Case I. Chemical Elements

The idea of elements existed for millennia but it is safe to say that Lavoisier gave the first rigorous definition of them. He proposed that elements are things that cannot be further decomposed by means of chemical analysis. Dalton postulated that elements are composed of ‘qualitatively identical atoms’, to which Mendeleev added that the property which all atoms of an element share is their atomic weight (Reference HendryHendry 2005: 32).Footnote ¹⁰ In the 1920s, it was discovered that elements can contain atoms of different atomic weights (i.e. isotopes). Given this, the International Union for Pure and Applied Chemistry (IUPAC) defined them to be distinguished by their atomic number; that is, the ‘number of protons in the atomic nucleus’ (IUPAC 2014: 123).Footnote ¹¹

Microstructural essentialism about chemical elements involves two claims. First, the property which identifies a kind-element is microstructural: it is a property that concerns the microstructure of atoms. Most proponents take this to be IUPAC’s defining property of elements: atomic number (e.g. Reference HendryHendry 2006a; Reference PutnamPutnam 1975). Second, the microstructural property is essential to its kindhood. What is meant by ‘essential’ diverges in the literature, but one could contend that there are (at least) two interpretations.Footnote ¹² First, ‘essential’ confers the idea that it is necessary for members of a kind to possess that property: if they do not possess it, they are not members of that kind.Footnote ¹³ For example, if a sample does not consist of atoms with atomic number 79, it does not qualify as an instance of gold even if it exhibits all other properties that are standardly associated with gold (such as colour and texture) (Reference HendryHendry 2005: 33). The second interpretation takes a property to be essential in that it is necessary and sufficient for members of a kind (e.g. Reference HäggqvistHäggqvist 2022: 32). On this view, a sample consisting of atoms with atomic number 79 is an instance of gold even if it does not exhibit the properties that one generally expects of gold (such as being shiny or malleable).

A different account of microstructural essentialism for elements is formulated by Reference HarréHarré (2005), who bases his account on Locke’s distinction between nominal and real essences. Harré takes nominal essences to refer to a set of properties that have been selected by the scientific community at a specific historical period to pick out members of a kind. He views them as practical criteria to identify members of a kind. Real essences are the necessary and sufficient criteria for an instance to be member of a kind. Real essences are often unobservable properties and are conferred by theoretical hypotheses that are empirically confirmable and thus revisable. In the case of elements, Harré argues that atomic number ‘is meant to express an aspect of the real essences of elementary substances’ (Reference Harré2005: 19).

Objections are raised against microstructural essentialism when applied to chemical elements.Footnote ¹⁴ These objections are (implicitly at least) addressed against the second interpretation of microstructural essentialism as they point out chemical examples in which atomic number is insufficient for correctly identifying members of an element-kind. First, take isotopes. Isotopes are ‘(n)uclides having the same atomic number but different mass numbers’ (IUPAC 2014: 794). This means that while all members of an element possess the same number of protons in their nucleus, they can possess different numbers of neutrons. For example, the element hydrogen can be found in stable form with either zero, one or two neutrons. These three cases correspond to distinct isotopes of hydrogen: protium, deuterium and tritium, respectively.Footnote ¹⁵ Given this, it can be argued that atomic number does not distinguish correctly between kinds because, based on this property, members of the same element-kind exhibit differences in their chemical and physical behaviour. This leads to the following dilemma: we either admit that members of the same element-kind exhibit different observable properties or we deny that atomic number is sufficient to correctly pick out members of a kind.

In response to this, Hendry claims that chemists rightly do not distinguish isotopes as different kinds (Reference Hendry2006a: 868). Indeed, protium, deuterium and tritium are regarded as instances of the same element (hydrogen), occupying a single space in the periodic table. This is empirically justified because while hydrogen exhibits chemical and physical differences in its three isotopic forms (including in some instances, in its toxicity, boiling point, density and reactivity), most differentiations in mass numbers have negligible observable differences. As Hendry states, ‘the isotope effect in hydrogen is an extreme case: a monster, not a paradigm’ (Reference Hendry2006a: 868).

However, Bursten points out that there are also other properties (apart from isotopy) that lead to observable differences among members of an element-kind. These concern the size, shape and dimensionality of the collection of atoms that makes up a pure substance (Reference BurstenBursten 2016: 14). For example, a collection of 100 gold atoms (suspended in a prepared solution) exhibits different properties from a collection of a billion gold atoms (Reference BurstenBursten 2016: 1). The texture and appearance of the two collections differ: the lump of a billion gold atoms is shiny and yellow, but the hundred gold atoms in a solution are red or black (Reference BurstenBursten 2016: 2). Moreover, at the nanoscale, differences in size, shape and surface lead to differences in the material’s physical properties (such as conductivity and ductility), and to differences in chemical properties (including chemical reactivity). According to Bursten, this is a problem for microstructural essentialism because ‘(a)ll this is to say that the macroscopic kindhood of my collection of gold atoms is underdetermined by solely specifying the identity of the atoms involved’ (Reference Bursten2016: 2). So, one is faced with a similar dilemma as in the case of isotopes: either accept that an element-kind exhibits different macroscopic properties depending on the size, shape and surface of the corresponding collection of atoms or deny that atomic number is sufficient to differentiate between observably distinct kinds of matter (Reference BurstenBursten 2016: 2).

In light of this, Bursten proposes reactivity as the correct property to pick out members of a kind.Footnote ¹⁶ As she states, ‘fundamental chemical kinds should be individuated such that no two kinds enter into all the same chemical reactions and no two members of one kind enter into different reactions’ (Reference Bursten2014: 639). Interestingly, despite dismissing microstructure as essential to chemical kinds, she retains its importance in the sense that it explains the reactivity of chemical kinds. She claims that microstructure and reactivity form an asymmetric relationship: microstructure grounds, justifies and explains the reactivity of a kind (and not vice versa) (Reference BurstenBursten 2014: 644).

Note also that for Bursten microstructure should not be understood as referring solely to the atomic number of an element, but to a richer set of microstructural information (Reference Bursten2014: 639). She distinguishes between two types of so-called Chemical Microstructural Properties (CMPs): monadic and relational CMPs.Footnote ¹⁷ Monadic CMPs concern the individual properties of atoms and include, apart from atomic number, the number of neutrons (and thus isotopic information) as well as electronic structure. Relational CMPs include properties concerning the relations among atoms, such as the ratio of species of atoms in a molecule and the geometric properties of molecules. Both proposed revisions offer a more complete account of what microstructure involves. As such, one could wonder why this amended understanding of microstructure does not resolve Bursten’s objection to microstructural essentialism. After all, if these properties are included in our understanding of microstructure, can we not argue that this enriched notion is sufficient to being member of an element-kind?Footnote ¹⁸ We return to this in the discussion of chemical compounds.

Case II. Chemical Compounds

While IUPAC does not offer a definition of compounds, compounds are standardly understood as collections of identical molecular entities. Similarly to element-kinds, microstructural essentialism for compound-kinds takes that a chunk of matter is member of a compound-kind in virtue of its microstructural properties. For example, a jug of liquid is member of the kind-water because of its microstructure; namely, it consists of H₂O molecules. This idea is often conferred in the literature by the phrase ‘Water is H₂O’ or ‘Water = H₂O’ and has prompted extensive criticisms. While I do not restrict my analysis of this view to either of the two interpretations of ‘essential’ presented at the beginning of this section, it is interesting to note that insofar as ‘=’ is understood as a symmetric identity relation, statements of the form ‘Water = H₂O’ may be understood as taking H₂O to be both necessary and sufficient to being water.Footnote ¹⁹

This reading is further reinforced by the fact that most objections seem to (implicitly) address (again) the second interpretation of ‘essential’. First, take the problem of isotopes, which carries over to the case of compounds. Isotopes form distinct isotopic compounds (also called isotopic isomers; Reference Weisberg, Baird, Scerri and McIntyreWeisberg 2006). For example, there are three isotopes for hydrogen and three for oxygen, resulting in different combinations between them that produce different isotopic variants for water. The problem with this is not that substances with distinct isotopic properties are all members of the same compound-kind (i.e. the kind-water). This is to be expected from a microstructural essentialist perspective as the latter regards distinct isotopes to be members of the same element-kind. Instead, the problem with isotopic compounds is that certain combinations of isotopes lead to different macroscopic properties that are not standardly associated with the compound-kind of which they are members. For example, consider a substance consisting mainly of deuterium oxide, D₂O (called heavy water). This is an isotopic variant of H₂O and, as such, microstructural essentialists regard it a member of the kind-water. However, this compound is highly toxic and undrinkable. Therefore, it exhibits an important observable divergence from the properties usually associated with water (Reference HendryHendry 2012a: 62–3). So, the dilemma is similar to that previously raised about element-kinds: we either admit that members of the same compound-kind exhibit different observable properties (due to their isotopic variance) or we deny that being H₂O is sufficient to being water.

Despite this, Hendry maintains that ‘being H₂O is the only chemical requirement that is relevant to being water; it is the only requirement of any kind that is necessary to being water’ (Reference Hendry2012a: 63). As with the case of isotopes, he points out that water is mostly found as a drinkable non-toxic substance and the microstructural properties which describe its elemental composition successfully explain the standard properties associated with water. This view is more generally based on what he calls the ‘core conception’ of a chemical element, which consists of three assumptions: (a) elements survive chemical change; (b) compounds are composed of elements; and (c) the elemental composition of compounds explains their behaviour (Reference HendryHendry 2006b). On this view, if we accept these assumptions, then we can maintain microstructural essentialism about chemical compounds.Footnote ²⁰

However, apart from isotopic compounds, there are also isomers which seem to reinforce the problem for microstructural essentialism. An isomer is ‘(o)ne of several species (or molecular entities) that have the same atomic composition … but different line formulae or different stereochemical formulae and hence different physical and/or chemical properties’ (IUPAC 2014: 784). Consider ethanol and methoxymethane (Reference HendryHendry 2006a: 869). Both compounds consist of the same type and number of atoms: two carbon atoms, six hydrogen atoms and one oxygen atom. However, the atoms in each case are bonded differently, resulting in the line formulae CH₃CH₂OH and CH₃OCH₃, respectively. Isomers are problematic for the microstructural essentialist because they show that elemental composition fails to distinguish between compounds that not only have different physical and chemical properties but also – more importantly – are regarded by scientists as distinct kinds of compounds.

This problem can be resolved if ‘microstructural properties’ include not just information about the elemental composition of compounds but also structural information about atomic connectivity and molecular structure (e.g. Reference McFarlandMcFarland 2018; this is also similar to adopting Bursten’s notion of relational CMPs). After all, structure is a collective term which includes all properties that specify the spatial arrangement of the atoms that constitute a molecule, such as the number and types of chemical bonds, bond length, bond angles and so on. By enriching the notion of microstructural properties, one can retain the thesis that the essence of compound-kinds (including isomers) is conferred by their microstructure.

A third problem for the microstructural essentialist arises with mixtures, as the specification of microstructure does not seem to suffice to distinguish mixtures from compounds. A mixture is a ‘portion of matter consisting of two or more chemical substances’ (IUPAC 2014: 941). According to Needham, a microstructural essentialist cannot distinguish between – say – water and a homogeneous mixture of hydrogen and oxygen that has the same elemental proportions as water (Reference Needham2011: 11). This is because both samples have the same elemental composition and in practice scientists distinguish them by specifying their macroscopic differences, such as their melting points and reactivities (Reference NeedhamNeedham 2011: 11–12). One plausible reply to this is that Needham’s point expresses an epistemic (and perhaps semantic) difficulty in identifying compound-kinds. From a metaphysical perspective, a mixture of hydrogen and oxygen is distinct from water in terms of its microstructure, regardless of whether in practice we invoke macroscopic properties to differentiate between them.

A more pressing worry is that microstructural essentialism does not conform to our best scientific understanding of the chemical world. As Reference NeedhamNeedham (2011) and Reference HäggqvistHäggqvist (2022: 32) point out, the physical and chemical properties of compounds are influenced by factors other than their elemental composition or even structural properties. The thermodynamic conditions under which a substance is placed and its phase (i.e. solid, liquid or gas) make a difference to its observable properties (such as boiling point and density), but also to its microstructure. Consider water. In its solid phase, its microstructure is different from that in its liquid or gaseous phase. Bond lengths and angles differ, and the way H₂O molecules dynamically interact with each other in each instance (transforming back and forth into ions of H₃O⁺ and OH^-) is different, with variations in the concentration of ions depending on the thermodynamic conditions of the sample (Reference NeedhamNeedham 2011: 9). This suggests that there is no ‘the microstructure of water’ (as Needham puts it), but variations of microstructures depending on the macroscopic conditions in which the sample is found.

A last challenge for microstructural essentialism is that resorting to microstructural properties is not even necessary to being member of a compound-kind (Reference NeedhamNeedham 2011: 8–9). If this is correct, then one could argue that microstructural properties are not essential to chemical kindhood, under either of the two readings of ‘essential’ property (i.e. as necessary, or as necessary and sufficient). Specifically, Reference NeedhamNeedham (2011) claims that one can distinguish between members of different chemical kinds by invoking solely macroscopic properties. Thermodynamics offers both theoretical grounds and specific criteria for distinguishing between chemical compounds (whether in pure substances or in mixtures). For example, the unique triple point of chemical substances theoretically distinguishes between distinct isolated chemical substances.Footnote ²¹ Moreover, the Gibbs phase rule offers criteria to distinguish between chemical substances in a mixture (Reference NeedhamNeedham 2011: 8).

However, dismissing microstructure as being necessary to chemical kinds overlooks an important idea about microstructure; namely, that it has some form of metaphysical priority (e.g. Reference GoodwinGoodwin 2011; Reference TobinTobin 2010b). Put differently, one cannot dismiss that the elemental constitution of a compound is what largely explains (if not somehow determines) its resulting behaviour (Reference HäggqvistHäggqvist 2022: 32; Reference Hoefer and MartíHoefer and Martí 2019: 12). Hendry makes a similar point when he states that H₂O molecules should be seen as the ‘ingredients’ in water that need not persist yet are essential in forming the compound water (Reference Hendry2006a: 872). So, dismissing microstructure as necessary to the identification of a chemical kind distorts an important fact about the role of microstructure in chemistry.

Overall, what sort of property correctly distinguishes between chemical kinds and whether (and in what way) there is an essential property to them have been one of the most debated questions in philosophy of chemistry. This debate is ongoing and there are regularly new responses. The next section moves to a connected yet distinct question about chemical kinds: do they correspond to natural kinds, or do they represent artificial groupings?

Case III. Acids

An acid is a ‘molecular entity or chemical species capable of donating a hydrogen (proton) (see Brønsted acid) or capable of forming a covalent bond with an electron pair (see Lewis acid)’ (IUPAC 2014: 21). Apart from the Brønsted and the Lewis acid, IUPAC presents additional concepts and definitions of acidity, including for hard acids, soft acids, carboxylic acids, oxoacids and sulfonic acids. According to Reference ChangChang (2012a), this definitional and conceptual plurality is indicative of a ‘messiness’ in how acids are understood and grouped into categories. This messiness arises because there is no unique set of properties that is commonly shared by acids simpliciter. Instead, there is a multiplicity of distinct and incommensurable concepts associated with the term ‘acid’. Acidity lacks a uniform definition that applies to all recognised instances of acids, but more importantly ‘a unified theory’ that explains their behaviour (Reference ChangChang 2012a: 697). The only reason why ‘acid’ is still used is due to ‘the persistence of the quotidian concept’ (Reference ChangChang 2012a: 690). In this context, acids seem to fail a central requirement for natural kinds; namely, that all its members share a set of common properties. Therefore, acids do not correspond to a natural kind.

One can resist this claim in different ways. First, even if acids do not correspond to natural kinds, this does not imply that we cannot accept subtypes of acids as natural kinds. For example, we could argue that there are different kinds of acids, each representing a natural category (this would include the Lewis acid and the Brønsted acid as distinct kinds). This is in line with Dupré’s ‘promiscuous realism’, which he defends for biological kinds (Reference Dupré1993; also Reference HendryHendry 2006a: 865). On this view, there is no unique privileged way of grouping things in the world. One can taxonomise objects in countless ways, all of which are natural.Footnote ²³

Alternatively, one could maintain that acids simpliciter correspond to a natural kind. This could be supported by accepting Scerri’s objections against the empirical basis of Chang’s argument. Scerri claims that the Brønsted and Lewis acids are not distinct, incommensurable concepts of acidity. This is because the Lewis definition picks out all members of the acid-kind, including those of the Brønsted acid-group (Reference ScerriScerri 2022: 14–15). So, the Lewis definition identifies the correct property that is shared by all instances of acids.

Another way to resist Chang’s claim is by pointing out that it is not necessary that we successfully pick out the members of a kind by invoking their true common property. This is broadly based on Locke’s distinction between real and nominal essences, where real essences are ‘the very being of any thing, whereby it is, what it is’ and nominal essences are those (observable) features that help us distinguish between substances (Locke 1689: III.iii.15).Footnote ²⁴ According to Locke, while nominal essences follow from real essences, one need not know the real essences of a kind in order to pick out its members. Instead, members of a kind are usually picked through their nominal essences.

One can apply this idea to acids. Via the Lewis and Brønsted acids, scientists develop descriptions that involve reference to various observable properties which they invoke depending on the needs and uses they have. Such properties may not be suitable for picking out every and all members of the kind-acid. Nevertheless, their success to identify a subset of those members may be due to the real (yet unknown) property that unifies all instances of that kind. Therefore, the messiness of acids need not be viewed as evidence of them not being a natural kind. Instead, it could be indicative of an epistemological messiness where different descriptions pick out correctly some (not all) instances of acids.

This concludes the analysis of acids as candidate natural kinds. It revealed that identifying the unifying property of membership to a kind is not straightforwardly satisfied by all chemical kinds. There are also other requirements that may not be met by candidate chemical kinds. The remainder of this section discusses two such criteria and shows that they are not uncontroversially met by even the most paradigmatic cases of chemical kinds.

The first is that kinds are categorically distinct (e.g. Reference EllisEllis 2001). That is, there is a clear-cut distinction between kinds; there cannot be a ‘smooth transition from one kind to another’ (Reference Bird, Tobin and ZaltaBird and Tobin 2022). Ellis claims that chemical elements satisfy this requirement because distinct element-kinds are clearly separated by their atomic number (Reference Ellis2002: 26). Element-kinds are distinguished by their atomic number, which is a natural number. Starting with atomic number 1 (for hydrogen), they are arranged in the periodic table in increasing atomic number. So, elements which are positioned next to each other in the periodic table have no hidden element between them.

If we accept this as a criterion for natural kindhood, then it does not apply to a paradigmatic example of chemical kinds; namely, chemical compounds. Recall that some compound-kinds only differ in terms of their structure; they are distinct isomers. In these cases, Reference NeedhamNeedham (2000) and Reference Van Brakelvan Brakel (2000) point out that there is no clear microstructural distinction between isomers. Even if we incorporate molecular structure as part of the essence of compounds, there will always be some overlap between members of seemingly distinct (isomer) compound-kinds. This is because molecular structure is a vague concept: there is no clear line separating one isomeric structure from another when differentiating them in terms of quantitative differences in their bond angles, nuclear distances and so on. This reveals a general problem with compound-kinds. Structure is a dynamic property: the spatial arrangement of atoms in a molecule is continuously changing and the structures which are depicted by chemical representations are nothing more than idealised freeze motion images. If we require for natural kinds to be distinct, as Ellis does, then this is evidence that compounds are not natural kinds.

One could reply that this is problematic only if we assume, from the microstructural essentialist perspective, that microstructure is both necessary and sufficient for kindhood. However, if we admit macroscopic properties as part of the essence of compound-kinds, then this suffices to distinguish isomer-kinds (i.e. by invoking macroscopic differences). While this seems to solve the semantic problem (of how to pick out members of a kind), it may not resolve the metaphysical issue, which is whether there exist distinct categories of isomeric structures. If structure is a vague concept then – at least when it comes to compounds that differ only in terms of their structure – there does not seem a way out of the fact that isomers are not distinct kinds.

Another requirement for natural kindhood is that the property which unifies all members of a kind is natural.Footnote ²⁵ What we mean by ‘natural’ allows many interpretations and we would exhaust the length of this Element to analyse it. To avoid this, I assume that whatever ‘natural property’ means, it is a property whose value is not determined by the pragmatic purposes of the scientists. I explain this by means of an example. Specifically, I explicate how members of compound-kinds are unified by what we might think of as an unnatural property; namely, their stability. If this is the case, then it constitutes further evidence that compounds may not be natural kinds.

Regardless of whether we accept only microstructure as essential or take macroscopic properties as necessary to picking out members of compound-kinds, chemists always identify a compound-kind when it is thermodynamically stable. That is, they dismiss an unstable substance as a kind. However, the choice of when a substance is stable or not is a pragmatic choice, determined by the heuristic considerations of scientists. Put differently, stability – as a property of compound-kinds – is an unnatural property. This is because its value is determined by the choices of scientists.

Stability ‘expresses a thermodynamic property which is quantitatively measured by relative molar standard Gibbs energies’ (ΔG; IUPAC 2014: 1432). For example, ‘a chemical species A is more stable than its isomer B if Δ_rG° > 0 for the (real or hypothetical) reaction A -> B under standard conditions’ (IUPAC 2014: 1432).Footnote ²⁶ This shows that a chemical species is stable with respect to ‘some explicitly stated or implicitly assumed standard’ (IUPAC 2014: 1432). The standard is set by convention and usually to the thermodynamic values that are ‘characterized by a standard pressure, molality or amount concentration’ (IUPAC 2014: 1438).

So, whether a compound is stable depends on a thermodynamic property (i.e. the Gibbs energy, G), whose value is determined by the specific thermodynamic conditions in which we consider that compound. The problem with this is that there is no principled reason why a given set of thermodynamic conditions should be selected where some compound is stable whereas another is not. Under different conditions, the reverse is plausible: the formerly stable compound is unstable, and the latter is stable. Why should we pick one set of conditions over another? Couldn’t we consider – say – ions of NH₃ (such as ammonium NH⁺₄) as compound-kinds if there are some conditions in which they are stable?

Could we dispense of stability if we invoke a different property to unify members of compound-kinds, such as Bursten’s proposal of reactivity? The same problem arises. IUPAC’s definition of reactivity is this: ‘A species is said to be more reactive or to have a higher reactivity in some given context than some other (reference) species if it has a larger rate constant for a specified elementary reaction. The term has meaning only by reference to some explicitly stated or implicitly assumed set of conditions’ (Reference Bursten2014: 1261).Footnote ²⁷ This suggests that whether a compound is reactive is determined by the conditions in which it is considered: under some conditions it is more reactive than another compound, and under different conditions it is less. Which thermodynamic conditions we consider as standard is a pragmatic choice. More importantly, there does not seem to be any principled metaphysical priority of one set of conditions over another.

Could a similar worry be expressed about element-kinds? No. Elements are not standardly identified as stable entities; far from it.Footnote ²⁸ Many elements in the periodic table are highly unstable under standard conditions. The admittance of radioactive elements (i.e. elements which undergo spontaneous nuclear transformations) is an illuminating evidence of this. Certain radioactive elements, such as francium, are so rare that there are only 30 g found on earth’s crust. Oganesson, with atomic number 118, does not naturally occur on earth and has a half-life of 1.8 milliseconds! So, whether and under what conditions elements are considered stable does not determine their admittance as element-kinds. Therefore, at least with respect to the requirement for natural properties, element-kinds are not threatened by a similar worry to that about compound-kinds.

These points far from settle whether elements and compounds fulfil the requirements for natural kinds. Even if the challenges I present are correct, there are probably ways in which one could maintain their natural kindhood. What these ways are is left for another occasion. In any case, an important conclusion is drawn from this analysis. Despite the extensive discussion about chemical kinds, there is still a lot to be said to convincingly claim that a chemical classification corresponds to a natural kind. One needs to look at the exact requirements for natural kindhood and examine whether they correctly apply to each chemical case. It might turn out that even the most paradigmatic cases of chemical kinds do not correspond to natural categories. Or, we might have to review how we think of the natural/artificial distinction between kinds.

Case IV. Macromolecules

Certain chemical compounds are identified as kinds not in terms of their microstructure, but in terms of a function they serve. That function may be chemical or biological. When chemical, a function is typically conferred to organic compounds by so-called functional groups, that is, ‘an atom, or a group of atoms that has similar chemical properties whenever it occurs in different compounds’ (IUPAC 2014: 605). Examples of functionally defined compound-kinds include alcohols, carboxylic acids, amines and ketones. When biological, a function is typically conferred to macromolecules (though not exclusively) that figure in physiological processes and is said to serve evolutionary or etiological considerations (Reference TahkoTahko 2020: 800).Footnote ²⁹ Examples include proteins, genes and vitamins, and are often called biochemical kinds. Such groupings are invoked to describe biological behaviour and figure in inductive generalisations and explanations of biological phenomena.

The problem with functionally defined compound-kinds is that (at least part of) their unifying property is their function, undermining microstructural essentialism.Footnote ³⁰ Tahko spells out this problem in terms of ‘multiple realisation’ and ‘multiple determination’. Multiple realisation occurs when ‘(t)here may be a difference between (entities) A and B which explains why, even though each is capable of performing a certain function, they each do so in a different way’ (Reference Tahko2020: 814). For example, ‘haemoglobin’ refers to a group of macromolecules with different microstructures whose members are unified by their shared ‘ability to bind and release oxygen’ in an organism (Reference TahkoTahko 2020: 808). Such examples of multiple realisation putatively show that microstructure is not necessary for compounds to belong to a kind (thus undermining both interpretations of ‘essential’; see Section 2.1).

Multiple determinability occurs when a microstructure realises multiple (biological or chemical) functions. An example is moonlighting proteins which have one primary structure (i.e. they are formed of the same sequence of amino acids) but fold up in different ways, thus resulting in different three-dimensional structures, each identified as a distinct kind (Reference TahkoTahko 2020: 804; Reference TobinTobin 2010b). This is considered problematic for microstructural essentialism because (primary) microstructure is not the unifying property of protein-kinds. In fact, Tobin argues that moonlighting proteins are additionally problematic because they are ‘intrinsically unstructured’ or disordered, thus undermining the essential role of structure in conferring them as members of a protein-kind (Reference Tobin2010b: 41).

There are also organic molecules that exhibit multiple determinability: an organic molecule can have a specific structure yet be considered a member of multiple chemical kinds depending on the chemical function it serves. For example, some compounds are classified as both alcohols and carboxylic acids (or, as both amines or amides). So, a compound’s membership to a kind can be conferred by different chemical functions and not by its microstructure, thus undermining microstructural essentialism for chemical compounds (Reference GoodwinGoodwin 2011).

Several responses have been offered to these challenges. First, one could argue that this is evidence of some form of pluralism about natural kinds, such as Dupré’s promiscuous realism (see Case III) or Slater’s macromolecular pluralism. Reference SlaterSlater (2009) claims that there is no principled way to invoke structure to distinguish between proteins; instead, there is a plurality of equally legitimate biochemical classifications. Reference BartolBartol (2016) defends a ‘dual theory about kinds’ (see also Reference LongyLongy 2018). This theory purports that there are two distinct kinds of kinds: the chemical kind and the biological kind (and no biochemical kind). In this context, multiple determination putatively shows that a member of a chemical kind can contain multiple members of biological kinds. Multiple realisation shows that a member of a biological kind can contain multiple members of chemical kinds (Reference BartolBartol 2016: 549). In contrast to this theory, Reference BellazziBellazzi (2022) argues that we should think of such groupings as genuinely biochemical kinds; that is, kinds whose membership is conferred by their microstructure and by their function.

Lastly, there are ways to defend microstructural essentialism too. Reference GoodwinGoodwin (2011) for example argues for the ‘fundamental role’ of structure. Based on an analysis of organic chemistry, he claims that molecular structure is fundamental because it explains why a functional group classification is appropriate at a particular instance, and because a compound’s modal capacity to function a certain way is in virtue of its structure (Reference GoodwinGoodwin 2011: 538–40). (This is similar to favouring a sort of dispositionalist view about kinds.) Alternatively, one could adopt the ‘powers-based subset strategy’, which takes the causal powers of a (biological or chemical) function to be the proper subset of the powers of the microstructure of the compound that has that function (Reference TahkoTahko 2020: 806). This way, microstructural essentialism is not undermined by multiple realisability or multiple determinability because microstructure is (in the sense specified by Tahko) ontologically prior to the relevant function (Reference TahkoTahko 2020: 822).

Overall, whether chemical kinds are natural can only be answered on a case-by-case basis. It is likely that different chemical case studies warrant different answers as to whether they correspond to natural groupings in the world, with some representing natural kinds and others not. Moreover, as the example of chemical compounds showed, even the most paradigmatic chemical case studies for natural kinds are not definitively settled. Furthermore, this analysis may also prompt a revisionist attitude towards the very notion of natural kinds and its distinction from artificial kinds. Which route to select is left for the reader to choose!

Case V. Atoms and Molecules

Let’s start with atoms and molecules. In the eighteenth century, Dalton postulated that atoms – that is, indivisible chunks of matter – make up different elements and combine to form molecules. While Dalton’s theory of atoms allowed chemists to gain a better insight into elements and how they differ from each other, many chemists were sceptical as to their reality. This is partly because Dalton’s theory contributed mostly by offering for the first time a visual representation of atoms. He used images and wooden balls to show how atoms combine to form molecules – something that Dalton himself considered more of a teaching tool than a depiction of reality (Reference BallBall 2021: 141). In general, up until the beginning of the twentieth century, scientists viewed atoms and molecules as hypothetical entities, leaving open the possibility that they have no ontological import and that they just help describe, predict and explain chemical and physical phenomena (Reference HendryHendry 2018: 110).

This attitude is said to have changed with Perrin, who claimed to have empirically established the reality of atoms and molecules (Reference Perrin1916). He supported this claim by illustrating how the same value for Avogadro’s number can be calculated with relatively close agreement by thirteen different methods applied to a diverse range of phenomena (Reference NyeNye 1972).Footnote ³⁹ The domain of inquiry within which Perrin undertook his calculations was very broad as it included ‘the measurement of the coefficient of diffusion; the mobility of ions; the blue color of the sky (the diffraction of the sunlight by the atmospheric molecules); the charge of ions; radioactive bodies; and the infrared part of the spectrum of the black-body radiation’ (Reference PsillosPsillos 2011: 355). Based on the empirical success of his analysis, Perrin stated:

Agreement between calculations that were conducted within different domains of inquiry, and by employing different experimental methods, constituted empirical evidence that atoms and molecules are real. Perrin was subsequently awarded the Nobel Prize in Physics for establishing the ‘physical existence’ of those entities.Footnote ⁴⁰

It is no surprise that Perrin’s work is discussed in the debate about scientific realism. Philosophers became particularly interested in spelling out Perrin’s reasoning behind his claim that atoms and molecules are real. Reference Salmon, Rescher and RescherSalmon (1985), for instance, argues that Perrin’s realist argument is an application of the Principle of the Common Cause. According to this principle, apparent coincidences are explained by the occurrence of a common cause (see Reference ReichenbachReichenbach 1956). Applied to the case in question, the fact that distinct calculations of Avogadro’s number coincided on the same value is explained in virtue of a common cause; that is, the existence of the entities posited by the underlying theoretical hypothesis. Reference AchinsteinAchinstein (2001), Reference ChalmersChalmers (2011) and Reference PsillosPsillos (2011) each take Perrin’s realist claim to be an example of the ‘robustness argument’. According to this argument, the ‘empirical results indicate the reality of unobservables if these results are generated by a variety of empirical methodologies’ (Reference HudsonHudson 2020: 34). On this view, the reality of unobservable entities is supported by the fact that diverse and different empirical methods produce the same value for Avogadro’s number.Footnote ⁴¹

On the other hand, van Fraassen argues that we should not interpret Perrin’s work as establishing the reality of atoms and molecules, but as showing the empirical adequacy of the atomic and molecular hypothesis. This view is based on a more general anti-realist stance held by van Fraassen, called constructive empiricism. According to this, ‘(s)cience aims to give us theories which are empirically adequate; and acceptance of a theory involves as belief only that it is empirically adequate’ (Reference van Fraassenvan Fraassen 1980: 12). In this context, the empirical evidence which is produced in support of a theory need not be construed as indicating the reality of that theory’s unobservable entities, but only as supporting its empirical adequacy (Reference Van Fraassenvan Fraassen 2009: 23). (This, of course, relies on some definition of the observable that does not allow atoms to count as such.)

Van Fraassen supports this argument for the case of atoms and molecules in large part through a historical analysis of the relevant scientific period. He claims that realists promote a distorted historical narrative of how scientists investigated and understood atoms and molecules in the eighteenth and nineteenth centuries. Realists misinterpret scientists’ views of the time by employing terms in their narratives that scientists themselves did not use or did not understand the way realists do today (namely, ‘empirical adequacy’) (Reference Van Fraassen2009: 7). Moreover, Perrin’s models for the calculation of Avogadro’s number were allegedly based on a problematic understanding of molecules as perfectly elastic and hard spheres – an assumption which scientists had already called into question due to Rutherford’s insights on nuclear structure (Reference Van FraassenVan Fraassen 2009: 8). All in all, he claims that realists exaggerate the ontological weight scientists (including Perrin) assigned to atoms and molecules.

Another challenge to the reality of atoms and molecules is the problem of unconceived alternatives. Reference DuhemDuhem ([1914] 1991) noticed that theory choice often proceeds through eliminative reasoning: scientists choose among competing hypotheses or theories by eliminating those that they believe are less tenable. He pointed out that this eliminative reasoning can only be reliable in one’s pursuit for the true theory if among the alternative theories considered there is the true one too. Following Duhem’s reasoning, Stanford argues that history contains numerous instances in which scientists failed to conceive alternative theories that ‘were both well confirmed by the evidence available at the time and sufficiently plausible as to be later accepted by actual scientific communities’ (Reference Stanford2006: 27). That is, we cannot be confident that among the theories that scientists conceive, the true theory is one of them. Therefore, eliminative reasoning is not reliable and we ought to be sceptical as to the truth of the theory that has been selected via elimination.

Reference StanfordStanford (2009) and Reference RoushRoush (2005) have debated whether this argument applies to atoms. Roush argues that in the case of Perrin’s analysis, there weren’t any other alternatives to the atomic hypothesis that could equally well explain Brownian motion.Footnote ⁴² On her view, the randomness of motion cannot be explained by anything else but the existence of particles. This is because a random Brownian motion implies the existence of particles that perform that motion (Reference RoushRoush 2005: 219). Note that unlike previous realist arguments, Roush’s focus is not on all the phenomena that Perrin empirically examined to corroborate the atomic hypothesis. Rather the argument is that in the single case of Brownian motion, there are no other plausible theoretical hypotheses that could explain it. Therefore, the problem of unconceived alternatives doesn’t arise.

Stanford makes two points against this argument. First, there were alternative hypotheses at the time (including the electromagnetic view of matter) which were considered plausible explanations of Brownian motion (Reference StanfordStanford 2009: 260). Second, eliminating the possibility of alternative hypotheses which haven’t been conceived is itself an instance of eliminative reasoning, which in turn is an unreliable method of argumentation. He purports that historically scientists have been often wrong when they assumed that there are no other ways to explain some phenomenon, and this is evidence that eliminative reasoning is unreliable. Given that Roush similarly bases her argument on eliminative reasoning, it follows that her conclusion is also unreliable, or so Stanford argues (Reference Stanford2009: 262).

Reference HendryHendry (2018) considers another chemical case where the problem of unconceived alternatives may apply. Since the 1860s, chemists have developed different representations of the spatial arrangements of atoms in molecules, called structural formulae. Different formulae were proposed over the decades (such as Kekulé’s sausage formulae and Hofmann’s glyphic formulae) with different explanatory and empirical aims (Reference HendryHendry 2018: 110). The case of interest here is van’t Hoff’s representation of organic molecules which exhibited distinct stereoisomeric structures. The appropriate formulae had to depict the spatial arrangement of these molecules in such a way as to agree with the empirical information regarding the right number of isomers. To decide as to the appropriate structural formula, van’t Hoff followed an eliminative reasoning: he considered alternative representations and eliminated those that he regarded less tenable. In this process, he chose a tetrahedral structure because it successfully differentiated between the right number of isomers. Had he selected the square planar arrangement, a surplus of alternative stereoisomeric structures would have been produced which was against empirical evidence.

This, according to Hendry, is an example of eliminative reasoning in chemistry which proved to be reliable. Its reliability was supported not only by the observations van’t Hoff had readily available; it was further corroborated through the development and use of future spectroscopical and other experimental results (Reference HendryHendry 2018: 114). So, in contrast to Stanford, whose analysis of historical episodes in science putatively illustrates the unreliability of eliminative reasoning, Hendry takes the analysis of alternative structural formulae in the nineteenth century to illustrate the reliability of eliminative reasoning in chemistry.Footnote ⁴³

This is not where the debate around realism in chemistry ends, far from it. Moving beyond atoms and molecules, it is worth looking at the general arguments formulated within the scientific realism debate, and present how our metaphysical understanding of chemistry has and can be further informed by such arguments.

Case VI. Phlogiston

The most characteristic defence of realism is via the No-Miracles Argument (NMA). As Putnam famously put it: ‘the positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle’ (Reference Putnam1975: 73). Specifically, the reality of unobservable entities is supported by the argument that – were they not real – it would be miraculous that the theories which posit them are so successful in predicting and explaining phenomena. Put differently, the best explanation for the fact that our scientific theories are empirically successful is that they correctly identify the unobservable entities in the world (Reference LadymanLadyman 2012: 213).

One cannot deny that chemistry is a hugely successful science in terms of explanation and prediction. It accurately does both for the results of chemical reactions and the chemical properties of matter, through a constant process of experimental analysis via diverse methodologies. It has also contributed to the advancement of other sciences, including physics, biology, geology and astronomy. It has led to the development of applications in chemical engineering, medicine, nanotechnology and agriculture with enormous effects on our health and lifestyle. Chemists have predicted new phenomena, proposed novel applications and discovered (and also synthesised) previously unknown elements and substances. Following the NMA, it would be miraculous if chemistry had achieved all this and yet was wrong about the entities and properties that make all this happen.

Of objections to the NMA perhaps the most important is the Pessimistic Meta-Induction argument (PMI). According to Reference LaudanLaudan (1981), the history of science offers several examples of theories which were at some point in time empirically successful but were later rejected or whose entities were discarded. Given that such revisions are quite common in the history of science, by induction one should expect that in the future the theories we regard as true today will be similarly revised or rejected. So, we are not justified in believing in the unobservable entities posited by our best current science.

To support the PMI, Laudan invoked an episode from the history of chemistry; namely, the Chemical Revolution (Reference Laudan1981: 29). The Chemical Revolution refers to the period during which chemists abandoned the so-called phlogiston theory and accepted Lavoisier’s theory of combustion. Until the eighteenth century, phlogistonists believed that combustion is the result of a principle or element called ‘phlogiston’. The term was inspired by the Greek word for ‘set on fire’, and first posited in Stahl’s theory of combustion articulated in 1703 (Reference BallBall 2021: 66–8). Very briefly, Stahl claimed that substances contain different amounts of phlogiston which are released into the air whenever these substances burn. This hypothesis was invoked to explain why matter weighed less after being burned, and why lighted candles in closed containers would eventually go out. Phlogiston was also supposed to explain other phenomena, including respiration and acidity, and it was posited by Stahl to be what all metals have in common, making them similar in their properties.Footnote ⁴⁴

For some time, the theory agreed quite well with empirical observations; however, disagreements with observations eventually accumulated (Reference Ladyman, Slater and YudellBlumenthal and Ladyman 2017). Among other things, chemists discovered that certain substances gained, instead of lost, weight when they burned – an empirical fact that contradicted the phlogiston theory. Eventually the phlogistonists started to disagree radically about how phlogiston related to the known behaviour of acids, bases, metals, salts and water, as well as to the growing list of newly discovered substances, including hydrogen, oxygen, carbon dioxide and nitric oxide. Around the same time in the 1780s, Lavoisier argued that there is no such thing as phlogiston and proposed an account of combustion according to which when substances burn, they absorb or combine with an element in the air which he called ‘oxygen’.

This episode in chemistry is an example of how a previously successful theory posited something that was later rejected. As such it has been invoked as one of several episodes in the history of science during which scientists posited unobservable entities they later discarded. In this context, one raises a serious anti-realist worry about chemistry. Given that chemists at the time had sufficient empirical grounds to believe in the existence of phlogiston, how can we be sure that chemists today – who equally base their beliefs on empirical evidence – do not believe in fictitious entities?

There are different responses a realist could offer. First, one could argue that unlike today, chemistry during the time of the phlogistonists was not a mature science. What is today a thorough empirical practice was back then guided by outdated qualitative ideas inherited from Aristotle and the Renaissance period. It was not a mathematicised science and phlogistonists did not have the ability to precisely measure masses and volumes to corroborate their hypotheses (Reference LadymanLadyman 2011: 91). Given this, it is to be expected that past chemical theories were incorrect, and it would be unfair to generalise from this that modern chemistry will be equally false in the future. Chemistry today has undergone extensive empirical scrutiny and thorough experimental analysis; chemical hypotheses have been tested by multiple experimental techniques and with growing precision.Footnote ⁴⁵ So it is safe to believe that the entities posited by our current chemical theory of combustion, including oxygen, are real.

Another way to deal with the PMI is to admit that phlogiston is real; that is, it correctly refers to something in the world. Even if phlogistonists did not realise it, ‘phlogiston’ referred to at least some of the properties and causal powers that are responsible for combustion, respiration and calcination.Footnote ⁴⁶ Accepting this allows us to be realists about our currently posited unobservable entities because it admits that past theories were in some sense correct as well, thus defeating the main idea of the PMI. However, it comes at a cost, as we not only have to admit that phlogiston is real but also do so in a way that is in danger of triviality. As Reference LaudanLaudan (1984) points out, any past theoretical entity can be said to be real to the extent that we take it to refer to whatever it is that causes the relevant phenomena (regardless of whether we have discovered those causes or not).

A more nuanced response is to say that some parts of the phlogiston theory are true and other parts are false. The parts which are true have been retained in the newly accepted theory of combustion, whereas those that are false have been discarded. This sort of continuity between past and present theories allows us to circumvent the PMI and retain a realist stance. Psillos calls this the ‘divide et impera move’. According to this view, ‘when a theory is abandoned, its theoretical constituents … should not be rejected en bloc’ (Reference PsillosPsillos 2005: 108). There are parts of those theories that were essential to their empirical success and – as such – are retained in our current theories. That this is plausible is supported by looking at the empirical success of the phlogiston theories. Indeed, phlogistonists were not completely wrong about everything and even made novel predictions, such as predict new acids which were subsequently retained by the new theory (Reference LadymanLadyman 2011: 99). So even though chemists today do not use the term ‘phlogiston’, the theory which posited it captured some aspects of the world correctly, even if partly. If we accept this claim, then this allows us to circumvent the PMI and thus be realists about currently posited unobservable entities.

Interestingly, there are disagreements about what exactly is retained from past to present theories and these disagreements produce different ontological commitments with respect to past theories. For example, Psillos claims that phlogiston as a material entity is not real as it was not essential to the theory. On this view, phlogiston ‘refers to nothing’; that is, there is no material stuff in the world that possesses the properties assigned by phlogistonists to the entity called ‘phlogiston’ (Reference PsillosPsillos 2005: 291).Footnote ⁴⁷ Reference KitcherKitcher (1993) agrees that phlogiston doesn’t refer to anything, but contends that ‘dephlogisticated air’, under some of its past usages, successfully referred to something in the world (namely, to what we call today ‘oxygen’).Footnote ⁴⁸ Ladyman also believes that there is no thing released during combustion called phlogiston. However, he does not believe that phlogiston was inessential to the phlogiston theory of combustion. Instead, since (among other things) the theory was correct that ordinary combustion, the calcination of metals and respiration are all the same kind or process, it ‘did to some extent correctly describe the causal or nomological structure of the world’ (Reference Ladyman2011: 100). In this context, there is something real captured by the phlogiston theory, namely, modal structure, even though there is not a material entity released during combustion.Footnote ⁴⁹

By establishing some form of continuity between past and present chemical theories, several philosophers have responded to the PMI and thus retained their realism. However, there is also a different way to be a realist about chemical stuff which substantially diverges from the general spirit of the previous views. It is called `pragmatic realism’. On Chang’s view, phlogiston is ‘as real as tables-and-chairs and cats-and-dogs are in our daily lives’ (Reference Chang2016: 118; also Reference ChangChang 2012b). In fact, phlogiston is real in the same way that oxygen is, even though the two entities are posited by theories that are inconsistent with each other.Footnote ⁵⁰

While this seems like a strong metaphysical view in the sense of being ontologically committed to phlogiston, it substantially diverges from the traditional spirit of scientific realism. This is because it understands the truth of scientific theories in terms of coherentism. Standardly, coherentism takes truth to amount to nothing more than a set of propositions being logically consistent with each other (e.g. Reference AustinAustin 1962). The truth of a proposition is not defined by whether it corresponds to something in the world, but by whether it logically coheres with the rest of the propositions with which it is put together. Even though Chang follows the spirit of coherentism, he amends his understanding of truth in his account of pragmatic realism. Specifically, he claims that truth is granted not to a set of propositions, but to a scientific practice which succeeds in meeting its aims. As he states: ‘I define (pragmatist) coherence as a harmonious fitting-together of actions that leads to the successful achievement of one’s aims’ (Reference Chang2016: 112).

Based on this understanding of truth, Chang argues that phlogiston is real because it is part of a scientific practice which was very successful in achieving its aims. Not only did phlogistonists pursue a well-defined coherent set of aims (such as to phlogisticate or de-phlogisticate air) when they analysed the relevant phenomena, but they often considered these aims as being successfully met. Chang presents historical evidence that purportedly shows this to be the case. Based on this, he argues that to the extent that phlogistonists considered their practice a success, we should admit their theory as true and regard the entities which they posited as real.

There are two replies one can formulate against this view. First, one can deny that the aims set by phlogistonists were fulfilled or deemed successful by them. This objection is based on an examination of the history of phlogiston theories. Historical work has revealed that there were numerous disputes and empirical problems that phlogistonists faced and could not resolve in the context of their accepted theory (e.g. Reference Ladyman, Slater and YudellBlumenthal and Ladyman 2017, Reference Blumenthal and Ladyman2018). As Blumenthal and Ladyman argue, phlogiston theories eventually ‘reached impasses due to internal problems or included features which made them unacceptable even to other phlogistians’ (Reference Blumenthal and LadymanBlumenthal and Ladyman, 2018: 169). A second objection is that pragmatic realism misses what truth and realism are supposed to capture.Footnote ⁵¹ Even though Chang claims that phlogiston is real, the notion of reality that he advocates is far from the defining idea of realism; namely, that there is an external world in which there are things which exist independently of how we conceive them.

As a possible response to this last objection, we could invoke Chang’s normative point about truth and reality. Chang argues that we should amend our notion of truth and realism and assign to them different meanings altogether. This is because traditional understandings of realism and truth are ‘dead metaphors’: we do not have access to the external world and thus we shouldn’t take our descriptions of the world as literal (Reference Chang2016: 109–10). Now this is a perfectly admissible metaphysical view which is traditionally advocated by philosophers from the anti-realist camp.Footnote ⁵² The only difference with Chang’s account is how this idea is branded. But regardless of how one wishes to define the terms ‘realism’ and ‘truth’, the case remains that under pragmatic realism one is not ontologically committed to the mind-independent existence of scientific entities or even to the existence of an external world. Put differently, the pursuit of discovering what exists in the world independently of us eludes pragmatic realism.

All in all, the analysis of scientific realism from the perspective of chemistry reveals something very interesting about our understanding of chemical ontology. If we want to claim that the entities chemists posit in their modern theories are real, we must account for the entities which chemists invoked in the past but now reject. We cannot have a complete metaphysical account based solely on modern chemistry; we also need to consider the historical evolution of chemical ontology.

But even this does not suffice to settle the reality of chemistry. The realist question is (at least) two dimensional. So far, I have sketched the first axis, which concerns the historical evolution of chemical ontology. The second axis concerns chemical constitution. In this context, I address the third question at the start of this section: should we believe in the reality of chemical entities given that they are composed of other (physical) things?

Case VII. Molecular Structure

Quantum physics is taken to describe the properties of atoms and molecules by solving the Schrödinger equation. Τhe Schrödinger equation calculates the interactions of each and every subatomic particle that makes up a system. From this it is possible to derive the system’s observable properties, including its chemical ones. While this could prima facie serve as evidence that chemistry is reduced (in Nagel’s sense) to quantum physics, philosophers of chemistry have argued against this. This is because quantum physics does not satisfy a supposedly key requirement for Nagelian reductionism; namely, that derivability is realised from first principles.Footnote ⁶⁰

Derivability is not realised from first principles because in practice a solution to the Schrödinger equation always involves making idealisations and approximations to the equation. These idealisations and approximations have a physical justification and are based on prior empirical knowledge of the system and its chemistry. Nevertheless, they are taken to suggest the irreducibility of chemistry. This is because, had they not been used, quantum physics would have been unable to produce the expected results about the system.

The most characteristic example invoked to illustrate this is molecular structure. Molecular structure refers to the spatial arrangement of the atoms that constitute a molecule. The quantum mechanical identification of a molecule’s structure is standardly achieved after implementing the Born-Oppenheimer approximation (BO) to the Schrödinger equation. Applying this approximation results in a quantum mechanical representation ‘of the complete wavefunction as a product of an electronic and a nuclear part where the two wave-functions may be determined separately by solving two different Schroedinger equations’ (IUPAC 2014: 179). This amounts to disregarding the interactions that take place between a system’s nuclei.Footnote ⁶¹

The use of the BO approximation putatively supports the irreducibility of chemistry for three reasons. First, the assumptions that are made via this approximation are structural (Reference Hendry, Woody and HendryHendry 2012b: 373; Reference WoolleyWoolley 1976). The BO ‘fixes’ the nuclei in space and thus presupposes a particular position for them. This means that one assumes and imposes some structural information to the equation, before identifying the overall structure of the system. Second, the structural information that is transcribed via the BO approximation is drawn from the chemical examination of the system (Reference Hendry, Woody and HendryHendry 2012b; Reference ScerriScerri 1998). This means that the higher-level theory has been used to presuppose information in the lower-level description. Third, these assumptions are putatively necessary for the identification of structure; they are not merely an indication of an inability to solve a very complicated equation (Reference HendryHendry 2010: 186; Reference Woolley and SutcliffeWoolley and Sutcliffe 1977). Even if it were possible to solve the equation without applying the BO approximation, the relevant solution would not identify any structure to the system (more on this later in this section). This suggests that quantum physics is in principle unable to identify chemical properties; that is, quantum physics alone cannot derive chemical properties.

As already mentioned, some philosophers argue that this is evidence of the failure of chemistry’s Nagelian reduction (Reference ScerriScerri 1994). Others argue that it is evidence that chemical entities are somehow distinct or autonomous from the physical entities that make them up (see the following paragraphs). I do not critically analyse the arguments against the epistemic reduction of chemistry. Instead, I focus on the metaphysical implications that are drawn (at least in part) from this antireductionist argument.

There are two metaphysical views that have been proposed: strong emergence and ontological pluralism. Strong emergence claims that the use of the BO approximation for the identification of molecular structure is evidence that structure is a strongly emergent property (Reference HendryHendry 2010, Reference Hendry, Woody and Hendry2012b). There are three features to this view which specify the precise form of strong emergence that is advocated by Hendry.Footnote ⁶² First, in line with other emergentist accounts, there is a hierarchy of levels. Nature is divided into distinct energy, length and time scales within which different entities are found. Second, structure depends on the interactions of the subatomic entities which make up the molecule. Hendry spells out this dependence in terms of supervenience (Reference Hendry2010: 185). Very briefly, structure (just like any chemical property) supervenes on the relevant quantum physical entities and their interactions in the sense that whenever there is a change in a molecule’s structure there is also some change in the quantum physical entities of that molecule. Third, structure is causally autonomous. There are different ways one can spell out causal autonomy (e.g. Reference Wilson, Bigaj and WüthrichWilson 2016). In the context of Hendry’s account, structure is causally autonomous in the sense that it possesses causal powers that are not token identical to any set of powers of the relevant quantum physical entities. This is further spelled out in terms of downward causation. That is, structure possesses downward causal powers: it partly causes the way in which the subatomic particles of the molecule interact with each other (Reference HendryHendry 2010: 185).

While Hendry argues for strong emergence only for the case of molecular structure, his overall framework and its subsequent metaphysical implications produces a very interesting image of chemical ontology. On his view, a molecule’s structure is not ontologically reducible to its lower-level physical parts: structure is not identical to, nor the complete result of interactions among the molecule’s physical parts. Instead, structure is a distinct property which doesn’t exist at the scale where quantum physical entities are found; it exists at a different scale (Reference HendryHendry 2010: 186)

Moreover, structure is said to have a downward causal effect on how the molecule’s physical constituents behave. Just like the movements of every participant in a sirtaki dance is partially determined by the geometry and rhythms that a sirtaki adheres to, so the interactions of each subatomic particle are determined by the overall structure of the entire system. It is in virtue of the ability to exert downward causal powers – that is, to causally influence the lower-level constituents – that structure is distinct and non-reducible to its physical parts. This implies that strong emergence makes for a realist position about higher-level entities. If one accepts Alexander’s dictum that to be is to cause, then it follows that molecular structure is real.Footnote ⁶³

The second metaphysical account is ontological pluralism. Lombardi and Labarca take the inability of quantum mechanics to identify a molecule’s structure as suggestive of chemistry’s autonomy. They spell out chemistry’s autonomy in terms of ontological pluralism; that is, the thesis that ‘permits the coexistence of different but equally objective theory-dependent ontologies interconnected by nomological, non-reductive relationships’ (Reference Lombardi and Labarca2005: 146). Based on Putnam’s internalist realism, they reject that there is an external world to which we can gain access via our scientific descriptions. Instead, the world and its objects are dependent on how we perceive and conceptualise them. Put differently, the world is contingent on and determined by the theory within which we describe it, rejecting what is standardly called the ‘God’s eye view’, which purportedly discovers the objective, mind-independent world.Footnote ⁶⁴

There are several implications of their view. First, there is no external world that one aims at discovering (as per traditional scientific realism). Instead, there is a plurality of ontologies which can be inconsistent to each other yet carry the same ontological weight (i.e. they are all equally real). In the case in question, the entities postulated by quantum physics ‘co-exist’ with those of chemistry. There is no metaphysical priority of physical entities over chemical ones. Physical entities are not more fundamental. There is no hierarchical relation between the chemical and physical levels, as accepted by Hendry’s strong emergence or by the standard hierarchical image introduced by Reference Oppenheim, Putnam, Feigl, Scriven and MaxwellOppenheim and Putnam (1958).

There are conceptual and empirical challenges to both strong emergence and ontological pluralism. One conceptual issue with strong emergence is how exactly to understand causation when talking of downward causation. Given the multiplicity of causal accounts in terms of production, counterfactuals or mechanisms, it is an open question which (if any) of these accounts fit in the context of Hendry’s strong emergence (see Reference SeifertSeifert 2020: 23). Another issue has to do with whether downward causation is a synchronic or diachronic relation between a cause and its effect (Reference SeifertSeifert 2020: 5–11). This is important because some philosophers argue that synchronic causation is incoherent: an effect cannot occur at exactly the same moment that the cause occurs (e.g. Reference KimKim 1999).Footnote ⁶⁵ With respect to ontological pluralism, it is not entirely clear how it understands the dependence relation between a molecule and its parts. If we understand chemistry and quantum physics as offering distinct ontological pictures of the world, then how can we make sense of connections that the relevant sciences advocate for them?Footnote ⁶⁶

From an empirical perspective, strong emergence and ontological pluralism face a common challenge.Footnote ⁶⁷ Can the use of the BO approximation be interpreted in ways that do not require the postulation of downward causes or distinct ontologies? If so, then both antireductionist views are undermined by adhering to Occam’s razor. According to this principle, ‘a theory that postulates few entities, processes, or causes is better than a theory that postulates more, so long as the simpler theory is compatible with what we observe’ (Reference SoberSober 2015: 2). In this context, if there is a metaphysical view that is more parsimonious compared to strong emergence and ontological pluralism, then it should be preferred.

Indeed, there is evidence towards that direction. Reference Franklin and SeifertFranklin and Seifert (2020) point out that the use of the BO approximation is a result of the measurement problem in quantum mechanics. The measurement problem arises because quantum physics predicts certain systems to be in superposition states relative to a measurement basis even though the measurement of those states produces determinate outcomes. If we assume that the Schrödinger equation offers a complete description of a quantum state, this reveals an apparent inconsistency, which is referred to as the measurement problem (e.g. Reference MaudlinMaudlin 1995).

According to Reference Franklin and SeifertFranklin and Seifert (2020), the measurement problem is central to understanding why the BO approximation is used for the identification of molecular structure. Without applying the approximation, quantum physics predicts that the ground state of certain types of molecules corresponds to a superposition of their structures.Footnote ⁶⁸ For example, this is the case with optical isomers: their predicted ground state corresponds to a superposition of all their possible isomeric structures. Given that we only observe a determinate structure, and that the quantum physical description of isomers is assumed to be complete, it follows that this is an instance of the measurement problem. Therefore, Franklin and Seifert conclude that the apparent inability of quantum physics to identify molecular structure from first principles is a special case of the measurement problem.

In light of this, different avenues become available to interpret quantum physics’ apparent inability to identify structure (also referred to as the problem of molecular structure). By identifying the problem of molecular structure as a special case of the measurement problem, it follows that a solution to the measurement problem constitutes a solution to the problem of molecular structure. To this day, there is no consensus as to what the solution to the measurement problem is. Nevertheless, several solutions have been proposed in the context of alternative interpretations (and theories) of quantum mechanics, including the Copenhagen interpretation, the many-worlds interpretation and the de Broglie–Bohm theory. In this context, the crucial question becomes whether an adherence to any of these interpretations allows one to adopt a more parsimonious view of chemical ontology that does not require positing distinct ontologies (as per ontological pluralism) or downward causal powers (as per strong emergence).Footnote ⁶⁹

Another interesting result produced by Franklin and Seifert’s thesis is that we need to distinguish between isolated and non-isolated systems when discussing how systems relate to their constituents (Reference Franklin and Seifert2020: 2; also Reference SeifertSeifert 2020, Reference Seifert, Lombardi, González and Fortin2022a). The case of structure is quite revealing of this as certain quantum physical interpretations suggest that structure may not be instantiated by isolated molecules; it only arises after interaction with some environment. If this is the case, then the question of reduction and emergence becomes moot for the case of isolated systems. If there is no structure for quantum physics to derive (in isolated systems), then strictly speaking there is no apparent inability of quantum physics to identify structure (as purported by antireductionism). This could render a very large part of the empirical basis for antireductionism out of place.

Admittedly, this is a brief discussion of how considerations around quantum physics can affect metaphysical questions about chemistry. Nevertheless, an analysis of quantum mechanics is crucial to formulating an empirically well-informed account of how chemistry and quantum physics relate. Thus, a metaphysics of quantum physics goes hand in hand with a cogent metaphysics of chemistry.

Case VIII. Chemical Bonds

Given that the available accounts on unity are under-explored in the philosophy of chemistry, the view which I present is only one way to support unity and reflects my own views on how to understand it with respect to chemistry. Specifically, I focus on the chemical bond and argue that bonds are related to their physical constituents in the sense that they are real patterns of interactions among subatomic particles (Reference SeifertSeifert 2022b). This understanding of chemical bonds offers a way of defending their reality while maintaining the ideal of unity.

The idea that bonds exist when atoms form stable independent molecular entities has been of perennial importance to understanding chemical transformation and the properties of matter (IUPAC 2014: 257). Despite its value to science, there is a persisting debate in science and philosophy about the bond’s nature and reality (Reference WeisbergWeisberg 2008: 932–3). To this day, scientific papers are published that try to understand what bonds are (e.g. Reference Song, Yin and WangSong et al. 2019; Reference Zhao, Pan, Holzmann, Schwerdtfeger and FrenkingZhao et al. 2019). Diverse views have been proposed as to whether bonds refer to material things, energetic facts or mere fictions. Lewis (who first posited covalent bonds) took a strong ontological stance about bonds when he said that ‘in the mind of the organic chemist the chemical bond is no mere abstraction; it is a definite physical reality, a something that binds atom to atom’ (Reference Lewis[1923] 1966: 67). On the other hand, Coulson took the development of quantum models to show that bonds are nothing but mere fictions. He stated that ‘a chemical bond is not a real thing: it does not exist: no-one has ever seen it, no-one ever can. It is a figment of our own imagination’ (Reference CoulsonCoulson 1955: 2084).

In light of all this, Reference HendryHendry (2008) proposes two alternative conceptions to the chemical bond: the energetic and the structural. The energetic conception takes bonds to refer to molecular-wide phenomena that correspond to states of energetic stabilisation of a molecule (Reference HendryHendry 2008: 919). The structural conception takes bonds to be ‘material parts’ that are localised between pairs of atoms and are responsible for those atoms’ pair-wise relation (Reference HendryHendry 2008: 917).

While both conceptions offer valuable insights as to the nature of chemical bonds, neither makes clear what the dependence relation is between a bond and its physical parts, nor whether the bond is real. Under the structural conception, the chemical bond is ‘responsible for spatially localized submolecular relationships between individual atomic centers’, suggesting that it is real (Reference HendryHendry 2008: 917). Nevertheless, this statement does not involve any claims about whether bonds conform to the ideal of unity. On the other hand, the energetic conception is compatible with understanding bonding both as a property of the entire molecule, and as a fictitious entity (Reference SeifertSeifert 2022b: 13). So, the question about the reality of bonds remains open.

Understanding bonds as real patterns answers both questions. First, it specifies the dependence relation in terms of the notion of patterns. Second, it advocates that bonds are real. These claims are based on an idea formulated by Reference DennettDennett (1991) and later adopted – with certain additions – by ontic structural realists (e.g. Ladyman and Ross 2007; Reference Ross, Ross, Brook and ThompsonRoss 2000).

Very briefly, Dennett’s account is the following. A system may be described by various methods, some of which are more efficient than others. Among them is the least efficient method of describing the system called the ‘bit map’. Efficiency can be understood in different ways, but for sake of brevity I understand it in terms of degrees of freedom (Ladyman 2017: 157; also Reference SeifertSeifert 2022b: 21). Specifically, a description is more efficient than another if fewer independent parameters need to be specified to produce that description, compared to the number of parameters required for the other. In this context, a pattern exists if there is a way of describing a system that is more efficient than the bit map. This pattern is identified via the concepts employed by the more efficient description.Footnote ⁷⁸

For example, consider a collection of black and white dots. Its bit map is the description which identifies the position of each and every black and white dot (Reference DennettDennett 1991: 32). However, suppose also that the black dots can be viewed as forming shapes in the frame, such as a series of black boxes. This makes it possible, instead of counting each and every black and white dot, to describe the frame by identifying the size and distance of the black boxes. Such a description would be more efficient than formulating the bit map because it requires specifying fewer variables. Following Dennett, this suffices to claim that there is a pattern in the way the black and white dots are positioned. Put boldly, the black boxes are (real) patterns of black dots in the frame.Footnote ⁷⁹

Dennett’s account successfully applies to molecules (Seifert 2022: 16–18). The bit map description of a molecule corresponds to solving its Schrödinger equation from first principles. This is because solving this equation requires identifying the interactions of each and every electron and the nucleus that comprises the molecule, without disregarding any of the entities or interactions. Moreover, in quantum chemistry and chemistry, a molecule is described by more efficient methods than this. In quantum chemistry, the use of approximations and idealisations reduces the degrees of freedom of the quantum models employed to describe molecular systems. The implementation of the BO approximation alone suffices to support this, as this approximation amounts to disregarding the interactions among the nuclei of a system. Similarly, chemistry has fewer degrees of freedom compared to the bit map because it describes molecules in terms of the number and types of bonds that form between its atoms. This involves the specification of the electronic configuration of the atoms in a molecule which in turn is based on an analysis of only those electrons that are found in the atoms’ outer shells.

This allows us to claim that chemical bonds are patterns of interactions between subatomic particles. This is because the more efficient descriptions employed in chemistry and quantum chemistry invoke bonds to describe molecules. In the process of describing the subatomic interactions of a molecule, quantum models (employed in quantum chemistry) identify chemical bonds in terms of electron clouds, bond paths or electron charge distributions (e.g. Reference Macedo and HaidukeMacedo and Haiduke 2020). In chemistry, the number and types of bonds that are posited among specific atoms (such as covalent, ionic and metallic bonds) are central to the specification of a molecule and its structure. Therefore – like the boxes of black dots – bonds are real patterns.

While Dennett’s account has been criticised on the basis of implying instrumentalism or pluralism about patterns, it has also been used as a way to understand the dependence of higher-level entities to lower-level ones. Ontic Structural Realism (OSR) as formulated by Ladyman and Ross adopts Dennett’s idea of patters to offer an account of non-reductive unity which maintains the reality of higher-level entities.Footnote ⁸⁰ On this view, descriptions identify real patterns not only because they are more efficient than the bit map but also because they make counterfactual and nomological generalisations that successfully explain and predict phenomena (Ladyman 2017: 154).

Indeed, bonds satisfy this criterion. By positing, for instance, covalent bonds, chemistry makes counterfactual and nomological generalisations about how classes of molecules react and form stable entities. The covalent bonds between carbon atoms explain the stability of organic molecules, the formation of macromolecules and the energetic facts around specific classes of chemical reactions. Similarly with other types of bonds.

Adopting an OSR view of bonds allows to maintain both the ideal of unity and the reality of bonds. Unity is maintained because OSR – applied to the case of bonds – posits a compositional relation between bonds and their subatomic entities that is diachronic and dynamic (Ladyman 2017: 152). This understanding of dependence is consonant with accepted scientific knowledge that the interactions of electrons and nuclei (which form a bond) are dynamic: subatomic particles move around the molecule and occupy different orbitals at different times. By advocating this non-static understanding of dependence an important feature of chemical bonding is thus illuminated: bonds are diachronic and dynamic, and result from subatomic particles which interact via (mostly) Coulomb forces.

That it is a realist account follows from Dennett’s understanding of patterns, as he takes that to be a pattern is to be real. This of course can be resisted; why does being a pattern automatically imply that patterns are real? While this seems to be taken by Dennett as a primitive fact about patterns, the additional requirement of OSR that real patterns figure in nomological and counterfactual generalisations offers sufficient support as to their reality. This is because, similarly to strong emergence, the realist feature of OSR is based on the acceptance of Alexander’s dictum (i.e. that to be is to cause).

Admittedly, this is a very short exposition of how an account of unity can be applied to a case in chemistry and invoked to support its reality. There are many questions and problems that this (and any) account needs to address before we can convincingly argue that it should be accepted. In any case, I take the purpose of this presentation to be fulfilled. I showed that it is possible to maintain the unity of chemistry with quantum physics without holding an eliminativist stance on chemical ontology. This goes against the received view in the philosophy of chemistry and opens new avenues for research around the metaphysics of chemistry.

Finally, can the account of real patterns or any other account of (dis)unity be generalised to all chemical ontology? To answer this, it is essential to examine each chemical entity separately, including molecules, structure, orbitals and electronegativity. My suspicion is that each case relates differently to its physical constituents, or at least requires its own account of how it relates to them. This is because any account should be informed by the scientific details regarding how precisely chemistry and quantum physics each describes, explains and represents the chemical entity in question. As the case of the chemical bond illustrates, the specific details help us understand an entity’s relation to its physical parts and offer empirical evidence to support a metaphysical position. Without looking at the models, representations, explanations and concepts that scientists use in order to understand and describe a chemical entity, one cannot offer an accurate metaphysical account of it.

So, before defending a specific metaphysical worldview about chemistry, we should remain neutral and examine the body of knowledge offered by the relevant sciences. It might turn out that different chemical entities relate in substantially different ways to their physical constituents: some may be reducible in a Nagelian (or other) manner, others may be patterns of physical interactions, or grounded to their physical parts. Still others may even be substantially independent of their physical constituents. From the perspective of the realist question, this implies that one may hold more than one view as to the reality of chemical stuff and its relation to physical stuff. Some chemical entities may be eliminable; others may be real because they are causally autonomous or real patterns; and still others may just be useful fictions. Identifying the ontology of chemistry is a fascinating multidimensional project.

Case IX. Periodic Table

The modern periodic table is a visual representation of all known chemical elements. The elements are positioned in the table in terms of increasing atomic number. Starting with hydrogen at the top left, the elements are positioned consecutively from left to right and top to bottom. Based on this ordering, chemists distinguish between sets of elements in the table: the elements found in the same horizontal line are said to form ‘groups’ and the elements found in the same vertical line form ‘periods’. The identification of groups and periods is useful in chemistry because members of a group or period have specific chemical or physical properties in common. This allows chemists to make inferences, predictions and explanations about chemical and physical phenomena.

Reference to a ‘periodic law’ emerged from the very beginning of the inquiry into the classification of chemical elements (Reference PulkkinenPulkkinen 2020). In the nineteenth century, Newlands used several times the term ‘periodic law’ to refer to his proposed classification of elements, and in his attempt to claim priority over Mendeleev and Meyer’s classifications, stated:

In 1871, Mendeleev published his paper ‘Periodic Law’, where he proposed ‘the law of periodicity … that was applicable to study the relations between the properties and the atomic weights of all of the elements’ (quote from Reference PulkkinenPulkkinen 2020: 196). Even though Newland’s, Meyer’s and Mendeleev’s versions of the table have been discarded, the term ‘periodic law’ is still used with respect to the modern table. One need not go further than Wikipedia to find that the table is defined as ‘a graphic formulation of the periodic law, which states that the properties of the chemical elements exhibit an approximate periodic dependence on their atomic numbers’.Footnote ⁸⁷

Despite the metaphysical significance of laws, philosophers have either not picked up on or undermined the periodic table’s relevance to the discussion of laws (e.g. Reference ScerriScerri 2012, Reference Scerri2020). An exception is Reference Woody, Soler, Zwart, Lynch and Israel-JostWoody (2014), who has stated (without further argument) that the periodic table could be viewed as a candidate law from the perspective of Reference MitchellMitchell’s (2000) pragmatic account. In general, however, the periodic table has been investigated either as a theory (Reference Hettema and KuipersHettema and Kuipers 1988; Reference WeisbergWeisberg 2007) or as a taxonomic representation (Reference ScerriScerri 2012, Reference Scerri2020; Reference Shapere and SuppeShapere 1977).

So, how can we argue that the periodic table is a representation of a law of nature? I argue that there are several regularity relations identified by the table and which should be viewed as candidate laws. These regularity relations are much more precise than what is standardly understood as ‘the periodic law’ and are expressed by multiple statements that are embedded in the table. These statements include for example that ’Actinium reacts rapidly with oxygen’; ‘Halogens undergo redox reactions with metal halides in solution’; and ‘Lanthanum reacts with the halogens at room temperature.’ That is, the periodic table is a (visual) depiction of regularities between individual elements, between sets of elements and between elements and sets of elements. The visual depiction of elements in a specific ordering, together with the posited classifications into groups and periods, allow chemists to form statements about the chemical and physical properties of different sets of elements.

So, if the periodic table represents a law of nature, it represents many laws of nature. This shouldn’t come as a surprise; the table identifies 118 elements, 18 groups and 7 periods, positing various regularity relations between them about – among other things – their chemical reactivity, their (non-)metallic character, their electron affinity and ionisation energy.

Note that, I claim, the periodic table represents (or identifies) laws of nature. An equivalent way I state this is this: non-accidental regularity relations are expressed by statements that are embedded in the periodic table. Here, these are taken as equivalent ways for saying that there are laws in the periodic table. I do not adopt a philosophically informed understanding of ‘representation’ in spelling out this claim. I employ the terms only to bring forward the idea that chemists employ the periodic table as a means to visually depict and empirically examine regularity relationships between elements.

Moving on, even if we admit that there are many empirically observable regularity relations expressed within the table, we need an argument for why these regularities have lawful status. After all, apart from accidental regularities in nature (such as about the size of gold spheres mentioned previously), there are regularity relations posited by science which are not granted lawful status. As Reference Carroll and ZaltaCarroll (2020) notes, ‘the regularity of the ocean tides, the perihelion of Mercury’s orbit, the photoelectric effect, that the universe is expanding’ do not have the lawful status of – say – Newton’s laws or the laws of thermodynamics.

To this end, there are certain features that are taken to be suggestive of a lawful regularity.Footnote ⁸⁸ These features are generally accepted to be found in candidate laws regardless of how philosophers further understand – or disagree upon – the precise nature of laws (e.g. as per the regularity or necessitarian views). I show that they are exhibited by the regularity relations identified in the table.Footnote ⁸⁹

First, statements of laws are used to make empirically successful inferences about instances of matter (Reference Van Fraassenvan Fraassen 1989: 29). This applies to the law-like statements of the periodic table. For example, that ‘gold is unreactive’ allows inferring that one’s golden necklace is unreactive. Second, law-like statements allow predictions of behaviour of instances of matter in the past, present and future. Indeed, one can predict that her golden necklace will never rust based on the law that gold is unreactive.Footnote ⁹⁰ Third, laws unify the behaviour of prima facie disparate things in the world. Statements about oxygen, for instance, unify how we understand the behaviour of matter, whether it is found in the sky of Athens, in a chemical laboratory in Zurich or on Mars. In turn, this implies that laws allow scientists to systematise empirical facts. Information about the chemical properties of any particular in the world (for instance of any gold substance found in jewellery, computers, mines etc.) is systematically organised by the relevant law about gold. These features are often taken to indicate that laws are universal (or statistical) claims: they hold at every time and place in the universe, and for all relevant instances of matter. Indeed, in the case of statements about (sets of) elements, these statements are taken to hold for all instances of chemical elements found anywhere and anytime in the universe (under specific conditions).

Moreover, unlike accidental generalisations, laws support counterfactual reasoning in the sense that they make counterfactual statements true (or false).Footnote ⁹¹ Indeed, this seems to be applicable to the law-like statements of the periodic table. For example, ‘If a chunk of matter were made of gold, then it wouldn’t rust’ is made true by the periodic law that ‘gold is unreactive’. Lastly, laws are taken to explain phenomena. How to spell out explanation is an issue in its own right, but it is generally agreed that laws should explain phenomena. For example, that my great-grand-mother’s necklace has not corroded after 100 years is explained by the law that gold is unreactive.Footnote ⁹² Given the controversy over the periodic table’s explanatory power, I return to this point.

Note that my view diverges from standard understandings of the ‘periodic law’. Unlike Newlands, Mendeleev and modern usages of the term in both science and philosophy, I do not take ‘periodic law’ to refer to the existence of a periodic dependence between the properties of elements (i.e. between elements and their atomic number, as per the modern understanding of ‘periodic law’). Instead, I take that there are multiple laws expressed within the table and which identify regularity relations between properties of (sets of) elements.Footnote ⁹³

While this is a brief analysis of the main indications of lawhood, I take this to be a good step towards believing that the law-like statements embedded in the periodic table express laws of nature. Note that this is not the first time one highlights these features of the periodic table:

Interestingly, while Mahan refers to the periodic law as standardly construed (i.e. as referring to the periodic dependence of elements on their atomic number), Woody points out that it is ‘implausible’ that this is what he means, as this understanding of ‘periodic law’ is too imprecise to have the requisite explanatory and predictive power (Reference Woody, Soler, Zwart, Lynch and Israel-Jost2014: 135). I take this to reinforce my view that if we are to construe anything as the periodic law, it must be the regularity relations posited between specific properties of specific (sets of) elements.

Note that one need not be a realist about laws to admit that the regularity relations expressed in the table are legitimate candidates of laws. Consider for example the problem of ceteris paribus laws. According to Reference CartwrightCartwright (1983), there are no laws of nature because all law-like statements in science hold ceteris paribus; that is, there are no true exceptionless regularities. Regardless of whether this criticism holds, it can be applied to the law-like statements of the table in the same way it is applied to other paradigmatic candidates of laws, such as Coulomb’s law or Newton’s laws. Take for instance the law-like statement ‘Lanthanum reacts with halogens at room temperature.’ This is a ceteris paribus statement because it posits a regularity relation between instances of lanthanum and halogens that only holds under specific thermodynamic conditions.Footnote ⁹⁴ Of course, there are philosophers who – contrary to Cartwright – maintain that there are exceptionless law-like statements in fundamental physics which as such can be admitted as representing laws (Reference Earman and RobertsEarman and Roberts 1999). In this context, the statements in the periodic table would be denied lawful status.Footnote ⁹⁵ In any case, the fact that the law-like statements of the periodic table can figure in such discussions demonstrates that at the very least they are as good candidates as other paradigmatic candidates of laws (that are not exceptionless).

All in all, my claim is far from uncontroversial and requires a detailed exposition of its main tenets. In addition, it requires addressing issues raised by philosophers who take the table to be nothing more than a classificatory scheme (e.g. Reference ScerriScerri 2012, Reference Scerri2020). The remainder of this section briefly presents four putative problems against the periodic table representing laws.

The first problem concerns the predictive power of the periodic table. Recall that the ability to make predictions is an important feature of law-like statements. The periodic table has been lauded for its ability to not just accommodate known facts but also predict previously unknown empirical facts. Specifically, the acceptance of Mendeleev’s periodic table – which is the precursor of the modern periodic table – is attributed to its ability to predict new elements, including gallium, scandium and germanium:

However, Scerri and Worrall claim that ‘the impression of consistent predictive success for Mendeleev’s scheme is a complete misrepresentation of history’ (Reference Scerri and Worrall2001: 419). Among other things, Mendeleev posited the existence of at least two elements that are lighter than hydrogen, as well as six new elements between hydrogen and lithium. Both predictions turned out to be false (Reference Scerri and WorrallScerri and Worrall 2001: 420–1). Moreover, there were several unsuccessful predictions of the properties of known elements, including about the melting point of gallium and the solubility of aka-boron (Reference Scerri and Worrall2001: 422). In addition, Scerri and Worrall challenge the predictive success of Mendeleev’s table on methodological grounds, arguing that ‘Mendeleev … was operating within a general and rather loose framework, underpinned by no very definite theory, and was feeling his way towards making particular predictions rather than being in possession of a theory that makes them willy nilly’ (Reference Scerri and Worrall2001: 440).

On the other hand, Reference WeisbergWeisberg (2007) maintains that the successful prediction of new elements by Mendeleev is evidence that the table is not a classificatory scheme (but a theory). On his view, the methodology by which Mendeleev predicted those elements was not an exercise to fill missing gaps; it was based on hypothesising missing elements and analysing the theoretical structure Mendeleev had created via his proposed ordering of elements (Reference WeisbergWeisberg 2007: 214).

The second problem concerns the explanatory power of the periodic table. Reference ScerriScerri (2020) claims that the periodic table lacks genuine explanatory power because quantum physics, and in particular reference to the electronic configuration of elements, does all the explaining of the relevant phenomena. Therefore, the table is explanatorily redundant. While this worry is not addressed against what I take here to be the candidate laws of the periodic table, it is nevertheless a relevant worry as it is a standardly accepted feature of laws that they explain.

A possible reply is that we need to distinguish between what a law explains and how a law is explained. Take for instance a paradigmatic candidate law: PV = nRT (the ideal gas law). Granted, the law itself does not explain why this mathematical relation holds between pressure, volume and temperature. One could even claim that statistical mechanics offers an explanation of why this relation holds between these properties. Nevertheless, one can still maintain that this law-like statement has explanatory power as it explains how particular instances of matter behave when we increase – say – their temperature. A similar response can be formulated about the regularities expressed within the table. Take for instance ‘actinium reacts rapidly with oxygen’. The electronic configuration of actinium and oxygen may explain why they react the way they do. Nevertheless, this does not diminish the statement’s explanatory power with respect to observed instances of chemical transformations. That is, the observed course of chemical transformation of any particular instance of actinium is explained by invoking this statement. A similar response is offered by Woody who states:

In fact, it is worth noting that – contrary to Reference ScerriScerri (2020) – Woody maintains that the periodic table is explanatory and even connects its explanatory power with its status as a law. She claims that the table identifies patterns among chemical elements, which play a vital (though not sufficient) role in the explanations invoked in chemical practice (Reference Woody, Soler, Zwart, Lynch and Israel-Jost2014: 141). Woody’s idea that the table identifies patterns complements nicely how certain philosophers spell out lawful regularities in terms of real patterns (as per Reference DennettDennett 1991, see Section 3; e.g. Reference Kimpton-NyeKimpton-Nye 2022; Reference Ladyman, Ross, Spurrett and CollierLadyman and Ross 2007; Reference PsillosPsillos 2014: 23). While this is by no means a sufficient analysis, this point further reinforces the legitimacy of viewing the table as a representation of laws of nature.

However, an additional problem is prompted by considering the role of quantum physics in explaining chemical behaviour. This problem has been raised against special science laws in general, and is partly based on the adoption of a reductionist perspective towards the special sciences (e.g. Reference Fodor and NedFodor 1980; Reference KimKim 2010). The worry is often formulated (though not exclusively) in terms of the overdetermination problem. According to this problem, if we accept that every non-physical event supervenes on a physical one and that – construed as an effect – the physical event always has a physical cause, then we cannot accept that this same effect also has a non-physical (say chemical) cause, because then we would have the (unacceptable) result that an effect has more than one causes. Therefore, we should reject that there is anything else than physical causes. If we further assume that explanations track causal relations (i.e. they are statements about how effects come about by causes), then we are lead to conclude that there are no special science explanations and hence no special science laws. Instead, everything is explained by physical laws.

Evidently, this issue boils down to the question of whether there are special science laws or only fundamental laws. The motivation for this scepticism against special science laws is that if special science regularities are somehow ‘grounded’ on more fundamental physical regularities, then perhaps we shouldn’t grant to the former lawful status (e.g. Reference Davidson, Moser and TroutDavidson 2002; Reference FodorFodor 1989; Reference PsillosPsillos 2014). As Kim states:

Note that this problem involves many assumptions regarding how we should construe laws, causes, explanations and reductions. Philosophers have analysed extensively the relations between these ideas and reviewed these relations to offer different responses. While I do not present these responses here, it is evident that the postulation of laws in the periodic table hinges on how we respond to these general worries about special science laws.

One last challenge arises if we accept – as some do – that laws are regularities between natural kinds (Reference Bird, Tobin and ZaltaBird and Tobin 2022). If this is the case, one has to offer support not only for the claim that chemical elements correspond to natural kinds. One has to also support the claim that sets of elements correspond to kinds. This is because some of the law-like statements in the table concern relations between groups or periods (such as alkali metals and noble gases). And arguing that groups or periods correspond to natural kinds may not be as uncontroversial, especially if one adheres to the hierarchy requirement for natural kinds (see Section 2.2).Footnote ⁹⁶ Therefore, it might turn out that not all law-like statements in the table correspond to laws of nature.

All in all, there is evidence in favour and against the claim that the regularities identified within the table are laws of nature. Whichever position one maintains, whether the periodic table represents any laws is an interesting question to raise. To answer it, we need to pursue (a) a historically informed analysis of the table; (b) a scientifically rigorous analysis, especially in terms of the table’s relation to quantum physics; and (c) a careful conceptual analysis of laws and the subsequent metaphysical commitments involved.

Case X. Chemical Reactions

It is hard to overstate the importance of chemical reactions in understanding nature and sustaining life. From lighting fires and fermenting bread to breathing, developing life-saving drugs and creating (and tackling) climate change, there are few activities in our everyday life that are not the result of naturally occurring or synthetic chemical reactions.

Chemical reactions refer to transformations of chemical substances that do not involve changes in the atomic number of the substances’ constituting elements. I distinguish between two forms of reaction statements in chemistry. First, there are statements of reactions that occur between specific chemical substances under specified thermodynamic and environmental conditions, and which lead to the production of specific substances (henceforth called ‘individual reactions’). For example, solutions of hydrochloric acid react with sodium hydroxide to produce sodium chloride and water: HCl + NaOH → NaCl + H₂O.

Second, there are statements which describe chemical transformations between types of substances within a range of conditions (henceforth called ‘general reactions’).Footnote ⁹⁷ For example, the above reaction is a special case of the acid-based reaction which occurs between an acid and a base to produce an ionic salt and water: HA + BOH → BA + H₂O.

So far, philosophical and historical works on chemical reactions concern issues in chemical education: the history of chemistry; conceptual analysis; the relation of chemistry with biology; and even the metaphysics of chemistry (Reference HarréHarré 2008; Reference MartinsMartins 2019; Reference MorettiMoretti 2015; Reference ŠimaŠima 2013; Reference VillaniVillani 2017). However, none of this work offers an account of what chemical reactions are, nor draws insight from the extensive body of knowledge on causation and laws of nature. In fact, there is little overlap of the philosophical study of chemical reactions with the literature on metaphysics of science. In part this is because the philosophy of chemistry primarily focuses on the analysis of chemical elements and substances, atoms and molecules, chemical bonds and the relation of chemistry with quantum physics. While these issues offer valuable insight on chemical reactions, an understanding of the nature of chemical reactions requires investigating them in their own right. Chemical reactions hold an ineliminable role in conveying what it is that determines the course of a chemical transformation, and this role cannot be substituted by only identifying the entities and properties of the reactants.

From the perspective of chemical reactions, it is central to examine whether reactions identify genuine causal relations, and which specific understanding of causation best applies to them. Different candidate notions of causation are available within the broad distinction between Humean and anti-Humean accounts. These include the regularity view of causation, the counterfactual account, the mechanistic account and the power-based account of causation. The metaphysical implications of each account affect our understanding of chemical reactions as causal relations because each specifies differently how reactants cause the formation of their products.

Investigating chemical reactions as causal relations prompts questions about reactions representing laws of nature. In philosophy, the connection of laws and causation is highly contestable. Nevertheless, an analysis of existing accounts of laws can help inform whether, in what way, and if all types of chemical reactions represent laws in nature. For example, can individual reactions be appropriate candidates of laws, if laws correspond to relations among universals (see Section 4.1)? Additionally, how should we make sense of individual reactions in the context of the ceteris paribus view of laws (e.g. Reference CartwrightCartwright 1983)? Moreover, focusing on the unique features of chemical reactions can lead to novel insight on causation and lawhood. To demonstrate this, the remainder of this section briefly presents four such features.

First, a typical chemical reaction is not an event where chemical substances irreversibly transform into other substances (just like – say – a rock would irreversibly cause the shattering of a window). Instead, a reaction is a dynamic process which – once at equilibrium – results in a state where the system continuously and at a constant rate transforms into the products and reverses back into the reactants. This is a highly interesting feature of reactions when viewed from the perspective of causation. It suggests that reactions exhibit causal loops and as such they either should not be considered as genuine causal relations or they pose a challenge for those Humean and non-Humean accounts of causation that require the temporal priority of causes (e.g. Reference Mumford and AnjumMumford and Anjum 2011).

Second, any account of causation applied to chemical reactions needs to accommodate the role of catalysts in the realisation of reactions. A catalyst is a ‘substance that increases the rate of a reaction without modifying the overall standard Gibbs energy change in the reaction’ (IUPAC 2014: 220). Their presence can be said to partly cause a reaction (as their absence often explains why a reaction does not take place), even though they do not substantively participate in the reaction (because they do not transform into products). This explains why chemists include them as both a reactant and a product in a chemical reaction statement. However, it raises the question of whether they should be construed as genuine causes of a reaction or as part of the environment which accommodates the reaction’s realisation.

Third, chemical reactions are products of multi-level theories. The description of a chemical reaction in terms of the standard arrowed equation (i.e. A + B → AB) is the result of a body of knowledge that comes from a combination of higher- and lower-level theories, most notably quantum physics and thermodynamics (e.g. Reference Keeler and WothersKeeler and Others 2003). This makes them a unique example from the perspective of special science causation and lawhood as it raises the question of whether chemical reactions are eliminable or reducible to more fundamental causal relations and laws in physics.

Lastly, any account of causation needs to accommodate the role of reaction mechanisms in describing chemical reactions. Reaction mechanisms are descriptions of the process the reactants undergo during a chemical transformation. They specify the properties of intermediary entities and transition states formed during a reaction (IUPAC 2014: 902). The prevalence of reaction mechanisms in the explanation of chemical reactions has prompted philosophers to advocate a mechanistic view of chemical explanation (e.g. Reference Goodwin, Hendry, Needham and WoodyGoodwin 2012; Reference Weininger, Klein and ReinhardtWeininger 2014). While such a view suggests that a mechanistic account of causation is plausible for chemical reactions, this has not been explicitly examined.

So, thinking of chemical reactions from the perspective of causation can be extremely informative not only for those who wish to understand the natural of chemical reactions but also for those who are interested in forming a scientifically well-informed view of causation. Admittedly, causation is one of the most controversial ideas in metaphysics, with many philosophers dismissing it as ‘a relic of a bygone age’ (Reference RussellRussell 1912). Perhaps thinking of it from the perspective of chemical reactions will offer a novel way to understand causation that even its most persistent critics could accept.