Part 1 of this post argued that the historical relations between natural scientific and economic thought require additional attention. It suggested that in the Enlightenment period both were subsumed within the epistemology of philosophical systems-building and the generic argumentative structure of “economy”. Although David Hume’s theory of morals was not economics, per se, in a separate post I used his example to demonstrate how the argumentative construction of a social economy had to face similar intellectual problems as chemistry, botany, and (what was thought of as) physics.
Part 2 emphasizes the importance of logical or argumentative space in economic thought, as exemplified by — but by no means limited to — mathematical inquiry. I want to argue that economics continued to adhere to the argumentative strategy of system-building familiar from 18th-century natural and political philosophy. Meanwhile, though, most natural sciences took a separate path toward argumentative rigor applied to a tightly constrained space of argumentation, such as that defined by laboratory phenomena. Political economists were deeply influenced by the natural sciences’ newly enhanced commitment to rigor, but interpreted that commitment in novel ways within the relatively unconstrained argumentative space of political economy.
In the 18th century, mixed mathematics (or rational mechanics) developed a deeply nuanced methodology, which, attached only to Newton’s three laws, attained a new level of predictive mastery over celestial phenomena. Most historians no longer pay much mind to celestial mechanics, perhaps because the high bar mathematical astronomy set for scientific advance was for too long seen as a paradigm of scientific method, thus making it an imperative to study everything else.
This blog advocates that even if a topic appears to be tapped out (though I doubt many topics in the history of science actually are), it is nevertheless wise to continually refresh our interest in it, lest our appreciation of its nuances erode. In particular, it is important to keep in mind that the success of celestial mechanics was quite singular, and that other areas of rational mechanics, such as hydrodynamics, remained — and would remain — analytically detached from most experiment.
Mathematics, circa 1800, remained a subject more closely attached to argumentative rather than predictive precision. By 1900, (advanced) optics, electromagnetism, and heat were all combined into a body of precision-tested, mathematically defined knowledge grounded in basic principles. At that time, mathematics was only beginning to make its way into economic thought. This era is a staple of the history of economics literature: E. Roy Weintraub’s How Economics Became a Mathematical Science (2002) does not provide a complete account of the transition, but it’s a good place for the novice to start.
The intervening period of the 19th century provides an enormously rich vein of scientific practice, political thought, and epistemological debate, which needs to be taken seriously to understand why economic thought developed in the ways that it did. As late as the middle of the 19th century, mathematics, as applied to physics, still mainly connoted clarity of argument. Stating a physical argument in mathematical terms allowed one to explore the logical consequences of a set of assertions, and to distinguish possible implications so as to parse whether one or another explanation for a phenomenon was preferable.
My favorite discussion of this use of mathematics remains Jed Buchwald’s account of the importance of Fresnel’s rigorous mathematical arguments as the basis for presenting a clear preference for the wave theory of light as an explanation for certain polarization phenomena. The wave theory would be held up as an analytical triumph by proponents of the reform of mathematical education at Cambridge, including Charles Babbage, John Herschel, George Peacock, and George Airy. However, while the mathematical wave theory’s success was tied to its ability to describe precision experiment, physical experiment would not itself be emphasized at Cambridge until much later in the century.
A key aspect of a mathematical education, I would argue, was the skills it fostered in approximation and legitimate idealization in reasoning and argumentation — a point that may be intuitive to those who have studied physics, though it is rarely emphasized. Nineteenth-century mathematics education at Cambridge has been analyzed at length by Andrew Warwick. Many questions on Cambridge’s mathematical tripos exam involved deriving results related to decidedly obscure mechanical arrangements. Such argumentative forms would be used in the latter half of the century by physical theorists, for example, to interject their thermodynamical knowledge into geological discussions about the age of the sun and earth — a topic most extensively studied by Crosbie Smith.
However, the mathematical tripos was considered appropriate beyond the education and epistemic elevation of future mathematicians and physicists (an increasingly used term). It was also thought to have virtue as a general form of elite education. See John Gascoigne’s 1984 discussion “Mathematics and Meritocracy” (paywall), which focuses on the emergence of the tripos as a dominant part of Cambridge education. The first part of the tripos was taken by all Cambridge students. Much later economists Alfred Marshall (1842-1924) and John Maynard Keynes (1883-1946) were actually among the wranglers (the top finishers) in the mathematical tripos examination. Some economists actually took their models directly from physical theory: Philip Mirowski has traced the very direct links between thermodynamics and the economic theory of value.
This is not simply about economics impersonating physics. The point should prompt a deeper consideration of what such an impersonation would and would not imply about the presumed epistemology of a mathematical economics circa 1900.
I believe the crucial point to keep in mind when considering the historical epistemology of economics is that political and economic phenomena will be talked about. Therefore, the question is not so much: how can you talk about complicated and undetermined economic systems at all, or with certainty? but: what ways of talking about these systems are to be preferred in comparison to others?
Calls in that era to raise political economy to the level of science in this context should not necessarily be considered equivalent to a call to reduce political economy to a laboratory science. The most important thing in the arena of a self-proclaimed scientific political economy was to avoid specious argumentation. Specious argumentation allowed any conclusion to be (apparently) justified by recourse to accepted principles. Avoiding speciousness could be achieved by ensuring that conclusions followed from presuppositions. Logic and mathematics stood (as they long had) as ideal forms of argument in this respect.
However, mathematics aside, there were a number of other candidates in the nineteenth century for ways of speaking scientifically about social and economic phenomena. Karl Marx, for an important instance, grounded his thinking in the belief that society occupied certain definable states, which, due to internal contradictions or instabilities, would — like arguments themselves — resolve themselves by proceeding to a new state. However, this was not simply a feature of communist thought: see also many of Chris Donohue’s posts on this blog about the theories of society and civilization that were prevalent in this period.
A little later, in Austria and Germany, Carl Menger, who had a legal education, confronted Gustav Schmoller’s “Historical School” over the legitimacy of abstracting more localized economic behavior from a more complete understanding of culture. Their arguments revolved around whether or not a historically rich understanding of differences in national cultures was a preferred means of analyzing and prescribing economic policy. (The story goes that the Historical School’s inability to give concrete advice in World War I led to their political marginalization.) Max Weber’s understanding of his brand of sociology, grounded in “ideal types” as a means of analyzing empricial observations, drew heavily on Menger’s arguments for the legitimacy of economic theory.
Whether we are discussing mathematical models or ideal types, I think the specific connections between scientific and economic (not to mention legal) thought, which are in the most need of renewed study, are the epistemological affinities and differences between different cultures of theory. Although analytic philosophy, mathematical and statistical thought, the philosophy of experiment design, economic theory, social science, anthropology, cognitive psychology, computation, evolutionary theory, genetics, and the search for axiomatic foundations in science all have their historians, I would like to see both a deeper exploration of what appear to be labyrinthine connections and tensions between these areas, as well as a conscientious comparative description of the various intellectual projects involved.
In most the accounts I know of, critical characterizations of theoretical projects are often grounded in polemics historically hurled between proponents of these projects, which unfortunately obscures the methods, goals, and ambitions of each project’s proponents. As with “Newtonianism” it is important to distinguish programs from the polemical labels that have been affixed to them.
Of course, in a post-Latour science studies, it has become especially difficult to separate actual historical methods of theorizing from the ubiquitous historical accusations of rationalism applied to them by, say, Austrian School economist Friedrich Hayek (or even by someone as close to us as Karl Popper). It appears as though the possibility of a polemic of rationalism is thought to have only become available with the 1970s-era overturning of historical ideas about a culture-free access to nature and truth. Therefore, it is too often assumed that historical projects can be sufficiently described as rationalistic, because rationalism would have been understood as a legitimate intellectual strategy in the pre-1970s era, without taking seriously the point that that was a label applied by critics at the time.
(Incidentally, obtaining such an understanding is also useful in appreciating points such as that, in yesterday’s column lauding a “new humanism”, conservative NYT columnist David Brooks is essentially the latest figure to recycle 200-year-old conservative polemics, complete with a stab at the French Enlightenment, to explain whatever political evils happen to be prevalent in any day and age.)
In my limited forays into this area, I have found that theorists usually pursue particular problems because of their peculiar intellectual interest, which perhaps has a loose connection to, and thus no direct implications for, real policy problems. Theories are valued in terms of their contribution to an existing body of theory; thus their legitimacy is judged not in terms of its truth as a sort of principle of nature, but in comparison to the contents of existing theory.
Further, if we want to understand, for example, why theoretical economics is chock-full of things like existence and uniqueness proofs, it is because economic thought is grounded in a long tradition where the ability to speak coherently about a subject is deeply valued, and where logical-mathematical argument is viewed as the basis of argumentative coherence. Again, it is coherence between axioms and conclusions that fuels the claim that economic ideas are universal and objective.
Does this theoretical coherence rationalize political authority? Contrary to received notions in science studies, I have seen no indication that it did or does. This particular story is not about trust in numbers. In fact, theoretical concerns have usually been sufficiently arcane to arouse political suspicions when they come into too close contact. Economists themselves make clear distinctions between positive and normative economics. (I have, by the way, intentionally left positivism out of my brief account of the 19th-century for no good reason except that this post is too long anyway.) Some economists’ much-noted confidence in political advocacy often seems to be based more in the idea that, when compared to the intellectual content of competing policy arguments, their arguments take additional points into account, which suggests a preference for their arguments over the competing arguments.
However, the more general point here is that there is a profound need to distinguish between cultures of theory and cultures of advice, and to understand the distinct forms that ideas take within each culture, to investigate the sources of these ideas as well as the sources of the distinct etiquettes that govern each culture, and the social and intellectual ways in which ideas have and have not flowed between them.