Reductive Explanation and Mechanistic Explanation

Abstract

Reduction reconciles diversity and directionality with strong unity, without relying on elimination. Unity is achieved by identification; diversity is conceptual or descriptive in nature; but what about directionality? Directionality can be accounted for in terms of explanation. The present and the following chapter motivate this idea and connect it to the thesis that reductive diversity is conceptual diversity. To get an idea of what reductive explanation consists in, it is compared to recent models of mechanistic explanation. It is shown that reductive explanation is a cognate of mechanistic explanation. It is argued that characterizations of mechanistic explanation fail in several respects – for example, the alleged importance of differences between ‘by’- and ‘because’-explanations in recent models of mechanistic explanation is overestimated, and the ontological dimension of mechanistic dependence is often misinterpreted.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reduction reconciles diversity and directionality with strong unity, without relying on elimination. Unity is achieved by identification; diversity is conceptual or descriptive in nature; but what about directionality? Directionality can be accounted for in terms of explanation. The present chapter and the following chapter motivate this idea and connect it to the thesis that reductive diversity is conceptual diversity.

1 Reduction – A First Explication

Consider, again, our standard example: Water reduces to H₂O. I propose the following reconstruction of this sentence’s truth-conditions: Water reduces to H₂O iff for every x, if x is water then (x is water because x is H₂O), and being water = being H₂O. We should add that no conceptual explanation is involved; otherwise, all conceptual explanations, what was briefly gestured at in Sect. 2.2.3, such as ‘this is a drake because this is a male duck’, would turn out to be reductive explanations. Mere identity of properties does not suffice for conceptual constitution or analysis, or whatever conceptual dependence consists in – we cannot account for the concept of water in terms of the concept of H₂O. Note that one may want to introduce a broader notion of reduction that encompasses both sorts of reduction, conceptual as well as non-conceptual reduction. These kinds of explanation may even bear striking similarities. Here, we are concerned with the non-conceptual case of reductive explanation only.¹ This yields a first explication of the notion of reduction, here restricted to the reduction of types or kinds.

(Explication I – Kind Reduction) :

F-ness reduces to G-ness iff

• (i) for every x, if x is F then (x is F because x is G), and

• (ii) F-ness = G-ness.

Condition (i) is, thus, to be interpreted as a non-conceptual explanation. Instances of it do not illuminate the concept expressed by the predicate in the position of ‘F’. Note again that the logical form of ‘water reduces to H₂O’ is maybe not perfectly captured by ‘F-ness reduces to G-ness’ – one might expect a quantified phrase, rather than a phrase containing terms referring to properties or kinds. However, sentences such as ‘water reduces to H₂O’ are used to express the idea that the kind water is identical to and reduces to the kind H₂O; thus, deviating from what might seem to be the grammatical surface structure seems justified (to repeat: we are dealing with a technical term, where occasionally, the intended use weighs more than grammatical surface-structure).

This candidate explication suffices, in a sense, for a full-blown explication of the concept of (property-)reduction. It guarantees strong unity because of condition (ii). Note that due to this condition, we do not have to add a necessity operator in condition (i). Condition (i) captures directionality, and it ensures conceptual diversity: In condition (i), we face the interesting case where explanans and explanandum of an explanation are intensionally equivalent, but do not yield conceptual analysis. This can be illustrated referring to the idea of Russellian propositions: The Russellian proposition expressed by ‘this is water’ and ‘this is H₂O’, when uttered in an appropriate context that fixes the meaning of ‘this’, is, roughly, <the object referred to by ‘this’, being water> in both cases. The difference between explanans and explanandum in virtue of which we get explanatory dependence is conceptual in nature.²

This definition clearly distinguishes reduction from other dependence relations such as causation on the one hand, and conceptual dependence on the other. Causation is incompatible with condition (ii) – without an appropriate time-index, the properties alluded to in a causal explanation have to be distinct. One may want to hold that one is a smoker now because one was a smoker last year, and that this explanation can be given a causal interpretation. Removing reference to times, however, radically changes the situation. No one’s being a smoker at t₁ causally depends on her being a smoker at t₁, in any sense. The relation of this and similar definitions to characterizations of ontological dependence or grounding will be discussed below (see Sect. 9.3). For the moment, suffice it to say that we adequately characterized one form of identity-based reduction in terms of a specific sort of explanation.

But can’t we say more about this sort of explanation? Sometimes, philosophers have intuitively described reductive explanation as mechanistic explanation (Fodor 1974; Chalmers 1996; Kim 2008) – an idea also alluded to in the intuitive descriptions assembled in Chap. 2 (Wimsatt 2006). The remainder of the present Chapter is dedicated to a discussion of the relation between reduction, as captured by (Explication I), and what has been intensively discussed under the title ‘mechanistic explanation’ within the past few years. Building on this discussion, the next chapter suggests that differences in meaning in reductive explanation reflect differences in modes of presentation, or differences in the way an object is presented as having specific properties.

Mechanistic explanation is usually described in terms of ‘by’-explanations. Before turning to the details of the relation between reductive and mechanistic explanation, let me firstly argue that there is a variant of (Explication I) which comes in ‘by’-format as well.

2 Reductive ‘By’-Explanations

Craver and others deny that mechanistic explanation is reductive (see below). To tentatively motivate the idea that there is a tight connection between reductive and mechanistic explanation, consider candidates for reductive ‘by’-explanations: ‘things freeze by forming lattice structures’, and ‘things pump blood (naturally) by the rhythmic contraction of muscles in an appropriate environment.’³ Here are the corresponding reduction statements:

• (1) Freezing reduces to lattice-structure formation, and:

• (2) (Natural) pumping of blood reduces to rhythmic muscle-contraction in an appropriate environment.

Even (1) and (2) express falsehoods, we can learn something about reduction pretending that they are true. And here are the truth conditions, now in terms of ‘by’-explanations:

• (1) Freezing reduces to lattice-structure formation iff

  • (i) For every x, if x freezes, then x freezes by forming lattice structures, and

  • (ii) Freezing = Lattice structure formation.

• (2) Natural pumping of blood reduces to rhythmic muscle contraction in an appropriate environment iff

  • (i) For every x, if x pumps blood (naturally) then x pumps blood by the rhythmic contraction of muscles in an appropriate environment, and

  • (ii) the natural pumping of blood = rhythmic muscle contraction in an appropriate environment.

So, prima facie, some by-explanations figure in truth conditions for at least some reduction statements. We thus arrive at a characterization of the reduction of events (here, again, construed as types):

(Explication II – Event-Reduction) :

ϕ -ing reduces to ψ-ing iff

• (i) for every x, if x ϕ -s then (x ϕ-s by ψ-ing), and

• (ii) ϕ -ing = ψ-ing.

The importance of the distinction between event-reduction and kind-reduction should not be overestimated. It will be shown that reduction, which can be defined in terms of ‘by’-explanations can also be defined in terms of ‘because’-explanations. The idea is that if x ϕ -s by ψ-ing then x ϕ-s because x ψ-s (Schnieder 2009, Sect. 4.5 suggests that the relevant ‘by’-statement implies a sentence of the form ‘it is true that x ϕ-s because it is true that x ψ-s’, Schnieder 2009, 666) and, building on this idea, if x ϕ-s because x ψ-s and, in addition, if (x’s) ϕ -ing = (x’s) ψ-ing, then x ϕ -s by ψ-ing (see below, Sect. 4.5.2). However, since in the debate on mechanisms, grammatical differences between ‘because’- and ‘by’-explanations have often been emphasized, it is worth noticing that at least some reductive explanations, and truth-conditions for reduction statements, can come in the ‘by’-format. Thus, the claim that reductive explanation is mechanistic is not obviously mistaken.

3 Mechanistic Explanation – The Background

Is reductive explanation basically mechanistic in nature? To evaluate this point, we need some background on approaches to mechanistic explanation first. One common criticism of Nagel’s model (and similar approaches to reduction) is that it is concerned with theories (and sciences) only (for an attempt to show that this criticism is misguided, see my (van Riel 2011b)). According to Wimsatt (1976), Darden and Maull (1977), and Schaffner (1993, 2006), this poses a problem especially for sciences that do not contain full-fledged theories, such as biology. A more general worry was that explanations, as construed by Nagel and what one might call the reductive tradition, interpreted explanations as instantiating argument-schemata – what was to be explained was regarded as being derivable from the material that served as (or expressed) the explanans. This covering law model of explanation (basically any variant of the DN-model) was rejected for several reasons we do not have to go into here (a summary can be found in Craver 2007, chapter 2). This sort of criticism inspired philosophers working on mechanistic explanation (Kauffman 1970; Cummins 1975, 1983, 2000; Bechtel and Richardson 1993; Bechtel 1994; Glennan 1996: Machamer et~al. 2000; Craver 2005, 2007). Mechanistic explanation comes under many different labels. Sometimes it is described as constitutive or structural, and it seems to be related to functional explanation. The main idea is nicely captured in the following quote taken from Salmon (1984):

A constitutive explanation is an exhibition of the internal causal structure of the explanandum; such an explanation exposes the causal mechanism within the explanandum. (Salmon 1984, 270)

Constitutive or mechanistic explanation explains something in terms of its constituents, or its underlying mechanism. But what is a constituent, or a mechanism of something?

In a first step, I will discuss the notion of a mechanism as conceived of within the debate on mechanistic explanation. In a second step, the role of specific question-answer pairs for the individuation of the relevant kind of explanations will be examined. Intuitively, these two aspects correspond to two different ways of characterizing an explanation – an ontological and a grammatical one. In a third step, I will point to some problems these candidate characterizations face, and a solution to these problems will be offered. Finally, a characterization of a kind of explanations will be given that covers reductive explanation as a special case.

Before entering the debate, let me briefly mention what I will not focus on, too: Epistemological and pragmatic issues of this kind of explanation will largely be ignored. A great deal of the work of philosophers who describe scientific endeavors as being related to mechanistic explanation consists in the investigation of actual scientific procedures. To this extent, these philosophers work with a paradigm that has been widely accepted in the Post-Nagelian tradition, and which has been described as being based on extension first approaches to reduction in Sects. 2.2 and 2.3. The target explicitly is the description of aspects of scientific investigation (Craver 2007, vii; Bechtel 2008, ix, though Craver assumes that his proposal has normative consequences as well).⁴ These rich debates on actual examples especially in biology and cognitive science will be neglected. Thus, the structure I impose on the debate – the distinction between ontological and grammatical characterizations – has the status of a reconstruction. In the debate, these are intertwined with each other as well as with discussions of other aspects of mechanistic explanation.

3.1 The Ontological Characterization of Mechanistic Explanation

A mechanism is, according to one standard interpretation, a complex entity, consisting of constituents that are organized to do something.⁵ An appropriate description of a mechanism explains the occurrence of the phenomenon to be explained. Characterizing mechanistic explanation in terms of what it is concerned with, i.e. in terms of how it relates to the worldly stuff whose interconnections give rise or correspond to mechanistic explanations, is characterizing it in ontological terms. It is similar to characterizing causal explanation giving an account of causal dependence, and it is similar to characterizing conceptual explanation in terms of the relations between concepts conceptual explanations allegedly track. This is an important (implicit) assumption: That on the one hand, we have explanations, whereas on the other, there are worldly relations corresponding to explanations, in virtue of which explanations are true or false. On this picture, a causal explanation is causal only insofar as it is (purportedly) about or corresponds to a causal relation, and it is true only if (and if so, in virtue of the fact that) the relevant causal link is instantiated out there. A conceptual explanation is conceptual only insofar as it is (purportedly) about or is concerned with a conceptual link, and it is true only if (and if so, in virtue of the fact that) the relevant conceptual link holds. Let us refer to such relations as ‘explanatory relations’. They are explanatory in the sense that if they hold, there is at least one corresponding explanation that is true in virtue of the fact that this explanatory relation is instantiated. Consider the following explanation: He drank the water because he was thirsty. The explanation is a true causal explanation if and only if (and if so, in virtue of the fact that) his being thirsty, the event, caused his drinking the water, another event (the target of the explanation). We characterize an explanation referring to a corresponding relation that is explanatory in nature.⁶

On this view, we can distinguish between kinds of explanations by appealing to corresponding explanatory relations. Conceptual explanations are different from causal explanations insofar as they correspond to different explanatory relations.⁷ This is one of the two main strategies pursued by philosophers who work on mechanistic explanations. They describe mechanistic explanations in terms of the worldly relation purportedly corresponding to mechanistic explanations. Let us call this relation ‘mechanistic dependence’. An explanation is mechanistic if and only if it is (supposed to be)⁸ about or concerned with a mechanistic dependence relation.

For what follows, it will prove useful to mark a distinction between the explanandum (and an explanans) as a proposition, and the entity that figures as the target of an explanation. Explanans and explanandum are here conceived of as conceptual contents. Consider again the following example: He drank the water because he was thirsty. The explanans is the proposition that he was thirsty; the explanandum is the proposition that he drank the water. The target of the explanation is his drinking the water – an event. This is a verbal point; one may want to label the target ‘explanandum’. Some such distinction is needed to reconstruct the relevant aspect of the discussion about mechanistic explanation, although it is not always clear what the target or object of an explanation is supposed to be. Intuitively, the target of an explanation is the entity the explanandum of an explanation is about. For some cases, it will be relatively easy to identify the target of an explanation. In an explanation of why a specific Tsunami occurred, the target is the occurrence of a specific Tsunami. Asking how humans are able to cognize the actions of others as intentional, the target is the human ability to cognize the actions of others as intentional. Sometimes, however, things are more complicated. What is, for example, the target of an explanation of why salt dissolves in water? Is it the disposition of salt to dissolve in water? Or is it an event type, i.e. the event of salt dissolving in water? Or is the target just the proposition or the fact that salt dissolves in water? These questions may not pose insurmountable problems; but trying to answer them would take us too far from our actual target. Let us rely on an intuitive understanding of the notion of a target of an explanation – we will need it for heuristic purposes only.

On the ontological interpretation of what it is for an explanation to be mechanistic, we have to give an account of mechanistic dependence. A mechanism is what is supposed to do the explanatory work in a mechanistic explanation; intuitively, a mechanism is what gives rise to the target. There are a number of different characterizations of what a mechanism is. I will work with a minimal characterization. First of all, it is important to note that mechanisms are mechanisms of some phenomenon (Glennan 1996, 2002; Craver 2001, 2007) to be explained by that mechanism. This motivates tying the notion of a mechanism to what it does, an idea reflected in Craver’s characterization:

Mechanisms are collections of entities and activities organized together to do something. (Craver 2005, 385)

On most accounts, the notion of a mechanism depends on the notion of organization (cf. Bechtel and Richardson 1993; Glennan 1996, 2002; Machamer et~al. 2000; Bechtel and Abrahamsen 2005; Bechtel 2007). This is what gives, on these accounts, rise to the explanatory link. The explanatory relation is instantiated by the target and what gives rise to the target. The heart pumps blood by the orchestrated interaction of its constituents. The constituents are organized to give rise to the heart’s pumping blood.

For what follows, we should rely on an intuitive understanding of organization (we do not get more than that in the debate on mechanistic explanation): Computers and their functioning, perceptual systems, cells, and bodily parts are organized to do something.⁹ For mechanistic explanation, we can then rely on Cravers description, giving a sketch of the notion of a mechanism (the notion of an entity is here used in a wide sense, such that we do not have to mention activities in addition): Something is a mechanism iff it is a collection of entities, which are organized to do something. ¹⁰ And something is a mechanistic explanation iff it corresponds to the instantiation of a mechanistic dependence relation, where ‘correspondence’ just mimics the intuitive ‘being (purportedly) about’.

The characterization of mechanistic dependence is, however, still rather meager. We may hope to learn more considering the notion of a component in or of a mechanism. As Craver puts it:

Mechanistic explanations are constitutive or componential explanations: they explain the behavior of the mechanism as a whole in terms of the organized activities and interactions of its components. (Craver 2007, 128)

We should take this literally: Reference to capacities of components is required to make an explanation mechanistic. So, what is a component of a mechanism?

Components of mechanisms are supposed to be mechanisms themselves (with the possible exception of components at some fundamental level). To avoid long exegetical remarks, I suggest the following interpretation: A mechanism, an ordinary object or entity, is a collection of other ordinary entities,¹¹ which, together, engage in an event that explains the event produced by the mechanism or by another object the mechanism belongs to. Not every proper part of the object that produces the phenomenon to be explained needs to be a component in the mechanism. The entire mechanism may be a proper part of another object that performs a certain task that depends on the functioning of the mechanism. Consider a watch and its mechanism. A watch represents times successively. Representing these times successively is an event. A watch contains proper parts. These objects – gears, screws etc. – engage in doing something, they are bearers of events, the occurrence of which brings about the functioning of the watch. Some parts of an ordinary watch belong to its mechanism, whereas others do not. Assume that one of the gears in our watch bears the watchmaker’s signature – a physical object consisting of, say, ink. This may be a proper part of the watch, but it does not contribute to its functioning. In this case, the mechanism is a proper part of the watch. Other objects may have a mechanism as an improper part. In that case, the object is identical to the mechanism. There could be a watch that is identical to its mechanism, representing times successively by the mechanism being in different states. The functioning of both kinds of watches mechanistically depends upon the events its mechanism’s components produce.

Often, it is suggested that the relation of being a component is non-causal (Bechtel 2007; Craver 2007): The functioning of the constituents of V1 (an area processing visual information) does not cause V1 to process information – these constituents and their functioning constitute V1’s processing information. Thus, we have a relation between a complex, encompassing event, the processing of information by V1, and the events underlying or constituting this event. Giving an appropriate description of the mechanism in terms of its components or constituents, we should mention the causal organization of the mechanism’s constituents (Craver 2007, 62, this also underlies Salmon’s 1984 and, in a similar fashion, Causey’s 1977 conception of constitutive explanation), because it is their causal functioning that explains the functioning of the whole. Thus, it is assumed that it is the component’s causal organization that gives rise to the mechanism’s behavior. This idea of giving rise to something – an explanatory notion, as the quote from Craver suggests – is crucial: It is the notion corresponding to mechanistic dependence we need in order to come up with an appropriate characterization of mechanistic explanation (on the ontological conception). The idea seems to be this: A part x of an object that has mechanism M to produce E is a constituent or component of M if and only if x produces some event y, such that M’s producing E occurs (partly) in virtue of the occurrence of y.

Note that here, we make use of the notion of ‘in virtue of’ in order to define the notion of a constituent, which, in turn, enters the characterization of a mechanistic explanation; this is somewhat similar to the way in which ‘reduction’ was defined in (Explication I) above. This is obviously not to say that this isn’t an interesting definition of what a component in a mechanism is supposed to be. However, following this line of thought, we must not hope to come up with a “reductive” definition of mechanistic explanation, unless we possess a general strategy to get rid of ‘in virtue of’- and other explanatory talk.

To sum up: On the ontological account of mechanistic explanation, an explanation is mechanistic iff it corresponds to the instantiation of a mechanistic dependence relation. Correspondence is still an intuitive notion: Just like the explanation that he drank water because he was thirsty is causal in virtue of somehow corresponding to an alleged causal relation, mechanistic explanations are supposed to correspond to mechanistic dependence relations.

The relata of a mechanistic explanation are events – one event the mechanism (or another object) is the bearer or the subject of, and an event its components are the bearers or the subjects of. To clarify this jargon: Persons are the “bearers” of their actions, houses are the “bearers” of their burnings, and watches are the “bearers” of their representing times. In the light of this, we can characterize mechanistic dependence: one event mechanistically depends on another event if and only if the latter is an event the bearer of which is a component in the mechanism to produce the former. And when is an object a component in a mechanism? We already gave the sketch of an answer above. To keep things simple, let us focus on the case where the mechanism is identical to the object that produces the target phenomenon. Here is the characterization again, in a more precise form (schematically):

(Components of Mechanisms): :

x is a component in the mechanism, y, to ϕ iff y ϕ -s (partly) by the ψ-ing of x.

One may want to add a nomological necessity operator to the right hand side, so as to ensure that no arbitrary, merely temporal dependence relation is covered. In the context of the life sciences, we might hope to substitute this talk by ‘being selected for’-talk; and in the case of artifacts, such as watches, we might want to limit this talk to talk about intended use, or de-facto use within a social group. Thus, one may add a conjunct that x was selected, or chosen for ψ-ing. For present purposes, this characterization is sufficient. It yields an ontological characterization of mechanistic explanation in the sense that it enables us to characterize mechanistic explanation in terms of a corresponding ontological relation of mechanistic dependence, which, in turn, rests on the notion of a component in a mechanism. There is, however, another strategy in the debate: That of characterizing mechanistic explanation in terms of certain grammatical surface-properties of sentences that express these explanations.

3.2 The Grammatical Characterization of Mechanistic Explanation

In an ontological characterization, kinds of explanations are distinguished in terms of corresponding ontological relations. On what I have labeled ‘grammatical accounts’, explanations are distinguished in terms of different linguistic features exhibited by different explanations.

Following Craver and Bechtel, mechanistic explanations are constituted by answers to certain ‘how’-questions (in a non-evaluative sense, as one should hasten to add (cf. Schnieder 2009)). Such questions take the form ‘How does x φ?’ A corresponding explanation is, then, a ‘by’-explanation of the following form ‘a φ-s by (b’s) ψ-ing’. Reference to ‘b’ is relevant insofar as we sometimes face explanations such as ‘the heart pumps blood by the organized contraction of its constituent muscles’. To connect this to the less precise talk above: In the position of ‘a’ or ‘b’ we substitute an expression that designates the bearer of an event; in the case of ‘a’, it is the mechanism, in the case of ‘b’ it is the component, or the collection of components. Note again that this characterization perfectly matches the idea that what is to be explained is the occurrence of an event.

But does this grammatical characterization suffice? It does not, as long as we intend to capture mechanistic explanation only. Two possibly problematic cases have been recognized in the debate: that explanations that refer to mere models as well as non-mechanistic functional explanations may come in the same format. Therefore, the grammatical description is flanked by additional requirements:

Firstly, mechanistic explanations correspond to, as Craver has recently pointed out, pairs of ‘how-actually’-questions and their answers. Intuitively, a ‘how-actually’ question is to be distinguished from a ‘how-possibly’ question in that an answer to a ‘how-actually’ question has to refer to the actual mechanism which in fact produces or constitutes the phenomenon to be explained (Craver 2007, Chapter 4 – here, one also finds a detailed discussion of the distinction between these two kinds of questions). Mere models in science give answers to ‘how-possibly’ questions. Now, Craver conclusively argues that it is this aspect that increases the explanatory power of mechanistic explanations (Craver 2006, 2007, chapter 4). Following Robert Cummins (1975, 1983), Daniel Dennett (1994), and Herbert Simon (1969), Craver argues that giving descriptions in terms of homunculi, sub-systems, reverse engineering, decomposition or functional organization is a useful guide to the relevant sort of constitutive explanation. He argues that these strategies have to be accounted for in terms of aiming at explanations that reveal what actually happens.

Here is an interesting side effect: Knowledge of answers to ‘how-actually’ questions will increase the manipulability of the phenomenon we are interested in (it gives, intuitively speaking, a more detailed list of possible nodes we can influence) (Craver 2006). This is an interesting epistemological and pragmatic point: If we were able to give a detailed description of the causal organization of a phenomenon, we would be in the position to give a more detailed list of possible interventions (Woodward 2003; Pearl 2000). Based on mere models, this will be difficult: The objects postulated by a mere model just do not exist. An ideal mechanistic description would give us all the relevant aspects of mechanistic organization (Craver 2006). Mechanistic descriptions we are able to give do less than that, but they nevertheless increase our understanding of how things work and, thus, increase the ways in which we can intentionally intervene on them – a topic picked up again in Sect. 9.4.

Secondly, asking how Oswald killed Kennedy, we may seek an answer in terms of the actions he performed that constituted his killing Kennedy. An appropriate answer to this question is this: He killed Kennedy by shooting him.¹² This is an instance of a ‘how-actually’ explanation, but it is not a mechanistic explanation. Rather, it is what is sometimes referred to as a functional explanation. In another context, this has been recognized by Craver (2007, 129), who takes this point from Cummins (1983). I suggest that nevertheless, constitutive explanation should be regarded as a variant of functional explanation. Recall: it is the constituents’ causal functioning that explains the functioning of the whole. The moral to be drawn from these points is rather important: characterizing mechanistic explanations as corresponding to pairs of ‘how’-questions and their answers does not fully capture the notion of mechanistic explanation. Moreover, as already indicated in Sect. 4.2, it will turn out that there is no sharp distinction between ‘by’-explanations and ‘because’-explanations (see Sect. 4.5.2). If there are no further grammatical differences available, an appropriate characterization of mechanistic explanation has to build on ontological criteria, say, concerning the difference between constituents on the one hand, and what is reflected in the debate on action-individuation as the accordion effect on the other.¹³ As will become apparent below, there are further difficulties with this characterization: First of all, ‘how’ questions do not play the prominent role they purportedly play in the context of mechanistic explanation, and a family of explanations, namely, reductive explanations, transcends the boundaries determined by the focus on organization and the rather demanding notion of components.

This notion of mechanistic explanation in mind, let us turn back to the question of how mechanistic explanation relates to reductive explanation. Based on the rough characterizations just given, it will now be argued that mechanistic explanation perfectly matches the idea that we get diversity in terms of differences in conceptual material, unity in terms of identity, and directionality in terms of explanatory dependence. In order to see how unity relates to mechanistic explanation, let us first consider the notion of mechanistic levels – it forms the guide to understanding unity in models of mechanistic dependence.

4 Identity in Mechanistic Explanation

Is reductive explanation mechanistic explanation? If so, the conception of mechanistic levels ought to be compatible with strong unity in a mechanistic hierarchy. The following bi-conditional states the suggested connection between level-talk and the property of being a component of a mechanism:

X’s φ-ing is at a lower mechanistic level than S’s ψ-ing if and only if X’s φ-ing is a component in the mechanism for S’s ψ-ing. (Craver 2007, 189, similarly in Craver 2005, 389 and in his 2007, 170)

Levels of mechanisms are thus to be understood as levels of components which, in turn, can be accounted for in terms of their components, which, in turn, can be accounted for in terms of their components, and so on.¹⁴ Based on the relation of being a component in, we get the following picture of hierarchies of mechanistic levels: Let us call the mechanism we want to explain on a given occasion the target-mechanism (just like in general, what we want to account for in an explanation the target of that explanation). A component in one mechanism may be the target of another mechanistic explanation.¹⁵ A mechanism’s components are organized in a hierarchical structure: Some constituents of the target mechanism are themselves constituted by other mechanisms, which in turn are constituted by other mechanisms and so forth. The constitution-relation gives an idea of a hierarchical organization of levels of mechanisms. It also matches the idea of explanation: We explain a complex in terms of the arrangements and interactions of its parts (and their properties). Building on this picture, we may now turn to the question of whether or not mechanistic explanation is compatible with reduction, as conceived of here: Is it (conceptually) possible that the relevant object an explanandum is concerned with is identical to the object relevantly referred to in the explanans? Is it the case that necessarily, if S φ-s by the ψ-ing of some of its constituents, then S’s φ-ing ≠ S’s constituents’ ψ-ing?

Craver (2007) shifts between reductionist and anti-reductionist descriptions of mechanistic (here figuring as ‘constitutive’) explanations. On one occasion, he writes:

There are two dominant and broad traditions of thought about constitutive explanation: the reductive tradition and the systems tradition. My view is a development and elaboration of one strand on the systems tradition. (Craver 2007, 108)

Thus, “his view” opposes reductive interpretations of mechanistic explanation. Some pages later, however, the following intuitive characterization of the system approach is given: It is ‘to reduce a capacity to the programmed exercise of sub-capacities’ (Craver 2007, 110). So, is mechanistic explanation reductive, or isn’t it? One might suggest solving this tension in the spirit of Kim (2008) and others (Chalmers 1996, 43, Fodor 1974, 107) who give an idea of reductive explanation as opposed to (identity-based) reduction in terms of mechanistic explanation. According to this view we can have reductive explanation without reduction as being based on identity. Kim goes a step further, claiming that we cannot have both at the same time: identity-based reduction and reductive explanation (conceived of as closely tied to mechanistic explanation) contradict each other. This would nicely fit Craver’s way of talking – that mechanistic explanations do not yield reductions, but, nevertheless, reductively explain some capacity.

4.1 Kim’s Worry

This is Kim’s worry: Given that a = b, and a reduces to b, and a is to be explained in terms of b, we face a problem: Since nothing can be explained by itself (Kim 2008, 102 f., 106), we cannot have both at once, identity-based reduction and the corresponding reductive explanation. Put differently: Reductive explanation would essentially be trivial; any such explanation would be plainly false. Here is, however, a rival intuition:

What reduction needs […] is the idea that the ‘reduced phenomenon’ is made more comprehensible or intelligible by being shown to be identical with the ‘reducing phenomenon’. (Crane 2001, 54)

If, say, water is made more intelligible by being shown to be identical to H₂O, then it seems that water (or its behavior) is thereby somehow explained. But how can an explanation foster our understanding and, at the same time, be trivial? This is impossible. So, who is right?

Kim’s argument rests upon a misunderstanding. An explanation is trivial only if its explanandum is relevantly contained in its explanans. One straightforward kind of this containment is this: Explanations of the form ‘p because p’ are trivial and false (if ‘p’ is not relevantly ambiguous and disambiguated on both occasions). There might be more subtle kinds of problematic containment of the (parts of the) explanandum in the explanans. However, brief reflection upon what the relevant material, that is contained in the explanandum, is will help solve this problem: The connection between triviality of an explanation and containment of fragments of the explanandum in the explanans concerns, at best, the conceptual level, i.e. ways in which things are presented by the meaning of an expression.¹⁶ It does not concern the ‘metaphysical level’, i.e. what is represented by the meaning or the conceptual content.

4.2 Kim’s Mistake

What Kim misses is this: Explanations are not individuated by the properties and individuals their constituents pick out in order to explain, but rather by the way they present us with these properties and objects. This is pointed out by Ned Block (who uses the term ‘fact’ in the way I would use ‘proposition’):

Just as knowledge of the fact that freezing happened is not knowledge of the fact that lattice-formation happened, so also an explanation of the fact that freezing happened is not an explanation of the fact that lattice-formation happened. By contrast: just as the time at which freezing happened is the time at which lattice-formation happened, so the cause of freezing is also the cause of lattice formation. (Block forthcoming)

Block’s point is that we can give different explanations which both refer to the same objects (cause) in the explanans. He argues that the cause of freezing = the cause of lattice formation. However, the explanation of why lattice-formation happened is different from the explanation of why freezing happened. This is so because the explanans and the explanandum have, in both cases, different meanings, although they give access to the same state of affairs, or law-like connection. For an explanation to be trivial, meaning identity, or identity of conceptual content, or identity of Fregean sense is required. This is Block’s point, or so it seems: knowing that freezing happened is not knowing that lattice-formation happened, because ‘lattice formation’ and ‘freezing’ have different meanings. So, the principle that nothing explains itself seems to require quantification over entities as presented by a certain meaning. It should be clear that conceptual difference between explanans and explanandum is a requirement for the truth of explanations such as the explanation of the human capacity to cognize the other as social in terms of mirror neuron mechanisms. Similarly, nothing is water because it is water, though, in the spirit of (Explication I) one may want to suggest that water is water because it is H₂O. Thus, conceptual difference is, again, the relevant point here: Even though water is identical to H₂O, H₂O can, in some sense, “explain water”. H ₂ O comes in the appropriate conceptual shape. Thus, difference in meaning is a pre-requisite for reductive explanation. But conceptual difference does not necessarily translate into ontological difference. The principle Kim seems to allude to, that nothing explains itself, is, as he interprets it, misguided.

4.3 Identity

There is, at least prima facie, no reason to assume that reductive explanation is incompatible with identity-based reduction. It is at least conceptually possible that the freezing of water just is the formation of lattice structures by H₂O-molecules. Thus, one candidate reason for denying the possibility of cross-level identities in explanatory hierarchies has been dismissed. Even if nothing can be explained by itself (no explanans should be identical to its explanandum), an explanans and an explanandum may still refer to or be about the same object.¹⁷ But isn’t there positive reason to assume that mechanistic explanation allows for the relevant cross-level identities?

S’s φ-ing is explained in terms of an underlying mechanism, which consists of entities that engage in certain events, which, together, give rise to S’s φ-ing. ‘S’s φ-ing’ is an expression that designates an event in a mechanistic explanation. A mechanistic explanation is an explanation of an event-type, some S’s φ-ing, which is explained by interactions of components of S. Recall the idea of a component: A component is the bearer of an event in virtue of which the relevant activity of the overall-mechanism occurs. Components are parts of mechanisms. But what is the relevant relation between their orchestrated interaction and the event with respect to which they count as components of the mechanism (unlike other parts of the object the mechanism is a mechanism of, like the signature that belongs to the watch, but does not belong to its mechanism)? Here is a thesis: At least for some mechanistic explanations, the event described in the explanandum is identical to the event described in the explanans. And here are three arguments:

4.3.1 The First Argument

The first argument is based on the observation that for some explanations, which are not paradigmatically mechanistic, this idea makes perfect sense. Assume that the freezing of water is nothing but the lattice-structure formation of sums of H₂O molecules. Now, how does water freeze? It does so by the formation of lattice structures of H₂O molecules. Assume that pain is identical to C-fiber stimulation. How do pains occur? They do by the occurrence of C-fiber stimulations. This matches one of the more intuitive examples for reductive explanation. Nagel suggests that when:

… the detailed physical, chemical, and physiological conditions for the occurrence of headaches are ascertained […] an explanation will have been found for the occurrence of headaches. (Nagel 1961, 366)¹⁸

Similarly, assume that our cognizing others as social beings is nothing but the activation of mirror-neurons in motor-regions of our brains. How does the relevant mechanism enable us to cognize others as social beings? It does so by the activation of mirror-neurons in motor regions of our brains. And at least prima facie, there is no reason to assume that this does not generalize to other cases: The mechanism by way of which a watch represents times successively is nothing but the sum of the relevant components, and the event by way of which a clock represents times is nothing but the concerted activation of these components. First of all, it is conceptually possible. Secondly, from the point of the reductionist, it seems economical: Why should we postulate additional events when we have perfectly analogous cases that suggest the economical interpretation? In our paradigm cases, there is no reason to postulate a difference between the events described in the explanans and the explanandum. Why should we postulate a difference, without further ado, in the present case? Thus, we shift the burden of proof. One argument against the compatibility of mechanistic explanation and cross-level identities has been dismissed. Secondly, there are cases that suggest the identity-interpretation.

4.3.2 The Second Argument

The second argument supports the idea that at least sometimes, the identity-interpretation is correct. The Davidson-Anscombe thesis (see, for example, Davidson1963, 1967; Anscombe 1957) states that if x φ-s by ψ-ing, then x’s φ-ing = x’s ψ-ing. According to this view, someone’s pushing a button could be identical to her causing the death of a million people (namely, if that person killed a million people by pushing the button), my driving a car is identical to (a part of) my contribution to the pollution of earth, and so forth. This line of thought has, however, recently been disputed by Schnieder (2009). Roughly, Schnieder argues that instances of ‘x φ-s by ψ–ing’ could be true, even if a corresponding instance of ‘x’s ϕ –ing = x’s ψ–ing’ (which is implied by the Davidson-Anscombe thesis) is false. The idea is that for a ‘by’-explanation to be true, the event relevantly related to the explanans could be a mere constituent, or a “part” of the event relevantly related to the explanandum. Identity is not required. For the present context, suffice it to say that nevertheless, there is reason to assume that at least sometimes, or possibly a sentence of the form ‘x φs by ψ-ing, and x’s φ-ing = x’s ψ–ing’ expresses a truth. This would be sufficient to establish the point we are concerned with here. The generality of the Davidson-Anscombe thesis might be mistaken; this does not imply that necessarily, it is never the case that this form of explanatory dependence goes together with identity, at least under a reading of events as particulars.

4.3.3 The Third Argument

I think that one of the intuitions that play a major role in the reduction debate is this: We can sensibly ask questions such as ‘What is (the nature of) water?’ Or: ‘What is (the nature of) the mechanism that keeps the watch running?’ Or: ‘What is (the nature of) the mechanism that enables us to cognize others as social?’ Sometimes, questions of this sort seek a conceptual explanation. But they may also aim at an answer that reveals the nature of an object, a property, a fact, or an event. If naturalism is true, then answers in terms of molecule-structure, in terms of the interaction of gears and screws, of mirror neurons and synchronization of synaptic activity are promising candidates for appropriate answers. And they may be accompanied by a ‘nothing but’. Water is, accordingly, nothing but H₂O. Hence, it is identical to H₂O. The mechanism that keeps the watch running is nothing but the structured object consisting of gears, screws and the like. And, although the content of this claim may be disputable, some have claimed that the mechanism that enables us to cognize others as intentional agents is nothing but the mirror-neuron mechanism. On a weak interpretation, ‘by’-explanations are at least compatible with corresponding ‘nothing but’ statements. Hence, they are not incompatible with the relevant identity-links. On a more thorough interpretation, it is the search of what these things really, or ultimately are, what their nature is, that gives rise to or justifies the relevant by-explanations. Both interpretations suit the point to be established here: ‘by’-explanations are compatible with the relevant cross-level identities.

Thus, it seems perfectly sound to assume that at least some mechanistic explanations are such that they reconcile conceptual diversity with strong unity. Even if reductive explanation is not basically mechanistic, it is at least a cognate of mechanistic explanation in the sense that mechanistic and reductive explanation overlap. In a mechanistic reductive explanation, the relevant directionality stems from an explanatory relation. What has been proposed as a reductive ‘by’-explanation in Sect. 4.1 seems to be a cognate of mechanistic explanations. Nevertheless, there are important differences. First of all, reductive explanation does not hinge upon the idea that things are organized to do something – this teleological aspect is irrelevant to the broader notion of reductive explanation. Some obviously non-mechanistic explanations, explanations that do not involve reference to organized things, such as the explanation of the occurrences of the freezing of water, are reductive. Moreover, the focus on ‘how’-questions and ‘by’-explanations does not play the role in reductive explanation it is supposed to play in mechanistic explanation according to the model presented above. Emphasizing ‘how’-explanations seems to be a result of the focus on events in theorizing about mechanistic explanation. Reductive explanation should be construed more liberally – that a dollar bill is money may reduce to its being accepted as money, water reduces to H₂O, and the fact that this particular amount of water freezes reduces to the fact that this particular sum of H₂O molecules forms lattice structures. In these cases, no events are alluded to. Let us address these points, before applying some of the lessons drawn from a discussion of mechanistic explanation to a more detailed model of reductive explanation in the next chapter.

5 Mechanistic and Reductive Explanation

We now consider the model of mechanistic explanation as a candidate for a model of reductive explanation of events in general. Does mechanistic explanation, if appropriately combined with identity, make for reductive explanation? Identifying aspects in the characterization of mechanistic explanation that distinguish it from reductive explanation enable us to fully characterize the relation between reductive and mechanistic explanation.

5.1 Teleology

Relying on the characterization given above, a mechanism is necessarily organized to do something. If the freezing of water reduces to lattice-structure formation of H₂O-molecules, and if the notion of a reductive explanation hinges upon the notion of a mechanism, then water-molecules are organized to form lattice structures. This is absurd. Thus, we should get rid of teleology.¹⁹ I suggest replacing the notion of a mechanism by the notion of a constitutive-structure.²⁰ The notion of a constitutive structure is supposed to cover that of a mechanism. Thus, the mechanism of a watch is, with respect to its functioning, its constitutive structure. The mechanism of human social cognition is a constitutive structure with respect to events of social cognition, namely the structure that constitutes events that are instances of social cognition. But whatever the freezing of water depends upon, it is not a mechanism. Water just freezes without being organized to freeze. It freezes because it is constituted in a certain way, without being organized to do something in a way. In a constitutive explanation, we should describe an object in terms of its constituents and in terms of these constituents’ properties. However, a constituent is not necessarily a component in a mechanism.

The thesis is, then, this: Reductive explanation is constitutive explanation plus identity. If identity comes with constitutive explanation for free (a question not to be pursued here), then reductive explanation just is constitutive explanation (with the contention that partial reductions, as defined below, do not amount to, but can be defined in terms of identity-based reduction). But how does constitutive explanation relate to the ‘grammatical’ aspect of theories of mechanistic explanation?

5.2 Grammar

It has been assumed that mechanistic explanations that are constituted by answers to how-questions do not translate into ‘because’- statements. Philosophers sometimes claim this to be a virtue of their mechanistic accounts (see, for example, Craver 2007): They argue that classical approaches to explanations like the DN-model, or unificatory models (one versions of which, namely Kitcher’s 1981, 1989, is discussed and – rightly – dismissed in Craver 2007, chapter 2), miss the point of a great deal of explanations given in science.²¹ Let me briefly point to a problem here. It seems that for a question of the form: ‘How does a φ’, that requires an answer of the form ‘a φ-s by ψ-ing’, there are corresponding questions that come in the ‘why’-format and seek a ‘because’-explanation; or, as Schnieder put it, if ‘[t]hat x ψ-s explains how x φ-s’, then ‘[i]t is true that x φ-s because it is true that x ψ-s’ (Schnieder 2009, 666). Here are two candidates, and the corresponding explanations:

• (i) ‘Why does a φ?’

  ‘a φ -s because a ψ-s’

• (ii) ‘Why did a’s φ-ing occur?’

  ‘a’s φ –ing occurred because a’s ψ-ing occurred.’

Consider the question ‘Why is this a water-constituent?’²² The answer is this: ‘This is a water-constituent because it consists of two hydrogen molecules and one oxygen molecule.’ In response the question ‘How did the heart pump blood?’ we can say that ‘the heart pumped blood by expanding and contracting regularly’. A similar explanation, now using the connective ‘because’, can be given in response to ‘why’-questions: ‘The heart pumped blood because it expanded and contracted regularly’, and, less intuitive but, I submit, equally true: ‘the heart’s pumping blood occurred because its expanding and contracting regularly occurred’. Thus, reductive ‘by’-explanations are covered by the explication given above:

(Explication I – Kind Reduction) :

F-ness reduces to G-ness iff

• (i) for every x, if x is F then (x is F because x is G), and

• (ii) F-ness = G-ness.

We can easily transform the explication reserved for reductive ‘by’-explanations, namely (Explication II):

(Explication II* – Event Reduction) :

ϕ -ing reduces to ψ -ing iff

• (i) for every x, if x ϕ -s then (x ϕ-s because x ψ -s), and

• (ii) ϕ -ing = ψ -ing.

Thus, it is not at all clear what the grammatical difference amounts to. To be sure, there are aesthetic and, maybe, pragmatic differences between these question-answer pairs. Maybe, ‘because’ triggers expectations as to causal explanations, at least if the explanandum deals with an event; and causal explanations cannot be rephrased in terms of ‘by’. ‘Because’ allows for such constructions, ‘by’ does not (cf. Schnieder 2009). This may suffice to grant a semantic difference between the two. However, a reductive ‘by’-explanation can be characterized in terms of a ‘because’-explanation plus identity, thereby canceling the possibility that a causal relation backs up the explanation. It seems far-fetched to claim that the question-answer pairs, together with the additional information, differ fundamentally in informational content. At least for practical purposes, knowing that the pumping of blood of the heart occurred because its expanding and contracting regularly occurred, and that the former is identical to the latter, is equivalent to knowing that the heart pumps blood by its component muscles contracting regularly, and the former is identical to the latter. Thus, the difference between ‘because’ and ‘by’-explanations does not suffice to show that reductive ‘by’-explanations are informationally or otherwise relevantly different from the corresponding ‘because’-explanations plus the relevant identity statement (which excludes the causal interpretation of the ‘because’ statement).

Note that in the debate on mechanistic explanation, we seem to be confronted with somewhat deviant cases. The basic idea is that, intuitively, two different objects may play a role in the explanation – the one being the object that does something which is to be explained, and the other being the object (or objects) which (together) give rise to the target that is to be explained. Here is an example: ‘The heart pumps blood by organized contraction of heart muscles.’ Can such an explanation be given a straightforward reductive interpretation? The identity clause in a characterization of reductive explanation would commit us to plural identities. Schematically:

• 1. F-s φ by the ψ-ing of G-s

• 2. a φ-s by the ψ-ing of b ₁ , b ₂ , b ₃ , …

Corresponding reductive interpretations suggests themselves:

• (1*) The φ-ing of F-s reduces to the ψ-ing(s) of G-s iff

  • (i) F-s φ by the ψ-ing(s) of G-s &

  • (ii) The φ-ing of F-s = the ψ-ing(s) of G-s.

• (2*) a’s φ-ing reduces to the ψ-ing of b ₁ , b ₂ , b ₃ , … iff

  • (i) a φ-s by the ψ-ing(s) of b ₁ , b ₂ , b ₃ , …, &

  • (ii) a’s φ-ing = the ψ-ing(s) of b ₁ , b ₂ , b ₃ , …

To fully account for this idea, we will need an elaborate notion of plural and partial reduction. A reductionist may wish to argue that the pumping of blood of a heart is nothing but the organized contraction of heart muscles (in an appropriate environment). If events are bearer-individuated, then the identity clause will require some sort of plural interpretation. This is a substantive issue, and one may want to hold that if this is so, then we should better reject the reductive interpretation of these explanations. A whole is more than its parts, and events a whole engages in are distinct from the events of the whole’s constituents. The reductionist commitment is that we can identify the latter with the former. So, an explication of reduction should make this commitment transparent; fortunately, an explication does not have to solve the issue of whether or not such reductions are feasible. Section 5.6.2 proposes a way to accommodate these doubts within a reductionist framework, defining a notion of partial as well as of plural reduction without requiring a notion of pluralidentity.

That said, let us turn back to the question of how this form of ‘by’-explanation relates to ‘because’-explanations. Again, it implies a corresponding ‘because’-statement. Schematically, if F-s φ (a φ-s) by the ψ-ing of G-s (of b ₁ , b ₂ , b ₃ , …), then F-s φ (a φ-s) because G-s (b ₁ , b ₂ , b ₃ , …) ψ. Grasping the ‘by’-explanation, we grasp that no causal relation is involved. This is not so for the ‘because’-version. However, together with the relevant identity claim, we can define the reductive interpretation of this form of ‘by’-explanation in terms of an identity claim and the corresponding ‘because’-statement.

Now, ‘why’ and ‘how’ questions do not exhaust the field of questions that seek for a reductive explanation. Remember the connection between ‘what’-questions and ‘by’-explanations tentatively suggested above. Let us push it a bit more: Why shouldn’t we say that answering the relevant ‘what’ questions is, or can be, part of an explanatory project? We may ask what the nature of an entity is and, thereby, seek an explanation. One way of phrasing a ‘why’-question is particularly interesting in this respect: Consider the question: ‘Why is this water?’ It may be interpreted as an epistemic question, seeking for a reason to believe that something is water. It can also be uttered to ask for a conceptual clarification – if one needs an update on the conceptual content of ‘water’. It can, however, also be asked to arrive at a reductive explanation. Depending on context, an appropriate answer to this question may be this: ‘This is water because it is H₂O’. Introducing a contrast, this becomes apparent: ‘Why is this water, rather than the watery stuff from twin-earth?’ Answer: ‘This is water (and it is not the watery stuff from twin earth) because it is H₂O, rather than XYZ.’ Similar questions could be asked for events. They can be captured as follows:

• ‘Why is this an F/a φ-ing’

• ‘This is an F/a φ–ing because it is a G/a ψ-ing.’

A ‘what’-question can be used in a similar fashion: ‘What is water (ultimately)?’ Answer: ‘Water is H₂O’. We may also ask what the cause of something was, thereby seeking an explanation. And we may ask what the concept of knowledge is, or what it consists in, thereby seeking a conceptual explanation. On a technical understanding of ‘explanation’, we do not get an explanation when answering such questions: when answering such questions, we do not get sentences that are or express explanations. There just is no term such as ‘by’, ‘in virtue of’, ‘because’ etc. occurring in these sentences. However, it should be obvious that in explanatory projects, ‘what’ questions may, if appropriately phrased, play a role quite similar to ‘how’- and ‘why’-questions. The moral to be drawn is this: We should not rely on the grammatical nature of questions, or the occurrence of expressions such as ‘by’ rather than ‘because’ in order to determine a kind of explanatory dependence, such as mechanistic or reductive dependence.²³

Here is an additional argument, namely, that the relevant ‘what’, ‘why’, and ‘how’ questions are interdependent in the following sense: they have similar answers whose truth-values stand and fall together, depending on the ontological make-up of our world. Consider these questions (other versions of ‘how’- and ‘why’-questions would work as well):

• 1. How does social cognition occur?

• 2. What is social cognition?

• 3. Why is this social cognition?

Once we vary the ontological make-up of the world in which these questions arise, the corresponding (correct) answers will take a different form simultaneously:

Let us turn the naturalist reductionist position upside down and let us check the interdependence of truth-values to answers to this set of questions. Assume that we live in a the caricature of a Cartesian world in which our soul, a non-physical substance, directly models other souls when coming into their trans-gravitational field (or whatever does the relevant job); let this event be an event of soul-modeling. In this case, we should give a different answer to the first question; How does social cognition occur? By soul-modeling. And what is social cognition? Soul-modeling! The same holds for the third answer: My seeing you as a social being would be an instance of social cognition because it is an instance of soul-modeling. Therefore, varying the relevant bit of ontology of our world, we vary the conditions on answers to these questions. At least to this extent, these questions are connected.

This makes room for broadening the focus. ‘How’-questions are concerned with events. There is no way of phrasing a question about the nature of, say, water in terms of a ‘how’-question (unless the nature of water is fully captured by the events in which water plays a role). Reductive explanation, however, should not only capture ‘by’-explanations, but also explanations such as ‘This is water because this is H₂O’, and ‘This is money because we accept it as being money’. Given the tight connection between ‘by’-explanations and ‘because’-explanations, and the idea that even ‘what’-questions can be explanation-seeking, we should not focus primarily on grammatical surface structure in order to individuate the right sort of explanation.

Mechanistic and reductive explanations at least overlap. The fact that mechanistic explanation has been explicated in terms of ‘by’ explanations does not ground a substantive difference between reductive and mechanistic explanation. Ignoring the difference between properties and event-types, the explication proposed in the beginning captures at least some mechanistic explanations (though plural versions still pose a problem):

(Explication I – Kind Reduction) :

F-ness reduces to G-ness iff

• (i) for every x, if x is F then (x is F because x is G), and

• (ii) F-ness = G-ness.

The connection between reductive and mechanistic explanation suggests an interpretation of the directionality of reduction: Intuitively, a mechanistic explanation gives access to the nature of the entity we are dealing with. So does reductive explanation, by presenting one and the same object in different ways.

6 Conclusion

We have explicated a core notion of reduction, according to which diversity is conceptual in nature, directionality is explanatory, and unity is cashed out in terms of identity. We are, thus, here:

Q1::

How can we reconcile diversity and directionality with strong unity?

…

Th. 3::

Directionality is explanatory in nature; reductive explanation is a cognate of mechanistic explanation.

Th. 4::

In this spirit, a core notion …. can be explicated.

…

The intuitive notion of reductive explanation has been contrasted with a conception of mechanistic explanation. In order to arrive at a cognate of the notion of reduction, we have to abstract away from three features of the notion of mechanistic explanation: we neglect teleology, we do not only focus on ‘how’-questions, and we do not only focus on events as the targets of the explanandum. The concept of kind-reduction has been characterized as follows (the explanation in (i) is non-conceptual in nature):

(Explication I – Kind Reduction) :

F-ness reduces to G-ness iff

• (i) for every x, if x is F then (x is F because x is G), and

• (ii) F-ness = G-ness.

In the light of the similarity between mechanistic and reductive explanation, we may now tentatively characterize the connection between the directionality of reductive explanation and the conceptual diversity involved in reductions as follows: The conceptual difference between the conceptual contents of ‘F’ and ‘G’ is a difference in the transparency to the object’s constitutive structure, or its nature.

Thus, reductive explanation differs from characterizations of mechanistic explanation in that it (i) extends the set of targets, (ii) replaces the notion of a mechanism by the broader (though still intuitive) notion of a constitutive structure, (iii) puts emphasis on the fact that there is a whole family of questions tied to this sort of explanation, and (iv) guarantees the reductive interpretation by stressing the identity-requirement. Dropping this identity requirement, we may arrive at a kind of explanation that covers reductive explanation as a special case. Thus, reduction reconciles descriptive or conceptual diversity and explanatory directionality with strong unity, which is cashed out in terms of identity. But can’t we get rid of explanatory notions in our characterization of the dependence relation? In the next section, I will suggest that even though we cannot, we can say a lot more about relevant features of the descriptive diversity in virtue of which the explanatory link is instantiated in cases of reduction.