Colligation in modelling practices: From Whewell’s tides to the San Francisco Bay Model

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Abstract

“Colligation”, a term first introduced in philosophy of science by William Whewell (1840), today sparks a renewed interest beyond Whewell scholarship. In this paper, we argue that adopting the notion of colligation in current debates in philosophy of science can contribute to our understanding of scientific models. Specifically, studying colligation allows us to have a better grasp of how integrating diverse model components (empirical data, theory, useful idealization, visual and other representational resources) in a creative way may produce novel generalizations about the phenomenon investigated. Our argument is built both on the theoretical appraisal of Whewell’s philosophy of science and the historical rehabilitation of his scientific work on tides. Adopting a philosophy of science in practice perspective, we show how colligation emerged from Whewell’s empirical work on tides. The production of idealized maps (“cotidal maps”) illustrates the unifying and creative power of the activity of colligating in scientific practice. We show the importance of colligation in modelling practices more generally by looking at its epistemic role in the construction of the San Francisco Bay Model.

Introduction

“Colligation”, a term first introduced in philosophy of science by William Whewell (1840a), today sparks a renewed interest beyond Whewell scholarship. In this paper, we argue that examining the notion of colligation in its original context, that is, as part of Whewell’s theory of induction and in relation to his work as a practicing scientist, can contribute to our current understanding of scientific models.

Throughout his philosophical work, Whewell showed a continuing interest in induction as the chief mental operation in the acquisition of scientific knowledge. He believed that science largely consisted in the combination of facts under “suitable Conceptions”, which he took as a fundamental part of induction called the “Colligation of Facts” (Whewell, 1847/2001, v. 5, p 36. Emphasis of the text).1 More generally, Whewell applied the term colligation “to every case in which, by an act of the intellect, we establish a precise connexion among the phenomena which are presented to our senses” (Ibid.). This paper focuses on the role of colligation in the context of modelling practices in science. It takes Whewell’s own practices as a tidologist in the mid-19th century, as well as the construction of the San Francisco Bay Model in the mid-20th century, as insightful cases in point. In so doing, we aim to uncover the actuality of Whewell’s ideas on colligation and, at the same time, offer an expanded interpretation of this notion in the light of recent work in philosophy of science in practice.

Section 2 provides a brief characterization of colligation from Whewell’s philosophical works and notes the recent interest in this notion among philosophers of science. We purposefully disengage with debates concerning the place of Whewell’s overall philosophical project in relation to other systems of knowledge, such as empiricism or transcendental philosophy, and instead push our research towards a more historical and practice-oriented understanding of colligation, building on recent works by Reidy (2008), Ducheyne (2010a, 2010b, 2011), and Snyder (2006, 2011).

Section 3 addresses Whewell’s scientific work on tides and proposes a novel account of how his ideas on colligation emerged from it. Whewell’s practices in tidology are reconstructed through the analysis of four crucial papers on tides (Whewell 1833, 1834, 1835, 1836). Especially the production of idealized maps (i.e. cotidal maps) and the use of graphical methods was a fundamental source for Whewell’s later conceptualization of induction and colligation. With hindsight, those maps and graphs exemplify the epistemic role of colligatory acts, which entail the creative integration of different components of modelling (empirical data, theory, useful idealizations, visual resources) as to produce novel generalizations.

Lastly, section 4 expands our analysis of colligation to the context of recent model studies. It examines the case of the San Francisco Bay Model (SFBM) in detail, in order to show how the activity of colligating can play an important role at specific stages of the construction of scientific models. In the case of the SFBM, scientists’ acts of colligation facilitated the production of novel generalizations about hydraulic phenomena in the San Francisco Bay (and beyond) through the use of creative visual resources.

Seeking a genuine integration of philosophy and history of science, we advance a reappraisal of Whewell’s ideas on colligation in connection to his scientific work, and we hope that more instances of colligation in contemporary modelling practices can be further investigated.

Section snippets

Colligation in philosophy of science

The notion of “colligation” was originally proposed by William Whewell in the Philosophy of the Inductive Sciences in 1840. Whewell saw colligation as a part of induction, together with the “Explication of the Conceptions”, which is the operation of clarifying the unifying conceptions that are employed in colligation (1847/2001, v. 5, p 46). Induction, more broadly, was “usually and justly spoken of as the genuine source of all our real general knowledge respecting the external world”

Whewell’s tides: the development of colligation

The study of tides, the field to which Whewell gave the distinct name of “tidology”, was one of the scientific projects that caught his attention the longest. Indeed, Whewell possessed expertise and carried out observations in a variety of fields, from mineralogy to geology, biology, and astronomy (see Ruse, 1976). Because of the diversity of his contributions, his relationship with science has often been described as amateurish (Reidy, 2008, pp 126–128), or not significant enough in comparison

Colligation in model analysis: the San Francisco Bay Model

In this section, we expand the analysis of colligation from the context of Whewell’s cotidal maps to recent model studies. This move is motivated in part by Whewell’s intention to advance an account of colligation that could apply to a wide range of scientific contexts (1858/2001, v. 6, p 60), and in part by the thought that the production of cotidal maps was a modelling practice itself.

Conclusions

We have argued that Whewell’s notion of colligation was developed alongside his scientific research on tides. In its original philosophical exposition, colligation was meant to account for discovery and creative inferences made in scientific practice. While stressing the material background of colligation, which appears now directly related to graphical tools and maps in nineteenth-century scientific research, we tried to extract some of its more general implications, spelling out how

Declaration of competing interest

None.

Acknowledgements

The authors would like to thank the audiences of the Seventh International Conference on Integrated History and Philosophy of Science, celebrated at Leibniz University Hannover (July 2018), the Narrative Science Seminar Series, at the London School of Economics (November 2018), and the Early Career Seminar of the Max Planck Institute for the History of Science in Berlin (May 2020). Special thanks go to Hasok Chang, María de Paz, Dominic Berry, Lino Camprubí, Chiara Ambrosio and Mary Morgan for

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