A Unified Theory of the Second Scientific Revolution, Part 2: a Solution

Haüy's crystallography-what did it have in common with Coulomb's physics and Cuvier's zoology?

As I wrote last week, there are at least seven theories about the second scientific revolution (SSR), all of them claiming that science changed dramatically in the three decades on either side of 1800, none of them explaining how its assertions can be reconciled with those of the other six theories. Let’s assume for the moment that a reconciliation is possible and desirable. How might it be realised? How can we unite, in a single theory, the insights that are scattered across these seven different theories? Here is my proposal. It proceeds in three steps.


The first step is to clarify John Pickstone’s idea that natural history and natural philosophy were two ‘layers’ that came into contact in the SSR (see the end of this post for the details of Pickstone's article and of the other works mentioned here). Lavoisier and Cuvier and Coulomb did not just join together two activities that had previously been done separately. They did that, but in doing so, indeed in order to do so, they changed the two activities.

Take the crystallography of René-Just Haüy. Before Haüy, mineralogists had observed the different forms of natural crystals and explained these forms in terms of the way the crystals are formed in the earth. Like them, Haüy observed the natural forms of crystals. But, in addition, he observed the forms that resulted when he divided natural crystals along their lines of cleavage. And he explained the forms of the undivided crystals in terms of the divided ones.

Haüy’s observations were deeper than those of his precursors (as Michel Foucault's theory predicts) and his explanations shallower (as Hélène Metzger's predicts). This is why Haüy was able (as Pickstone's theory predicts) to bring the two into very close contact. This is also why Descartes’ version of ‘analysis’ was not that same as Haüy’s. Both explained wholes in terms of parts, but Haüy had seen his parts whereas Descartes had not seen his, because Haüy had taken his wholes apart. Likewise, Coulomb took his wholes apart when he measured forces between microscopic charges (or at least approximations thereof) rather than between macroscopic ones.


The second step is to extend Thomas Kuhn’s idea of a convergence of mathematics and experiment so that it encompasses sciences that did not become mathematical during the SSR, such as the sciences of plants, animals and minerals. The key here is to see that taxonomy bore the same relationship to plants, animals and minerals as mathematics bore to motion, heat, light, magnetism and electricity.

Consider the following parallels. Both taxonomy and mathematics had a long history of moderate success in certain domains—examples are Aristotle’s taxonomic treatment of animals and Euclid’s geometric treatment of light. Around 1700, both enjoyed some striking successes in their traditional domains—witness Huygens’ optics and Newton’s celestial mechanics on the one hand, and the botany of Ray and Linnaeus on the other. But both were unable to absorb certain theories and phenomena that came to the fore in 17th-century—compare the difficulty of absorbing the electricity of Hauksbee into the mathematical sciences and the difficulty of extending the anatomical findings of Edward Tyson to encompass all classes of animal. Yet, to a large extent, these difficulties were overcome in the decades around 1800—as Pickstone observes with respect to the comparative anatomy of Cuvier, and as Kuhn and Bachelard observe with respect to the electrical researches of Coulomb.

Like John Heilbron, Toré Frängsmyr, and Robin Rider, I say that taxonomy and mathematics were part of a single trend in the last third of the eighteenth century. But unlike them, I say that they shared more than a concern for rigour, order, and system. They shared a history of convergence with their empirical subject-matter, a convergence that was already apparent around 1700 but that was much more comprehensive in the decades around 1800.


The third and final step is to see that the first two steps are connected. Why did the conceptual tools of taxonomy and mathematics achieve such widespread success around 1800? Why did electricity become tractable to mathematics, and animals to taxonomy? Precisely because, in the study of animals and of electricity, observation had come into closer contact with explanation. By studying microscopic charges, Coulomb not only fitted his observations to his explanation but also ensured that his explanation could be mathematical in nature. That is one of Heilbron’s insights. He applied it to experimental physics, but it applies just as well to the study of plants, animals and minerals. Haüy, by cleaving crystals to reveal the geometry of their cores, paved the way for a classification of minerals in terms of their geometry. Cuvier, by studying skeletons, gave an account of animals that was both more closely grounded on observation, and more thoroughly comparative, than earlier accounts of animals.

To sum up, the SSR was characterised by three convergences. The first was between explanation and observation. The second was between (on the one hand) the formal tools of mathematics and taxonomy and (on the other hand) the natural phenomena to which these tools were best suited. The third was a convergence of convergences, the mutual reinforcement of the new ties between (on the one hand) explanation and observation and (on the other hand) between formal tools and natural phenomena.

***

So much for the theory. Is it true? Does it fit the facts? I don’t know, but I do know that it is derived from a set of theories that are based on extensive empirical research, namely the seven theories that I reviewed in the previous post. And the step from those theories to my theory is not a big one—for the most part, I have simply adjusted each of those theories in light of the others. I do not believe my theory, but I do believe it is a good working hypothesis.

Here then is one way of generating working hypotheses in history: review current theories on a topic, note the insights of each and the inconsistencies between them, and adjust them to preserve the former and eliminate the latter. This procedure may seem obvious, but it is not a common one in the history of science. It should be more common, because—as I will explain in the next post—it is both more important, and easier to implement, than we are led to believe.



References:

Metzger, Hélène. La genèse de la science des cristaux. Paris: Albert Blanchard, 1969.

Bachelard, Gaston. La Formation de l’esprit scientifique: contribution à une psychanalyse de la connaissance. Vrin, 1934.

Foucault, Michel. Les mots et les choses: une archéologie des sciences humaines. Paris: Gallimard, 1966.

Kuhn, Thomas. ‘Mathematical Versus Experimental Traditions in the Development of Physical Science’. Journal of Interdisciplinary History 7, no. 1 (1976): 1–31.

Heilbron, John. Electricity in the 17th and 18th Centuries: a Study of Early Modern Physics. Berkeley: University of California Press, 1979.

Frängsmyr, Tore, J. L Heilbron, and Robin E Rider, eds. The Quantifying Spirit in the 18th Century. Berkeley: University of California Press, 1990.

Pickstone, John V. ‘Ways of Knowing: Towards a Historical Sociology of Science, Technology and Medicine’. The British Journal for the History of Science 26, no. 4 (1993): 433–58.

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