2.1 From Logical Empiricism to Nagelian Reduction

Unity of science was a driving ideal in the logical empiricist tradition. It was closely tied to reductionism and an anti-metaphysical attitude, so the relevant sense of unity was primarily following the epistemic/pragmatic model of unity with a semantic focus on the language of science, but it may be considered to have had an implicit ontological element as well. The resulting picture is a combination of eliminative semantic unity and reductive ontological unity. We can see all these elements in Carnap’s (e.g., Reference Carnap1928, Reference Carnap1934) work, and indeed in his formulation of unity in the book entitled The Unity of Science: ‘all empirical statements can be expressed in a single language, all states of affairs are of one kind and are known by the same method’ (Reference CarnapCarnap 1934: 32).

While this formulation focuses on semantic and epistemic unity, it certainly suggests an ontological commitment to states of affairs of just one kind as well. However, I will omit an analysis of Carnap’s metaphilosophical position (for a related discussion, see Reference TahkoTahko 2015a). The important feature here is the apparently anti-metaphysical background, which meant that unity of science was conceived as an epistemological and methodological project attempting to establish that all higher-level, special science statements, predicates, and explanations are reducible into those of physics. The implicit ontological import would then be that all entities also reduce to those of physics. These ideas were clearly present in Carnap’s work. But instead of focusing on the well-reached history of the logical empiricist position and details of the work of its main architects, such as Carnap, we can directly jump to two of the core elements regarding the development of the logical empiricist tradition towards a systematic model of reduction and unity.

These two core elements are Reference HempelHempel’s (1942; Reference Hempel and Oppenheim.Hempel and Oppenheim 1948; Reference HempelHempel 1965) deductive-nomological (DN) model of explanation and Reference NagelNagel’s (1961) account of reduction. Both of these elements focus on explanatory connections. In brief, the DN model involves an explanandum, a sentence that describes the phenomenon we wish to explain, and an explanans, which is a class of sentences providing the explanation for the phenomenon. The deductive part of the model concerns the requirement that the explanandum must follow from the explanans by logical consequence. The nomological (i.e., ‘law-like’) part refers to the requirement that the explanans must contain at least one law of nature, and without it the deductive inference would not be valid. For example, take the universal generalisation that ‘all gases expand when heated under constant pressure’ (Reference HempelHempel 1965: 338), which may be regarded as a law. According to the DN model, we can use this law and the fact that a given sample of gas has been heated under constant pressure to explain why the sample of gas has expanded.

Now let us connect the DN model with Nagelian reduction. Here is a representative passage from Nagel himself: ‘A reduction is effected when the experimental laws of the secondary science…are shown to be the logical consequences of the theoretical assumptions (inclusive of the coordinating definitions) of the primary science’ (Reference NagelNagel 1961: 352). The basic form of a Nagelian reduction suggests that theory A reduces to theory B if and only if A is derivable from B with the help of any necessary ‘coordinating definitions’, which are more commonly known as bridge laws or bridge principles; these bridge laws can take the form of logical connections, conventions, or empirical hypotheses (Reference Nagel1961: 354). It is not difficult to see that the DN model and Nagelian reduction are closely connected. In effect, the Nagelian model suggests that the reducing theory explains the reduced theory (with the help of bridge laws).

The DN model and Nagelian reduction dominated the philosophy of science for a time, but they did also come under heavy criticism (see, e.g., Reference van Rielvan Riel 2014). We will not need to provide these details here, but it is important that we understand the sense of unity that emerges from this background: the upshot is that all higher-level science explanations ultimately collapse into those of physics. But while the DN model and Nagelian reduction both operate at the epistemic level of explanation, there does seem to be an implicit ontological commitment to the idea that all entities reduce to (fundamental) physical entities. However, the difference between these two aspects needs to be clarified. In Reference Oppenheim and PutnamOppenheim and Putnam (1958), which is the subject of the next section, we can find a clearer statement of the ontological view.

2.2 Oppenheim and Putnam on the Unity of Science

Reference Oppenheim and PutnamOppenheim and Putnam (1958) distinguish three different unity theses:

• Unity of language (epistemological reduction)

• Unity of laws (implies the unity of language)

• Unity of science (in the strongest sense, implies unity of laws and unity within a science)

Unity of language is described as the idea that all terms of science are reduced to one discipline, such as physics, whereby ‘reduction’ would most plausibly be understood definitionally. This would result in a type of epistemological reduction, where all the claims of the special sciences could, at least in principle, be translated into claims of some more fundamental science. It is worth taking a moment to pause and think what this would mean, if true. It would mean that the vocabulary used in the special sciences – terms such as covalent bond, cell wall, neuron, memory, and so on, could ultimately be replaced by ones of a unified science. The idea could be understood as semantically eliminative, in that all this higher-order vocabulary could be eliminated in favour of the language of, say, fundamental physics. But even if we could eliminate all higher-level language, it is a rather radical claim to say that we would do so. There are individual cases where this has happened, though. To provide just one example, the now thoroughly abandoned idea of vitalism suggested that there is something fundamentally different about living organisms – namely, they are non-mechanical, containing an ‘élan vital’ or vital force that gives life to inanimate material bodies. The theory of vitalism involved a sophisticated theory, but the notions employed by that theory, such as that of a vital force, have been completely eliminated by contemporary science. By the late nineteenth century, the experimental progress of developmental biology and emerging modern biochemistry, combined with the lack of any experimental support for vitalism, made it clear that vitalism has no future (see Reference GathererGatherer 2010 for a short history of vitalism). However, it should be noted that a plausible understanding of the unity of language should not entail full elimination of all higher-order vocabulary. Even if it were possible in principle to eliminate such vocabulary, it would surely be difficult – for instance, we do still talk about ‘life’ in a rather abstract fashion. Hence, there is room for non-eliminative semantic disunity.

Unity of laws, as defined by Oppenheim and Putnam, is a stronger thesis than unity of language. The thought is that all the scientific laws could be reduced to the laws of one unified science. On the face of it, unity of laws seems to be a more interesting thesis, as it does not focus on the individual terms used in science (albeit Oppenheim and Putnam do take it to imply unity of language). The precise meaning of ‘reduction’ is left open by Oppenheim and Putnam and I will do the same for the time being, but it appears that here we are moving towards an ontological model of unity. I will shortly discuss an example, but it may be helpful to do so in the context of the strongest sense of unity of science that Oppenheim and Putnam entertain, as it explicitly mentions also the connections within a discipline: ‘Unity of Science in the strongest sense is realized if the laws of science are not only reduced to the laws of some one discipline, but the laws of that discipline are in some intuitive sense “unified” or “connected”’ (Reference Oppenheim and PutnamOppenheim and Putnam 1958: 4).

They specify immediately that the required ‘connection’ between the laws should be something stronger than the mere conjunction of these laws. What might qualify as this type of unification? A plausible candidate is provided by electroweak unification – the successful effort to unify two of the fundamental forces (and hence the laws concerning them), the weak force and the electromagnetic force. In fact, the electromagnetic force itself already unifies two apparently distinct forces – namely, the electric force between charges which is governed by Coulomb’s law and the magnetic force. The Lorentz force law summarises both of these forces.

The unification of the weak and electromagnetic interaction is rather more complicated, as it involves further exchange particles, namely the W and Z bosons that are involved in weak interaction. Indeed, it was the prediction and discovery of the W and Z particles and the resulting unification of the weak and electromagnetic interaction that led to the 1979 Nobel Prize in physics being awarded to Weinberg, Salam, and Glashow. The press release announcing the award serves to highlight just how deeply ingrained the search for unity in science is:

As the press release makes clear, a key part of the unification of the weak and electromagnetic forces are the shared properties of the exchange particles. The next step is to explain the primary difference, which has to do with mass. The story continues with electroweak symmetry breaking, and the more recent discovery of the Higgs boson, but we need not enter these complications. What should already be clear is that the search for unity is one of the key values of scientific inquiry, and indeed of the Nobel Committee, and there are many celebrated examples of this in the history of science. No wonder, then, that Oppenheim and Putnam attempted to systematise this idea.

We have so far omitted one important detail: when we speak of unification in science or discuss cases such as the unification of the weak and electromagnetic forces, it is not obvious that we are talking about ‘unity’ in the same sense that Oppenheim and Putnam or contemporary philosophers always intend. There is clearly something in common with these cases, which is why I have used electroweak unification as an example of how the laws of physics might be ‘connected’ in the sense that Oppenheim and Putnam require. But we should keep in mind the distinction between ontological models of unity and epistemic/pragmatic models of unity. In particular, the case I have just described could be understood in the sense of theoretical unity (or unity of formalism), so we should consider this form of unity in more detail.

The idea behind theoretical unity is simply that we may discover a formal (mathematical) framework, which manages to approximately model a certain set of distinct phenomena. For a given purpose, it may be sufficient to use a simple unified formalism. To continue our previous example, consider the role of the electromagnetic force in holding together atoms and molecules. The electromagnetic force is by far the most significant force in determining atomic and molecular structure. It has an infinite range, just like gravity, but given the extremely small masses of particles in the atomic scale, gravity is negligible. The strong force, by contrast, is very strong indeed, but its range is very short – it holds the nucleus together. The weak force has an even shorter range, 0.1% of the diameter of a proton. If we are interested in the molecular range, it is really just the electromagnetic force that matters. So, for most calculations that we might wish to make concerning the molecular scale, it is entirely unnecessary to consider gravity, even though gravity is in effect at all scales. Thus theoretical unity has an element of interest relativeness, which is useful and even necessary for science, but it is not the type of ontological unity that some philosophers may be interested in.Footnote ⁴

In contrast, ontological models of unity concern the structure of reality rather than the structure of theories. Yet, so far, we have not specified a properly ontological as opposed to epistemological sense of reduction that might underlie such unity. Let us turn back to Oppenheim and Putnam, who also state that they wish to set aside epistemological versions of the unity thesis (cf. Reference Oppenheim and PutnamOppenheim and Putnam 1958: 5). Relying on previous work by Reference Kemeny and OppenheimKemeny and Oppenheim (1956), they take reduction to be a relation between theories. This may not quite capture the sense of ontological unity that I have just been alluding to, but we should not be misled by this, for Oppenheim and Putnam do specify that a key part of reduction is that a set of observational data explainable by one theory is explainable by the reducing theory. This explanatory connection, we may assume, is supposed to track the ontological relation between the phenomena that the theories describe. What is that relation? Oppenheim and Putnam call it micro-reduction. As they specify, this relation concerns the objects or entities that theories deal with, so it is ontological rather than epistemological in the intended sense.

The idea of micro-reduction is something that survives in contemporary philosophy (under different labels), so it is useful to consider it in some detail (cf. microstructural essentialism, which we will return to later; see also Reference TahkoTahko 2015b). Micro-reduction is transitive, irreflexive, and asymmetric. As Reference Oppenheim and PutnamPutnam and Oppenheim (1958: 7) observe, the transitivity of the relation is of particular importance since it establishes a hierarchy of reductive levels. The thought is that there must be more than one such level (rather than a ‘flat’ one-level reality), there is a unique lowest level (such as fundamental physics), and a common denominator for each level (any thing on one level, except for the fundamental one, must be composed of parts on the level immediately below it). In practice, this means that if psychology reduces to neuroscience and neuroscience to biochemistry, then in virtue of transitivity, psychology will also reduce to biochemistry. This strict hierarchical structure may seem controversial because sometimes it does seem that we have to consider two levels at more extreme ends. For instance, the field of quantum biology applies results from quantum mechanics directly to the realm of biological entities. But Oppenheim and Putnam insist that we better not ‘skip’ any levels in this process, say, by trying to explain psychology in terms of subatomic physics, as this would indeed be ‘fantastic’ (ibid.). We now arrive at Oppenheim and Putnam’s proposed account of the levels of science, represented by the pyramid in Figure 2.

Figure 2 A system of reductive levels (author’s own work)

Notice that a key idea driving reduction in Figure 2 seems to be a simple parthood or composition relation: social groups are composed of living things, which are composed of cells, which are composed of molecules, and so on. This is a type of ‘building blocks’ conception of nature that has survived a long time in philosophy and still enjoys support, e.g., in the form of a commitment to a fundamental compositional level (see Reference TahkoTahko 2018 for discussion). Note, however, that a commitment to a fundamental level does not by itself entail such a conception – for one thing, there could be just one level, in which case the ‘building blocks’ idea would not be a good fit. Moreover, if the various levels of entities in Figure 2 are thought to be genuinely existing, then the model at hand would be compatible with non-reductive ontological disunity, while eliminating the higher-level entities in favour of a singular level of elementary particles would entail reductive ontological unity.

The result, then, is a hierarchical picture of the levels of reality which is really driven by just one relation – namely, the parthood or composition relation. This is effectively what the idea of micro-reduction amounts to on the Oppenheim-Putnam line. However, it is worth keeping in mind that Oppenheim and Putnam did not claim (and presumably would not claim even now, more than sixty years later) that we already possess the tools to perform this type of micro-reduction. Rather, ‘[t]he assumption that unitary science can be attained through cumulative micro-reduction recommends itself as a working hypothesis’ (Reference Oppenheim and PutnamOppenheim and Putnam 1958: 8). By a ‘working hypothesis’, they mean that this idea should be justified on empirical grounds, if and when we are able to establish this type of reduction. They go on to support this idea (Reference Oppenheim and Putnam1958: 12ff.) in terms of theoretical virtues such as the simplicity of the hypothesis and the variety and reliability of the evidence in favour of it from the various sciences and successful inter-theoretic reductions. They also put forward case studies from each of the levels. Among the more famous case studies, partly because it was later picked up by Fodor, is the case of Gresham’s law in economics.

Gresham’s law, which states that bad money drives out good, can be illustrated with a simple example. In this example, ‘good’ money is money, such as gold coins, where the nominal value (the face value) of the coin is equal or close to equal to the value of the metal it is made of (the commodity value), in this case gold. ‘Bad’ money, on the other hand, is money which has a higher nominal value than commodity value. So, Gresham’s law states that when ‘bad’ money is circulating along with ‘good’ money of the same nominal value, it tends to drive out the ‘good’ money, since the higher commodity value of the ‘good’ money is an incentive to hold on to it. A consequence of this law was the practice of debasement, which could unlawfully be done by the public – for example, by scraping off small portions of gold from gold coins, while the coin retains its nominal value. The reeded edges on coins, still present in many modern-day coins (such as the two-euro coin), were intended to make this practice evident and hence allow the recipient to deny a payment in such ‘bad’ money.

Oppenheim and Putnam suggest that we can analyse cases such as Gresham’s law in terms of individual choices, where these choices are ordered by means of an ‘individual preference function’ (Reference Oppenheim and Putnam1958: 17). Economists can then attempt to explain the behaviour of social groups and the market in terms of these functions. Indeed, Gresham’s law does seem to simply confirm the individual preference to maximise profit: if you can pay for the same commodity with one of two coins of equal face value, then it makes sense to choose the coin with a lower commodity value. So, Oppenheim and Putnam take this to be a successful case of explaining a ‘law’ of economics in terms of a psychological ‘law’. But it is less clear how we can account for this individual preference in terms of its composite parts at a lower level – presumably the cellular level of neurons – as the micro-reductive account would ultimately require. Even putting this worry aside, there is an important caveat, one that later led Putnam to give up the reductionist account. This caveat concerns the phenomenon of multiple realisability: many higher-level things or phenomena can be realised by two or more lower-level things.

2.3 Fodor on Multiple Realisability and the Disunity of Science

Jerry Fodor, in two very influential papers (Reference Fodor1974, Reference Fodor1997), argues against a strong form of reductionism and in favour of the autonomy of the special sciences. The first of these papers reacts against the traditional Nagelian model of reaction described in Section 2.1, while the second addresses a rejoinder to Fodor’s original paper by Jaegwon Reference KimKim (1992). There are two important methodological points to note about this line of discussion that began in the seventies.Footnote ⁵ First, very much unlike the logical empiricist tradition or Oppenheim and Putnam’s traditional discussion, this new literature was concerned with metaphysics of science (even though this notion was not used): the focus is on notions of natural kind, property, realisation, and so on. These are metaphysical notions that rarely feature directly in scientific theories, and we will discuss their role in more detail later on. Second, despite the import from metaphysics of science, there is in fact a much closer interest to actual scientific case studies – a trend that we see continuing in contemporary metaphysics of science. The latter methodological point is especially striking, given the supposed scientific rigour of the logical empiricist tradition.

Fodor, in fact, starts by noting that the trend toward reductionism in philosophy of science (at that point in the seventies), while driven by scientific successes, is not thoroughly explained by it. Instead, Fodor thinks that many proponents of reductionism are motivated by the relative generality of physics when compared to the special sciences. But he thinks that this idea of the generality of physics should be separated from a stronger sense of ‘the unity of science’:

The thought that the special sciences ought to disappear as they succeed is indeed a rather strong doctrine. It reflects the strong reductionism of logical empiricism and it may or may not be the case that Oppenheim and Putnam were committed to something as strong as this, but such a view is certainly not very popular today, even among those who would call themselves reductionists (Reference RosenbergRosenberg 1994, e.g., may be an exception). So, Fodor’s target is a very strong sense of unity, and so is his understanding of reduction. He characterises it in terms of bridge laws, where predicates of the reducing and reduced science are connected via an identity relation – for example, every event which consists of x’s satisfying some neurological predicate S₁ is identical to some event which consists of x’s satisfying some biochemical predicate S₂ and vice versa (cf. Reference FodorFodor 1974: 100). The resulting picture looks like a combination of reductive ontological unity and eliminative semantic unity.

Let us return to Gresham’s law. One of Fodor’s central points is that not every natural kind corresponds to a physical natural kind. The notion of a ‘natural kind’ is here interpreted very liberally: it is a general term that captures something that is in common among the instances of a kind. We will return to the interpretation of natural kinds in much more detail in Section 3. So, monetary exchanges, which are what Gresham’s law concerns, could be regarded as a natural kind insofar as there is something in common among its various instances. Fodor (ibid., 103; original emphasis) states the following: ‘I am willing to believe that physics is general in the sense that it implies that any event which consists of a monetary exchange (hence any event which falls under Gresham’s law) has a true description in the vocabulary of physics and in virtue of which it falls under the laws of physics.’ But Fodor then points out that since monetary exchanges are realised by a vast variety of different realisers (not just euro coins but also dollar bills, cheques, and ‘strings of wampum’), the events being covered by the reducing science would have to be ‘wildly disjunctive’. The worry is that any disjunctive physical predicate that would be able to cover all these instances of monetary exchanges would not express a physical natural kind (and would not feature in laws of physics). Yet monetary exchanges presumably have something interesting in common despite the variety of different realisers. So, Fodor’s point is that there are other, higher-level natural kinds in addition to physical kinds: ‘A natural kind like a monetary exchange could turn out to be co-extensive with a physical natural kind; but if it did, that would be an accident on a cosmic scale’ (Reference FodorFodor 1974: 104). The upshot, according to Fodor, is that economics is not reducible to physics and hence there is no unity of science.

We have now arrived at a key turning point in the history of reductionism and indeed the search for a unity of science. Even though Fodor did not yet use the notion of multiple realisation in his Reference Fodor1974 paper, this is clearly the idea behind the ‘wildly disjunctive’ realisers of monetary exchanges. But in fact, Putnam had already discussed the idea of multiple realisation in the late sixties (Reference Putnam, Capitan and MerrillPutnam 1967). Reference FodorFodor (1974: 105) mentions Putnam’s ideas, but does not cite his work (indeed, he cites only Chomsky besides himself!). A little later in the paper (ibid., 108), he specifies that there is ‘an open empirical possibility’ that the realisers of a supposedly reducible higher-level natural kind predicate could turn out to be ‘a heterogeneous and unsystematic disjunction of predicates in the reducing science, and we do not want the unity of science to be prejudiced by this possibility’. Fodor’s focus on predicates is problematic though, for why should we think that any (or all) predicates of the special sciences should correspond to genuine natural kinds? Indeed, we should not think so, any more than we should think that Nelson Goodman’s famous predicate ‘grue’, which applies to all things examined before some future time t if and only if they are green but to other things observed at t or after it if and only if they are blue.

Of course, ‘grue’ is a perfectly legitimate predicate, and we can imagine that such a made-up predicate could have some use in a specific scenario. Yet there is no reason whatsoever to suppose that there should be a physical natural kind predicate that corresponds to ‘grue’. As we shall see, it is thus better to focus on properties rather than predicates, in order to avoid the clearly conventional elements associated with predicates. I take this to be a serious flaw in Fodor’s original criticism of reductionism. He concludes his Reference Fodor1974 criticism of strong reductionism by saying that it is not ‘required that taxonomies which the special sciences employ must themselves reduce to the taxonomy of physics’ (ibid., 114). But this is something that a friend of reductive ontological unity can agree with: ontological reduction does not concern the taxonomy of the special sciences. In other words, reductive ontological unity is compatible with non-eliminative semantic disunity. Admittedly, the strong version of reductionism originally pushed by the logical empiricists in the form of eliminative semantic unity does entail eliminativism regarding higher-level taxonomy, and this is Fodor’s main target, but it would be a mistake to regard the unity of science quite generally to be hostage to the unity of taxonomy.

2.4 Kim versus Fodor on Jade

Moving on to the next stage of the debate, we should take a closer look at Jaegwon Kim’s famous discussion of multiple realisation concerning the case of jade, along with Fodor’s reply to this case. This example was originally introduced by Reference PutnamPutnam (1975: 241), although for a slightly different purpose. Kim summarises the case as follows: ‘[W]e are told that jade, as it turns out, is not a mineral kind, contrary to what was once believed; rather, jade is comprised of two distinct minerals with dissimilar molecular structures, jadeite and nephrite’ (Reference Kim1992: 11). He then introduces a supposed special science law stating that jade is green and divides that into a conjunctive law, whereby jadeite is green and nephrite is green. Here, ‘jade’ is of course supposed to refer to a higher-level natural kind. But Kim, favouring reductionism, thinks that the special science law in question is not a genuine law, despite having the basic form of a law and being able to support counterfactuals. This is because the law is not projectible – it does not have ‘the ability to be confirmed by observation of positive instances’ (ibid.). Kim’s case in favour of this conclusion is the possibility that we only encounter one or the other of the realisers of jade when trying to confirm the law stating that jade is green. This would only support the projectibility of either jadeite or nephrite being green. The upshot, according to Kim, is that jade is a ‘true disjunctive kind’ (Reference KimKim 1992: 12).

Now we get to Kim’s famous challenge for Fodor: he argues that special science laws concerning ‘wildly disjunctive’ higher-level kinds are not genuine laws, because they do not deal with genuine natural kinds. They can be reduced to laws concerning lower-level kinds. But Fodor’s reply to this challenge is also forceful; he denies that jade is paradigmatically multiply realisable in the first place and, further, claims that the scenario Kim describes is just based on a sampling error. However, Fodor does admit that jade is a true disjunctive kind; what he denies is that this is the same thing as being disjunctively realised: ‘Jade is disjunctive because the only metaphysically possible worlds for jade are the ones which contain either [jadeite], or [nephrite] or both. By contrast, multiply based properties that are disjunctively realized have different bases in different worlds. Pain is disjunctively realized because there’s a metaphysically possible, nonactual, world in which there are silicon based pains’ (Reference FodorFodor 1997: 153).

For Fodor, the case of jade is not a genuine case of disjunctive realisation, so he agrees with Kim that it is not projectible in the required sense. Moreover, the disjunction is ‘closed’ in that in all cases we are dealing with either jadeite or nephrite, and there are no further candidates. This constitutes a case in favour of abandoning the special science law concerning jade and replacing it with lower-level laws concerning jadeite and nephrite. But if we are dealing with an ‘open’ disjunction, then there are metaphysically possible worlds in which a property has realisers that it does not have in the actual world – only this type of case counts as genuine multiple realisation for Fodor (Reference FodorFodor 1997: 156). So, the corresponding lower-level laws would also have to be open, and Fodor insists that ‘if there is a higher level property that subsumes all the disjuncts of an open disjunction, then we will want to state our laws in terms of it’ (ibid., 158).

The idea behind Fodor’s open/closed distinction is, I take it, to postulate higher-level kinds in order to get the desirable closed laws back, unless we can point to closed lower-level laws. Fodor’s claim, then, is that while the case of jade is closed, the case of pain (or other genuinely disjunctively realised functional kinds – kinds which are defined in terms of what they do) may be open and hence justify postulating higher-level kinds. Fodor summarises this idea with the following principle that he takes to govern our inductive practises: ‘Prefer the strongest claim compatible with the evidence, all else equal. Quantification over instances is one aspect of rational compliance with this injunction; reification of high level kinds is another’ (Reference FodorFodor 1997: 159).

One thing that is striking about this debate is just how little scientific detail it involves, especially when the key argument is supposed to be that it is science that gives us the criteria according to which we ought to judge higher-level kinds. This is particularly ironic since Kim and Fodor supposedly agree about the case of jade. What they do not seem to realise is that jadeite and nephrite, the supposed realisers of jade, are themselves higher-level kinds. In fact, Reference FodorFodor (1997: 154) makes a passing appeal to the commonly accepted Kripke-Putnam framework of microstructural essentialism, stating that jade’s being jadeite or nephrite is metaphysically necessary, just like it is metaphysically necessary that water is H₂O. According to this framework, kinds are defined in terms of their microstructural essence. That’s how Fodor arrives at the judgement that jade is not a genuinely disjunctively realised kind. But this goes against Reference KimKim (1992: 24), who suggests that jade is to be defined in terms of its macrophysical properties.

Fodor may think that his modal intuitions ‘are pretty clearly the right ones to have’ (Reference FodorFodor 1997), but it has been clear at least since Jaap Reference van Brakelvan Brakel’s (1986) work (see also Reference VanDeWallVandeWall 2007) – over a decade before Fodor’s snarky remark – that even the usual microstructural story about water is seriously wanting.Footnote ⁶ In particular, to arrive at the result that the case of jade is closed in Fodor’s sense, we must rely on the controversial assumption that the macrophysical properties of jade are irrelevant. This is the upshot of Fodor’s speculative scenario where someone recreates the macrophysical properties of jade from melted bottle glass. Fodor insists (based on the ‘pretty clearly right’ modal intuitions) that the result would not be jade. But this already assumes that the higher-level kind jade is genuine and to be defined in terms of the traditional microstructuralist story. Rather than take this assumption for granted, we would do well to consider what we know about jadeite and nephrite.

We know that jadeite and nephrite share many of their chemical properties yet differ in terms of microstructure. Jadeite and nephrite are not exactly identical in terms of their chemical properties. Jadeite (NaAlSi₂O₆) is somewhat harder and less prone to scratches due to its dense crystal structure and higher specific gravity – it is a pyroxene mineral. Nephrite (Ca₂(Mg,Fe)₅Si₈O₂₂(OH)₂) is a mineral in the actinolite-tremolite series. I would like to draw attention to one aspect of nephrite’s chemical formula: (Mg,Fe). This peculiar feature means that different samples of nephrite can have varying proportions of Mg and Fe. This is not just a feature of nephrite. Consider the common mineral olivine, which also occurs in two varieties, a magnesium-rich and an iron-rich variety; this is similarly reflected in its chemical formula, (Mg,Fe)₂SiO₄. The chemical properties of olivine vary according to whether it is Mg-rich or Fe-rich (e.g., only the latter can exist stably with silica minerals such as quartz). So, are olivine and nephrite disjunctive kinds like jade in that they are realised, in all possible worlds, either by the Mg-rich or the Fe-rich variety? Or are they genuinely disjunctively realised, like Fodor takes pain to be?

In fact, neither answer seems correct. The reason is that minerals such as olivine (and, more generally, feldspars and pyroxenes) are usually considered as mixtures rather than compounds; they are more appropriately understood as solid solutions.Footnote ⁷ A solution is a form of mixture, but in this case, the solution is of course much more rigid than the solutions we usually encounter. The principle, however, is very similar. Think of a vinaigrette emulsion, which is also a type of mixture: the olive oil and the vinegar are normally immiscible, which means that they do not naturally form a homogeneous mixture. But by shaking them into an emulsion, we have created a homogeneous mixture. This is a simple example of the type of mechanism that we have in the case of solid solutions as well.

The upshot is that we should define jadeite and nephrite as distinct kinds (if they are to be understood as kinds at all), which, as Kim suggests, have been classified as jade due to some superficial, macrophysical similarities rather than some shared microstructural basis. Hence, if we follow Fodor’s microstructuralist criteria, there are good, scientific reasons to think that these minerals are not genuine natural kinds at all; they are mixtures of two elements in close proximity on the periodic table that remain in a stable, homogeneous state, e.g., when combined with silica minerals (compare this with Reference VanDeWallVandeWall 2007 on the case of H₂O). This does not mean that the general microstructuralist approach that Fodor relies on must fail, but in the case of the particular example being discussed, Kim’s macrophysical approach is evidently much better supported by scientific practice. Insofar as we wish to postulate higher-level kinds such as jade, we ought to define them in terms of their macrophysical properties. In scientific practice, jadeite and nephrite are clearly distinguished, since they differ in terms of their chemical and many of their macrophysical properties, but note that it may nevertheless be possible to adopt a theory that allows genuine natural kinds to be macrophysically defined (cf. Reference HendryHendry 2010, Reference NeedhamNeedham 2011, and Reference TahkoTahko 2015b; see also Reference SeifertSeifert 2019).

It seems then that the case of jade certainly does not settle the debate between reductionism and anti-reductionism – in that, Fodor is correct. But Kim’s analysis of the case raises legitimate concerns about the anti-reductionist approach. Let’s see if we can put our finger on these concerns independently of the case of jade.

2.5 Are Higher-Level Kinds ‘Really There’?

Let us move on to an interesting analysis of the Kim-Fodor debate, by Louise Antony:

The crucial question is: what makes a kind ‘real’ and can disjunctive kinds indeed be ‘real’ in the relevant sense? Antony draws on a suggestion from Lenny Reference ClappClapp (2001), arguing that disjunctive properties can indeed be ‘real’ in cases where the disjuncts ‘have real commonalities’ (Reference AntonyAntony 2003: 10). The question then turns entirely on whether there is such a real underlying resemblance in the case of disjunctive predicates.

Somehow, the anti-reductionist must define an objective sense of higher-level ‘reality’. But I find Antony’s ultimate case for this unconvincing; she suggests, very much in line with Fodor, that there is a ‘strong abductive argument from the projectibility of higher-level predicates to the reality of the kinds they designate’ (ibid., 13). The idea is that the disjunctive predicates designating ‘real’ kinds are necessarily co-extensive with some projectible predicates (but she qualifies that this is merely a sufficient rather than a necessary criterion). Antony suggests that this is the case with many predicates ‘entrenched’ in human language – reflecting Nelson Goodman’s view in letter even if not in spirit (since Goodman was deflationary about projectibility). However, as Antony immediately acknowledges, there is an issue that might easily undermine such an argument: there are plenty of projectible higher-level predicates that are suitably entrenched in human language, but which we surely do not wish to reify as genuine, higher-level natural kinds. Two examples of this are ‘witch’ and ‘angel’ – predicates that we clearly do not believe to correspond with genuine natural kinds. However, both ‘witch’ and ‘angel’ may be projectible, because we can, for instance, make true generalisations about the women labelled as witches in the Middle Ages. It is just that those generalisations are not true because these women were witches with some supernatural skills, but rather because they were women who were all oppressed for some social or political reasons. So, what should we say about such cases?

Antony has an interesting suggestion about how to deal with this. One could try to deny that the abductive argument goes through (and hence deny the entrenchment of predicates like ‘witch’) in these cases, because there really have not been that many successful predictions made using these predicates. Or one could explain the entrenchment in terms of something else than what the supernatural connotations regarding ‘witch’ or ‘angel’ suggest, namely, in terms of socio-political groupings, as suggested previously. The reason why this suggestion is interesting is that it gives us a nice way to distinguish between eliminativism and reductionism:

Antony’s proposal nicely illuminates the eliminativism-reductionism distinction. Both are strategies to avoid including things like witches and angels among the genuine natural kinds. So, could one of these strategies apply in the case of jade?

Antony does not seem to think so. Like Kim and Fodor, she disqualifies jade from the class of ‘real’ natural kinds, appealing to Fodor’s argument (based on the distinction between open and closed disjunctions), which we outlined in the previous section: ‘It’s a mere accident that both jadeite and nephrite count as jade; there is nothing that the two mineral kinds [jadeite and nephrite] really have in common’ (Reference AntonyAntony 2003: 15). Or even if there is, she continues, it is not in virtue of the observable macrophysical similarities that we count jadeite and nephrite as jade, contra Kim – this reply reflects the case of witches and angels. But I think that here’s where the anti-reductionist strategy that Antony develops breaks down: ‘jade’ satisfies all the criteria that were given for ‘real’ kinds in Antony’s theory. It is entrenched in human language, and it is entrenched precisely because there is a set of higher-level, macrophysical properties that we associate with ‘jade’ and that we value, such as aesthetics and ease of working into exquisite objects (cf. Reference HackingHacking 2007a: 276; Reference LaPorteLaPorte 2004: 94–100). These properties are had both by jadeite and nephrite because, despite the differences in microstructure, both result in sufficiently (from the point of view of entrenchment) similar macrophysical properties. So, the abductive argument goes through here and it cannot be explained away by either of the strategies that Antony entertains. The reason for this is that we did not make any mistake here about what is projectible about jade – we were always interested in the macrophysical properties of jade, whereas in the case of witches we were, supposedly, interested in their dealings with the devil. Indeed, it is useful to refer to both jadeite and nephrite with the same term precisely because they share roughly the same, valued macrophysical properties, and it is these properties that secure its projectibility.

It should be getting clear what the upshot of all this is for the unity of science. Everyone agrees, we were told, that jade is not a ‘real’ natural kind, and hence not a legitimate counterexample to Fodor’s account of the disunity of science. But the criteria for ‘real’ make jade every bit as real as the postulated higher-level kinds that the anti-reductionists typically wish to reify. I think that a more systematic account of what it takes for something to be a genuine natural kind is needed. If it turns out that there really are genuine, irreducible higher-level natural kinds, then the traditional pluralist argument for the disunity of science is back in business. But if we can unify our theory of natural kinds and either reduce or explain away the supposedly irreducible kinds, then higher-level kinds do not threaten reductive ontological unity. Fortunately, there has been plenty of progress in our theory of natural kinds in recent years. In Section 4, we will return to the issue of natural kinds and its connection to unity. But first, we should discuss the state of the art regarding unity of science.

3.1 Biochemical Kinds and Special Science Laws

I will consider biochemical kinds such as proteins as the first example.Footnote ⁹ These kinds are at the intersection of biology and chemistry, making them an interesting case of potential cross-cutting and/or reduction/emergence (for discussion, see, e.g., Reference SlaterSlater 2009, Reference TobinTobin 2010b, Reference GoodwinGoodwin 2011, Reference BartolBartol 2016, Reference HavstadHavstad 2018). Proteins are macromolecules, and if macromolecules are considered to be chemical kinds, we would typically explain their chemical properties in terms of their physical structure, in line with traditional microstructural essentialism. But when considered to be biological kinds, the role of these molecules in physiological processes is important. This role is typically called the (biological) function of the kind. The function is also tied to evolutionary or aetiological considerations, given that biological functions are the result of a causal sequence of evolutionary processes.Footnote ¹⁰ The key question is of course the relationship between the complex biological aspects, which also involve extrinsic, historical properties, and the microstructural, chemical aspects. For instance, one might suggest that a protein’s three-dimensional structure supervenes on its amino acid sequence. This idea can be illustrated with simple textbook models of protein structure, such as the structure of haemoglobin in Figure 3.

Figure 3 Textbook model of haemoglobin.

Source: OpenStax College (2017): ‘Organic Compounds Essential to Human Functioning’ (CC-BY 4.0), available at https://legacy.cnx.org/content/m46008/1.8/.

But even though there is clearly a compositional dependence relation between the primary structure (amino acid sequence) of a protein and the resulting (tertiary and quaternary) three-dimensional structure, the exact relationship between these aspects is much more complicated. Indeed, many have argued that protein folding is a challenge even for weak forms of ontological unity, and accordingly provides a strong case in favour of disunity or pluralism (e.g., Reference DupréDupré 2012: ch. 9; Reference BartolBartol 2016, Reference HavstadHavstad 2018). Yet not everyone thinks that this case undermines ontological reductionism (OR) as we defined it at the beginning of Section 3 (e.g., Reference GoodwinGoodwin 2011, Reference TahkoTahko 2020).

William Goodwin’s case in favour of ontological reductionism draws on an analogy with organic chemistry, where we may classify molecules into distinct functional types, not unlike proteins. Organic molecules can be classified depending on their molecular and reactive environments, but their behaviour in these environments is nevertheless considered to result from molecular structure (which should also be conceived of three-, or in fact four-dimensionally because the structures are dynamic in time). In other words, chemical kinds, for better or worse, are just as ‘messy’, to use Joyce Havstad’s term, as biochemical (or biological) kinds (on ‘messy’ lab work, see Reference SchickoreSchickore 2008: 329; see also Reference RosenbergRosenberg 1985: 76). As Reference GoodwinGoodwin (2011: 543) puts it: ‘The tertiary structure of a protein, when there is one, represents the most energetically stable conformation available to the protein in the relevant biological circumstances.’ So, the process of protein folding, which can produce different tertiary structures from one primary structure, may be understood as being governed by complex interaction with the environment, aiming towards the most energetically stable conformation.

To illustrate that chemical kinds as well are ‘hostage’ to their environment, it might be helpful to briefly discuss a classic example of a rather problematic pair of chemical kinds: acids and bases (which are discussed in a slightly different context, e.g., by Reference Stanford and KitcherStanford and Kitcher 2000: 115–119). Acids were historically defined in terms of their macroscopic, phenomenological properties, such as their sour taste and corrosiveness. But chemists have struggled to come up with a proper definition of acids and bases, one reason being precisely contextual variation (on the history of acids, see Reference Chang and KendigChang 2016: 41ff.). The most commonly used account derives from the Brønsted–Lowry theory: acid-base reactions generally involve the transfer of a proton (an H+ ion) from an acid to a base. Hence, we could define acids as proton donors and bases as proton acceptors. However, the obvious problem in giving a general definition for acids is that a variety of substances can undergo these reactions and indeed some substances (called amphoteric substances), such as water, can react both as acids and as bases, depending on their environment. So, acting as an acid or as a base is something that cannot easily be defined without reference to a given context. A given substance may act as an acid in most environments, but there is nothing about the substance itself that guarantees its behaviour as an acid, the environment must also be considered. Following this line of thought, acids and bases could be understood as functional kinds.

An interesting feature of this case is that the relevant laws concerning acids and bases, like all special science laws, will be ceteris paribus laws – laws that allow for exceptions outside normal conditions. Now, let us grant (as, e.g., Fodor assumes) that laws do not need to be exceptionless to be ‘real’ (Reference FodorFodor 1997: 162, fn. 2). We still need to ask: what are the relevant normality conditions? Whatever these conditions are, they better not be determined, say, just by the experimental setup. If we were to introduce a law that states ‘All acids are proton donors’ based on experiments involving only water as the base, then the ceteris paribus clause would rule out water itself being an acid. In fact, this used to be the case with the definition of acids in the late 1800s, when the Swedish chemist Svante Arrhenius defined acids as compounds that increase the concentration of H+ ions that are present when added to water. Since water was used as part of the normality condition, it is obvious that water itself could not be classified as an acid or base according to this definition. Moreover, any laws to be derived based on this theory would not be able to account for cases where the reacting substances do not contain the relevant hydrogen ions. So, the correct ceteris paribus clause in this case would instead have to be based on the underlying chemical properties of the participating substances, and the Brønsted–Lowry theory enables this, since it is no longer necessary that a substance should be composed of hydrogen (H+) or hydroxide (OH-) ions in order to be classified as an acid or a base.

This brief example serves as our first warning sign: we should recognise that there could be differences in lower-level properties (here, the chemical properties of substances participating in acid-base reactions) that could make a difference in how we classify higher-level kinds (here, the classification into acids or bases). Otherwise, we may end up arbitrarily ruling out relevant lower-level differences based on nothing but the fact that we have not conducted any experiments where these differences would be observable. Therefore, an appeal to special science laws as the motivation to postulate distinct higher-level kinds is not enough on its own. I have previously labelled this as ‘the problem of lower-level vengeance’ (Reference TahkoTahko 2020).

The account that is emerging here plays into the hands of the ontological reductionist because higher-level kinds turn out to be dependent on lower-level kinds in precisely the way that the ontological reductionist claims. The fact that special sciences generally involve ceteris paribus laws introduces a prima facie challenge for the anti-reductionist, because the relevant normality constraints may also require reference to lower-level kinds, hence undermining the autonomy of the special science laws. Regarding the unity of science, the upshot is clear: We have to consider dependence relations all the way down to make sure that we have the full picture, to determine the complete set of identity-criteria of a given natural kind. These dependence relations are important for ontological models of unity, as they help us determine whether the relationship between higher-level and lower-level phenomena is ontologically reductive or non-reductive.

3.2 The Case of Haemoglobin

As a somewhat more detailed case study, I will consider the haemoglobin molecule.Footnote ¹¹ Haemoglobin binds and transports oxygen in blood, releasing it in cells. Roughly speaking, the biological function of haemoglobin is its ability to bind and release oxygen – more accurately, to carry oxygen from the lungs to the tissues and return carbon dioxide from the tissues to the lungs. The haemoglobin molecule is constituted by four polypeptide chains: two alpha chains (alpha helices) and two beta chains (pleated sheets), which have different sequences of amino acid residues but fold up to form similar three-dimensional structures (as in Figure 3). Only nine of the amino acid residues per globin chain in functionally identical haemoglobin molecules are present in all (functionally identical) haemoglobin molecules. Variations elsewhere in the sequence do not alter the functional profile. So, it appears that we are dealing with a case of multiple realisation, where several different microstructures can produce the same biological function.

In a biological context, we can take two distinct macromolecules (polypeptides) as two instances of haemoglobin, whereby both macromolecules are effectively treated as the same protein, despite microstructural differences. Hence, ‘haemoglobin’ might serve as a label for a class of proteins defined not only in terms of their microstructural features but also in terms of their functional profile.Footnote ¹² But we need some more detail about protein structure to assess the example. It is at the level of tertiary protein structure, the three-dimensional combination of alpha and beta chains, where we see the biological function of the protein. There can be several different primary structures that produce the same functionality. This is a common feature of proteins. Significantly different primary structures can produce very similar three-dimensional structures, sufficiently similar in order to produce the same functionality. This is true in the case of the various haemoglobin molecules as well. One aspect of variation in haemoglobin concerns its affinity for oxygen. For instance, since foetuses cannot breathe for themselves, the haemoglobin molecule active in foetal blood has a very high affinity for oxygen (there are three different haemoglobins in effect at different stages of foetal development). After birth, this affinity decreases. While it is important that haemoglobin has a high affinity for oxygen, it is also important that the oxygen gets released when needed. Accordingly, it is not surprising that the haemoglobins between adult mammals of different species may bear more similarities with each other than those between the adults and foetuses of the same species. In fact, haemoglobin can modify its affinity for oxygen depending on its chemical environment, since the adaptability of haemoglobin is tied precisely to its environment (compare this to the case of so-called moonlighting proteins, discussed in Reference TobinTobin 2010b). One property that influences haemoglobin’s affinity to oxygen is the pH value of the environment.

The question that the ontological reductionist faces is whether we can account for the capacities of the haemoglobin molecule in terms of its primary structure. If these capacities are present only at the level of tertiary structure, then this would appear to be a case of multiple realization which is problematic for the ontological reductionist. But why should one think that various primary structures do not all have the same functional capacities? Here we ought to recall Goodwin’s point: the case of proteins is analogous to that of organic molecules that may be classified according to distinct functional types. One way to think about these capacities is in terms of dispositional properties that may or may not manifest. The case of acids and bases which we discussed in the previous section is a good example. The initial problem with the simple idea that acids are proton donors and bases are proton acceptors is that a variety of amphoteric substances can act both as acids and bases, and this variation will depend on the environment. Yet it would be odd to claim that the capacity of an amphoteric substance to react as either an acid or a base is something over and above its microstructural properties, something that the substance gains only when the relevant environmental circumstances are in place. The thought here is that the capacity to behave in certain ways in different environments can be fully analysed in terms of the intrinsic properties of the substance. After all, both losing a proton (reacting as an acid) and gaining a proton (reacting as a base) are simple chemical reactions that are determined by the relevant molecular structures and we understand these reactions very well. There is no reason to think that we could not accurately capture acid-base interactions in terms of molecular structure, as the capacity to act as an acid or a base is contained, dispositionally, in that structure.

We are now in a position to give an analysis of one important aspect of haemoglobin’s functional profile in the lines of reductive ontological unity. Amino acids, which have a carboxylic acid group and an amino group (base), are also amphoteric. As we know, proteins are made up of amino acids, and accordingly they can also react as amphoteric substances. So, it turns out that at least some of the interesting capacities of proteins, some of their functional promiscuities, derive precisely from their amphoteric nature, which we have just explained in terms of molecular structure. This looks like a straightforward case of ontological reduction. So, the upshot of this case study is that the biological function of proteins like haemoglobin may, at least partially, be reduced to their microstructure. Indeed, in the case of haemoglobin, its amphoteric nature is in an important role when it comes to oxygen equilibrium; if we want to explain the oxygen affinity of haemoglobin, we will ultimately have to refer to its amphoteric nature.

So, it looks like we can give an analysis of this case that could satisfy the ontological reductionist. This contrasts with, for example, Jordan Reference BartolBartol (2016: 543), who recommends that we should adopt a ‘dual theory’ of chemical and biological kinds with respect to macromolecules such as proteins, driven by issues surrounding multiple realisation. This would result in non-reductive ontological disunity and entail a type of ontological pluralism about kinds. Note however that I do agree with Bartol when he points out that there could be pragmatic reasons to adopt different classificatory practices, so nothing we have seen above rules out pluralism modelled in the sense of non-eliminative semantic disunity. Continuing this line of thought, Havstad has argued that the primary structure of proteins is not sufficient to account for protein individuation in biological practice. She thinks that we need to consider the aetiological constraints as well and that these constraints are difficult to account for in microstructural terms. (I discuss this issue in more detail in Reference TahkoTahko 2020.) Moreover, even if we knew everything there is to know about evolution and were able to reconstruct this in microstructural terms, we might nevertheless prefer a taxonomy of the relevant biochemical kinds driven by considerations of biological practice. So, does this support disunity/pluralism? Yes, but arguably only of the epistemic/pragmatic type that enables semantic pluralism and can be reconciled with ontological reductionism. Let me now move on to another case study.

3.3 The Case of Electronegativity

This case study comes from the chemistry-physics interface. The question is, can we give an ontologically reductive analysis of chemical properties in terms of physical properties? We should start by making an observation about the distinction between chemical and physical properties quite generally, as this distinction is by no means uncontroversial. For instance, in the nineteenth century, the boiling and melting point were still considered to be physical properties, not necessarily connected with the chemical properties of a substance (Reference NeedhamNeedham 2008: 66–67). Moreover, Paul Needham notes that ‘[i]t was sometimes taken as an argument against the reduction of chemistry to physics that physics couldn’t possibly provide for the chemical characteristics of substances’ (ibid., 67). The situation changed once atomic numbers were understood as encompassing the crucial guidelines for chemical properties. Perhaps the simplest case that we can consider here is the reducibility of the chemical properties of a molecule to the molecule’s proper parts (and their properties), the elements and subatomic particles that compose the elements (for relevant discussion, see Reference Le PoidevinLe Poidevin 2005, Reference HendryHendry 2010, Reference van Brakelvan Brakel 2010, Reference NeedhamNeedham 2011, Reference SeifertSeifert 2017, Reference Seifert2019, and Reference TahkoTahko 2012, Reference Tahko2015b).

There are good reasons to start with the most discussed example in philosophy of chemistry: water. Water has special importance for us as living organisms, but it also has many interesting chemical properties despite its relatively simple structure. We also have a relatively good understanding of what the corresponding physical properties responsible for chemical properties like the boiling and melting point (of water) are. Water’s atypically high boiling point is explained by hydrogen bonding. When several water molecules are present, they form hydrogen bonds with each other, resulting in a network of hydrogen bonds. Similarly, many of water’s other interesting properties, such as its surface tension, derive from the polarity of the water molecule and the resulting bonding behaviour. All this is at the level of chemistry, but we can further analyse hydrogen bonding in terms of electronegativity. A hydrogen bond between two molecules forms when two electronegative atoms, such as hydrogen and oxygen, are close enough to attract each other. Electronegativity, according to the standard definition formulated by Linus Pauling, is the chemical property that acts as a measure of the tendency of an atom to attract a bonding pair of electrons. Figure 4 illustrates the electronegativity of oxygen (3,44) and hydrogen (2,20) atoms in an H₂O molecule. Figure 5 illustrates hydrogen bonding between H₂O molecules.

Figure 4 Permanent dipole of water molecule.

Source: Wikimedia Commons (2014): ‘Dipoli_acqua.png’ (CC-BY-SA-3.0), available at https://commons.wikimedia.org/wiki/File:Dipoli_acqua.png.

Figure 5 Hydrogen bonds between water molecules.

Source: OpenStax (2013): ‘Anatomy and Physiology’ (CC-BY 4.0), available at https://openstax.org/books/anatomy-and-physiology/pages/2-2-chemical-bonds.

This is where things start to get interesting. Electronegativity, which is generally understood as a chemical rather than a physical property, does not have an obvious reductive explanation in terms of more fundamental, physical properties, at least not in the sense that we could give a specific set of physical properties and identify these with electronegativity. There are two issues that we should consider here:

1. 1. Electronegativity is a relational property. It describes the magnitude of the interaction between an atom’s valence electrons – electrons on the outer shell – with those of another atom.

2. 2. As we already saw in the case of water, electronegativity is mainly relevant as a property of an atom as part of a molecule.

Both of these issues complicate the analysis of electronegativity, although they do not of course block ontological reduction entirely, since the configuration of the valence electrons clearly has a key role. We might say that whatever electronegativity is, it somehow derives from this configuration of the valence electrons. But the point is that we would struggle to replace the notion of electronegativity in chemistry with the configuration of valence electrons. An additional point of interest is that although the magnitude of electronegativity is influenced by atomic number and the valence electrons’ distance from the atom’s nucleus, electronegativity itself is not something that can be directly measured; instead, there are a variety of different methods of calculating it from other properties that the relevant atoms and molecules have. When I say that electronegativity cannot be directly measured, I mean that electronegativity must always be measured in relation to other properties, such as bond energies, and it does not have a unit. All this means that while electronegativity is clearly dependent on nuclear charge and electron configuration, it would seem problematic to simply replace it in chemical practice with these properties. This would misrepresent the relational aspects of electronegativity as well as its role in determining the chemical properties of molecules (i.e., some information would be lost).

This result speaks clearly in favour of the semantic anti-reducibility of properties such as electronegativity, and hence non-eliminative semantic disunity on the side of epistemic/pragmatic models of unity. More speculatively, on the side of ontological models of unity, this gives rise to the question of whether electronegativity could be an emergent property, introducing causal powers irreducible to fundamental physical properties, which would entail non-reductive ontological disunity. At the very least, the idea that we can see emerging from this discussion is that there plausibly could be chemical properties that are, in a sense, fundamental, due to being irreducible to more fundamental physical properties. And this is the case even though we know that there are more fundamental physical properties that influence, and perhaps determine, the relevant chemical property. Moreover, even though the presence of these more fundamental physical properties may be necessary for the relevant chemical properties, it might not be sufficient. It is not sufficient for the emergence of chemical properties such as electronegativity that all the relevant lower-level properties are present, since we have just observed that electronegativity is mainly relevant only as a property of atoms when they are a part of a molecule. So, as we have seen in other examples, we cannot define such properties without reference to their environment.

One question that we might like to ask, prompted by this case study, is how much do we need to know in order to conclude that some higher-level property is ontologically reducible? None of the examples that I have mentioned throughout this Element have demonstrated anything near a complete ontological reduction. But at some point, when we know enough about the dependence relations between a higher-level property and some set of lower-level properties, we seem to be in a position to say that a complete ontological reduction is possible or at least very likely, even if we were not yet (or ever) in the position to state all the relevant bridge laws. However, and in contrast, not just any dependence relation is enough. For instance, in the case of electronegativity, what I have said previously is hardly enough for a complete ontological reduction, even though we can point to a clear (compositional) dependence between electronegativity and the relevant valence electrons. In addition, we would need a much more detailed account of the underlying quantum chemistry (for discussion, see, e.g., Reference LloredLlored 2012). Still, the reason for favouring ontological reductionism is clear: so far, we have not encountered clear violations of it. For the friend of ontological unity, this is of course very good news: we can salvage as many higher-level predicates as we like, but at the end of the day, we know it to be very likely that there is a complex network of dependence relations that connects all of science, even if we cannot list all of these relations, and hence cannot eliminate the higher-level predicates – we can still be semantic pluralists.

I will conclude this section by noting that there is another line of argument available that challenges reduction at the chemistry-physics interface. This argument was introduced by Reference NeedhamNeedham (2011). Needham argues that there are no good reasons to accept microessentialism, the thesis that chemical substances must be characterised in terms of their microstructure. Instead, Needham proposes that we characterise chemical substances in terms of their macroscopic properties. Needham is mainly reacting against natural kind essentialism based on intrinsic (non-relational) properties familiar from the work of Saul Reference KripkeKripke (1980) and Hilary Putnam (e.g., Reference Putnam1975). Accordingly, I do not think that the argument is quite as damaging against more developed forms of natural kind essentialism (as discussed in Reference TahkoTahko 2015b). The important point here is the need to characterise chemical substances at least partly macroscopically. Philosophers of chemistry have long resisted natural kind essentialism’s poster child, namely, the over-simplified identification of water and H₂O. Needham’s central message can be captured with this striking quote: ‘A scientific characterisation needn’t be a microscopic characterisation’ (Reference Needham2011: 7; see also Reference WilliamsWilliams 2011 on the intrinsicness requirement; this point has more recently been bolstered in Reference HavstadHavstad 2018). But once we realise that the unity of science need not be supported by a commitment to such a strong form of reductionism, it should be clear that the question of microstructural versus macrostructural approach to chemistry does not settle the issue about ontological unity. Indeed, there may still be some hope for a qualified version of microstructural natural kind essentialism even if we do take Needham’s arguments onboard – namely, a version acknowledging that the context and environmental interaction of chemical substances need to be taken into account.

3.4 Unity of Science and Ontological Reductionism

The hope for unity of science was originally part of a logical empiricist dream of explicit eliminative semantic unity and implicit reductive ontological unity, the search for a simple relation of explanatory dependence, both at the epistemic and the ontological level. We have known for a long time that this dream was overly ambitious and indeed quite implausible, given the complexity of science and the need for semantic pluralism. But the notion of the unity of science should not remain tied to this long-abandoned endeavour. Given the complexity of science and indeed our own psychological limitations, we need to be open-minded about the various models, methodologies, and theoretical concepts employed in science. In this sense, pluralism – the disunity of science – is obviously alive and well. However, I hope that for those who have read the book this far, it should also be clear that relatively few arguments raised against reductionism and the unity of science, and in favour of pluralism, target the ontological dimension of unity. And even when the arguments are about ontology, I have tried to demonstrate that there is much controversy about whether the arguments establish that there is genuine ontological disunity or just epistemic shortcomings or pragmatic issues deriving from scientific practice. None of this is supposed to downplay the importance of such epistemic and pragmatic issues, but we should not be misled about what these issues amount to: they concern the ways in which we do science, not the underlying ontology of reality.

We may further clarify the two levels of inquiry that are intertwined here by focusing on two explanatory goals. One of these goals is at the level of ‘surface discourse’ (i.e., it is primarily pragmatic). I take the notion of ‘surface discourse’ from Reference GoodwinGoodwin (2011: 535), but I should note that Goodwin does not appear to use this notion of surface discourse in any pejorative sense. Rather, the idea is that the necessary preservation of certain higher-level predicates at the level of surface discourse suggests a commitment to semantic anti-reductionism, whereby the predicates of the special sciences can still serve an invaluable, even indispensable role (see Reference GillettGillett 2007: 195, Reference Gillett2016: 16).

Given the important role of the special science predicates, eliminative semantic unity now seems like a non-starter. But the ontological reductionist only insists that it is, at least in principle, possible to find lower-level truthmakers for the higher-level, special science talk, where ‘in principle’ can mean that we will never actually be able to do this, even if science were to be completed. Why is it so important to appreciate this difference? The reason for this is something that John Heil has captured in a very striking way: if we do not properly distinguish ontological matters from the semantic and epistemic import of science, there is a risk that we end up ‘reading off’ features of the world from features of our language (Reference HeilHeil 2003b: 218).Footnote ¹³ This does not mean that we should not pay attention to scientific practice or map the various competing models that science employs. Even when a number of these models turn out to be incompatible, they may nevertheless all turn out to be valuable in some way (cf. Reference MitchellMitchell 2002,2003 ). But there is just one world, and insofar as we do not find any genuine cases of strong emergence, then there is some consistent set of worldly dependence relations that ultimately underwrites all these models. Our models may turn out to be abstractions or idealisations that only capture some aspects of those worldly dependencies (cf. Reference KnoxKnox 2016) – and this is perfectly fine – but none of this undermines ontological unity.

Let me conclude this section with a conciliatory note. Even if we must be ontological reductionists to salvage the (ontological) unity of science, this does not take anything away from the practice of higher-level sciences like biology or chemistry. More generally, the status of a scientific discipline does not depend on there being a set of genuine, ontologically irreducible higher-level kinds or special science laws that we can associate with it. However, the ontological reductionist recognizes that the higher-level goings-on depend on the lower-level goings-on in some important respects even when there is higher-level autonomy with respect to certain degrees of freedom (cf. Reference WilsonWilson 2010). This means that even if higher-order scientific language includes some indispensable classificatory practices or natural kind predicates, this does not entail ontological pluralism about natural kinds.

The upshot is a modest type of ontological reductionism that is compatible with a similarly modest type of semantic pluralism. But there is one big issue that remains open, now that I have argued that we are still entitled to pursue ontological unity: where does that ontological unity stem from? I have hinted at a few alternatives, such as Gillett’s compositional reductionism, which suggests that we account for the ontological status of higher-level entities in terms of their component entities (but note that as Aizawa and Gillett (2019) argue, we should be pluralist about those compositional explanations as well). But this still leaves the ultimate ontology of those component entities open, and indeed we have many, many options regarding that ontology. My preferred strategy for laying out this ontology is by looking at the notion of a natural kind. This choice is easy to justify, since we saw that the notion of natural kind was central already in the original debate about unity between Fodor and Kim. But now we have the tools to make the underlying ontology much more precise.

In the next section, I will argue in favour of a unified theory of natural kinds – natural kind monism – as this enables us to preserve a core motivation for the old search for the unity of science as well.

4.1 The Naturalness and Kindhood Constraints

The starting point of the naturalness constraint (NC) is that what is ‘natural’ about natural kinds is their correspondence with the mind-independent joints of reality: natural kind terms aim to reflect the structure of reality. There are several ways to cash out the distinction between natural and non-natural properties in this sense (e.g., Reference LewisLewis 1983). For some, resorting to naturalness is so obvious that arguments in favour of it do not amount to much more than an appeal to ‘knee-jerk realism’ (Reference SiderSider 2011: 18).Footnote ¹⁶ However, one might think that relying on a David Lewis-style account of naturalness will not get us very far if we hope to define natural kinds quite generally, because the focus of the discussion is not so much on kinds, but rather on a nominalist account of properties – a nominalist account denies the existence of universals. Yet naturalness may nevertheless be the best candidate we have for clarifying the idea that not all properties are ‘on a par’, as Reference Dorr, Hawthorne, Bennett and ZimmermanCian Dorr and John Hawthorne (2013) put it in their lengthy discussion of naturalness.

Rather than discussing the history of naturalness, we should instead focus on the more pressing question of how we can put natural properties to use when it comes to identifying natural kinds. This is an important issue for any account that resorts to natural properties. Here, the most popular option seems to be projectibility. As Tobin puts it: ‘The naturalness of kinds makes them projectible; the observation of some instance of a natural kind Ka, licenses the inference that any future instance of K will be similar to Ka and gives credence to the belief that any future K will be similar to Ka’ (Reference Tobin, Mumford and TugbyTobin 2013: 165).

We first encountered projectibility in Section 2.3, when discussing the case of jade. We can clearly see the important role that it plays in discussions of naturalness and natural kinds. However, the key problem with projectibility is that the inductive inference described by Tobin in this quote can be upheld simply by virtue of shared natural properties between observed cases (cf. also Reference KornblithKornblith 1993). In other words, as we have already seen, projectibility by itself is not enough because it can give us false positives – cases where inductive inferences are upheld merely because of (perhaps accidentally) shared natural properties.Footnote ¹⁷ Tobin is careful to note that projectibility is only associated with giving some credence to the belief that Ks observed in the future will be similar to the previously observed instance. That’s because members of kinds need not be similar in all respects. But we should similarly be wary of cases where members of two distinct kinds share some properties. To control for this, we need the kindhood constraint.

The kindhood constraint (KC) will cause immediate controversy. One reason for this is the variation in the ontological weight that philosophers are willing to admit for natural kinds. But since the kindhood question is here separated from the naturalness question, perhaps we can make some progress. It is worth noting that we should also distinguish the kindhood question from the universalism/nominalism question.Footnote ¹⁸ This is despite the fact that I will operate in the realm of realism about natural kinds. We might compare this to the analysis of natural kind realism by Reference Hawley and BirdKatherine Hawley and Alexander Bird (2011: 206), who simply assume the existence of universals and hence dismiss nominalism altogether, limiting the discussion to those views that accept universals. I will focus on these views as well, but since we have distinguished the kindhood question and the naturalness constraint (NC), it may be possible to account for the relevant type of unity doing the work in KC in some other way than by postulating a universal. So, I think that one could be a realist with regard to KC but a nominalist with regard to NC – that is, to deny that either natural properties or natural kinds themselves should be understood as universals. The idea of unity of science should not be settled on this basis, but this issue will ultimately be faced by any account of ontological unity based on natural kind monism.

Even if we assume the existence of universals, a number of different options remain. For instance, kinds themselves might be considered to be particulars rather than universals, they might be considered as simple or complex universals (the latter option is preferred by Hawley and Bird), or they might be considered as sui generis entities, forming one of the fundamental ontological categories. Each of these approaches would give a somewhat different picture of what is responsible for shared kind membership. I will not discuss the details of these options. Instead, I shall focus on my preferred account. I favour the idea that natural kinds form one of the fundamental ontological categories – this would give them the highest ontological weight possible, and indeed I believe that this gives us a very neat sense of unity of science as well. But what does this mean?

Brian Ellis (e.g., Reference Ellis2001) and E. J. Lowe (e.g., Reference Lowe2006, Reference Lowe, Galluzzo and Loux2015) have provided the best-known accounts of kinds as a fundamental ontological category. Here we will collectively group these views under the label of natural kind fundamentalism. This use of ‘fundamental’ should not be confused with fundamental physics. Lowe specifies the idea as follows: ‘What does it mean to describe a certain ontological category as being “fundamental”? Just this, I suggest: that the existence and identity conditions of entities belonging to that category cannot be exhaustively specified in terms of ontological dependency relations between those entities and entities belonging to other categories’ (Reference LoweLowe 2006: 8).

An example may help, so let me borrow Lowe’s own example: if particulars consist of coinstantiated universals or perhaps from bundles of tropes, then the category of ‘particular’ cannot be fundamental in the relevant sense. That’s because in that case, the existence and identity conditions of particulars would be entirely specified in terms of the universals or tropes that constitute it (cf. Reference Keinänen and TahkoKeinänen and Tahko 2019). Lowe himself would include the category of ‘substance’ as one of the fundamental categories. It may be helpful to include an illustration of his four-category ontology (Figure 6), which, as the name suggests, postulates four fundamental categories.

Figure 6 The ‘ontological square’, modelled after Reference LoweLowe 2006: 22 (author’s own work)

We need not dwell on the details of Lowe’s ontology, but we may note that the top-left corner of Figure 6 (substantial kind universals) that is of particular interest to us. Relatedly, for Ellis, kinds feature in three of his six fundamental ontological categories, as substantive kinds (generic substantive universals), dynamic kinds (processes, events), and property kinds (Reference EllisEllis 2001: 97–98, 134). For Lowe, there are two types of universal – substantial and non-substantial – where the first corresponds with substantial kinds (i.e., natural kinds; Reference Lowe2006: 21, 33). So, in both ontologies, kinds feature among the fundamental ontological categories, although for Ellis they are distributed across several categories and hence perhaps better regarded as a subspecies of universals. In any case, I consider both Lowe and Ellis as proponents of natural kind fundamentalism.

Even if kinds were not fundamental entities in this sense, many would nevertheless consider them as entities of some sort. (Reference BirdBird [2018a] calls this view ‘strong realism’.) In particular, one might regard natural kinds as emergent entities. The homeostatic property cluster (HPC) theory familiar from the work of Richard Boyd (e.g., Reference Boyd1991, Reference Boyd and Wilson1999) could be seen as advocating this type of view. In this case, the resemblance among the members of the kind would seem to be derived from the role that kinds play in projectible, inductive generalisations. In other words, the resemblance between the members of a kind is manifested via a shared causal structure; each kind is a property cluster kept in homeostasis by a causal mechanism. But while this type of account has been very popular, it is also clear, and well-known, that the account is unlikely to apply to all (natural) kinds (see, e.g., Reference KhalidiKhalidi 2013: sec. 2.6, Reference MagnusMagnus 2012, Reference SlaterSlater 2015). For instance, it is difficult to see what kind of causal mechanism could be postulated to be responsible for the resemblance amongst chemical elements: a shared atomic number and nuclear charge are not mechanisms in HPC’s sense, but rather just individual (possibly essential) properties. The situation is different in the case of biological species, of course, where the HPC theory has proved to be quite popular (but see Reference KhalidiKhalidi 2013 for some critical remarks about this). In any case, it does seem that the HPC theory could at best offer only a partial account of kindhood – although various novel, more extensive versions of the framework have been proposed (such as Reference SlaterSlater 2015; Reference Hawley and BirdBird and Hawley 2011 also put the HPC theory to broader use).

Take Matthew Slater’s version, where resemblance is derived from Marc Lange’s (e.g., Reference Lange2009) idea of the stability of sets of laws under counterfactual suppositions (Reference SlaterSlater 2015: 398ff.). As Slater puts it, the idea is that ‘certain sets of truths are maximally invariant under counterfactual perturbations’ (ibid., 398). So, if we make a counterfactual supposition which is consistent with the members of a set, then we can reliably infer that, had the supposition been true, the members in that set would still have been the case. The resulting ‘non-nomic stability’ is important for Lange’s account of laws, but for our purposes, the important point is that, on Lange’s account, it looks like the set of laws is the only non-trivially non-nomically stable set. So, as Slater notices, there is ‘a sharp distinction between the facts that are laws and those that are accidents’ (ibid., 399). Now, what makes this interesting is that Lange, in reply to Rosenberg, has himself tried to apply this account of laws to produce a novel account of the autonomy of functional biology. But this requires more restrictive stability than we get with the set of all laws. All this will be easier to understand with an example, so let me cite a passage from Lange, which Slater also cites:

So, Lange’s suggestion is that we can restrict the relevant range of counterfactuals in terms of the interests of the special sciences – in this case, the medical sciences. Slater reports sympathy towards this basic idea, but he rightly points out that ‘there are some pressing concerns about the details of how interests apportion modal space’ (Reference SlaterSlater 2015: 400). This is also the concern that I have, because the upshot of Slater’s account of kinds seems to become, as he puts it, ‘domain-relative’ (ibid., 403), due to the fact that the definition of stability (on Lange’s account) is dependent on the interests of the relevant special sciences. Now, Slater prefers to formulate the account in terms of ‘relevance’ instead of ‘interests’ (ibid., 401), but the domain-relativeness is nevertheless at the very core of his account. It should be noted that Slater acknowledges all this – for example, ‘if some kinds are domain-relative, the question of what kinds there are tout court is not generally tractable’ (ibid., 404). But it is clear that this will not satisfy those sympathetic to natural kind monism, because it is precisely a singular – and realist – sense of natural kinds, tout court, that the monist requires.

Whether Slater’s account satisfies natural kind realism is a more controversial issue, but he does explicitly state, contra Reference LoweLowe (2006), that on his account, natural kinds are not an ontological category (Reference SlaterSlater 2015: 406). On Reference Kendig and GreyKendig and Grey’s (forthcoming) reading, Slater aims at a metaphysically neutral account of natural kinds – something that they regard as incomplete without explicit metaphysical presuppositions. Moreover, Slater’s account may violate what I regard to be a minimal criterion for natural kind realism – namely, that natural kinds reflect natural divisions in mind-independent reality. (I will return to the mind-independence criterion shortly.) Moreover, any account that offers only a partial solution to the kindhood question will be unable to account for the ontological unity of science.

One competing account that attempts to provide a more unified approach to natural kinds and is hence worth considering in this context is the one developed over many years by Muhammad Ali Khalidi (e.g., Reference Khalidi2013, 2018). Khalidi suggests that ‘epistemic practices [in science] aim to uncover the divisions that exist in nature’ (Reference KhalidiKhalidi 2013: 63). Or as he puts it some years later, ‘the ontological ground of projectibility is causation’ (Reference KhalidiKhalidi 2018: 1389). Khalidi’s ‘simple causal theory’ of natural kinds has many benefits over competing views and I find it to be one of the most clearly presented and detailed accounts of natural kinds overall, but it is his take on the kindhood question which I will take issue with. The reason for this is that Khalidi, like many others, ultimately takes projectibility to be the most important guide to kindhood. As we have already seen, this puts a lot of weight on the epistemic practices in science and it is this feature that I believe to have skewed our conception of the unity of science towards the epistemic/pragmatic rather than the ontological. So, there is no question that Khalidi’s account is supposed to be realist, but ultimately, any realist account will have to address the ontological dimension as well, and the relationship between properties and kinds is one of the most pressing issues here (see Reference KhalidiKhalidi 2013, sec. 6.2).Footnote ¹⁹ Here is how Khalidi first ties these together:

As Khalidi notes, this is surely not enough, as we also need an account of what unifies the properties associated with a kind. The problem of finding a reliable link between projectibility or inductive generalisations and natural kinds is of course not new; here we return to the debate between Fodor and Kim discussed in Section 2. Let me cite a passage from Ruth Millikan (whom Khalidi also cites) to illustrate:

Khalidi builds on this idea from Millikan by introducing the requirement that there needs to be ‘no shortage’ of projectible predicates associated with the kind K. So, the inductive inferences that natural kinds support need to have a certain robustness. What explains this robustness? Khalidi’s preferred answer is that there is a causal link between the properties. Thus it is this causal ‘network of properties’ that distinguishes natural kinds from non-natural kinds – Khalidi coins this idea by stating that kinds are the ‘nodes in causal networks’. In a little more detail, the thought is that there are some ‘primary’ or ‘core’ causal properties which are co-instantiated with ‘secondary’ or ‘derivative’ causal properties, because the primary properties directly cause the secondary properties. An example of this distinction that Khalidi gives is the case of gold atoms, where ‘the primary causal properties of gold include atomic number 79 as well as a disjunction of mass numbers, which give rise in turn to a cluster of other causal properties (e.g. ionization energies, atomic radius, etc.)’ (the latter being secondary properties) (Reference KhalidiKhalidi 2018: 1384). This is a sensible approach in that it allows for certain variation in the secondary properties (for instance, some secondary properties could be masked), while the causally prior primary properties would still be present. Hence, we should identify the kind with these primary properties, even if the kind is also associated with the secondary properties. The key question is of course how the primary properties become co-instantiated. Here, Khalidi is somewhat more tentative, but ultimately his account seems to be based on the idea that the causal networks track laws of nature: ‘it seems that all we can say is that some combinations of properties in the universe are allowable and others are not, and that is ultimately a matter of natural law’ (Reference KhalidiKhalidi 2013: 205).

The upshot of Khalidi’s account, it seems to me, is that we must reduce the kindhood question into a question about the laws of nature. But this, of course, requires an account of laws, which Khalidi is surprisingly silent about. Moreover, given the major role that causation plays in the account, there is a serious challenge that emerges from the old Russellian line, whereby causation is thought to be absent from the fundamental, microphysical level. This is, of course, a controversial matter, one that we cannot discuss in detail here (but see Reference KhalidiKhalidi 2013: sec. 6.3 for discussion). In any case, if microphysical causation is denied, this would seem to require one of two things: either we must give up microphysical natural kinds altogether or we must posit two classes of natural kinds and account for the fundamental physical kinds by some other means (an option that Khalidi considers, with reference to Ladyman, Ross et al. Reference Ladyman, Ross, Spurrett and Collier2007). But either option will be alarming for the friend of ontological unity framed in terms of natural kind monism, since they would both entail either giving up natural kind monism or leaving a part of science – and arguably the most fundamental part – out of the picture.

4.2 Mind-Independence, Cross-cutting Kinds, and the Hierarchy Thesis

Before I present my own preferred account of natural kinds in more detail, I would like to briefly discuss some pressing challenges for realism and monism about natural kinds. I shall start with the role of the mind-independence criterion for the naturalness of kinds. I have noted in passing that a common way to conceive of what is ‘natural’ about natural kinds within natural kind realism is their correspondence with the mind-independent joints of reality (and indeed I have defended this type of view before in Reference TahkoTahko 2012 and Reference Tahko2015b). But some might find this criterion unsatisfactory, primarily because there are supposed natural kinds that are at least partially mind-dependent, as we shall shortly see. Indeed, this is a potential threat for the idea that a unified account of natural kinds could truly support the ontological unity of science. For if there are higher-level sciences that are ruled out from this unified account of kinds by definition, then we are clearly not providing a complete unified picture. Now, proponents of natural kind fundamentalism might argue that such supposed higher-level kinds should be ruled out because they are subjective and/or reducible to lower-level kinds. But showing this is by no means straightforward. So, let us consider the issue in some more detail.

Two interesting cases of seemingly mind-dependent kinds are non-naturally occurring transuranic elements such as the element with atomic number 99 (Einsteinium), and psychiatric kinds such as mental disorders – the latter being mind-dependent by definition.Footnote ²⁰ However, I think that we need not worry about such cases that seemingly violate the mind-independence criterion; indeed, the thought that natural kinds need to exist mind-independently has sometimes been misunderstood or misrepresented.

Reference KhalidiKhalidi (2016: 228) has helpfully listed the following four different ways to understand the mind-independence criterion:

1. 1. Mind-dependence of the kind vs. its instances

2. 2. Causal versus constitutive mind-dependence

3. 3. Contingent versus necessary mind-dependence

4. 4. Mind-dependence versus theory-dependence

It is easy to see that kinds like Einsteinium will satisfy (1), given that the kind itself (say, understood as a substantial kind universal) may be considered mind-independent even if its instances (i.e., the specific Einsteinium atoms that humans have synthesised) are, in a sense, mind-dependent. However, the case of the various psychological and social kinds is more controversial, as one might think that without any minds at all, such kinds could not exist. The details will depend on whether one believes that kinds can exist without any instances – something that I would find questionable, being sympathetic to the Aristotelian view that all universals must be instantiated in the actual world (for discussion, see also Reference HommenHommen, forthcoming).

Regarding (2), the second of Khalidi’s suggested ways to understand mind-independence, the thought is that human minds may be causally involved in the creation of certain natural kinds, but these kinds may nevertheless be constitutively mind-independent. Clearly, kinds such as Einsteinium would count as mind-independent on this criterion as well, whereas mental disorders might not. (3) brings in explicitly the idea I mentioned in connection to (1), namely, that certain kinds, such as mental disorders, could not have come about without human minds, whereas we can perhaps allow for the possibility that kinds like Einsteinium could have been created spontaneously in the natural world. (This may be controversial, given the focused efforts required in creating such kinds.) Finally, the distinction suggested in (4) attempts to make the case for mind-independence in terms of ruling out social kinds such as money because their existence is dependent merely on there being a relevant theory (i.e., economics), but Khalidi questions this, noting that it is certainly not the case that all social kinds are entirely theory-dependent.

Indeed, Khalidi himself thinks that (1)–(4) are all problematic. Instead, he proposes a fifth formulation, whereby the distinction between mind-independent and mind-dependent kinds can be specified in terms of whether the instances of the relevant kinds require human mental activity to sustain them as members of those kinds. If such a need exists, the kind is mind-dependent. Even though this is Khalidi’s preferred way to understand the mind-independence criterion and it does seem to provide a way to distinguish social and psychological kinds from cases such as artificial elements, his main claim is that this distinction does not provide a good ontological account for distinguishing real or genuine kinds from ersatz kinds. More generally, he concludes that mind-independence of the provided varieties should be considered irrelevant to realism about kinds. I beg to differ.

In my view, the point of the mind-independence criterion for genuine natural kinds amounts to this:

So, what makes a set of properties ‘objectively unified’? This concerns the relevant unification principle, the manner in which the properties are unified. But it is, in fact, easier to say what makes a set of properties not objectively unified: if the set of properties that a kind term tracks is based on some human interests, then that set of properties is not objective and the kind in question is mind-dependent.Footnote ²¹ It may help to give an example. Consider the phenomenon of radioactive decay. When we say that something is radioactive and classify various isotopes in terms of this radioactivity, we have in mind relatively unstable nuclei. Nuclear stability comes in degrees, but we have never observed proton decay and we classify nuclides as stable when they do not spontaneously undergo radioactive decay. Yet this may all be because we have not had sufficient time to observe such decay – and likely never will. In a famous article, Freeman Dyson suggests that over a time scale of 10¹⁵⁰⁰ years, ordinary matter is radioactive – ultimately, all matter will decay into iron (Reference DysonDyson 1979: 452). But we are generally not interested in such incomprehensibly long time scales, and for good reason. Nevertheless, if Dyson is right, the objective property of ‘radioactivity’ is much more promiscuous than we ordinarily think – that is, when we have our interest-relative glasses on. Properly speaking, it is not the property of radioactivity that is interest-relative here, but rather the property of ‘nuclear stability’, as we ordinarily use it (not to be confused with Slater’s use of ‘stability’ discussed earlier). But it is clear that we would lose something if we stopped using the notion of nuclear stability, because for virtually all of our scientific interests, it makes absolutely no difference to us if a nuclide that we classify as ‘stable’ decays, say, in some 10¹⁰⁰ years.

The previous example hopefully serves to highlight that just because a kind or a property is mind-dependent does not mean that such a kind could not be useful or that it could not track some causal structures. Rather, such a kind or the associated set of properties satisfies some looser sense of cohesion or unity, say, given a particular epistemic goal (although this is not to say that the goals are purely epistemic). If we take the case of synthetic elements like Einsteinium, the proper mind-independence criterion, is easily fulfilled: there is an objectively unified set of properties (e.g., nuclear charge), which is associated with Einsteinium. The fact that the existence of any given instance of Einsteinium is dependent on human action is irrelevant. Moreover, the mere fact that social kinds and psychiatric kinds are mind-dependent is not the problem; rather, problems arise if the set of properties reified as a kind is picked up on the basis of our epistemic interests rather than some objective unification principle, whether or not the properties themselves are mind-independent.

For a natural kind realist, the main issue is that the kindhood constraint (KC) is satisfied and that it is satisfied because the kind is genuine (i.e., satisfies the objectivity requirement specified by MI). There are a number of ways that this genuineness can be captured, but according to my preferred account, genuine natural kinds are substantial kind universals. Such substantial kinds are associated with a given set of properties because the kind unifies these properties. Reference HommenHommen (forthcoming: [3]) puts this nicely: ‘[K]inds represent unified ways of being – both in an individual and in a collective sense: they account for the modal and temporal stability of character both within single particular objects and across what we then call different members of the same kind.’ This may be contrasted with the view that Mill may have held – namely, that at least fundamental natural kinds unify their properties as a matter of brute fact. In other words, there are no causal connections between, say, unit negative charge, half-integer spin, and the rest mass of electrons, even though all three of these are presumably definitive of the natural kind electron.Footnote ²² This bruteness approach may also be found, for example, in Reference ChakravarttyChakravartty (2007: 171), who suggests that fundamental natural kinds, such as electrons, have their core properties (mass, charge, spin) as a matter of brute fact. Yet this is not the account that Hommen is advocating. It may be the case that we cannot point to any causal mechanism or other clear explanation for why certain properties, especially those of fundamental natural kinds, cluster together. But instead of postulating this as brute fact, a natural kind fundamentalist can see this as a justification for postulating natural kinds as a fundamental ontological category. This is the account that Hommen seems to favour, and one that we can also see in the work of Ellis and Lowe. I shall outline this account in the next section, but first I would like to consider one more challenge for natural kind monism in general: the possibility of cross-cutting kinds.

The starting point of natural kind monism is that we can account for all natural kinds in terms of the same general identity-criteria. But an important addition to this, suggested by Reference EllisEllis (2001) is the thought that an entity can only belong to one (fundamental) natural kind. Probably no one is committed to this idea in its strongest possible sense – which Reference KhalidiKhalidi (2013: 69) calls the mutual exclusivity thesis, whereby there really is only a single natural kind that an entity can fall under. This would entail, for instance, that an entity cannot belong both to the kind proton and fermion, even though all protons are fermions. But it is, of course, very easy to weaken the thesis somewhat, so that an entity may indeed belong to several genuine kinds at once, as long as these are a part of a nested hierarchy. Since all protons fall under the more general kind fermion, it is easy to see that there is nothing here that threatens natural kind monism – indeed, this kind of hierarchy reminds us of Oppenheim and Putnam’s system of reductive levels. This idea has come to be known as the hierarchy thesis (Reference KhalidiKhalidi 1993, Reference Khalidi1998) and the key challenge to this thesis is the possibility of cross-cutting kinds (e.g., Reference Tobin, Beebee and Sabbarton-LearyTobin 2010a).

Some common examples of cross-cutting kinds come from biology and chemistry. In biology, such cases are extremely easy to find. Consider the notoriously tricky kind, mammal. Humans are mammals, and so are monotremes such as the platypus. The platypus is also oviparous, meaning that it produces offspring by laying eggs, like birds. But birds and humans cannot be classified together either as mammals or as oviparous. So, given the hierarchy thesis, something must give. Proponents of the hierarchy thesis, such as Ellis, may of course give up problematic biological kinds like a mammal. But the problem is that even if we were to rule out biological kinds as real natural kinds, there are examples further down the hierarchy as well. To borrow an example from Tobin, albumin and renin are both members of the kind protein, whereas renin and the hairpin ribozyme are members of the kind enzyme. However, the hairpin ribozyme and albumin do not fit together either as enzymes or proteins. Even though many enzymes are also proteins, not all of them are protein and hence they are not a subkind of proteins, and nor are proteins a subkind of enzymes (see Reference Tobin, Beebee and Sabbarton-LearyTobin 2010a for details; for comparison between biological and chemical kinds, see Reference HavstadHavstad 2018). This result has, unsurprisingly, been taken to favour pluralism over monism (cf. Reference DupréDupré 1995).

There are various ways in which friends of the hierarchy thesis could try to accommodate problematic cases, by modifying or weakening the thesis or by denying that the cases violating the hierarchy thesis amount to real natural kinds. One way to do so would be to argue that when two kinds do overlap in such a way that one is not a subkind of the other, then there must nevertheless be something shared between them, such as a common underlying structure. Tobin considers this strategy, applied to the case of enzymes and proteins:

Tobin goes on to make the point that reduction is not straightforward in cases such as this – the higher-level kinds here are multiply realised. Indeed, cases such as proteins and enzymes are particularly tricky, because of their complex three-dimensional structure which is responsible for a majority of their biological functions. (See Section 3 for further details on the case of proteins). As Tobin argues, classifying proteins and enzymes strictly in terms of the underlying chemical structure would leave out many important details that we do in fact need in science. This is a point bolstered most recently by Reference BartolBartol (2016) and Joyce Reference HavstadHavstad (2018). However, as I argued in Section 3, it is possible to accept this point – to admit that there are important scientific classifications that cannot be captured in terms of the underlying chemical structure and hence accept semantic pluralism – while also promoting ontological unity. Tobin suggests that in cases such as the one at hand, ‘Reduction is precluded by the fact that categories such as albumin and ribozymes are determinable categories’ (Reference Tobin, Beebee and Sabbarton-LearyTobin 2010a: 184). This is indeed evidence that points towards the indispensability of these categories in scientific practice, but arguably it does not prevent ontological reduction, which is compatible with theoretical or semantic anti-reductionism.Footnote ²⁴

What conclusion should we draw from the case of cross-cutting kinds? For the likes of Ellis, it means that we should abandon many higher-level kinds, even if they are accepted as real classifications. Another approach is to go for conventionalism about natural kinds, a view advocated by Reference HackingHacking (2007b) and dismissed by Tobin. This type of view suggests that classification is a matter of convention or agreement, perhaps based on our pragmatic interests. We saw this type of domain- or interest-relativeness with regard to Slater’s account of kinds as well, but the conventionalist could go much further and be explicitly anti-realist about kinds. Instead, the lesson that most realists about natural kinds would draw is one of pluralism, albeit the semantic and ontological varieties of pluralism sometimes seem to be confused here – Reference KhalidiKhalidi’s (2013: 72) take looks like a type of semantic pluralism given that he distances himself from Dupré’s apparent ontological pluralism. Tobin’s view is more conciliatory, as she argues that an acceptance of cross-cutting categories does not entail that the boundaries between them are arbitrary (Reference Tobin, Beebee and Sabbarton-LearyTobin 2010a: 189). So, in her view, one can be a realist about natural kinds while accepting that some cases are cross-cutting. I would agree that this is possible, as the hierarchy thesis itself is by no means definitive of natural kind realism. In fact, even fuzzy boundaries may be acceptable, as Reference KhalidiKhalidi (2013: 68) argues, and this certainly needs to be the case if one wishes to retain realism about categories such as biological species. Yet concessions at least to semantic pluralism may need to be made even in the realm of (bio-)chemical kinds, as the case of proteins and enzymes demonstrates. (For a related point about other chemical kinds, see Reference HendryHendry 2012.)

So, what is the upshot regarding the unity of science? The results clearly favour some kind of pluralism, but what kind? As I hope to have made clear, no one really believes in eliminative semantic unity in the sense that entails the denial of semantic pluralism. But some, like perhaps Dupré (e.g. Reference Dupré1995, Reference Dupré2012), might take the provided results to favour ontological disunity and hence ontological pluralism as well. It is not entirely clear just how strong Dupré’s sense of pluralism really is, but it is in any case stronger than what Khalidi, for instance, seems to have in mind (Reference KhalidiKhalidi 2013: 72). In my view, the resulting pluralism here is arguably nothing more than semantic or taxonomic pluralism of the type that we have already discussed in detail. If this is the case, ontological reductionism and reductive ontological unity are not immediately threatened, compatible as they are with semantic pluralism. It is now finally time to outline my preferred account of natural kind monism, which arguably provides a very plausible ontological basis for the unity of science.

4.3 Natural Kind Fundamentalism

I have already expressed my preference for natural kind fundamentalism – the view that natural kinds, as substantial kind universals, constitute one of the fundamental ontological categories (see also Reference Keinänen and TahkoKeinänen and Tahko 2019). The main interest for the view in the present context is that it provides an easy route to natural kind monism and thereby ontological unity: if the real or genuine natural kinds are only the kinds that can be associated with a substantial kind universal, then we have a very simple answer to the kindhood question, and hence a straightforward account of the identity-criteria for natural kinds. The properties clustered together in entities that are members of natural kinds do so because those entities are members of certain natural kinds. I should note that I understand universals as instantiated (sometimes labelled ‘Aristotelian’ instead of ‘Platonic’) – that is, there are no uninstantiated kind universals in a Platonic heaven. Rather, the instantiated universals are multi-located where their members are. This does invite further questions, of course. Let me anticipate one of them, regarding the status of kinds that have no actual members (e.g., potential transuranic elements that have not been synthesised). My view is that in such cases, we can often state what it is to be a (member of) the kind, but strictly speaking the kind does not exist, since there are no instantiated universals. But we may nevertheless say that were an entity of kind K to come into existence, it would have such and such properties because it is a member of kind K (say, a yet-to-be-synthesised transuranic element).Footnote ²⁵ This is the case even if no entity of kind K ever comes to exist in the actual world. Now, I would frame all this in essentialist vocabulary – that is, the identity conditions of the members of K state the general essence of kind K. But this is something that I will set aside here (see Reference LoweLowe 2008 and Reference TahkoTahko 2015b for more details regarding the essentialist formulation).

Of course, there are many other challenges that remain for natural kind fundamentalism, such as the question of our epistemic access to the genuine kinds. I cannot hope to settle all these challenges here, and indeed it is not my purpose to defend the view in detail (but see Reference Lowe, Galluzzo and LouxLowe 2015 and Reference HommenHommen, forthcoming, for two excellent defences). It might nevertheless be interesting to assess the view against some of the main competitors. One of them is the view outlined by Reference Hawley and BirdBird and Hawley (2011), whereby natural kinds are complex universals. On this view, natural properties may be understood in terms of property universals and natural kinds would thus be bundles (i.e., complexes) of such universals. Rather than engaging with this view in detail, let me raise a simple challenge to it: some of the best candidates for fundamental natural kinds do not comfortably fit into this picture. I have in mind fundamental physical kinds such as fermions and bosons, which appear to be definable (or at least distinguishable) in terms of just one natural property (namely spin: fermions have half-integer spin whereas bosons have integer spin). If this is the case, then it does not seem correct to understand these fundamental kinds as complex universals. Instead, we could say that there are at least some natural properties that constitute natural kinds on their own. Accordingly, we would lose at least some of the initial coherence of the view defended by Bird and Hawley. More importantly, we would struggle to address the original kindhood question: which bundles of properties are genuine natural kinds?

Reference BirdBird (2018a: 1420) makes a surprising suggestion regarding the connection between kinds and properties. He proposes that Boyd’s HPC theory, which suggests that properties cluster together (non-accidentally) in virtue of causal mechanisms, could be generalised to all natural kinds and not just biological kinds like Boyd himself perhaps intended. On this view, an HPC would be ‘a particular species of complex universal’ (Reference BirdBird 2018a: 1423). Now, the usual challenge for generalising the HPC theory to all kinds is that it is compositional in nature: the clustering together of certain higher-level properties is explained by a lower-level mechanism. But when it comes to fundamental physical kinds, there is evidently no lower-level mechanism to appeal to. Bird, however, expands the account by appealing to laws of nature in addition to mechanisms, and he considers this to ensure that when it comes to physical and chemical kinds, the clustering is in fact much more sharply defined. Yet this once again (as I argued in connection to Khalidi’s account) seems to reduce (or delegate) the kindhood question to a question about the laws of nature. We may ask: why do laws of nature cluster properties together in the way in which they do? Bird’s answer will be tied to his dispositional essentialist account of laws (in addition to the account of kinds as complex universals). My worry with this strategy of explaining property clustering in terms of causal mechanisms or laws, quite generally, is that this turns the explanatory order on its head. If the greatest motivation to postulate natural kinds is that they support inductive generalisations, then it is the fact that natural properties systematically do cluster together into kinds that explains why laws of nature hold. But if this clustering is again explained in terms of the laws, then the account is circular. I do not mean to suggest that Bird is committed to this type of circular explanation though – after all, he does have a distinct account of laws, but one that is only available to dispositional essentialists.Footnote ²⁶

My own view is closer to Reference LoweLowe’s (2006) picture, and in particular I adopt the distinction between two different kinds of universal: property universals (which we may understand as natural properties) and substantial kind universals (i.e., the natural kinds), as we saw in Figure 6. Any complete account of ontological categories should say something about how categories are related to laws of nature and Lowe has already developed a sophisticated theory about the relationship between laws and kinds (see also Reference TahkoTahko 2015c). More precisely, Lowe proposes that we should explain laws in terms of the natures of natural kinds (cf. also Reference EllisEllis 2001). The kind electron, for instance, has it as a part of its nature that its instances have unit negative charge. This essentialist fact can then help to explain various law-like regularities, such as the net negative charge of those ions that have extra electrons. Instead of considering laws as relations between property universals (like in the Dretske-Tooley-Armstrong theory, e.g. Reference ArmstrongArmstrong 1997: 223ff.), Lowe considers the truthmakers of laws as properties and relations that characterise kind universals. Consider electrons, which have a determinate mass, electric charge, and spin quantum number as their essential properties. What accounts for the clustering of these three property universals as necessary properties of the kind electron? As Reference Lowe, Galluzzo and LouxLowe (2015: sec. 6) points out, property universals and, say, the Armstrongian second-order necessitation relations between them cannot do the job. The main problem here is that a set of monadic property universals are clustered to constitute essential properties of a natural kind in some of their co-located occurrences but fail to occur together in others. For instance, muons can have the same spin quantum number and electric charge as electrons, but they have a considerably larger mass.

We can omit the details of Lowe’s four-category ontology here and just look at the basic structure, which introduces a kind of double primitivism: both natural properties and kinds constitute a fundamental category. Consider Figure 7.

Figure 7 The relationship between natural kinds and their properties (author’s own work)

An important feature that we can observe in Figure 7, even though it is of course overly simplified, is that all natural kinds (small circles) are linked to properties (triangles), but not all properties need to be linked to natural kinds. There could also be natural kinds that are linked to just one property, but the property and the natural kind are nevertheless distinct – hence the double primitivism. For instance, some fundamental physical kinds such as perhaps fermions and bosons might be definable in terms of just one natural property: spin. Obviously, such examples are controversial, but it is a benefit of the present picture that the possibility of natural kinds definable in terms of a single property is not ruled out. Although the picture does not illustrate it, there is, of course, nothing that rules out one property being linked to several different natural kinds; the property of spin, for instance, is linked to several kinds. Moreover, the dashed circles on the property side illustrate the ability of the kind to unify the properties – that is, the dashed circle may be regarded as the unification principle in the case of a given kind, be it a causal mechanism or something else. Based on this very simple framework, it is easy to explain why I have been emphasizing that we can make inductive inferences just based on properties rather than kinds. The reason is that there may be properties that are not directly linked to kinds (although they can be entailed by kinds), such as accidents or contingent properties – we may understand the ‘loose’ triangles to be such properties. A contingent property of a member of a kind may of course be ultimately linked to the kind as well, even if not directly through the kind’s unification principle.

To provide an example, consider the diffraction of water waves. Diffraction, the bending of waves around obstacles, is a feature of any wave, but it will of course only be apparent when we have a body of water rather than just one water molecule. Is diffraction a ‘core’ essential property of the kind water (if it is a kind) or just something that is entailed by the general essence of water? Well, one might think that it is not part of the essence of the kind water that water waves should diffract (even if it were part of the essence of the kind wave). If this is the case, we may say that water waves are disposed to diffract, but the core properties of water do not necessitate that water waves diffract. Now, all this should be taken with a grain of salt because the example is somewhat esoteric. But we may consider this to be a toy example, the main purpose of which is simply to illustrate the connection between kinds, their core or essential properties, and contingent properties that are dependent on the core properties.

One important upshot of this discussion is that even if there is a connection between inductive, law-like generalisations and natural kinds, this connection may not be necessary. In other words, there may be law-like generalisations which do not feature natural kinds, and hence the explanatory significance of natural kinds in certain inductive inferences does not, by itself, constitute a sufficient reason to postulate natural kinds. In fact, a case could be made to the effect that all the explanatory work required for inductive inferences could just as well be done merely in terms of natural properties, without assuming that the kindhood question requires an answer at all. Of course, this is not my own view, but it is perhaps worth considering, because it would wreak havoc for the important role of natural kinds in securing ontological unity as well.

Consider, for instance, inductive generalisations regarding the proportion of black ravens in a sample of ravens or the expectation that two positively charged particles will repel each other, in accordance with Coulomb’s law. Could we not explain both cases in terms of natural properties, regardless of whether we consider ravens or even charged particles to constitute a natural kind? In fact, it may be possible to explain at least the raven case without even any reference to naturalness, since a random sampling of sufficiently many cases could perhaps be considered a sufficient justification of the inductive generalisation, as Peter Reference Godfrey-Smith, Campbell, O’Rourke and SlaterGodfrey-Smith (2011) speculates (cf. also Reference StrevensStrevens 2012, who uses the raven case as an example). Be that as it may, the case of Coulomb’s law is of particular interest due to its wide applicability: it applies to all charged particles. Accordingly, if Coulomb’s law features a natural kind, this kind would have to encompass all charged particles. On the face of it, the natural kind ‘charged particle’ seems questionable, even ad hoc. One might think, following Ellis, that such cases have to do with ‘global’ laws that involve higher-order determinable natural kinds, even if they involve no fundamental natural kinds. Indeed, Ellis himself would have a further possible reply since he accepts ‘property kinds’ such as ‘charge’ and ‘mass’ (Reference EllisEllis 2001: 23). But these replies are controversial to begin with: Ellis’s hierarchical view of natural kinds, property kinds, and the idea of global laws involve heavy commitments and we have already discussed some of the problems of the hierarchical view in the previous section.

So, postulating a natural kind to do the job where simple correlations of natural properties are sufficient – as would seem to be the case with Coloumb’s law and charged particles – seems unwarranted, at least if we do it simply for explanatory purposes. Here I would agree with Bird, who states that associating natural kinds with inductive success ‘promotes an overly liberal conception of natural kinds’ (Reference Bird2018a: 1401). Having said that, explanatory significance may yet have a role to play in this discussion, but, in my view, only to recognize the ontological import of natural kinds. That is, natural kinds may ground the explanatory significance of some law-like generalisations, but not everything that is explanatory has to involve kinds.

There is much more to be said about the exact relationship between kinds, their properties, and the properties that are not directly linked to kinds as well as the relationship between kinds and laws (for discussion, see, e.g., Reference LoweLowe 2006, Reference Lowe, Galluzzo and Loux2015, Reference Keinänen and TahkoKeinänen and Tahko 2019, and Reference HommenHommen, forthcoming). It should also be acknowledged that none of this is immediately helpful for addressing the epistemic challenge of figuring out which natural properties indeed are linked to natural kinds, but I think some progress can be made if we have an idea about what the ontology could look like – we will leave the epistemic challenge for another day.

In conclusion, what I hope to take from this discussion is simply that natural kind fundamentalism provides one promising way to support my own take on the unity of science, namely a combination of reductive ontological unity and non-eliminative semantic disunity. The toolbox for this combination employs ontological reduction, semantic pluralism, and natural kind monism, the last of which I have just specified in terms of natural kind fundamentalism. This combination is certainly not the only way to defend ontological unity, but anyone who wishes to defend ontological unity does eventually need to give an account of the ontological basis of this unity, which is why a considerable part of this Element deals with the important question of how natural kinds fit into this picture.