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Formalization and the Meaning of “Theory” in the Inexact Biological Sciences

  • Thematic Issue Article: The Meaning of "Theory" in Biology
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Abstract

Exact sciences are described as sciences whose theories are formalized. These are contrasted to inexact sciences, whose theories are not formalized. Formalization is described as a broader category than mathematization, involving any form/content distinction allowing forms, e.g., as represented in theoretical models, to be studied independently of the empirical content of a subject-matter domain. Exactness is a practice depending on the use of theories to control subject-matter domains and to align theoretical with empirical models and not merely a state of a science. Inexact biological sciences tolerate a degree of “mismatch” between theoretical and empirical models and concepts. Three illustrations from biological sciences are discussed in which formalization is achieved by various means: Mendelism, Weismannism, and Darwinism. Frege’s idea of a “conceptual notation” is used to further characterize the notion of a form/content distinction.

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Notes

  1. For the ICZN, see http://www.nhm.ac.uk/hosted-sites/iczn/code/. For the ICBN, see http://ibot.sav.sk/icbn/main.htm. Consulted July 20, 2012.

  2. Compare Gould’s interpretation of Thompson as a theorist in his foreword to the (1992) Cambridge edition with Bonner’s more ambivalent introduction to the same edition. The former calls Thompson’s work a contribution to theoretical biology while the latter states that Thompson “was quite satisfied with a mathematical description or a physical analogy” (Thompson 2000, p. xv, emphasis added).

  3. A use is indirect if it is a change of use or “repurposing” from another. My belt buckle has a direct use in holding up my trousers, but an indirect use as a bottle opener because it happens that its structure is suited to that function as well, and I sometimes repurpose my belt buckle while traveling if I’ve forgotten my Swiss Army knife, which carries my regular bottle opener.

  4. On the mediating role of models, see Morgan and Morrison (1999).

  5. “Match” is used here to avoid more specific connotations of correspondence, isomorphism, or even similarity. I prefer the imagery of alignment, as in making railroad tracks laid from the west and from the east align in the middle so that trains can run smoothly in either direction. Alignment of models is like that: the aim is to connect phenomena and concepts smoothly. As Winsberg (2006, 2010) has argued, when models of different domains don’t align, scientists are willing to engage in various ad hoc “handshaking” arrangements to keep the trains running anyway. I think his points apply to models within domains of inexact sciences as well.

  6. Characterization of theory in terms of what theory does, materially, in relation to empirical content, has been emphasized recently by Love (2008 and 2012, this issue) and Brigandt (2010).

  7. On theory presentation, see van Fraassen (1980, p. 44); see also Griesemer (1984), and further discussion and elaboration in Love (2012, this issue).

  8. On challenges to the semantic view, see e.g. Morrison (2007, 2011); for a defense of the semantic view, see Thompson (2007). Critics make the compelling point that mismatch in the exact sciences appears to undermine the semantic view of theories. The exact sciences control their subject-matter domains precisely by means of formalized theories that delimit what count as proper subjects. The truth of formalized theories of a domain controlled by them is all too easy, since an object can belong to the domain only if it satisfies the theory. Hence Giere (1988; Giere et al. 2006) describes the role of theory as one of definition of a class of models. The problem arises for the semantic conception that scientific theories are intended to be true of their empirical subject matter as well, yet empirical contents of phenomena are related to models by relations of idealization and abstraction that, strictly speaking, render them false (Wimsatt 1987). On the semantic view, the theoretical models that precisely satisfy theories in the logical, Tarskian sense of model theory, cannot also be correct representations of empirical phenomena because empirical models must idealize and abstract from the phenomena in order to be useful representations. Empirical models, moreover, are often explicitly and intentionally false (i.e., partial, inaccurate) descriptions of phenomena, and often the models of a collection are intentionally designed to contradict one another as part of a research program to discover robust theorems (Levins 1966; Wimsatt 1987, 2007). Thus, if theoretical models satisfy theories and at the same time are expected to be idealized, false descriptions of empirical phenomena, even the best theories would have to aim at being both true and untrue of the empirical phenomena that the models describe. On the “twilight” of the perfect model model of science as aiming at exact natural laws that truly represent nature, see Teller (2001).

  9. Perini (2004), for example, argues that visual representations can bear truth, hence diagrams can function as theoretical models in the senses explored here.

  10. I resist the implication of the term “theorizing” of a one-way path from phenomena to theories—turning something that is not theory into something that is. I do not presuppose that is the only or even the primary path of “theory-ing.”

  11. Frege’s logicism is usually contrasted with the psychologism of Boole and other nineteenth century logicians. If psychologism is a form of “naturalism” about the subject domain of mathematics, Frege’s logicist program looks to be anti-naturalistic about mathematics and, in my extension of his use of conceptual notation to the idea of formalization in the natural sciences, anti-naturalistic about science. A Fregean (in my sense), however, can be pragmatic about conceptual notation (perspicuity is a pragmatic virtue) while logicist about theory (in Frege's case, about the logical theory of mathematics). Thus, Frege can be opposed to psychologism in mathematics and an anti-naturalist about mathematics and at the same time, pragmatic in his practice of logic. (Everyone is pragmatic about their own practice, even if logicists and reductionists deny pragmatism to everyone else in their practices!) So, one must distinguish the pragmatic role of an effective notation for logic from the role (logicist or otherwise) of theory about a subject-matter domain. Conceptual notations are means of formalizing theory and thus facilitators of formalism about theory, yet one's stance on theory can be autonomous from one's stance on notation.

  12. For an attempt to relate models of mechanism to theories, see Griesemer (2011a, b) and Love (2012, this issue).

  13. Love (2012, this issue) considers attempts to retain population genetics as a formal core of an exact science in the face of EvoDevo complications. Theoretical geneticists have also become interested in attempting to bring epigenetics under the umbrella of formal population genetics—e.g. Slatkin (2009); cf. Tal et al. (2010).

  14. See also Godfrey-Smith (2009) for a similar formalization around the idea of “Darwinian population.”

  15. “Investigative experience” is intended as a generalization of Suppes’ (1960, 1962) notion of “experimental experience,” allowing for a distinction between observation and experiment on the one hand, and experimental and theoretical investigations as empirical experiences on the other. For an “investigative practice” approach to science, see Waters (2008).

  16. On notational systems in general, see Goodman (1976, Chap. 4).

  17. Phenomena deemed similar enough to phenomena already in the domain are also counted as in the domain. Phenomena investigated because they result as products of prior investigations are also counted as in the domain. Phenomena that fit empirical models developed to describe other phenomena are counted as in the domain. This is not to say that exact sciences escape the politics of historical tradition, interest and patronage, but the locus shifts at least partially to theory and theory-ing from empirical practice.

  18. Thanks to Massimo Pigliucci for this last reference.

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Acknowledgments

Thanks are due to workshop organizers Massimo Pigliucci, Werner Callebaut, and Kim Sterelny, workshop participants, and the Konrad Lorenz Institute for Evolution and Cognition Research. I thank Roberta Millstein, Elihu Gerson, and the workshop organizers for valuable comments on a previous version of the manuscript and Ken Waters for encouragement. Support of a UC Davis Herbert A. Young Society Deans’ Fellowship, 2011–2014, is gratefully acknowledged.

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    James Griesemer

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Griesemer, J. Formalization and the Meaning of “Theory” in the Inexact Biological Sciences. Biol Theory 7, 298–310 (2013). https://doi.org/10.1007/s13752-012-0065-z

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