Challenging the traditional theory-centered view, the philosophy of science of the last decades has directed its attention to models, which play an essential role in scientific practice. From a widespread perspective, scientific models supply an approximate representation of the target system in terms of the concepts of the theory (da Costa and French 2003). Although models might vary in their degree of accuracy, representation is conceived as one of their essential features. However, this representational view of scientific models has been challenged by an artifactualist view, according to which models are not representational devices but material artifacts that provide information due to its manipulation and construction (Knuuttila 2005).
The debate about the nature of scientific models, as is typical to philosophical debates on science, mainly appeal to examples coming from physics, while other domains of science are overlooked.
The debate about the nature of scientific models, as is typical to philosophical debates on science, mainly appeal to examples coming from physics, while other domains of science are overlooked. As there is hardly a science in which models are employed as extensively as in chemistry, there is room to ask: what chemistry has to say about scientific models? By considering two examples coming from quantum chemistry, we will see that chemical models pose strong challenges to the representational view, but in a different sense than those posed by the artifactualist perspective.
The first example concerns the concept of chemical bond. Two approaches were developed in order to use the methods of quantum mechanics chemical bonding: the valence bond theory (VB) and the molecular orbital theory (MO). From the viewpoint of VB, a covalent bond is formed by the overlap of half-filled valence atomic orbitals; so, the bond structure is similar to a Lewis structure, in which bonding is due to the electrons shared between the two atoms. According to MO, atomic orbitals merge into a molecular orbital in which the greatest electron density falls between the two nuclei; this means that electrons in a molecule do not belong to individual atoms but are treated as moving under the influence of the atomic nuclei of the whole molecule. At present, both theories are extensively used in the practice of quantum chemistry.
Independently of technical details, the point to stress here is that each approach has its own way of modeling molecules, and the two ways are clearly different. EV models the molecule as a composite system in which component atoms, with their nuclei and electrons, can still be identified; in this sense, the picture is closer to that given by structural chemistry. In an MO model, by contrast, electrons do not correspond to a particular nucleus, but are delocalized in the molecule; therefore, the molecule is a whole that cannot be analyzed in terms of atomic components. It is apparent that these two kinds of models are incompatible: the target molecule cannot be accurately represented by the two pictures; so at least one of them must be conceived as a non-representational instrument for prediction and manipulation. Nevertheless, this fact does not undermine the central role that EV and OM play in contemporary quantum chemistry, and the fruitfulness of the models corresponding to those two theoretical approaches (for a different example of incompatible models in chemistry, see Accorinti 2019).
The second example refers to the so-called Born-Oppenheimer approximation (BOA). The ideal of quantum chemistry is to obtain the wavefunction describing a molecule by solving the well-known Schrödinger equation. However, beyond the molecule of hydrogen, such a task is unattainable: it is necessary to introduce different approximations to make the solution possible. The basic one is BOA, which consists in two steps. The first step is often referred to as “the clamped nuclei approximation”: the Schrödinger equation is solved by “clamping” the nuclei at definite positions. This procedure is repeated for different positions of the nuclei in such a way that the electrons are conceived as moving in an effective potential. So, in the second step the kinetic energy of the nuclei is reintroduced, and the Schrödinger equation is solved again. Again, independently of technical details, the point is that models based on BOA assume the nuclei as classical particles, at rest in definite positions. But this assumption contradicts the Heisenberg principle, according to which a quantum particle cannot be simultaneously assigned a definite position and a definite momentum (for a detailed discussion, see Lombardi and Castagnino 2010). In other words, the clamped nuclei approximation amounts to introducing a classical assumption into a quantum theoretical framework.
This means that, under BOA, a single model is constructed in terms of elements coming from incompatible theories, in this case, classical mechanics and quantum mechanics. The situation in which incompatible theories collaborate to build a single model not only challenges that theory-driven view of models (which endows theories with priority and makes models theory-dependent), but also seems to support the so-called “toolbox” view of scientific theories (Cartwright, Shomar, and Suárez 1995), according to which the main role of scientific laws is not to represent reality, but to lead to the construction of predictively and inferentially successful models.
These kinds of situations (incompatible models of a same target, incompatible theories in a single model) are not exceptional in the field of chemistry. Of course, they do not offer a definitive answer to the discussions about the nature of scientific models. Nevertheless, they show that philosophers of science would greatly benefit from considering the specificity of chemical sciences in their attempt to elucidate how science works.
References
Accorinti, H. (2019). “Incompatible models in chemistry: the case of electronegativity.” Fundation of Chemistry, 21: 71-81.
Cartwright, N., Shomar, T., and Suárez, M. (1995). “The tool-box of science.” Pp. 137-149 in W. Herfel, W. Krajewski, I. Niiniluoto, and R. Wojcicki (eds.), Theories and Models in Scientific Processes. Amsterdam: Rodopi.
da Costa, N. and French, S. (2003). Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning. New York: Oxford University Press.
Knuuttila, T. (2005). Models as Epistemic Artefacts: Toward a Non-Representationalist Account of Scientific Representation. Helsinki: University of Helsinki.
Lombardi, O. and Castagnino, M. (2010). “Matters are not so clear on the physical side.” Foundations of Chemistry, 12: 159-66.
* Hernán has a Research Scholarship from the National Council of Scientific and Technical Research, Argentina.
**Juan Camilo is Assistant Researcher of the National Council of Scientific and Technical Research, Argentina.