Toward an Integrated History and Philosophy of Diagrammatic Practices

Abstract

This article offers an overview of current approaches to the study of diagrams and their roles in scientific knowledge making. The discussion develops in three parts. The first investigates and questions historical and philosophical analyses of the suppression of diagrams in the nineteenth and twentieth centuries. It attempts to sketch an alternative historiography of diagrammatic practices in which the insights of advocates of diagrammatic reasoning in a time of “objectivity without images” take center stage. The second part turns to the American philosopher, scientist, and logician Charles Sanders Peirce as a representative defender of diagrammatic reasoning and diagrammatic representation in the late nineteenth century, and it investigates his legacy on current approaches to diagrams. The final part exposes a puzzling paradox in the literature, characterizing it as a false dichotomy between “the representational view” and the “object-based view” of diagrams. The article concludes that this dichotomy reveals more about the identities of scholars embracing particular disciplinary traditions than about diagrams themselves, and it suggests that this can be overcome by attending to diagramming as a practice at the intersections of representation, manipulation, and experimentation.

• diagrams
• scientific practice
• C. S. Peirce
• integrated history and philosophy of science

Acknowledgments

This article owes a great deal to a collegial and international community of scholars. I am grateful to Harro Maas for inviting me to contribute to this special issue, and for his careful and collegial critical commentary on an early draft of this piece. I benefited immensely from the activities of the “All-London Integrated HPS” reading group, which took place at the London School of Economics in the spring 2019. I am especially grateful to Mary Morgan, Dominic Berry, Roman Frigg, James Nguyen, and the members of the Narrative Science Project for agreeing to run a whole iteration of this annual event on the topic of diagrams, and for the lively and helpful discussion we had in each session. My PhD student Claudia Cristalli read an early draft of this article and provided precious comments, subverting once again in her unique way our supervisor-supervisee relationship. The indefatigable community of Peirce scholars, particularly Cathy Legg, served as my compass in a rather large field and guided my journey through the literature. Steven Wright at UCL Special Collections provided invaluable (and invaluably prompt!) support with the reproduction of the images from the American Journal of Mathematics; I am also grateful to the Houghton Library at Harvard for the reproduction of Peirce’s diagrams. Once again, and as always, Niall Le Mage kept track of the word count, commented every section, witnessed me agonize over word choices and image files resolution, and added a whole new list of diagram jokes to our repertoire.

Notes

¹ I follow the convention of citing Peirce’s unpublished manuscripts by manuscript number and page, as assigned in Robin 1967.

² Mary Morgan in this special issue also notes this tension and explicitly rejects it—see note 1 in her article.

³ I am grateful to Harro Maas for alerting me to how different the situation was in fields such as economics. Judy Klein (1997), for instance, situates the suppression of diagrams in economics in the first part of the nineteenth century, in conjunction with the discrediting of William Playfair’s work. Maas and Morgan (2002) connect the resurfacing of graphical methods in British political economy at the end of the nineteenth century to a broader shift in attitudes toward history and statistics—I will return to their work later on in this section.

⁴ The reception of Daston and Galison’s work has strangely overlooked their category of structural objectivity, mainly focusing on “truth-to-nature,” the attempt to idealize from instances in nature that preceded the establishment of the very notion of objectivity (Daston and Galison 2007: ch. 2), and especially on “mechanical objectivity,” the representative ideal that preceded structural objectivity and consisted mainly of “letting nature speak by itself” (120). See, for example, Jardine 2012; Pickstone 2009. Even Marcel Boumans (2016), who specifically focuses on graphs in assessing the role of economists’ expert judgment in inductive inferences, ultimately chooses mechanical objectivity as the foil of his argument (4).

⁵ Indeed, as Leo Corry (1996) has demonstrated, even the strictly mathematical formulation of “structure” was contested at this point.

⁶ Here the rejection of the visual as merely “psychological” crosses paths with the much broader debate on psychologism, on which see Kusch 1995.

⁷ See Schmidgen 2014 for an overview of reaction time measurements and the notion of temps perdu in Helmholtz.

⁸ Here and throughout the article, I use the conventional abbreviation “CP” to refer to the Collected Papers of Charles S. Peirce, in bibliography as Peirce (1931–38) 1958.

⁹ See Ambrosio and Campbell 2016 on the (much neglected) influence of chemistry and chemical education in Harvard on Peirce’s account of diagrammatic representations.

¹⁰ The article is reprinted in vol. 2 of the chronological edition of the Writings of Charles S. Peirce, henceforth “W” followed by volume number; in bibliography as Peirce (1982–). See W 2:282–84.

¹¹ For an excellent analysis of Peirce’s article and diagram see Campbell 2017: ch. 2.

¹² Incidentally, the journal had been just founded by the very Sylvester whose chemical-algebraic graphs I discussed above, and who was Peirce’s colleague at Johns Hopkins University. Indeed, Peirce’s own use of the term graph in logic is deeply indebted to Sylvester. In the “Prolegomena to an Apology for Pragmaticism” he explicitly states: “By a graph (a word overworked of late years), I, for my part, following my friends [William Kingdon] Clifford and Sylvester, the introducers of the term, understand in general a diagram composed principally of spots and of lines connecting certain of the spots” (CP 4:535). Peirce’s complaint that the term was becoming “overworked” signals that by 1906 it was stretching beyond its logical/algebraic use and coming to be associated with graphical representations such as the ones by Helmholtz and Whewell I discussed in the previous section.

¹³ My aim in what follows is not to give a detailed and technical account of Peirce’s diagrammatic system of Existential Graphs, on which there is a constantly growing literature. Instead, I hope to flesh out, from Peirce’s philosophical considerations, what his system has to offer to the broader historical and philosophical literature on diagrammatic representations. Technical studies of Peirce’s Existential Graphs began in the 1960s and 1970s with the works of J. Jay Zeman (1964) and Don D. Roberts (1974), and saw a revival from the late 1990s: see for example Barwise and Etchemendy 1996; Shin 2002; Pietarinen 2006; Stjernfelt 2007; Legg 2012; Legg 2013; Pietarinen and Bellucci 2016a and 2016b, and the forthcoming vol. 1 of the comprehensive edition of Peirce’s logical writings (Pietarinen, forthcoming).

¹⁴ See John Sowa’s detailed commentary on R 514, available online at www.jfsowa.com/peirce/ms514.htm.

¹⁵ This has often been interpreted as Peirce claiming that a relation of resemblance governs iconic representations. I have joined the host of Peirce scholars that have questioned the superficial account of resemblance implicit in these criticisms in Ambrosio 2014. See also, among the most notable defenders of iconicity, Dipert 1996; Hookway 2000: ch. 3; Stjernfelt 2000, 2007, 2011 ; and Legg 2012, 2013.

¹⁶ In a brilliant technical article, Cathy Legg (2012) shows that the notion of iconicity involved in Peirce’s Existential Graphs should prompt us to revisit the very foundational question of how we come to know mathematical necessity, for which she provides a phenomenological argument grounded in “the hardness of the iconic must.” Albeit Legg does not cite this specific passage, I believe her account illuminates precisely (among other things) the sense of “necessity” here invoked by Peirce.

¹⁷ I am grateful to Harro Maas for alerting me to this possible objection.

¹⁸ Interestingly, the special issue also features an article by Giardino (2018), which argues—among other things—that the view of diagrams as tools of reason should not be considered at odds with their representational nature.

¹⁹ A landmark study in this respect is Elkins 1999.

²⁰ Rudwick’s article had a large influence on the history of science and its methodology. For a recent review of its significance in the field, see Kusukawa 2016.

²¹ There is much more to Kaiser’s account than the brief sketch I provide here. The very title of his book on Feynman diagrams, Drawing Theories Apart, is an explicit rejoinder to Bruno Latour’s 1990 “Drawing Things Together”: The very idea of following a nonhuman scientific object around as an organising principle bears a certain Latourian signature. Yet, I follow a different line when it comes to the question of “immutable mobiles” . . . Whereas Latour emphasizes “optical consistency” (even “immutability”) as an essential feature of why diagrams and other scientific inscriptions carry so much force among scientists, I focus instead on unfolding variations within their work—on the production and magnification of local differences and the work required to transcend those differences. (Kaiser 2005: 7)

²² See for example Meynell 2008, which provides an answer in terms of representations to the claim that Feynman diagrams are calculational devices; Meynell 2018 takes up again the discussion about the representational nature of Feynman diagrams and relates it to a nonfactive account of understanding. Perini 2013 and Perini 2010 discuss diagrams and representations in biology; William Bechtel, Adele Abrahamsen Daniel Burnston and Ben Sheredos have worked for a long time now on representing biological mechanisms through diagrams—see for example Sheredos et al. 2013. On mechanism diagrams in cell biology, particularly apoptosis research, see Au 2016. On diagrams in relation to models and representations in economics see Morgan 2012, esp. ch 3. Giardino 2013 and 2018 place mathematical diagrams in dialogue with debates on representation in philosophy of science. Ambrosio 2014 contains my own contribution, via Peirce, to this expanding literature.

²³ This relation is usually construed as a similarity or (partial) isomorphism between a source and a target. Defenders of similarity (and selective similarity) comprise, among others, Ronald N. Giere (1988, 2004), Bas C. Van Fraassen (1980, 2008), and Paul Teller (2001). On the isomorphism (or partial isomorphism) side of the debate are Da Costa and French (2003). Van Fraassen’s (2008) “structural empiricism” hinges on a notion of selective similarity that ultimately is explained in terms of (structural) isomorphism, whereas Giere (2004) proposes a much weaker notion of similarity that refrains to appeal to “structure.”

²⁴ Practice-based accounts are a result of the most general “turn to practice” that has characterized philosophy of science starting from the 1980s. The forerunners of this approach are Peter Achinstein (1968), Max Black (1962), and Mary Hesse (1963). Nancy Cartwright (1983), Ian Hacking (1983), and Mary Morgan and Margaret Morrison (1999) pioneered the shift toward practice-based approaches to models; David Gooding (1990) importantly challenged the sharp divide between observing, experimenting and representing, whereas Soraya De Chadarevian and Nick Hopwood (2004) examined the historical context surrounding the production and use of models. Useful overviews of this debate are in Frigg and Hunter 2010 and Suárez 2010. The turn to practice in philosophy of science has a sociological counterpart in the accounts of representation in practice presented in Lynch and Woolgar 1990, and its recent revisited edition by Catalijne Coopmans et al. (2014), which features the brief commentary by Daston I presented at the beginning of this section.

²⁵ Eddy cites Michael Baxandall (1972), Svetlana Alpers (1983), and especially W.J.T. Mitchell (2005), as the pioneers of the compositionalist approach in history of art.

Additional information

Notes on contributors

Chiara Ambrosio

Chiara Ambrosio is associate professor in history and philosophy of science at the Department of Science and Technology Studies, University College London. Her research focuses on representations across art and science, nineteenth- and twentieth-century visual culture, the relations between classical Pragmatism and science, and the philosophy of Charles S. Peirce.