2.1 Definition

This definition is preliminary and requires clarification on two counts: what is meant by ‘same phenomenon’? And what is meant by ‘different lower-level systems’?

Following that clarification, in §2.2 I articulate what would be required for a reductive explanation of instances of MR which conform to this definition; and in §4 I relate this account of MR to others in the literature.

Phenomena are posited on the basis of experimental data and provide evidence for more general theories. Examples of phenomena include ‘weak neutral currents, the decay of the proton, and chunking and recency effects in human memory’ (Bogen and Woodward, Reference Bogen and Woodward1988, p. 306). Phenomena are individuated by the scientific theory that describes them, thus we may say it's the same phenomenon if it is well described by the same theory in the same conditions.Footnote ³

Importantly for compatibility with multiple realisability, phenomena are not individuated in terms of their realisers.Footnote ⁴ Thus, as discussed below, an entity may be identified as an electrical conductor because it satisfies aspects of circuit theory, but it's not consequently possible to infer its specific constitution. A principal feature of systems instantiating MR is that they may be identified at multiple levels where higher-level identification does not commit us to any specific realisation.

What is meant by ‘different lower-level systems’? Multiply realised phenomena are invariant with respect to certain changes in the lower-level system. I distinguish between two ways a system might be changed.Footnote ⁵ On the one hand, consider varying the particular microstate of a system – i.e. changes which the system might actually undergo. On the other, consider varying the very nature and make-up of the system itself – these are counterlegal or imagined changes.

Phenomena which are invariant with respect to the first kind of change are called ‘robust’ – some phenomenon is robust if and only if it's invariant with respect to changes allowed by the laws or dynamics at the lower level. For example, most thermodynamic phenomena are robust across a wide range of different molecular arrangements, where the molecular laws allow the system to transition from one to another arrangement.Footnote ⁶ The notion of changes allowed by the laws or dynamics is level-relative: when discussing the robustness or multiple realisation of a given phenomenon we (implicitly) specify a higher and lower level of description. Relative to such level-based descriptions a particular precision of description will be appropriate, and the allowed changes will be consequently defined.

Having set aside robustness, we can now refine the definition above:

This distinction will be further exemplified in the next section where I claim that electrical conductivity is multiply realised by, say, lithium and potassium, because no realistic process can convert a strip of lithium into a strip of potassium. On the other hand, the electrical conductivity exhibited by strips of either metal will be robust for a range of different changes: the macroscopic physical properties will be the same even where constituent atoms have moved about.

The aim in making this distinction is to ensure that MR is not absolutely ubiquitous: every higher-level phenomenon is robust with respect to some changes, but MR phenomena are thought to prompt special explananda.Footnote ⁷

Two further comments are relevant. First, non-fundamental levels are generically restricted both temporally and spatially; consequently, changes are nomologically impossible at some level if they happen so rarely that they fall outside the time-scale of that level. Therefore a phenomenon may count as multiply realised by two different systems even where, on sufficiently long time-scales, some set of changes would lead to both systems’ being well described by the same lower-level state. Thus, pressure in a sample of CO₂ gas is robust because there are various different microstates which realise the same pressure, and transitions between those microstates are allowed by the lower-level laws. On the other hand, pressure in gases is multiply realised because both CO₂ and Ne gases may realise the same pressure, but on timescales less than the age of the universe a sample of CO₂ gas cannot change into one of Ne gas.

Second, this distinction will not define a division between robustness and MR which always squares with our intuitions. For example, certain colour changes in metals will be allowed by the lower-level laws or dynamics while others will not; thus, differently coloured metals are, in some instances, trivial but genuine examples of MR. Any way of excluding such boring cases would be arbitrary. As soon as we can explain a given instance of MR, it may count as less surprising, or even boring; but the requirement that MR be surprising would effectively undermine the interesting philosophical and scientific projects of explaining MR – such a stipulation would beg the title question of the paper.

The distinction between MR and robustness is useful: it allows that, while there are genuine instances of MR in the world, not every higher-level phenomenon is multiply realised; however, I do not claim that the distinction is profound. The distinction is nonetheless crucial to those who wish to claim both that MR is instantiated fairly widely, and that it is by definition incompatible with reduction. If those philosophers fail to make this distinction they will have a very difficult case to argue; if all robust phenomena count as multiply realised, and multiply realised phenomena are irreducible, then all robust phenomena will be classed as irreducible. Every phenomenon and every kind term identified in any science is robust with respect to some changes: no phenomenon only exists at, say, a single real-number-valued temperature. The failure of reduction would thus be absolutely generic. As far as I know, such a claim isn't made by advocates of the MR argument, and it would leave their position rather more radical than is commonly acknowledged.

2.2 Explanation and Reduction

A further distinction is worth making at this stage between explanations that refer to MR phenomena, and explanations that tell us how MR is possible. One reason to take MR seriously is that the former kind of explanation is commonplace: many different scientific explanations refer to MR phenomena; that fact leaves it open whether or not explanations of MR are available. My project is non-eliminativist – consequently I think it inadvisable to attempt to purge science of reference to MR phenomena. In other words, I do not purport to replace explanations which refer to MR phenomena, rather I aim to explain why such reference is successful.

With that distinction in hand, there are two more kinds of explanation. First, one may explain a given phenomenon in terms of each of its individual realisers – call this specificity explanation; second, one may explain that the phenomenon is multiply realised in terms of the common features shared by each realiser, and the details which make such common features sufficient for the occurrence of the phenomenon – call this commonality explanation. Specificity explanations do not explain the multiple realisation of the phenomenon, they rather focus on the individual behaviour in each lower-level system; commonality explanations, by contrast, do explain multiple realisation. For example, specificity explanations will explain the particular conductivity of some metal, while commonality explanations will account for the multiple realisation of the conductivity.

This distinction corresponds to that employed by Batterman (Reference Batterman2017, p. 570): ‘There are two kinds of “why-questions” that one might ask about a pattern of [multiply realised] behavior.

• – Type I: One might ask why a particular instance of the pattern was realized.

• – Type II: One might ask why the pattern itself exists across its different realizations’.

It's the second type of question that commonality explanations address – these demonstrate how multiple realisation comes about, not just why some particular phenomenon is instantiated in some particular system.Footnote ⁸

In other words, one has merely restated the fact of multiple realisation if one demonstrates that system A exhibits phenomenon P and system B exhibits phenomenon P etc. As such, any system by system explanation will inevitably fail to address the type II explanandum. In order to explain the multiple realisation of phenomenon P it must be shown that all these systems display the same phenomenon in virtue of something which they share – that's why commonality explanations are required.

The way to offer a commonality explanation is, then, as follows: one explains the common behaviour by identifying an aspect or feature which is shared by the different systems, and one additionally demonstrates that the common features lead to the observed common behaviour in each case. While in some cases this second step may be left out, it is implicitly required.

When MR is instantiated and explicable, its realisers have both commonalities and heterogeneities; so, an explanation of MR must both identify the commonalities and demonstrate that the heterogeneities are irrelevant, in the sense that they do not make a difference to the MR phenomenon. That is, I claim that the only adequate explanations of MR are commonality explanations. Henceforth, all references to explanations of MR carry the implicit assumption that the explanation is a commonality explanation.Footnote ⁹

Now we have a general model for how to explain MR, we ought to ask whether such explanations are reductive: is MR explained from the bottom up?

Insofar as reduction is possible, for any given phenomenon, one may come to understand why it is the way it is from the bottom up. That is, reductions dissolve the explanatory gaps which motivate anti-reductionists. As further discussed in §4.2, I think that standard accounts of reduction, which predict the phenomena for each realiser in turn, only address type I explananda. Type II explananda are those which motivate puzzlement about multiple realisation, and, therefore no reductive explanation of multiple realisation is adequate unless it addresses one of these.

An explanation of a multiply realised phenomenon is, thus, reductive insofar as it explains why that phenomenon is multiply realised with reference solely to lower-level details. The reductive constraint on explanation of MR amounts to the stipulation that the identified commonalities are lower-level commonalities, and that the irrelevance of the heterogeneities is secured by lower-level facts or processes.

Such reductive explanations need not be eliminativist in the sense that the MR phenomena are to be excluded from our ontology once they are explained. In fact, many reductive explanations will establish that the MR phenomenon should be included in our ontology. That's because by identifying the commonalities and the real, physical processes which secure the irrelevance of heterogeneities, we establish that the multiple realisation is not a pure artefact of our descriptive practices. We haven't simply imagined that the phenomenon is multiply realised – we can derive that fact from details of the realising systems. Reductive explanations of MR thus underwrite the value of the unified multiply realised description even while they allow us to understand, from the bottom up, why the multiple realisation obtains.

Note that, at various stages through the process of seeking to explain commonalities, we may acknowledge that the commonality is not in fact out there in the world; that, instead, it's illusory, or that it's a consequence of our epistemic limitations, or an artefact of our organisation of the world; we might also acknowledge that the MR is purely coincidental or a statistical fluke.Footnote ¹⁰ Where any of that happens the demands for explanation, and the prospects for anti-reductionism (in the case that reductive explanation fails) are correspondingly lessened – this overlaps with the debate over scientific realism, and, because of this, will not be further discussed here.Footnote ¹¹

A reductive explanation of MR involves the identification of underlying common features and the demonstration, in lower-level terms, that such features are sufficient for the common behaviour. In the next section this framework for explaining MR is exemplified with a case study.

Note that different processes may be responsible in each realiser for securing the irrelevance of the heterogeneities. It's thus worth emphasising that, while the commonalities are in common, an account of each individual system is, in many cases, required in order to establish that the heterogeneities are irrelevant and, consequently, that the commonalities are sufficient for the MR phenomena to occur.

The upshot of this section is that MR is defined such that it is instantiated in the world and that reductive explanation is possible. I do not claim that all cases of MR can be offered reductive explanations; in my view, that's an empirically sensitive question, and reduction is hard! The advantage of my framework is that that question can be addressed, and, especially in mature sciences, reductive explanations of MR can be provided.

4.1 MR is Essentially Inexplicable

Some might object to my claim that MR can be reductively explained because they hold MR to be inexplicable by commonality explanations as a matter of conceptual necessity. As argued above and further developed in §4.2, commonality explanations are the only way to provide explanations of multiple realisation.

In this section I argue that it is a mistake to define MR as essentially inexplicable: the issues at stake in this paper ought to be settled by empirical investigation – facts about the world make it such that particular cases of MR are explicable and reducible, or not.

I resist the conflation of MR with inexplicability and irreducibility and argue that whether or not a phenomenon is MR is, at least to some extent, independent of whether or not it can be reductively explained. A major reason to maintain this distinction is that we may identify and discuss MR phenomena without thereby committing ourselves to an account of reductive explanation. Therefore by resisting the conflation we conserve a term for the interesting fact that various phenomena exhibit the confluence of commonality and heterogeneity which corresponds to MR. Whatever one's standards for reduction, it should be acknowledged that instances of MR still pose interesting and important explananda for scientific research.

Maintaining the distinction between inexplicability and MR allows reductionists and anti-reductionists alike to acknowledge that some phenomena are multiply realised, that these pose a challenge for reductive explanation, but that that challenge may not be insuperable. Whether or not the challenge can, in fact, be overcome is then to be decided on a case by case basis rather than in principle.

Polger and Shapiro (see their (Reference Polger and Shapiro2016); Shapiro (Reference Shapiro2018), and references therein) have done a great deal of work to demonstrate that, for various putative instances of MR, the realisers in fact share common causal structure. There is, thus, a sense in which their project can be construed as providing reductive explanations of MR. However, they are committed to the conflation just outlined. That is, they argue that putative cases of MR ought not to count as such insofar as they can be reductively explained by commonality explanations.

According to Shapiro (Reference Shapiro2000, p. 646):

Shapiro goes on to argue that MR is in fact rather rare, because in many putative instances of MR the two realisations don't differ with respect to causally relevant properties, they rather differ with respect to their causally irrelevant properties. For example, given the analysis in the previous section, his account implies that one ought not to say that the kind electrical conductor is multiply realised simply in virtue of the fact that both lithium and potassium conduct electricity. This is because the features which distinguish lithium from potassium might be claimed to be causally irrelevant to individuation qua electrical conductor.

This view is defended by Polger and Shapiro (Reference Polger and Shapiro2016) who consider a range of neurological case studies that have been described as instances of MR. They suggest that in almost all such cases the causal process which gives rise to the putatively multiply realised kind is identical.Footnote ¹⁵ For them, in order to qualify as MR, the relevant causal structure must be different.

While Polger and Shapiro have done significant and important work in bringing empirical considerations to bear on discussions of MR, it's unfortunate that they are committed to this account of MR. Not only does it make MR essentially inexplicable by commonality explanations (because such explanations would mean it no longer counted as MR), but it also undermines an important scientific project: that of accounting for how it is that there are so many instances of higher-level phenomena realised by multiple systems distinct at the lower level.Footnote ¹⁶ Important work in countering this aspect of Polger and Shapiro's project has been carried out by Aizawa and Gillett (see e.g. Aizawa and Gillett (Reference Aizawa, Gillett and Bickle2009)), who argue that multiple realisation is pervasive in the natural world, and provide a partial explanation of that fact for some biological systems. In addition, Aizawa (Reference Aizawa2013) also offers an explanation of the pervasiveness of MR in some physical systems.

Thus, my framework in §2.2 may be used to interpret aspects of Gillett and Aizawa's work as offering commonality explanations of MR.Footnote ¹⁷ However, their account is not explicitly targeted at reductive explanations of MR, and they do not discuss the type II explanandum. Consequently, their account is, in general, insufficient to address the anti-reductionists’ worries about MR, though that is not their explicit target.Footnote ¹⁸

In this paper, I show how a general framework for reductive explanation is compatible with MR, and that, once one recognises this fact, one can engage with the interesting project of identifying cases of MR, and assessing whether or not these can be reductively explained. Some of the explanations offered by Aizawa and Gillett fit into this framework and may be used to offer reductive explanations of certain instances of MR phenomena.

Polger and Shapiro differ from me, and from Aizawa and Gillett, in their account of multiple realisation. In my opinion, they err in claiming that once common causal structure has been identified, the phenomena in question should no longer count as multiply realised. If one were to accept Polger and Shapiro's analysis, one would be committed to categorising putative cases of MR as either inexplicable, or not multiply realised. By resisting the conflation, the category of MR-but-explicable is maintained and the interesting scientific explanations of how multiple realisation comes about are viable. In other words: once we accept that MR is reductively explicable in principle, we can engage in the framework laid out above which asks whether, in practice, particular instances of MR can be reductively explained.

On the account defended here, it's a discovered fact about the world that there are many phenomena which are identified independently of their realisation and are instantiated in multiple different kinds of system. Failing to acknowledge this as an explanandum would be to sidestep the substantial challenge to reduction which MR (or putative MR) poses; this line of reasoning is further defended in §4.2.

On my view, multiple realisation is fairly commonplace, but can be explained. Polger and Shapiro's view is that it's much rarer but can't be explained. In Polger and Shapiro (Reference Polger and Shapiro2016, p. 39), they defend their view by claiming that a more liberal view ‘entails an undesirable profligacy of distinct realizations for every kind, and undermines the significance of realization within debates over the autonomy of the special sciences’. While I agree that just any lower-level variation is insufficient for MR, I think that the MR-robustness distinction drawn above in §2 rules out ‘undesirable profligacy’. On the other hand, regarding autonomy, I'd argue that the autonomy of the special sciences is, in fact, closely related to multiple realisation as I define it: as Polger and Shapiro acknowledge (ibid., chapter 10.4), a system has some claim to autonomy if it provides for prediction and explanation at the higher level. Insofar as such autonomy can be explained, the threat to reduction is mitigated, but the debate over such cases is only confused by claiming that autonomy, or indeed MR, is rare but mysterious.

Lastly, even if Polger and Shapiro's approach is taken to provide an explanation of MR, their explanatory strategy is somewhat lacking. That's because, while they rightly emphasise the importance of demonstrating what's in common between the realisers,Footnote ¹⁹ they do not require that we also demonstrate that the heterogeneous features are irrelevant; and it is precisely this extra step that is required to dispel the apparent mystery that different systems exhibit common behaviour.

It's the very fact that different systems act similarly which is so remarkable – that's what motivates Fodor (Reference Fodor1974) in his discussion of the multiple realisation of currency and Putnam (Reference Putnam1975) in his discussion of the multiple realisation of square and round pegs. That there is MR is a consequence of the fact that genuinely different systems do, in some circumstances, exhibit identical phenomena notwithstanding their differences. MR is thus explained by showing both that such systems have features in common, and that, in those circumstances, their differences are irrelevant. By failing to offer explanations of this form, those who conflate inexplicability with MR cannot adequately respond to the anti-reductionist's challenge.

In part, my commitment to the distinction between MR and inexplicability stems from analysis of case studies from physics. In this context, we have phenomena which are quantitatively identical across a range of different systems; therefore there is good reason to think that multiple realisation is not an artefact of our classificatory practices. Examination of cases from physics also helps establish that reductive explanations of multiple realisation are the subject of active scientific inquiry.

The examination of case studies from the physical sciences is particularly helpful in these fraught philosophical discussions. Cases drawn from the biological sciences are far more complex and, consequently, reductive explanation is harder to come by. Therefore, in such contexts it's difficult to distinguish whether the source of apparent irreducibility is multiple realisation, or some other feature of the target system. Physics examples are, in general, more susceptible to reductive explanation, and the MR challenge can, thus, be assessed independently of confounding factors. However, the discussion in the philosophy of physics literature has led to a different objection to an approach like my own.

4.2 Commonality Explanations of MR are Anti-reductionist

I claimed in §2.2 that specificity explanations of MR phenomena are inadequate to address the MR explanandum. Once we have a reductive explanation for why lithium is a good electrical conductor, and why sodium is a good electrical conductor we still have an explanatory demand: what common feature of group I metals leads to the phenomenon that they all conduct electricity? Where the same phenomenon is observed in all these different systems we have multiple realisation and thus we have an explanandum for which the reductionist ought to be able to provide a reductive explanation.

Some might argue that no reductive explanation could address such explananda. For example, Batterman's view (e.g. (Reference Batterman2000; Reference Robert W2018)) is that there is MR, and that it can be explained, but that MR can only be explained anti-reductionistically.Footnote ²⁰ Consequently he denies the potential for the kind of reductive explanatory strategy outlined above. An important insight due to Batterman, on which I build in this paper, is that the MR explanandum requires a sui generis explanatory strategy. While I have argued that carrying out such a strategy can provide evidence for reduction, and Batterman disagrees, I follow him in claiming that once one acknowledges that there is MR in the world, a novel explanandum follows.

It's particularly worth highlighting this set of claims due to Batterman because they serve to undermine the explanatory pluralism advocated by Sober (Reference Sober1999):

Sober argues that multiple realisation need not trouble the reductionist. He does so by observing that different kinds of explanation are useful or applicable to different ends. He observes that adding content to an explanation does not stop its being an explanation and that reductions – which offer bottom-up explanations – will generally be of interest even if the higher-level explanations are adequate in some contexts.

Sober's arguments are well-taken: it's certainly the case that proportionate higher-level explanations are often superior qua explanations of higher-level explananda. However, not just any kind of explanation is adequate to explain MR. Given that Sober is talking about multiple realisation and explanatory approaches thereto, it seems fair to say that he has missed the anti-reductionist's point. This observation is emphasised by Batterman (Reference Robert W2018; Reference Batterman2000), who identifies an explanandum which is missed by many reductionists:Footnote ²¹

I agree with Batterman that standard reductionist approaches miss the MR explananda.Footnote ²² The question labelled MR prompts us to look at the distinct realisers of multiply realised phenomena and ask why all of these different underlying systems realise the same higher-level phenomenon. Batterman counters Sober's explanatory pluralism by arguing that, in certain cases, answers to MR are incompatible with reduction. He claims that universality is multiple realisation and that the full explanation of universality necessarily proceeds at the higher level. Batterman's contention is that lower-level and higher-level explanations are not equally adequate for understanding cases of MR. In fact, specifically for certain such cases the higher-level (or multi-level) explanations are the only ones which are able to address the principal explanandum.Footnote ²³

While I disagree with Batterman's anti-reductionist conclusion, I accept his more general assertion: that it's not good enough simply to say, as Sober does, that different explanations are good for different ends. The different descriptions and explanations of electrical conductivity – some in terms of abstracted circuit theory, and others in terms of the microscopic details of each metal – do not lead to an answer to MR. And it is that question which really provides the motivation for the anti-reductionist. Sober's pluralism is inadequate to refute the assertion that multiple realisation is inexplicable from the bottom up.

I have argued in this paper that MR may nonetheless be answered reductively. That is, I claim that, if we adduce the commonalities among lower-level realisers and identify the lower-level processes which make the heterogeneities irrelevant to the common behaviour, then we have provided a reductive explanation of MR. Therefore the anti-reductionist's motivations may be addressed, and the compatibility of MR with reduction may be established. MR poses an explanandum which requires a sui generis explanation; it's just that reductive explanations of MR are available.