"I have no great faith in political
arithmetick, and I mean not to warrant the exactness of either of these
computations." Adam Smith (1776) Wealth of Nations.
As it happens, Adam Smith's two best friends in old age, James Hutton and Joseph Black, the editors of his posthumous (1795) work, Essays on Philosophical Subjects (EPS), understood what was at stake. For, in 1785 Hutton gave a public lecture, “Concerning the System of the Earth, Its Duration, and Stability,” at University of Edinburgh. Due to Hutton's illness, Black gave the lecture on Hutton’s behalf. In the lecture Hutton used geological and fossil evidence to argue that the Earth was almost certainly older than 6000 years. We do not know for sure if Smith attended the lecture, although he was in town.The argument was elaborated in far greater detail in Hutton's (1788) Theory of the Earth, which made him an international celebrity. The significance of this episode to the history of geology and Darwinism is much studied.
But what does this have to do with the history of economics?
Smith's closeness to Hutton may provide additional clues for one of the enduring mysteries of the history of economics: why did Adam Smith forsake the deployment of a mathematical model in the Wealth of Nations (1776)?
From arranging and methodizing the System of the Heavens, Philosophy descended to the consideration of the inferior parts of Nature, of the Earth, and of the bodies which immediately surround it. If the objects, which were here presented to its view, were inferior in greatness or beauty, and therefore less apt to attract the attention of the mind, they were more apt, when they came to be attended to, to embarrass and perplex it, by the variety of their species, and by the intricacy and seeming irregularity of the laws or orders of their succession. The species of objects in the Heavens are few in number; the Sun, the Moon, the Planets, and the Fixed Stars, are all which those philosophers could distinguish. All the changes too, which are ever observed in these bodies, evidently arise from some difference in the velocity and direction of their several motions; but the variety of meteors in the air, of clouds, rainbows, thunder, lightning, winds, rain, hail, snow, is vastly greater; and the order of their succession seems to be still more irregular and unconstant. The species of fossils, minerals, plants, animals, which are found in the Waters, and near the surface of the Earth, are still more intricately diversified; and if we regard the different manners of their production, their mutual influence in altering, destroying, supporting one another, the orders of their succession seem to admit of an almost infinite variety. If the imagination, therefore, when it considered the appearances in the Heavens, was often perplexed, and driven out of its natural career, it would be much more exposed to the same embarrassment, when it directed its attention to the objects which the Earth presented to it, and when it endeavoured to trace their progress and successive revolutions.--Adam Smith, History of Ancient Physics. [Emphasis added]
The passage is from Smith's brief "History of Ancient Physics." In this work, it is not always easy to figure out when Smith adopts the perspective of those he is discussing and where he is speaking in his own voice. But this happens to be the first paragraph, and In the past, I have assumed that Smith is putting forward his own views. In particular, Smith makes a three-fold distinction, in which celestial phenomena are simple; phenomena in the atmosphere more complex; while terrestrial phenomena are infinitely complex. The simple phenomena are clearly capable of being subject of a science, but the terrestrial phenomena are, if they are subject to science, of a very different kind. And, indeed, if there are literally infinite variety of fossils and minerals then there is a Spinozistic point lurking here (Letter on Infinite, etc.); if there are literally an infinite variety of phenomena in a domain then the application of mathematics to it, may give false confidence in our ability to discern the genuine underlying connections. We may discern a robust, even causal pattern without doing justice to the complexity of the larger whole.
In the quoted passage above Smith is silent about mathematics. but the passage is the bridge between the history of astronomy, which has historically always been a mathematical and the history of physics, which historically was a qualitative science of body (not part of mechanics). The the kind of distinction that Smith proposes above is in historical context a crucial feature of a species (the so-called "containment strategy") of what I call "anti-mathematics." A containment strategy restricts the application of mathematics to a fairly limited domain of scientific inquiry.* By "anti-mathematics" I mean the expressed reservations about the authority and utility of mathematical sciences. So, Smith may, in fact, be agreeing with Locke (see Mary Domski's brilliant paper), Mandeville (here and here), Diderot, and Buffon that mathematical science is appropriate for the celestial sphere and much less so for terrestrial sphere, and by implication human affairs. (Hume offers a more global anti-mathematics.) All of these figures are not anti-science, but they are reserved about the deployment of mathematical techniques outside astronomy, celestial mechanics, and optics.
Now, one reason to think that Smith is speaking in his own voice in the quoted passage is the emphasis on infinite variety of fossils and minerals. Clearly Hooke’s “many other” is not the same as Smith’s “infinite variety.” But Hutton emphasizes the “infinite variety of mineral productions which we find in nature,” (vol 1, 90; according to Mizuta’s catalogue of Smith's library, Smith owned this book, but not the dissertation abstract of the 1785 lecture.) Smith, Hutton, and Black met weekly in the Oyster Club dinners. Smith’s interest in biology and botany is well attested. As Spencer Pack (2010: 105) has emphasized there is evidence in WN that Smith also took an interest in species extinction (4.7.a.11, 560; citing the authority of Buffon).
It is generally assumed that Smith wrote his "history of ancient physics" (and the companion essays on astronomy and metaphysics) in the 1740s well before Hutton was born. Now, it is not impossible that that the passage above was included by Smith as a late addition in response to scientific developments by Hutton--a bridge passage, but that has never been suggested before. So, it is not impossible that Hutton was nudged toward his view in his discussions with Smith. Now, Spinozists were not the only ones that emphasized infinite variety (E1P16: necessitate infinita infinitis modis). Leibnizians, who emphasized the law of continuity, did so, too. One way to distinguish an eighteenth century Leibnizian from a Spinozist is the existence of a robust strain of anti-mathematics, which is more common among the Spinozists.