Mathematics and materiality in Latour and Bourdieu’s sociology of science

by Sebastian Benthall

Our next reading for I School Classics is Pierre Bourdieu’s Science of Science and Reflexivity (2004). In it, rock star sociologist Bourdieu does a sociology of science, but from a perspective of a sociologist who considers himself a scientist. This is a bit of an upset because so much of sociology of science has been dominated by sociologists who draw more from the humanities traditions and whose work undermines the realism the scientific fact. This realism is something Bourdieu aims to preserve while at the same time providing a realistic sociology of science.

Bourdieu’s treatment of other sociologists of science is for the most part respectful. He appears to have difficulty showing respect for Bruno Latour, who he delicately dismisses as having become significant via his rhetorical tactics while making little in the way of a substantive contribution to our understanding of the scientific process.

By saying facts are artificial in the sense of manufactured, Latour and Woolgar intimate that they are fictious, not objective, not authentic. The success of this argument results from the ‘radicality effect’, as Yves Gingras (2000) has put it, generated by the slippage suggested and encouraged by skillful use of ambiguous concepts. The strategy of moving to the limit is one of the privileged devices in pursuit of this effect … but it can lead to positions that are untenable, unsustainable, because they are simply absurd. From this comes a typical strategy, that of advancing a very radical position (of the type: scientific fact is a construction or — slippage — a fabrication, and therefore an artefact, a fiction) before beating a retreat, in the face of criticism, back to banalities, that is, to the more ordinary face of ambiguous notions like ‘construction’, etc.

In the contemporary blogosphere this critique has resurfaced through Nicholas Shackel under the name “Motte and Bailey Doctrine” [1, 2], after the Motte and Bailey castle.

A Motte and Bailey castle is a medieval system of defence in which a stone tower on a mound (the Motte) is surrounded by an area of pleasantly habitable land (the Bailey), which in turn is encompassed by some sort of a barrier, such as a ditch. Being dark and dank, the Motte is not a habitation of choice. The only reason for its existence is the desirability of the Bailey, which the combination of the Motte and ditch makes relatively easy to retain despite attack by marauders. When only lightly pressed, the ditch makes small numbers of attackers easy to defeat as they struggle across it: when heavily pressed the ditch is not defensible, and so neither is the Bailey. Rather, one retreats to the insalubrious but defensible, perhaps impregnable, Motte. Eventually the marauders give up, when one is well placed to reoccupy desirable land.

In the metaphor, the Bailey here is the radical antirealist scientific position wherein facts are fiction, the Motte is the banal recognition that science is a social process. Schackel writes that “Diagnosis of a philosophical doctrine as being a Motte and Bailey Doctrine is invariably fatal.” While this might be true in the world of philosophical scrutiny, this is unfortunately not sociologically correct. Academic traditions die hard, even long after the luminaries who started them have changed their minds.

Latour has repudiated his own radical position in “Why Has Critique Run out of Steam? From Matters of Fact to Matter of Concern” (2004), his “Tarde’s idea of quantification” (2010) offers an insightful look into the potential of quantified sociology when we have rich qualitative data sets that show us the inner connectivity of the societies. Late Latour is bullish about the role of quantification in sociology, though he believes it may require a different use of statistics than has been used traditionally in the natural sciences. Recently developed algorithmic methods for understanding network data prove this point in practice. Late Latour has more or less come around to “Big Data” scientific consensus on the matter.

This doesn’t stop Latour from being used rather differently. Consider boyd and Crawford’s “Critical Questions for Big Data: Provocations for a Cultural, Technological, and Scholarly Phenomenon” (2012), and its use of this very paper of Latour:

‘Numbers, numbers, numbers,’ writes Latour (2010). ‘Sociology has been obsessed by the goal of becoming a quantitative science.’ Sociology has never reached this goal, in Latour’s view, because of where it draws the line between what is and is not quantifiable knowledge in the social domain.

Big Data offers the humanistic disciplines a new way to claim the status of quantitative science and objective method. It makes many more social spaces quantifiable. In reality, working with Big Data is still subjective, and what it quantifies does not necessarily have a closer claim on objective truth – particularly when considering messages from social media sites. But there remains a mistaken belief that qualitative researchers are in the business of interpreting stories and quantitative researchers are in the business of producing facts. In this way, Big Data risks reinscribing established divisions in the long running debates about scientific method and the legitimacy of social science and humanistic inquiry.

While Latour (2010) is arguing for a richly quantified sociology and has moved away from his anti-realist position about scientific results, boyd and Crawford fall back into the same confusing trap set by earlier Latour of denying scientific fact because it is based on interpretation. boyd and Crawford have indeed composed their “provocations” effectively, deploying ambiguous language that can be interpreted as a broad claim that quantitative and humanistic qualitative methods are equivalent in their level of subjectivity, but defended as the banality that there are elements of interpretation in Big Data practice.

Bourdieu’s sociology of science provides a way out of this quagmire by using his concept of the field to illuminate the scientific process. Fields are a way of understanding social structure: they define social positions or roles in terms of their power relations as they create and appropriate different forms of capital (economic, social, etc.) His main insight which he positions above Latour’s is that while a sociological investigation of lab conditions will reveal myriad interpretations, controversies, and farces that may convince the Latourian that the scientists produce fictions, an understanding of the global field of science, with its capital and incentives, will show how it produces realistic, factual results. So Bourdeiu might have answered boyd and Crawford by saying that the differences in legitimacy between quantitative science and qualitative humanism have more to do with the power relations that govern them in their totality than in the local particulars of the social interactions of which they are composed.

In conversation with a colleague who admitted to feeling disciplinary pressure to cite Latour despite his theoretical uselessness to her, I was asked whether Bourdieu has a comparable theory of materiality to Latour’s. This is a great question, since it’s Latour’s materialism that makes him so popular in Science and Technology Studies. The best representation I’ve seen of Bourdieu’s materiality so far is this passage:

“The ‘art’ of the scientist is indeed separated from the ‘art’ of the artist by two major differences: on the one hand, the importance of formalized knowledge which is mastered in the practical state, owing in particular to formalization and formularization, and on the other hand the role of the instruments, which, as Bachelard put it, are formalized knowledge turned into things. In other words, the twenty-year-old mathematician can have twenty centuries of mathematics in his mind because formalization makes it possible to acquire accumulated products of non-automatic inventions, in the form of logical automatisms that have become practical automatisms.

The same is true as regards instruments: to perform a ‘manipulation’, one uses instruments that are themselves scientific conceptions condensed and objectivated in equipment functioning as a system of constraints, and the practical mastery that Polanyi refers to is made possible by an incorporation of the constraints of the instrument so perfect that one is corporeally bound up with it, one responds to its expectations; it is the instrument that leads. One has to have incorporated much theory and many practical routines to be able to fulfil the demands of the cyclotron.”

I want to go so far as to say that in these two paragraphs we have the entire crux of the debate about scientific (and especially data scientific) method and its relationship to qualitative humanism (which Bourdieu would perhaps consider an ‘art’.) For here we see that what distinguishes the sciences is not merely that they quantify their object (Bourdieu does not use the term ‘quantification’ here at all), but rather because it revolves around cumulative mathematical formalism which guides both practice and instrument design. The scientific field aims towards this formalization because that creates knowledge as a capital that can be transferred efficiently to new scientists, enabling new discoveries. In many ways this is a familiar story from economics: labor condenses into capital, which provides new opportunities for labor.

The simple and realistic view that formal, technical knowledge is a kind of capital explains many of the phenomena we see today around data science in industry and education. It also explains the pervasiveness of the humanistic critique of science as merely another kind of humanism: because it is an advertising campaign to devalue technical capital and promote alternative forms of capital associated with the humanities as an alternative. The Bailey of desirable land is intellectual authority in an increasingly technocratic society; the Motte is banal observation of social activity.

This is not to say that the cultural capital of the humanities is not valuable in its own right. However, it does raise questions about the role of habitus in determining taste for the knowledge as art, a topic discussed in depth in Bourdieu’s Distinction. My own view is that while there is a strong temptation towards an intellectual factionalism, especially in light of the unequal distribution of capital (of various kinds) in society, this is ultimately a pernicious trend. I would prefer a united field.