Another mistaken criticism of set theory and set-theoretic methods

For some time now, a discussion has been raging about the pros and cons of set theory and the use of set-theoretic methods (STM) in the social sciences (e.g., in Sociological Methodology and the APSA Newsletter). Following up on a critical discussion by Paine and a constructive, comparative discussion of STM and regression analysis by Thiem, Baumgartner and Bol (TBB), Comparative Political Studies organized a symposium on STM. With this symposium, Gerardo Munck joins the debate, taking the side of the critical voices by concluding that we should set aside STM because “STCM’s approach to formalizing and testing causal relations is problematic”. (This and other papers write about set-theoretic comparative methods; I drop the “C” in STCM because it strikes me as redundant.)

Munck makes several points that are worth considering in more detail but here, I leave it with the compatibility of set theory/STM with process tracing. He argues that “process tracing is not part of STCM” and, in the conclusion, says that advocates of STM have not “justified why qualitative researchers should embrace STCM”. First of all, one needs to get straight who is being addressed here and who is not. These claims are valid if one thinks of people like Mahoney, who is firmly anchored in a set-theoretic worldview and is also a fan of process tracing (see the Two Cultures book, for example). But in general, I do not know that many people who contend that process tracing must have a set-theoretic basis. Instead, discussions take (implicitly) the form of “If one takes a set-theoretic view, then one has to do process tracing like this and this” (that’s my view, at least).

In any case, my reading of the part about process tracing is that STM are wrongly characterized. Munck explains that process tracing is not “a matter of ascertaining if there is a causal effect and how strong it is, but rather of learning how a causal effect is transmitted”. This point has been made a couple of dozen times during the last 10-15 years and is not contested in the qualitative literature. More importantly, it does not contradict the adoption of a set-theoretic view. Beach/Pedersen, and I in my case study book, for example, explain how a causal explanation can be couched in set-theoretic terms and analyzed with process tracing. It seems that Munck implicitly and incorrectly equates STM with Qualitative Comparative Analysis (QCA) and the measures of consistency and coverage that are irrelevant in process tracing. (In this debate, I believe it is often not clear whether we speak about set theory, set-theoretic methods, or QCA in particular.)

The problem that Munck identifies with applying set theory and that underlies his rebuttal of STM is not a problem at all. Referring to TBB, he contends that set theory forces one to take a static view that makes it impossible to relate a change in X to a change in Y. This ignores that Mackie and Mahoney, for example, illustrate how to blend a set-theoretic view with the method of difference the defining feature of which is to link a difference on X with a difference on Y. (I know that the method of difference does not have many supporters, incorrectly, in my view, but that is another matter.)

Regarding mechanisms and process tracing, Carsten Schneider and I explain in the context of set-theoretic multi-method research the way in which a counterfactual view on causal inference can inform empirical research on causal mechanisms (see also my paper on process tracing). This coincides with and, in fact, draws upon a broad debate in philosophy of science connecting a counterfactual view on causation with the analysis of mechanisms. Since a counterfactual is, by definition, about differences, the charge of taking a static view when applying STM is without any basis. In the empirical analysis, we then might do a counterfactual imagining the consequences of a change in a given factor, or do process tracing as part of an overtime/longitudinal/before-after comparison. (I would guess TBB agree with this and that Munck misinterprets their paper in this respect.)

For these reasons, Munck’s conclusion that the “discussion of STCM be brought to a close and that energies turn to other options” is misplaced when it comes to process tracing. Process tracing does not have to be set-theoretic, but it can be.


About ingorohlfing

I am Professor for Methods of Comparative Political Research at the Cologne Center for Comparative Politics at the University of Cologne ( My research interests are social science methods with an emphasis on case studies, multi-method research, and philosophy of science concerned with causation and causal inference. Substantively, I am working on party competition and parties as organizations.
This entry was posted in causal inference, causal mechanism, causation, comparative, process tracing, QCA, qualitative, Qualitative Comparative Analysis, set relation, set theory and tagged , , , , , , , . Bookmark the permalink.

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