, which show the difference between my and Hennig’s approach:
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An epistemological question: ”What kind of explanation is involved?”
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An ontological question: ”What is going on in the world?”
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1.
I don’t claim that this is what Aristotle indeed had in mind, but rather that this is a plausible way to interpret the passage.
Grimm does so in order to argue that, like in physics, understanding-as-grasping-structure is understanding enough for understanding people.
The situation for electromagnetism looked a bit different: especially in Britain, physicists early on presupposed a mechanism for the electromagentic field, of which Maxwell’s vortex model was a prominent example (Siegel 1991, 2014), while in Germany Wilhelm Weber’s action-at-a-distance theory was popular until it was challenged by Helmholtz and Hertz at the end of the 19th century (Steinle, 2013; Buchwald, 2013).
Max Abraham and Gustav Mie pursued a different strategy to build a unified theory of gravity by implementing gravity directly into special relativity (Norton, 2007; Smeenk & Martin, 2007). This project was finally abandoned for theoretical and empirical reasons. I thank Dennis Lehmkuhl for this example.
Thanks to an anonymous reviewer for raising this concern.
The concept of entropy found its way into thermodynamics only in 1854 in a paper by Rudolf Clausius (1822–1888), but it took another decade for Clausius to come up with the name “entropy” (Purrington, 1997, p. 95).
This was also one of the main motivations for David Bohm to develop his own quantum theory, which he himself preferred to call the ontological interpretation, although it was empirically equivalent to standard quantum mechanics (see van Strien, 2020, for a detailed discussion).
Max Planck later changed his mind when he used Boltzmann’s idea of quantizing energy for his work on blackbody radiation. Albert Einstein, although studying Boltzmann’s work, was still too young a student at the ETH Zürich at this time.
Although often the same people worked also in electromagnetism, positivism didn’t seem to be so prevalent in this theory. A rival theory to the field theory of electromagnetism was Wilhelm Weber’s action-at-a-distance theory. It would be worthwhile to find out how this theory was influenced by positivism (see, for instance, Hon & Goldstein, 2016).
I thank an anonymous reviewer for raising this idea.
There are other definitions of entropy: the Gibbs entropy in statistical mechanics, the von Neumann entropy for quantum systems, and the Shannon entropy for information. Robertson (2021) shows how the Gibbs entropy relates to thermodynamics; Myrvold (2020) discusses how the von Neumann entropy relates to thermodynamics; and Carcassi et al. (2021) do so for the Shannon entropy.
It suffices for our purposes to characterize reversible processes as minimally (that is, quasi-statically) changing the physical system so that they can be conducted in the reverse order (see Norton, 2016b, for a detailed discussion).
A thermodynamic process is called cyclic, if it returns to its initial state (Norton, 2016b, p. 48).
An adiabatic process is a process in which the physical system is closed, that is, it does not exchange heat or matter with an outside system. The word adiabatic comes from the Greek word adiábatos, which literally means impassable (from a “not” + diabatós “to be crossed”).
Thermodynamic equilibrium is defined to be a state in which the macroscopic variables of a system, like pressure, volume, temperature, and entropy, do not change over (sufficiently long) time (Robertson, 2021, section 3.1).
This definition of entropy is written on Boltzmann’s tomb, although Boltzmann actually defined entropy in a different mathematical way, even if similar in spirit. This formula for entropy was due to Max Planck (Darrigol & Renn, 2013, p. 783) and taken up as the foundation for the neo-Boltzmannian project of statistical mechanics (Callender 1999; Goldstein 2001; Lebowitz1993a, 1993b, 1994, 2008, Penrose 1989).
One may think that because of the imaginary ensembles Gibbsian statistical mechanics (which is the most popular formulation among physicists) does not specify a mechanism—I thank an anonymous reviewer for raising this concern. First, Robertson (2021) argues that ensembles are not essential for Gibbsian statistical mechanics; they are rather introduced to interpret the probabilities as hypothetical frequencies. Second, Gibbs introduces a probability measure over sets of microstates, which specify the probability in which particular microstate the system is. In this sense, Gibbs presupposes a mechanism or, at least, the existence of microstates. It seems, however, that a Newtonian mechanism does not play such a prominent role for Gibbs as it does for Boltzmann, whose entire project is to derive statistical mechanics from Newtonian physics. Since Gibbs follows a more pragmatic approach than Boltzmann, Frigg and Werndl (2019) call Gibbsian statistical mechanics an effective theory and Boltzmannian statistical mechanics a fundamental theory.
I thank an anonymous reviewer for pushing me on this point.
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Acknowledgements
I wish to thank Frederick Eberhardt, Christopher Hitchcock, and Tim Maudlin for their support and many helpful discussions. I also thank the audience of the Caltech Philosophy of Physics Reading Group for their comments. Special thanks go to Joshua Eisenthal and Maaneli Derakhshani their help on the passages on Einstein and to Charles Sebens and Federica Malfatti for thoroughly reading and commenting on previous drafts of this paper. Lastly, I wish to thank two anonymous reviewers for their constructive criticism and many suggestions for improving the paper.
Funding
Funding for this research was partially provided by the Swiss National Science Foundation as part of the Early Postdoc.Mobility Fellowship, grant no. 174745.
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Hubert, M. Understanding physics: ‘What?’, ‘Why?’, and ‘How?’. Euro Jnl Phil Sci 11, 85 (2021). https://doi.org/10.1007/s13194-021-00399-w
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DOI: https://doi.org/10.1007/s13194-021-00399-w