This section presents three challenges to Hendry’s account of strong emergence that have remained unnoticed in the literature. Identifying and resolving these challenges is essential for rendering Hendry’s account a viable and convincing position about the nature of molecular structure as a strongly emergent property.
Incoherence with respect to Supervenience
First, there is an incoherence between one of the main tenets of strong emergence (namely supervenience) and the empirical support of the strong emergence of molecular structure. For Hendry, DC is supported by how the Coulombic Schrödinger equation (via the resultant Hamiltonian) describes a molecule. He disregards the success of the configurational Hamiltonian in distinguishing molecules in terms of their structure. This is because, ‘(w)ithout a quantum-mechanical justification for the attributions of structure (and the lower symmetry)’ configurational Hamiltonians ‘simply assume the facts about molecular structure that ought to be explained’ (Hendry 2010b:186).
This leads to incoherence in Hendry’s account, because, it equally undermines the grounds for thinking supervenience holds, which is one of the core elements of Hendry’s understanding of strong emergence. Consider, for example, the two isomers ethanol and methoxymethane; they are chemically distinct and thus have different chemical descriptions (Hendry 2010a: 214). The resultant Hamiltonians, and thus the Coulombic Schrödinger equations which quantum mechanically describe the two isomers, are the same. Therefore, ethanol and methoxymethane have different higher-level descriptions, whereas their respective lower-level descriptions (as specified by the Coulombic Schrödinger equation) are the same. In sum, if as Hendry recommends, we disregard a molecule’s configurational Hamiltonian, then it follows that there are molecules whose chemical descriptions are different, whereas their quantum mechanical descriptions are the same. So, supervenience would not hold.
Based on the above, one needs to justify whether and why the configurational Hamiltonian is used as putative empirical evidence for supervenience. If one accepts the use of the configurational Hamiltonian for the empirical support of supervenience, then one needs to justify why the configurational Hamiltonian can be used as putative empirical evidence for supervenience, but not as putative empirical evidence for the existence of structure at the quantum mechanical scale. On the other hand, if one argues that the configurational Hamiltonian of a molecule cannot be invoked for the empirical support of supervenience, then one needs to explain why, despite the fact that the resultant Hamiltonian describes different isomers in an identical manner, supervenience is accepted within one’s understanding of strong emergence.
The assumption of determinate nuclear positions
A second problem in the defence of strong emergence concerns the assumption of determinate nuclear positions.Footnote 16 Recall that quantum mechanics standardly describes a molecule’s structure via the configurational Hamiltonian which, unlike the resultant Hamiltonian, makes assumptions about the structure of the examined molecule (see subsection 2.3). Among those assumptions is that the nuclei that comprise the molecule hold determinate positions.Footnote 17 The fact that quantum mechanics makes this assumption in order to explain molecules (and their structure) constitutes putative evidence for the strong emergence of molecular structure.
This section shows that there are three plausible and alternative ways that one can interpret Hendry’s claim that the need for this assumption supports strong emergence:
If quantum mechanical explanations are conditioned on assumptions that are not derivable from quantum mechanics, then this constitutes evidence for strong emergence.
If quantum mechanical explanations are conditioned on assumptions that are based on results from or are justified by higher-level theories, then this constitutes evidence for strong emergence.
If quantum mechanical explanations are conditioned on assumptions that are ad hoc, then this constitutes evidence for strong emergence.
In Hendry’s work on strong emergence there are passages which are suggestive of each of these three interpretations; the remainder of this section demonstrates this by means of textual evidence.Footnote 18 In this way, this section shows that it is not clear how the assumption is supposed to support strong emergence. Moreover, this section evaluates the tenability of each interpretation and discusses potential challenges that could be raised against them. It is concluded that, in its present form, Hendry’s account has not convincingly shown how the assumption of determinate nuclear positions supports the strong emergence of molecular structure.
Interpretation (1): If quantum mechanical explanations are conditioned on assumptions that are not derivable from quantum mechanics, then this constitutes evidence for strong emergence.
The following passage suggests that Hendry has in mind something along the lines of interpretation (1):
The complaint is not that there are no explanations of empirically determined molecular shapes, or even that the explanations are ad hoc, or of poor quality. Rather it is that the explanation is conditioned on determinate nuclear positions: if electronic motions are constrained by a stable nuclear backbone, then the energy dependence is such that such-and-such is the lowest energy configuration. (Hendry 2006: 184-185)Footnote 19
According to this interpretation, assuming determinate nuclear positions shows that quantum mechanics is not otherwise sufficient to derive an explanation of the examined molecule. That is, quantum mechanics underdetermines facts about molecular structure. This indeed undermines intertheoretic reduction to the extent that the latter requires lower-level theories to derive the properties of the examined system from the bottom-up.
Moreover, if the purported inability of quantum mechanics to derive molecular structure is not solely understood as an in-practice feature of quantum mechanics, then strong emergence may be reinforced. Indeed, as mentioned in 2.3, Hendry takes quantum mechanics to be in principle unable to derive molecular structure; it is not just the case that molecular structure is not derived by quantum mechanics, but that it is not derivable by it.Footnote 20 This is a more serious problem in the sense that it could also challenge non-reductive physicalism and thus further support strong emergence (Hendry 2010a: 212–213).
Nevertheless, if this is how Hendry invokes the use of this assumption in quantum mechanics, then more has to be said about why quantum mechanics is in principle unable to derive molecular structure. Stating that this inability is simply due to the fact that molecular structures ‘are not there to begin with’, is not sufficient (Hendry 2010b: 186). This is because, even though quantum mechanics (in the form of resultant Hamiltonians) does not identify the particular structure a molecule is observed to have, it does specify the possible structures of the molecule in the form of superposition states (Claverie and Diner 1980: 59; Scerri 2012; Woolley 1998). Hendry admits this:
The spherically symmetrical states could perhaps be regarded as superpositions of asymmetrical states with opposite orientations, just as the spin states of a silver atom may be regarded as superpositions of spin-up and spin-down, or the quantum state of Schrödinger's cat can be regarded as a superposition of ‘cat-alive’ and ‘cat-dead’ states. (2010a: 214)
In fact, there is a close connection between the putative empirical evidence for strong emergence and foundational problems in quantum mechanics. Scerri illuminates this connection quite clearly for the case of isomers:
According to quantum mechanics, molecules can be said to be in a superposition of a number of possible structures. For example, C2H6O1 can be regarded as a superposition of quantum states representing the structures of quantum states representing the structures of C2H5OH and CH3OCH3. Woolley, and now Hendry, concentrates on the fact that until an observation is carried out, neither of these structures has been actualized. The inference they draw from this state of affairs is that there is no intrinsic structure in the molecule, which—if it were true—would indeed mean that structure is not fundamental. However, the study of decoherence has shown that it is not just observations that serve to collapse the superpositions in the quantum mechanical equations. The collapse can also be brought about by the molecules interacting with their environment, something that Hendry occasionally mentions but quickly dismisses.Footnote 21 (Scerri 2012: 23)
Scerri’s formulation of Hendry’s argument suggests that the inability of resultant Hamiltonians to describe molecular structure is based on the fact that they identify superpositions of quantum states with alternative corresponding molecular structures. From this it follows that quantum mechanics’ in principle inability to identify structure is conditioned on some understanding of superpositions, as well as of the collapse of the wavefunction (also referred to as the measurement problem (Cushing 1998: 309)).
However, how to interpret superposition states and the collapse of the wavefunction are not settled issues within science and philosophy, and various proposals have been offered to explain them (Myrvold 2018). Given this, one cannot simply assume that a quantum mechanical description of molecular structure in terms of superposition states is not a description which adequately explains a molecule’s observed structure. Given that different metaphysical understandings of superposition states are debated in the literature, the strong emergentist needs to justify how she understands superposition states and why such states do not in principle explain structure.
Of course, establishing such a connection between the putative evidence for strong emergence and these foundational problems in quantum mechanics requires a much more detailed analysis that this paper cannot offer.Footnote 22 Nevertheless, it is interesting to note that other philosophers of chemistry also connect quantum mechanics’ inability to identify structure with foundational problems in quantum mechanics (see Chang 2015; Lombardi and Castagnino 2010). If Hendry’s argument in favour of strong emergence is similarly based on considerations of foundational problems in quantum mechanics, then a lot more has to be said regarding how the strong emergentist interprets superpositions and deals with the measurement problem. If, on the other hand, Hendry does not assume a connection with foundational problems in quantum mechanics then this interpretation seems to be lacking sufficient empirical evidence as it is no longer clear on what grounds quantum mechanics (in the form of resultant Hamiltonians) is in principle unable to identify structure.
In sum, a lot more has to be said regarding quantum mechanics’ inability to identify structure in order to invoke this as support for strong emergence. If quantum mechanics’ inability to identify structure is based on the fact that it identifies superpositions of molecular structures, then a central question that Hendry needs to address is how superposition and collapse are interpreted. This, in turn, leads to questions about the classical-quantum divide, the measurement problem and its standard putative solutions. None of these issues have been considered by Hendry in the context of evaluating the strong emergence of molecular structure.Footnote 23
All in all, while this interpretation of Hendry’s argument holds significant strength, there is an important feature missing for the argument for strong emergence to be sufficient. In the context of this interpretation, quantum mechanics’ inability to derive molecular structure is connected to foundational issues in quantum mechanics. This connection should be brought into light and relevant views on these issues should be taken into account in order to convincingly claim that molecular structure strongly emerges.
Interpretation (2): If quantum mechanical explanations are conditioned on assumptions that are based on results from or are justified by higher-level theories, then this constitutes evidence for strong emergence.
Hendry states the following which is suggestive of interpretation (2):
To solve the Schrodinger equations for more complex atoms, or for any molecule, quantum chemists apply a battery of approximate methods and models. Whether they address the electronic structure of atoms or the structure and bonding of molecules, these approximate models are calibrated by an array of theoretical assumptions many of which are drawn from chemistry itself. (Hendry 2010a: 212)Footnote 24
That this is a sensible interpretation of Hendry’s argument is also supported by the following passage:
To invoke one important constituency, among the chemists who founded quantum chemistry, there were many temperamental non-reductionists, who saw the quantum-mechanical explanation of chemical structure and bonding as a process that drew equally of physical principles and chemical knowledge, adapting quantum mechanics significantly in the process. (2010b: 187)
On this interpretation of Hendry’s argument, strong emergence is supported because the assumption of determinate nuclear positions is in some sense based on results from or justified by chemistry. Prima facie, this suffices to support that molecular structure strongly emerges at the chemical scale; if the assumption which is built into the quantum mechanical formalism somehow involves reference to chemical results or justifications (especially about molecular structure), then this could motivate the claim that molecular structure strongly emerges. However, there are no sufficient grounds to claim that this assumption is based on results from or justified by chemistry.
First, the assumption of determinate nuclear positions is formulated exclusively in terms of lower-level (i.e. quantum mechanical) entities, properties, etc. The entities, etc. that are invoked for the application of this assumption are physical. No chemical entity or property is invoked for the application of this assumption to the Schrödinger equation. This is evident by how the BO approximation is defined:
Representation of the complete wavefunction as a product of an electronic and nuclear part (Ψ ( r, R ) = Ψe( r,R ) ΨΝ( R )) where the two wave-functions may be determined separately by solving two different Schroedinger equations. The validity of the Born–Oppenheimer approximation is founded on the fact that the ratio of electronic to nuclear mass (…) is sufficiently small and the nuclei, as compared to the rapidly moving electrons, appear to be fixed. The approximation breaks down near a point where two electronic states acquire the same energy. The BO approximation is often considered as being synonymous with the adiabatic approximation. More precisely, the latter term denotes the case when Ψe diagonalize the electronic Hamiltonian. Thus, the adiabatic approximation is an application of the BO approximation. (IUPAC 2014: 179)
Secondly, assuming determinate nuclear positions does not amount to assuming a higher-level property, namely molecular structure. That nuclei hold determinate positions does not imply that the entire molecule has a particular structure. This is because a given set of nuclear positions corresponds to more than one structure. Each set of nuclear positions is compatible with different quantum states of the system because the electrons behave in more than one possible way, thus resulting in more than one structure. Quantum mechanics itself specifies which quantum state of the molecule (and thus which structure) corresponds to the stable state of the molecule.Footnote 25 Therefore, the conclusions drawn from quantum mechanics about how a molecule is structured, are not presupposed by assuming determinate nuclear positions.Footnote 26
Given the above, the only reasonable way this assumption can support strong emergence in the context of interpretation (2) is that it somehow appeals to higher-level (i.e. chemical) facts.Footnote 27 In order to illustrate this, consider how this assumption is applied to quantum mechanics. Within the BO approximation, one can in principle formulate the Hamiltonian operator by positioning the nuclei at all the possible determinate positions. Each set of nucleonic positions corresponds to different quantum states of the system (hence to different wavefunctions) and to different values of the total energy, E, of the molecule. However, in practice this process is not followed. By having prior knowledge of the quantum system that is under examination (in this case, by knowing the chemical properties of a molecule), only particular nucleonic conformations are considered when constructing the Hamiltonian operator. It is only in this sense that the assumption of determinate nuclei positions may be considered to be based on results from chemistry. This however is an epistemic feature of quantum mechanics; it concerns how the assumption is applied to the Schrödinger equation. In principle, it is possible to apply this assumption by considering all possible sets of nucleonic positions and thus without invoking chemical facts about the examined system (Atkins 1974: 29).
Given all the above, unless one proposes a different way to cash out interpretation (2), this interpretation of Hendry’s argument is not a convincing way of defending the strong emergence of molecular structure.
Interpretation (3): If quantum mechanical explanations are conditioned on assumptions that are ad hoc, then this constitutes evidence for strong emergence.
Lastly, while Hendry states that ad hoc-ness is not the source of his ‘complaint’ against reductionism, there are other parts where he suggests that the use of ad hoc assumptions is in fact problematicFootnote 28:
The Coulomb Schrödinger equation for an n-molecule ensemble of hydrogen chloride molecules has precisely the same symmetry properties as a Coulomb Schrödinger equation for a 1-molecule system. If the particular form of the symmetry-breaking addition is not justified, then it is just ad hoc: a deus ex machina. (Hendry 2010a: 215)Footnote 29
This quote prompts the investigation of the use of ad hoc assumptions and how they should be evaluated when it comes to the investigation of metaphysical positions such as strong emergence. There is extensive literature about what constitutes a hypothesis ad hoc, and in what instances it is unacceptable for the theory that assumes it. Without analyzing it in detail, certain points can be drawn from the relevant literature. Specifically, it is argued that while the particular assumption is a hypothesis which is neither derived nor required by the theory in which it is assumed, it is not ad hoc in the sense of being an ‘unacceptable’, ‘arbitrary’, ‘contrived’, or ‘strange’ hypothesis (Hunt 2012: 11).
First, according to Hunt, if ‘an auxiliary hypothesis turns out to make a novel prediction about which the progenitor of the idea was not aware’, it should not be considered ad hoc in the unacceptable sense of the term (Hunt 2012: 3; see also Grünbaum 1964: 1409). Indeed, the addition of this assumption allows the quantum mechanical description to make novel predictions about a molecule’s structure. These predictions have not only contributed to the empirical verification of the theory, but also to the formulation of novel explanations about molecular structure. Quantum mechanics has revealed the effect of electron delocalisation on the overall stability of a molecule’s structure (Weisberg 2008: 939–943); it has specified atomic structures and led to the prediction of novel elements (Needham 2004: 213); and quantum models have made novel predictions about, among others, pericyclic reactions (Hendry 2004: 1057), large molecules, and metals. This undermines the claim that this is an ‘unacceptable’ assumption to make in quantum mechanics.
Secondly, it is important to take into account the role and prevalence of ad hoc assumptions in science, when evaluating metaphysical claims which are supported via those scientific practices. Quantum mechanics more often than not employs information from classical physics or the special sciences in order to describe some phenomena. Depending on the particular system which it is set to describe, quantum mechanics draws information from the relevant classical or special science theories, in order to derive the properties of the system in a manner consonant to experimental evidence. An example is the case of wavefunction scarring, as discussed by Bokulich (2008a). She examines how semiclassical mechanics explains quantum phenomena in classical systems which are chaotic (2008a: 219). Similarly to the case of molecular structure, the explanation of the behaviour of quantum systems is provided by reference to classical structures. This is allegedly problematic because ‘the classical structure that they appeal to do not, strictly speaking, exist in these quantum systems’ (Bokulich 2008a: 217). Another example concerns quantum electrodynamics. In this context, ‘(i)t has become conventional to interpret experiments on the electromagnetic properties of leptons in terms of ad hoc modifications introduced in the formulas of quantum electrodynamics’ (Kroll 1966: 65).
In light of the above, the supporter of strong emergence could say that these are further examples of strong emergence. On this view, it is not only molecular structure which strongly emerges; various properties of a system, as these are described by classical physics or the special sciences, strongly emerge from its quantum mechanical behaviour. On the other hand, one could say that the prevalence of such examples indicates that something not so special is going on; this is merely how scientific explanations are derived from our theories. For example, Bokulich argues that while a purely quantum mechanical explanation of the phenomenon (i.e. ‘without reference to classical structures’) is ‘in some sense deficient’, ‘the classical trajectories do not cause the scarring’ (2008a: 219 and 228). If strong emergence is to be supported by the ad hoc assumptions about molecular structure, then the overall use of ad hoc assumptions in quantum mechanics has to be addressed.
One last point against the idea that the use of ad hoc assumptions gives empirical support to strong emergence, concerns the role of ad hoc assumptions in the construction of a molecule’s resultant Hamiltonian. Hendry’s argument for strong emergence assumes that the Coulombic Schrödinger equation (via the resultant Hamiltonian) makes no prior assumptions about the system it describes, and it is based only on the main postulates of quantum mechanics (Hendry 2010a: 212–213). However, this is not the case. The construction of the Coulombic Schrödinger equation is based on prior knowledge of the behaviour of particles. For example, the fact that the equation is spherically symmetric is something that is not derived from basic principles of physics but is an ad hoc assumption that is made in order to formulate the equation. Therefore, if one understands Hendry’s argument as being based on the use of ad hoc assumptions, then one must conclude that strong emergence is untenable because the spherical symmetry of the Coulombic Schrödinger equation is an ad hoc assumption as well.
This concludes the examination of the possible ways that Hendry’s argument can be interpreted. Each interpretation is vulnerable against particular challenges that potentially undermine the support of strong emergence. So it is crucial that one spells out exactly how the assumption of determinate nuclear positions supports strong emergence.
The nature of causation in downward causation
So far, this paper assumed an understanding of causation in terms of a primitive notion of production. It pointed out that Hendry does not explicitly state which notion of causation he assumes when referring to DC. Nevertheless, Hendry presents a counternomic criterion which, according to him, sufficiently supports DC. Specifically, Hendry takes that this criterion supports DC because the quantum mechanical description is nomologically sufficient for specifying the structure of a molecule, only after the use of ad hoc assumptions. Put differently, DC is understood by Hendry as a relation of nomological sufficiency.
The problem with such an understanding of DC is that, even if the quantum mechanical system at t1 is not nomologically sufficient for the occurrence of the quantum mechanical system at t2, this does not necessarily imply that the chemical system at t1 determines the quantum mechanical system at t2. For DC to be tenable, it must also be argued that the chemical entities, etc. at t1 are nomologically sufficient for the determination of the quantum mechanical entities, etc. at t2. That is, the chemical system must go through the same level of scrutiny that the quantum mechanical system at t1 goes through and allegedly fails. For that to be the case, it must be that the chemical description alone is nomologically sufficient for the occurrence of the quantum mechanical system at t2.Footnote 30
This subsection argues that the chemical entities, etc. at t1 are not nomologically sufficient for the determination of the quantum mechanical entities, etc. at t2. It introduces Hall’s account of ‘causation as production’ and argues that, within Hall’s account, the chemical entities, etc. are not nomologically sufficient at t1 for the determination of the quantum mechanical ones at t2 (Hall 2004).
According to Hall, a system M, understood as a set of all the entities, properties, processes, etc. that define M, sufficiently produces a system M’, just in case M’ follows from:
the premise that all the members of M occur at t1; and,
the premise that no other events occur at t1.Footnote 31
Hall does not examine ‘causation as production’ with respect to systems that are described within different scales, so this subsection makes three clarifications. First, since the description of all systems is scale dependent, the laws that are employed in order to describe each system must include all and only those concepts, theoretical postulations, explanatory mechanisms and laws of nature that are relevant to that specific scale. Secondly, the members of M are taken to include all and only those entities, properties, causal powers, etc. which completely specify the system at the relevant scale.Footnote 32 That is, neither the laws nor the entities, properties, etc. should belong to a different scale from that in which the respective system is specified. Thirdly, in the case under examination, there are two systems that are taken to be causally related via diachronic reflexive DC. The first system is that of an isolated molecule at t1 (i.e. system M). M is the set of all and only those chemical entities, properties, causal powers, etc. that occur at t1 and specify the molecule.Footnote 33 The second system M’ occurs at t2, and is the set of the quantum mechanical entities, properties, etc. at t2. Notice that the change that has been produced to the quantum mechanical entities, etc. from t1 to t2 has not led to a change in the chemical properties of the molecule at t2. The structural properties of the molecule produce changes to certain of its quantum mechanical properties in such a way that does not change those structural properties. Put differently, the structure of the entire molecule produces certain aspects of the behaviour of the electrons and nuclei in such a way that maintains this structure.
In order for M to causally produce a reflexive diachronic change, it must be the case that the set M, in accordance with the chemical laws, are sufficient for a change at the quantum mechanical level to occur at t2. This must follow from:
the chemical laws;
all the members of M that occur at t1; and,
no other events outside of M occurring at t1.
However, the chemical laws, together with the set M at t1, are not sufficient for determining the quantum mechanical description of the system at t2. This is for two reasons. First, it is not possible to derive the quantum mechanical description of system M’ at t2 from the chemical description of system M at t1, and the relevant chemical laws. The chemical laws and chemical entities, etc. cannot derive the sort of fine-grained description required for the full specification of the quantum mechanical system at t2. Therefore, this model of production collapses and, consequently, diachronic reflexive DC in terms of production is not epistemically supported.
A possible reply to this objection is that, although it is not possible to derive the quantum mechanical description of the system at t2 from the chemical description, laws, etc. of the system at t1, this doesn’t preclude the possibility that chemical systems cause quantum mechanical changes. This reply to the first objection leads to the second objection against DC. Due to multiple realisability, it is possible that a molecule, as this is described in chemistry, supervenes on more than one quantum mechanical state. Put differently, there are more than one possible quantum mechanical states of M’ on which the molecule (both at t1 and at t2) supervenes. In light of this, it is not possible that the chemical system alone, without ‘taking into account’ the particular lower-level entities that occur ‘within’ it at that particular time, can determine the state of its lower-level entities, etc..
A possible reply to this objection is that the set M includes all possible members of the basis on which M supervenes, and not only the actual set of entities, properties, etc. on which the molecule supervenes at that particular time. If M is understood this way, then the set M suffices for the production of the quantum mechanical change.Footnote 34 However, this would not be equivalent to stating that a molecule at t1 produces quantum mechanical changes on its supervenience basis at t2, but rather that the molecule together with its supervenience basis at t1 produce such changes at t2.
Based on the above analysis, the chemical system at t1 is not nomologically sufficient for the production of the quantum mechanical system at t2. It should be noted that, in the context of Hall’s account, the configurational Hamiltonian and its respective Schrödinger equation cannot be regarded as the higher-level description that supports the nomological sufficiency of the chemical system. The configurational Hamiltonian that is used for formulating the quantum mechanical description of a molecule, is neither a chemical description of that molecule at t1, nor is it based on the application of chemical laws pertaining to the molecule. Indeed, some assumptions and approximations that are used in order to construct the configurational Hamiltonian have been based on the respective chemical description of the system at t1. However, the configurational Hamiltonian is still part of a quantum mechanical description because the entities, properties, etc. that are postulated, as well as the interactions that are described, are found at the quantum mechanical scale.
A possible way out for the supporter of strong emergence is to propose a different notion of causation. This however requires a detailed presentation of how the proposed notion of causation supports the metaphysical claims that (1) the quantum mechanical entities, etc. at t1 do not determine certain aspects of the system’s quantum mechanical behaviour at t2, and also that (2) the chemical entities, etc. at t1 determine certain aspects of the system’s quantum mechanical behaviour at t2.