Introduction

It is perhaps just a happy coincidence that educational identity theory and the inferentialist proposals in the philosophy of science developed during more or less the same years, namely the turn of the twenty-first century. For, in fact, there is no evidence that the educational theorists involved were acquainted with the work of the philosophers interested in scientific representation (nor, unsurprisingly, the other way around). On the other hand, these two approaches are coherent with the same intellectual outlook. They respond to an emphasis on the social interactions that make possible any human activity or institution. From this perspective, both scientific representations and students’ conceptions are better understood as tools to be employed in specific contexts, according to certain social conventions and practices.

In this work I present a preliminary study of this parallelism. I will focus on some conspicuous examples of scientific representations, Lewis structures (LSs). In the following section I present an outline of an inferentialist account of LSs. In Sect. 3 I review the notion of science identity. In Sect. 4 I delve into the notion of chemistry identity, as it has been employed in the recent educational research, i.e., the facet of an individual’s identity consisting in being considered a “chemistry person”. I argue that this notion is coherent with an inferentialist vision of LSs. Finally, in Sect. 5 I conclude that, at least in the case of chemistry, inferentialism and educational identity theory can be seen as two complementary sides of the same wider program. I propose that the latter can shed some light on how LSs are validated and transmitted, while the former provides a fundamental framework for the research in chemistry education.

An inferentialist account of Lewis structures

Lewis structures (LSs) are schematic descriptions of the structure of molecules in terms of the valence electrons of the atoms that make them up. I will employ the term LS to refer to both planar and three-dimensional molecular representations.

To understand the role of LSs, a distinction must be drawn between the part of chemistry that tries to address the question “What makes a chemical statement true?” and that that simply aims at providing insightful accounts of chemical phenomena. The first program is characteristic of what is usually called physical chemistry (hereafter, for short, phys-chemistry), while the second is typical of what Joachim Schummer called, in a happy expression, “the chemical core of chemistry” (Schummer 1998). We shall refer to this specifically chemical approach as chemical chemistry (chem-chemistry). The role of LS’s in phys-chemistry is ancillary. They are employed as pictograms to represent the different chemical species, but they play no role in the theorizing. On the other hand, LSs are instrumental to any explanation within chem-chemistry. In this paper I shall focus on the latter.

The modelization of a reaction within chem-chemistry is closely linked to the notion of reaction mechanism. The usual way of representing a mechanism is graphical, in terms of LSs. Let us see it in a standard organic chemistry example, the reactions of electrophilic aromatic substitution (Fig. 1). In this example, A+ is a cationic electrophile and B is a nucleophile. The curved arrows are employed to represent a displacement of an electronic pair to generate (or to break) a bond.

Fig. 1
figure 1

Electrophilic aromatic substitution (License notice for the image: V8rik at English Wikipedia https://commons.wikimedia.org/wiki/File:BasicAromaticSubstitution.svg, “BasicAromaticSubstitution”, https://creativecommons.org/licenses/by-sa/3.0/legalcode)

Full size image

An eloquent token of how deeply this technique of representation is ingrained within chemical theory is that it has been given a proper name: arrow pushing (see, for example, Levy 2008). Besides its explanatory power, this way of graphical reasoning also has some predictive value. For example, it can be used to study the influence of a substituent group on the relative yields when more than a species can be produced in an electrophilic aromatic substitution. Similar arguments can be found in any introductory textbook for almost any organic reaction. Moreover, a quick review of the current chemical research publications shows that this explanatory scheme is far from being a mere introductory aid with didactic purposes. It is not an exaggeration to say that being a competent pusher is a necessary condition for a person to be a chemist.

LSs seem obvious candidates for an inferentialist account of scientific representations. In this work, I will adhere to the inferential conception of scientific representation put forward by Suárez (2003, 2004). In this view, the concept of representation is characterized by two necessary conditions: its directionality and its capacity to allow surrogate reasoning and inference.Footnote 1 Both conditions are linked by the notion of representational force. A source system or object A represents a target system or object B by means of its representational force, which, in the words of Suárez himself:

[…]is the capacity of a source to lead a competent and informed user to a consideration of the target. Force is a relational and contextual property of the source, fixed and maintained in part by the intended representational uses of the source on the part of agents: No object or system may be said to possess representational force in the absence of any such uses (Suárez 2004, p. 768).

From this point of view, for a scientific representation to be effective, some intended uses by an agent are required, and this implies some pragmatic considerations in the interpretation of the sources. There are also pragmatic skills involved in the appropriate descriptions of the targets and in how sources can be employed to draw inferences regarding them. The conditions for a correct molecular representation, the Meccano-like vision of the molecular frame as a three-dimensional construction that can be dismantled and re-arranged, and the rules of arrow-pushing are part of the minimal common pragmatic background shared by all post Lewis chemists that enables the representational force of LSs. On the other hand, literally instantiating features of a molecule, as it occurs in nature, as it were regardless of description, is not within the purview of LSs.

From an inferentialist point of view, it is not just an anomaly that, despite their instrumental role in chemical thinking, there seems to be no consensus about some aspects of LSs that are far from being mere details. To give a quite significant example, after a century of publications on LSs, it is not clear whether the octect rule has a preference over the avoidance of formal charge separation in the determination of the most stable resonant form for a given molecule (See 2009). Among other implications, this means that there is no agreement on how to determine the bond order of a molecule. This is, to say the least, surprising, since this notion is crucial in any chem-chemical mechanistic reasoning. In my opinion, this oversight can only be understood by considering that chem-chemists assume that the role of LSs is not providing a realistic, if simplified, depiction of molecules, but, instead, making inferences about their properties and reactivity. As long as the alternative rules for constructing and employing LSs do not lead to incompatible inferences, they can be overlooked. A similar argument can be given to account for the shocking fact that very little attention has been paid to relationship between LSs and the quantum mechanical description of molecules.Footnote 2 It can be said that, though implicitly (or even, perhaps, unconsciously), chemists have accepted that the role of LSs is not iconic, but symbolic.Footnote 3 I will get back to this point in Sect. 4.

This apparent negligence towards the physical implications is revealing of yet another pragmatic competence required to draw inferences from LSs. In any use of LSs by chem-chemists it is always implicit that they are ceding to phys-chemists the task of deciding about the truth value of their eventual conclusions regarding the properties of a substance, including its reactivity. Let us see this in another example. Any chem-chemist can infer, by using some simple structural rules based on three-dimensional LSs, about the polarity of a substance, and thus, about its solubility in different solvents. On the other hand, her or his conclusions are only qualitative. At best, and only in certain cases, a group of substances can be ordered according to their polarity. That is, in chem-chemistry the polarity of a substance is treated as a nominal or, only in some cases, ordinal variable. My point is that even this basic property must be experimentally tested by means of phys-chemical methods. The relative order of polarity of a group of substances could be assessed, for example, by comparing their respective solubilities in water. But this time-honoured, seemingly simple method rests on the theoretical principles and experimental methods of thermodynamics. And this approach is essentially different from the visual reasoning of chem-chemistry (see, for example, Birch et al. 2019; for an introductory review, see Reus et al. 2023). Similar arguments can be done for any other inference made from LSs.

Put briefly, any argument based solely on LSs provides, at most, a proof of the consistency of a given inference with the rest of the accepted chem-chemical knowledge, but not an absolute measure of its validity. Designing and performing these validity tests is the task of phys-chemistry. My point is that, since the arbiter role of physics is implicit in any chem-chemical argument, this epistemic deference is yet another pragmatic competence that enables LSs as a source of meaningful chemical inferences. Without it, chem-chemistry would degenerate into a self-referential game and its conclusions could not be deemed as inferences, but as interpolations.

In sum, an inferentialist approach to LSs provides a fresh approach to the problem of the relation between chemistry and physics. In this view, this relation is not to be found in the realm of ontology, nor in that of epistemology, but instead in pragmatics.

Science identity in education

To explore the interactions between inferentialism and chemistry education, it may be interesting to review one of the most influential lines in current educational research: the studies of science identity.

The notion of identity is central in contemporary sociology. Identity theory was introduced to provide a unified vision of the self that could account for both macro and micro processes in the interplay between the individual and their environment (Stryker, 1987). In this view, the self is reflexive, it classifies itself according to categories taken from the environment of the individual (McCall and Simmons 1978; Turner et al. 1987). Since, in general, an individual can adopt several of these availabe roles, the self is a multifaceted construct, and its components are usually referred to as identities. The categorization of the self as an occupant of a role, and the interiorization of the meanings and expectations associated with that role are instrumental in the formation of an identity (Turner 1978; Stryker and Serpe 1982).

In an influential article, James Paul Gee proposed that the notion of identity can be used as an analytical lens to study education (Gee 2000). Gee pointed out that some educational categories, such as, for example, being an ADHD child, can be understood as specific role identities in a school context. The ways in which the different educational actors perceive these identities strongly conditions not only how the individual to whom the identity is attributed is treated, but also her or his behaviour. Carlone and Johnson (2007) employed the ideas developed by Gee to study the identity formation of a group of North American women of color who had succeeded in taking on a professional career as scientists. These authors focused on their late college and early career paths to conclude that a relevant factor in their academic success was that they all had developed a scientific identity, that is, that they have come to be acknowledged as “science persons” at some point in their careers. In Carlone and Johnson’s view a science person is an individual who is able to perform some required tasks in a specific context, thus making their scientific competence evident, so that she or he is recognized by others as proficient in a scientific discipline.

Carlone and Johnson put an emphasis on the social performance of relevant scientific practices in the formation of a science identity, thus bringing an obvious pragmatic twist in the study of science education. Besides, if we consider the representational uses specific in a scientific discipline as one of the competencies required for a person to be recognised as a practitioner in the field, then the notion of science identity gains an obvious inferentialist reading. A science identity would imply, among other things, being competent in the use of certain kinds of representations to draw inferences, according to some rules commonly held by the agents who take part in a scientific context.

Carlone and Johnson’s model is the starting point of other approaches that employ the notion of science identity to account for different socio-educational issues (Chemers et al. 2011; Estrada et al. 2011; Stets et al. 2017). It has also been adapted to several scientific fields, including mathematics, physics and chemistry, by defining specific identities for each discipline. I will focus on these disciplinary identities, that are particularly relevant to my purposes in this article. In a much-cited paper on physics identity, Zahra Hazari and co-workers reformulated the notion of science identity so that it can be extended to non-professional scientists, such as students who were non-physics majors or earlier in their physics academic career (Hazari et al. 2010). Regarding chemistry, Hosbein and Barbera (2020a, b), have gone further on the way opened by Hazari, by explicitly resorting to Albert Bandura’s Social Cognitive Theory (SCT; Bandura and National Institute of Mental Health, 1986) to define the components of chemistry identity for tertiary education. Besides, they employ an adaptation of the Middle School Mathematics Self-Efficacy Scale (Usher and Pajares 2009), an instrument based on SCT, to quantify these components, while in Hazari and co-workers’ original work the performance in physics is measured by using SAT or ACT scores.Footnote 4 This is an evident improvement in terms of internal consistency, at the price of compromising its external validity, since it is not clear to what extent the instruments employed by Hosbein and Barbera can be applied to settings other than those studied by them. In particular, the questions of the Middle School Mathematics Self-Efficacy Scale explicitly refer to ‘math’ (in the adapted version, to ‘chemistry’), in general. For example, we find, among others, questions such as: “I make excellent grades on math tests” (question 1); “People have told me that I have a talent for math” (question 14); “My mind goes blank and I am unable to think clearly when doing math work” (question 22). The problem here, as I see it, is that while it seems sensible to assume that the meaning of ‘maths’ is basically uniform, that of ‘chemistry’ may vary strongly with the context in which it is employed. Does ‘chemistry’ imply the same in, let us say, England as it does in India, or in Nigeria, given the obvious educational and cultural differences among these countries? Moreover, Hosbein and Barbera’s approach is so strongly focused on tertiary education that it hardly says anything about chemistry identity in other contexts. The connotations, and perhaps even the denotation, of ‘chemistry’ are so divergent if the word is used by a middle school student and by, let us say, an organic chemist, that the validity of the instrument across the different contexts in which chemistry is employed is problematic.

I want to stress that I do consider that Hosbein and Barbera’s is an important contribution to the understanding of chemical education. On the other hand, the instruments that they employ do not show a clear validity outside the restricted sphere of (American) tertiary education. To extend their approach, it is necessary to explore whether there are identity traits that are valid along the whole career of any chemist, and across all the areas and activities into which chemistry unfolds.

Representational competence

There is no need to be a staunch inferentialist to acknowledge that a relevant part of the least common pragmatic ground that defines chemistry as a discipline are its representational practices. It is not an exaggeration to say that after Lewis, being able to produce and interpretate LSs, and so being recognized, is an indisputable necessary condition for a person to be acknowledged as a chemist. I do not think that much argument is required to support this position, but, if required, an empirical proof of the importance of LSs can be found by randomly leafing through the chemical literature, from educational textbooks to state-of-the-art research papers. If this evidence is not enough to convince the reader, the instrumental role of representations in current chemistry can be supported by appealing to authority. For example, Roald Hoffmann, one of the most influential chemists of the twentieth century, co-authored with Pierre Laszlo, a notable researcher and divulgator, a paper significantly entitled Representation in Chemistry (Hoffmann and Laszlo 1991). The very first two sentences of this article are:

Chemical structures are among the trademarks of our profession, as surely chemical as flasks, beakers, and distillation columns. When someone sees one of us busily scribbling formulas or structures, he has no trouble identifying a chemist (Hoffmann and Laszlo 1991, p.1).

Given the relevance of the authors, and since the guild of chemists has been traditionally reluctant to reflect on their own practice, it may be interesting to briefly review this paper.

Although Hoffman and Laszlo include assertions such as “Naive realism asserts that chemical formulas resemble reality: they do” (Hoffmann and Laszlo 1991, p. 5), this position is qualified in other parts of the article. For example, two pages above, they write: “Perhaps chemical drawings do not need to be realistic representations because they are symbols, signs, that in a chemist’s mind are reconstructed into the three-dimensional structure, or at least the ball-and-stick model.” (Hoffmann and Laszlo 1991, p. 3). It seems, therefore, that the authors use the term ‘chemical formula’ to refer to three-dimensional models of molecules. These spatial representations are what, in their view, realistically stand for the actual molecules. But the way they use the notion of chemical formula is, in fact, far more complex: “A chemical formula is at once a metaphor, a model (in the sense of a chemical diagram), and a theoretical construct. A chemical formula is part pure imagination, part inference.” (Hoffmann and Laszlo 1991, p.10). That is, despite their naïve realist statements, Hoffmann and Laszlo do acknowledge that formulae are not figurative depictions, and thus, that they are not essentially different from other forms of representing molecules.

Let us focus on their vision of the way chemists employ graphical representations. In the first pages of the article, it can be read:

Chemical structures are then part of a chemical language. What is interesting about language (it doesn’t matter whether it is German or English or...) is that (1) despite its impreciseness, people communicate with it and (2) it, language, inevitably brings us complications, ambiguities and richnesses that we did not expect. Or perhaps that we subconsciously intended (Hoffmann and Laszlo 1991, p.3).

As I interpret this paragraph, Hoffmann and Laszlo underline, albeit in an unelaborated way, the pragmatic character of the use of molecular representations. On the same page, they put an emphasis in molecular representations as tools of opportunity for the communication of chemists: “It is critical that chemists easily communicate this structural information [about molecules] among themselves. Via what’s at hand, which are two-dimensional media-paper, a screen”. (Hoffmann and Laszlo 1991, p.3). Below in the article, the authors point out the role of the graphical representations in the chemical practice: “In an important sense, chemistry is the skillful study of symbolic transformations applied to graphic objects” (Hoffmann and Laszlo 1991, p. 11). For reasons of space, I cannot include more quotations, but the text abounds with phrases pointing in the same direction.

Hoffmann and Laszlo’s article is not a work of philosophical research, but I think that it is philosophically relevant. Its interest lies, in my opinion, in that the authors have expressed out loud some basic ideas that most chemists, not to say all of us, implicitly, or even unconsciously, share. In particular, Hoffmann and Laszlo admit that chemical representations are primarily instruments for surrogate reasoning and inference in chemistry. Thus, in sum, regardless of the somewhat ingenuous Platonism than sprinkles the article, the authors adopt a position compatible with an inferentialist account of LSs. This implicit inferentialism can also be detected in the current educational research and practice. To fully understand this point, it may be convenient to take a short walk on the pedagogical side.

During the last decades, the educational focus has been shifted from the pieces of the content knowledge of a subject to be taught, to some specific abilities, usually covered transversally across different subjects, that the students are expected to develop over their educational years. In the jargon of pedagogy, the emphasis is now put on the competencies as the core of education. The notion of educational competence has an evident pragmatic character. In the definition of ‘competence’ that can be found in the web site of the UNESCO’s International Bureau of Education, we read:

Competence indicates the ability to apply learning outcomes adequately in a defined context (education, work, personal or professional development). Competence is not limited to cognitive elements (involving the use of theory, concepts or tacit knowledge); it also encompasses functional aspects (involving technical skills) as well as interpersonal attributes (e.g. social or organizational skills) and ethical values (UNESCO. International Bureau of Education 2023)

In this view, the goal of education is thus not just the apprehension of some ready-made pieces of information but rather the inculturation within some social practices.

The shift towards competencies, that informs most of the contemporary curricular approaches, has of course reached chemistry education. For example, as of January 28, 2023, the search engine of the Journal of Chemical Education yields 287 entries for the term ‘competencies’, 237 of them published in the twenty-first century, 222 in the last decade, 41 in 2022, and 4 in the first four weeks of 2023. Narrowing the search, ‘representational competence’ yields 60 entries, all of them published in the twenty-first century, 51 in the last decade, 9 in 2022, and two in 2023. Let us focus on these most recent works. In the introduction to a paper entitled “The Picture Is Not the Point: Toward Using Representations as Models for Making Sense of Phenomena”, the authors insist that the purpose of teaching molecular representations in organic chemistry is to enable students to explain and predict chemical phenomena (Stowe and Esselman 2023). In fact, this article is a clear, though implicit, act of endorsement of inferentialism in chemistry. The explanatory role of LSs is also stressed as inherent to a representational competence in chemistry by other authors, who focus on their use in reaction mechanisms (Dood and Watts 2022, 2023). Similar arguments can be found in other recent references of the list yielded by the search engine.

In conclusion, if chemical literature, both technical and educational, is a reliable mirror of the chemical practice, then it is evident that LSs play a crucial role in what being a chemist means. If there is such a thing as a chemistry identity, then being competent in the usage of LSs is a central part of it. Further, the way chemists rationalize these representational practices is fully compatible with an inferentialist account of LSs.

Conclusions: the tandem program

In the previous sections I have argued that the inferentialist view of scientific representation accounts for the role of LSs in chemical theory. I have also shown that the use of LSs as tools for making inferences is a central part of chemistry identity. These two conclusions, taken together, suggest that an inferentialist approach to LSs and the analysis of chemical education from the point of view of the students’ identity can be studied in parallel. I will call this complementarity the tandem program.

Within the tandem program, the inferentialist analysis contributes a theoretical framework for defining, at least partially, what being a “chemistry person” means. Specifically, it gives an a priori justification of the importance of the representational practices in the formation of a chemistry identity. Moreover, from an inferentialist point of view, “chemistry people” are individuals on whom the representational force of LSs acts, thus suggesting a method for detecting them. Besides, inferentialism brings support to a didactic approach in which the emphasis is put on the representational competencies of the students. In this view, learning chemistry, at least in part, consists in becoming competent in the usage of LSs as tools for inferring about chemical species and processes (see Stowe and Esselman 2023). The implications of this didactical side are one of the questions that I will study as a follow-up to this article.

On the other saddle of the tandem, research in chemistry identity can be seen as an experimental philosophy approach to inferentialism in chemistry. For, in fact, the way chemists (most of them, as it seems sensible to assume, fully unacquainted with the recent contributions of the philosophers of science) use molecular representations can be seen as an empirical confirmation of inferentialism. Besides, the study of the process of formation of chemistry identity can provide data on how the rules for the production and manipulation of LSs are codified and transmitted. Finally, it is not unreasonable to think that the origin of these representational practices has to do with the way chemistry is taught. In this view, LSs would be visual aids originally intended to teach chemistry that have been assimilated into the representational tools of professional chemists. In support of this hypothesis there is the fact that most of the information about LSs, not to say all of it, is in didactic texts, and that this is not a contemporary trend. Just to point out a rather significant example, the very first in-depth comprehensive presentation of LSs is included in a work with an explicit vocation of textbook: G.N. Lewis’ Valence (Lewis, 1923).

If the way LSs are used in chemistry has an educational origin, then chemistry would be a case of what could be called disciplinary neoteny, the preservation within the professional practice of a discipline of models and ideas specifically coined for the education in this discipline. This process, if actual, would grant chemistry education, understood as the process of formation of a chemistry identity, a new and unexpected meaning. It would be in fact more than the transmission system of the chemical ideas validated by the research community. Education would play an active role in the configuration of chemistry as a discipline. Testing the hypothesis that LSs are didactical aids festered within the professional identity of chemists is the second research path I set out to follow in further works.