Duhem’s Aim and Structure of Physical Theory

Aside from his work as an eminent physicist, Pierre Duhem (1861–1916) produced “massive groundbreaking” publications on medieval science (which I have yet to read) and a classic book on the theory of science, La théorie physique, son objet et sa structure. The original (1906) is available on Archive.org, and so is the excellent German translation by Friedrich Adler on which this review is based, Ziel und Struktur der physikalischen Theorien (1908). I did not find a free edition of the English translation, The Aim and Structure of Physical Theory, so it seems this translation is still under copyright.

What can a 1906 book on physical theory teach as today? Quite a lot, as it turns out. Duhem clearly perceives the precarious balancing act of physics between immediate observation on one hand and mathematical deduction on the other, and demonstrates its meandering progress with a wealth of historical observations. Ultimately, he dissects the naive view of physics as a certain and inherently truthful “mathematical” science that still holds sway today. I would recommend this compact and highly readable book to everyone with an interest in the history and practical reality of science. The following is an overview of major points, ignoring Duhem’s numerous historical notes for the sake of brevity.

Explanation or Classification

Duhem opens with the epistemological dichotomy that drives his analysis: do physical theories explain a group of experimentally discovered laws, or do theories merely combine and classify such laws, without claiming to offer an explanation? “Explanation” implies that physical theories uncover the truth behind physical reality, whereas “classification” is an act of arbitrary creativity which might or might not reflect any underlying reality.

Once the goal of explanation is dropped, there is logically nothing wrong with using several incompatible theories to describe different groups of physical laws, or even the same group [p.130f]. Obviously this is most unsatisfying to every physicist’s inherent drive to unify his science under a single theory, which is why using incompatible theories was considered unacceptable throughout most of history [p.134]. Indeed most physicists strove to present some all-encompassing theory of the world alongside their experimental discoveries, whether based on the four elements, atomic bodies, etc.

But as Duhem dryly notes, these explanatory efforts offered no sufficient foundation for the same physicist’s experimental discoveries. Rather their connection is “weak and artificial,” with the explanation forming a “parasite” on the discoveries [p.37f]. Steady scientific progress builds on observation and experimentation, while attempts at universal explanations are routinely discarded by later generations. Duhem acknowledges the drive to unify and simplify physical theories as much as possible, and hope to attain a mirror-image of reality in this way. This desire is only imposed by “common sense,” however, and cannot be logically deduced [p.135].

Theory and Experiment

Theories are to an inevitable degree arbitrary not only with regard to an unknowable physical reality, but even with regard to the practical facts observed by an experimenter. Theoretical statements assert precisely bounded geometries, exact temperatures, and so on, whereas practical observations always involve somewhat irregular bodies and approximate measurements. Given this inherent inexactness and the consequent necessity of allowing for error bounds when attempting to impose theories on observations, it follows that innumerable different theoretical facts can map to the same practical fact [p.174f].

Another consequence of the uncertainty of phyiscal facts is a much greater difficulty of deducing theorems from one another. Claiming that one statement is strictly true if another is strictly true – the usual procedure of pure mathematics – is quite useless in physics, as no premise is actually strictly true in practice. Rather, one must build deductions in such a way that the conclusion remains approximately true whenever the premises are approximately true, which is the best physics can offer [p.187].

The difficulties continue. Physical experiments rarely involve only direct human observations. Rather, they rely on measurements performed by mechanisms which are themselves the result of applied physical theories, such as the one that correlates a thermometer’s readout to the temperature supposed to be measured. In summary [p.192]:

A physical experiment is the precise observation of a group of phenomena combined with its interpretation; this interpretation replaces the concretely given […] with abstract and symbolic representations. Their correspondence relies on theories which the observer considers acceptable.

Reliability of Physics

From the above follows that the results of physical experiments are less certain than ordinary unscientific statements, which are obvious and easily verified. Instead, physical laws provide a greater number and precision of details [p.215]. This precision must be qualified by their approximate nature, however. Laws of common sense are simple statements, either true or false, e.g. the sun rises every day in the east. Physical laws are symbolic: they are theoretical constructs that aggregate observations within certain error bounds. A multitude of different symbols can represent the same observed facts. Therefore they cannot be said to be “true” or “false,” only more or less useful approximations [p.222f].

Being approximate and symbolic, every physical law is also temporary (provisional). Unlike statements based on direct observations, physical laws can be adequate today but too inaccurate tomorrow, as new experiments with better instruments produce additional data with smaller error bounds [p.227f]. Moreover, sometimes the very symbols used to express a physical law can become inadequate to describe new experiments, such as when gas habitually described by density, temperature, and pressure is discovered to be also affected by electric fields [p.230f].

“There is a trade-off between precision and certainty: one can only incrase as the other decreases.” [p.237] Physical laws are much more precise but therefore also much less certain than laws of common sense. They must be constantly adjusted to ensure their continued usefulness as experimental technology improves. “The history of physics shows quite often how the human mind was led to shatter axioms recognized for centuries as inviolable, and rebuild physical theories on new hypotheses.” [p.284]

No hypothesis can be assumed as definitely proven, and neither is there an “experimentum crucis” to definitely disprove one particular hypothesis. A failed experiment might reject any or all of the theories used in its attempted description; further research must uncover the necessary modifications [p.248f]. The infinity of potential theories that could be tailored to any given set of observations also prevents proof by reductio ad absurdum, as in pure mathematics. Any number of physical theories being false does not prove one specific other being true [p.252f].

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