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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A Unified Theory of the Second Scientific Revolution, Part 1: the Problem

Gaston Bachelard (1882-1962) forming the scientific mind.

There are two kinds of conference paper: the ones we give, and the ones we would have given if only we had been able to do enough research to back up our seductive hunches and our bold conjectures. At the 3 Societies conference in Edmonton in July, I gave a modest talk about an experimenter in 1730s France who had a notion of ‘exactitude’ that applied equally well to qualitative and quantitative research. The talk I would have given is much more sweeping and provocative. Frankly I would have preferred to listen to the ambitious talk, and not the modest and sensible one, but academic caution got the better of me. Here then is the sweeping and provocative talk, in summary form, safely packaged as a speculative blog post (or two).

What was the second scientific revolution, or SSR for short? Many historians of science believe that something dramatic happened to the natural sciences in the decades around 1800. According to no less an authority than the Oxford Companion to Modern Science, this period witnessed ‘the transition to modern science.’ But there is no agreement on how to characterise this all-important event, as we can see be reviewing some of the literature on the topic (see the end of this post for citations of the books and articles I have in mind).

Hélène Metzger, writing about the history of crystallography, thought that this was the period when naturalists abandoned the search for the causes of crystal form and focused on describing that form, preferably in mathematical terms.

Gaston Bachelard extended this account to physics and chemistry. He made much of Coulomb’s discovery of the inverse-square law of electrical force. For Bachelard, this discovery marked a shift from a qualitative, allegorical, diffuse physics to a quantitative, abstract, precise physics.

Michel Foucault’s account was almost the opposite of Metzger’s and Bachelard’s. According to Foucault, it was the first two-thirds of the eighteenth century that was obsessed with abstraction and classification (witness Linnaeus’ natural history) and it was the period around 1800 that saw the rise of a historical and causal natural history, one that studied the inner constitution of bodies and not just their surface appearances (witness the comparative anatomy of Cuvier).

Thomas Kuhn had little to say about classification or inner constitutions or the historical sciences, but he had much to say about physics and mathematics. He characterised the SSR (he was one of the first to use the phrase) as the period when terrestrial physics became quantitative. Astronomy had been quantitative for millennia, and some branches of terrestrial physics (such as optics) had a long history of geometric treatment. But what of chemical processes, electricity, heat, and magnetism? As Kuhn pointed out, it was only in the last third of the eighteenth century that these phenomena were measured with precise instruments and described with mathematical theories.

John Heilbron, in one guise, has put his finger on what was needed to apply Newton’s approach to celestial mechanics to terrestrial phenomena, and especially to electricity and magnetism. The key to establishing Coulomb’s law of electrical force, for example, was to see that the forces between macroscopic charges are complicated aggregates of the forces between the microscopic charges. Coulomb found a simple force law because he measured the forces between insulated spheres whose separation was large compared to their diameters.

John Heilbron, in another guise, and in concert with Tore Frängsmyr and Robin E. Rider, has argued for the existence and importance of a ‘quantifying spirit’ in the last third of the eighteenth century. Heilbron and his co-authors define this spirit broadly to include not just precise instruments but also systematic methods of classifying plants, animals and minerals.

Finally, John Pickstone argued that the key to events around 1800 was what he called ‘the analytical way of knowing.’ His best example was chemistry. The chemical revolution initiated by Lavoisier and co. was defined above all by the idea that substances are what they are made up of, where ‘what they are made up of’ does not mean ‘what philosophers consider fundamental’ but ‘what you get when you take them apart.’ Pickstone generalised this point by saying that the SSR saw the convergence of natural history, in the sense of surface descriptions of phenomena, and natural philosophy, in the sense of deep explanations of phenomena. Whereas these two activities had been practised separately before, as two ‘layers’ of knowledge, now they were practised as one.

***

The problem with these seven theories of the SSR is that they are hard to reconcile with each-other. Metzger and Bachelard detect a shift away from causes and towards surface description, whereas Foucault detects a shift in the opposite direction. Pickstone gestures towards Foucault with his talk of ‘deep causes’, but unlike Foucault he thinks that the novelty was not the interest in deep causes per se but the convergence of that interest with the description and classification of natural bodies.

It gets worse: three of the above authors (Kuhn, Metzger, Bachelard) think that mathematics was an important part of the story, whereas two others (Pickstone and Foucault) give it a secondary role.

Pickstone’s thesis is probably the pick of the bunch, but it is far from perfect. He claims that natural history and natural philosophy were separate in the eighteenth century, whereas other historians maintain that the grounding of natural philosophy on natural history was the main achievement of seventeenth-century science. And if analytical thinking means understanding a whole in terms of its parts, as Pickstone sometimes suggests, surely this applies as much to the metaphysics of Descartes as it does to the chemistry of Lavoisier?

My sweeping and provocative idea is this: we can resolve these conflicts, and get a more unified account of the SSR, by weaving together the best ideas of the six thinkers I have just reviewed. The unification proceeds in three steps, to be outlined in the next post.



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.

Expand post.

Malheureusement je ne traduis plus tous les posts que j'écris sur ce blog. Si vous voudriez lire les posts qui ont été traduits, veuillez cliquer ici.

Agrandir ce message.