Recently, Piccinini and Craver (2011) have stated three theses concerning the relations between functional analysis (hereafter, FA) and mechanistic explanation (ME) in cognitive sciences. First, they deny the functionalist truism in philosophy of cognitive sciences according to which FA and ME are distinct kinds of explanation (
In this paper, I aim to make a very specific point concerning the mechanist approach to the relations between FA and ME proposed by Piccinini and Craver (2011). I will show that there is a minimalist sense in which
Given this context, I argue that a mechanist stance in the vein of Piccinini and Craver (2011) faces a problem (section 4). Either generality is an explanatory ideal of mechanistic explanations, or it is not. If the latter is the case, then FA is not a kind of ME. In that case,
2. Explanation by Scientific Models
Piccinini and Craver (2011) argue against what they call “the received view” in philosophy of cognitive sciences regarding the relationships between functional analyses and mechanistic explanations. The received view can be stated by two different, but related, theses. The first tenet is
In the context of the cognitive sciences, FA is the analysis of some cognitive capacity, such as visual perception or episodic memory, in terms of the functional components of a system and their organization. Some functional analyses individuate the relevant components both in functional and structural terms, but, crucially, other functional analyses individuate the components only in functional terms, that is, in terms of the causal/ functional profile of each of the purported components of the system. 1 What these latter analyses aim to describe is the abstract functional and dynamical organization of the system, disregarding, at least temporarily, the details of the concrete realization of that functional superstructure. The explanatory interest of a FA is partially determined by the relative complexity of the organization of the components attributed to the target system (Cummins 2010, p. 292).
In contrast, ME is the analysis of a cognitive phenomenon in terms of the constitutively relevant parts, the causally relevant activities of those parts, and the relevant organizational aspects of those parts and activities in the mechanism that produces the phenomenon (Machamer, Darden and Craver 2000, Craver 2007). The component parts in an acceptable ME must be real parts, which means that they should have a stable cluster of properties, they should be experimentally and theoretically robust, it should be possible to use them in interventions into other parts of the mechanism, and they should be physiologically plausible (Craver 2007, p. 132). Piccinini and Craver admit that, especially in the case of complex biological systems studied by the cognitive sciences, the neurobiological realization of a functional component (its corresponding “structural component”) might be so distributed and diffuse as to defy the decomposition and localization heuristics essential to ME. Crucially, the mechanist conception of explanation is supposed to be compatible with the multiple realizability of functional kinds. It should be possible for the same functional component to be realized in different neurobiological kinds (Craver 2007, p. 198; Piccinini and Craver 2011).
The idea I have in mind is that both FA and ME are explanations by scientific models or “model explanations.” The key feature of model explanation is that the
There is some diversity among the articulation of the additional conditions that have to be added to this analysis of model explanation in order to distinguish between non-explanatory or “phenomenological” models and potentially explanatory models. The importance of this distinction is highlighted by Craver as follows:
What conditions must be met by scientific models for them to be explanatory? Morrison (1999) holds that models are potentially explanatory to the extent that they exhibit certain kinds of “structural dependencies” to the represented system. Bokulich (2011) holds that a model
According to Woodward, then, explanatory models enable us to answer a wide range of counterfactual questions concerning how the system would behave if the factors cited in the
An adequate proposal regarding scientific model explanation must be able to distinguish not only between phenomenological and potentially explanatory models, but also between possible explanations and genuinely acceptable explanations of some phenomena. The idea is that not all model-based explanations are equally acceptable. They must be evaluated relative to the representational/explanatory goals that govern and guide the practice of model-building in that domain. Generality, simplicity, precision, empirical support, and coherence with the rest of scientific knowledge are some of the most cited explanatory ideals of model-based science (Levins 1966, Weisberg 2007). I will describe some of the relations among these explanatory ideals in section 3.
What I would like to stress is that if FA and ME make essential references to scientific (idealized) models, then they are to be considered model explanations, and therefore, there is a clear (although minimal) sense in which both FA and ME belong to the same kind of explanation. There is a great deal of evidence that supports this minimal assertion. First, a mechanistic explanation of some
Furthermore, many paradigmatic functional analyses in cognitive sciences involve the deployment of representational or “cognitive models.” A cognitive model aims to explain some psychological capacity by postulating several kinds of (usually subpersonal) mental representations, computational processes that manipulate and transform those representations, and several resources that can be accessed by those computational processes. Some exemplars of cognitive model explanations are Treisman’s theory of feature
Paradigmatically, then, functional analyses of psychological capacities involve the exhibition and development of some representational/cognitive models. Since both FA and ME make reference to idealized scientific models, both of them can be seen as model explanations.
A remarkable feature of this (minimal) negation of
Indeed, Piccinini and Craver (2011) accept that functional modeling and mechanistic modeling are “autonomous” to the extent that each one of these practices is allowed to choose which phenomena to explain, which experimental designs to apply, which conceptual resources to adopt, and the precise way in which they are constrained by scientific evidence from adjacent fields. It seems to me that these four kinds of autonomy render functional modeling quite autonomous from mechanist modeling. 3
Of course, one could argue that there is a more robust or stringent sense in which
1In this paper, I adopt the characterization of functional explanation developed by Cummins (2010). Of course, it is not the only view concerning this subject. Alternatively, one could adopt the “etiological” conception of functional analysis developed by Wright (1973) and then assess the prospects of that explanatory pattern as a kind of mechanistic explanation. I favor the discussion in terms of Cummins’s proposal because it seems to be the main philosophical target of Piccinini and Craver’s arguments. 2Of course, there are ongoing debates in philosophy of biology concerning the very existence and status of laws of nature. It is not my intention to advance any bold claim concerning this topic here. If one is unsympathetic to the idea that there are natural laws governing the biological realm, it is perfectly acceptable to interpret the “laws” that appear in optimality models and other covering law model explanations as “principles” that govern, in any case, the modeled world, in the vein of the semantic conception of scientific theories (cf. van Fraassen 1989; Giere 1999). 3Since the “methodological” varieties of autonomy mentioned in this paragraph are explicitly acknowledged by Piccinini and Craver (2011), it is evident that these comments do not constitute an argument against their position. I mention these kinds of autonomy in order to put them aside and concentrate on the key to Integration being possible according to Piccinini and Craver; namely, that FAs are supposedly (bad) mechanistic explanations.
3. Sketchiness, Generality, and Explanatory Tradeoffs
Piccinini and Craver (2011) maintain that FA in cognitive sciences (typically, the specification of representational models in cognitive psychology) is a kind of mechanistic explanation. This thesis is controversial, since we have seen that functional analyses usually characterize the components of a system only in terms of their functional/causal roles in that system, while mechanistic analyses demand not only specification of the functional profiles of the purported components, but also a detailed description of the concrete structures in which those functional properties are realized. In consequence, these authors develop a sophisticated version of
What are the features common to FA and ME that justify this sophisticated version of
The argument behind the sophisticated version of
Let us consider the first dimension: plausibility. How-possibly models are not phenomenological models, but “loosely constrained conjectures” about the structure and function of the target system. They may exhibit some kind of dynamical organization of parts and activities, but the modeler cannot be sure if those components are real or if they are organized as the model describes. How-actually models, on the other hand, describe all and only real parts, activities, and organizational features of the mechanism that are relevant to the production of the
We can now turn to the second dimension of assessment: completeness. The mechanists seem to rely on a pre-analytical or intuitive notion of completeness. A mechanism sketch is a model that may specify some parts and activities of the target system, but that leaves various representational gaps for components whose functional or structural properties are unknown. On the other extreme of the continuum, an ideally complete model does not incorporate any “filler terms” and describes all the features that are relevant for production of the
I will expand upon this characterization of completeness as a regulative ideal in the following section. Here, I would simply like to stress that the mechanists tend to limit the discussion of the explanatory goals of modeling to the ideals of plausibility and completeness/precision.
The second tenet of Piccinini and Craver’s argument for
I would like to argue that, even if one accepts that cognitive models intend to represent the same multilevel mechanisms that mechanistic models do, and even if one concedes that cognitive models represent their target mechanisms without maximizing precision, it does not follow that they are unsatisfactory explanations of the phenomena they intend to explain. My argument in favor of the acceptability of “sketchy” cognitive models relies in the philosophical work of Weisberg and colleagues concerning the structure of tradeoffs in model building (Weisberg 2006, 2007, Matthewson and Weisberg 2008,
The ideas of this research tradition in philosophy of science were advanced by Levins in the sixties. According to Levins (1966), when confronted with the task of theoretically representing the structure and internal dynamics of complex systems, the modeler has two main options or approaches. First, she can adopt a “brute-force approach” in which the aim is to build as much of the target system’s complexity into the model as possible; that is, to build a model which is “a faithful, one-to-one reflection of this complexity” (Levins 1966, p. 421). The representational ideal associated with this brute-force approach is
Levins (1966) mentions three main problems with the brute-force approach to complex systems: there would be far too many parameters to measure, the dynamical equations would be insoluble analytically, and, even if they were soluble, the results of those equations would have no meaning for us. Considering these obstacles, a modeler may disregard the ideal of
The first ideal is generality. It is a
The second ideal is realism. The term “realism” is used, though not clearly explained, by Levins (1996). Weisberg (2006) construes this ideal as being related to the dynamical fidelity or accuracy of the
Finally, the third representational ideal is precision. It corresponds to the fineness of specification of the parameters, variables, and other parts of model’s descriptions (Weisberg 2006). Matthewson and Weisberg (2008) represent a parameter value as the central value for the parameter plus or minus the uncertainty associated with it. The idea is that precision increases as uncertainty decreases. This ideal of precision, in conjunction with realism, seems to be presupposed in the diatribe of mechanists against the use of “black boxes”, such as those that are common in purely functional cognitive models.
A crucial feature of the idealization approach to scientific modeling is that there are several tradeoffs among the representational/explanatory ideals mentioned above. It would be perfect to maximize the three
Relevant to my present interests is the well-established fact that there exists a strict tradeoff between precision and P-generality. It is impossible to increase the magnitude of these attributes at the same time; if there is an increase in precision, there follows a decrease in P-generality and vice versa. To present the argument these authors advance in favor of this thesis, it is indispensable that we introduce the distinction between model descriptions, models, and the target of models (Matthewson and Weisberg 2008, p. 178). Any model description selects a set of models considered as mathematical or abstract structures. A single model description may pick out several models, and one single model may be selected by several descriptions. It is important to bear in mind that precision is an attribute of model descriptions. Suppose that a model description
The fact that there is a strict tradeoff between precision and P-generality leaves two available strategies for the idealization approach to model building. A modeler can either sacrifice generality to gain precision and realism, or she can sacrifice precision to gain generality and realism. The first strategy is very similar to the brute-force approach. Indeed, according to Weisberg (2006), they are indistinguishable. The sacrifice of generality amounts to the search for a complete and detailed representation of particular phenomena. The second strategy (maximizing generality and realism in detriment of precision) is the one favored by Levins and Weisberg. The reason is that, as I have mentioned, P-generality seems to be directly linked to the explanatory strength of the model. A general characterization of the causal structure of a target system allows us to capture similar but distinct phenomena under the principles or equations of the model (Weisberg 2006). Thus,
Now, we must remember that mechanists such as Piccinini and Craver (2011) emphasize the representational ideals of realism (accuracy) and precision in the assessment of potentially explanatory models. From that point of view, mechanists criticize purely functional cognitive models as inadequate or faulty explanations, since the modelers who defend cognitive models tend to concentrate on the causal/functional superstructure of the target system while omitting the structural details of the realization or implementation of the functional aspects they identify. It seems evident that modelers of cognitive models are adopting the strategy favored by Levins and Weisberg; that is, those modelers make the strategic choice to maximize the attribute of generality in detriment of the precise details concerning the neurobiological implementation of the abstract system they describe.
I believe that the main reason or rationale behind the strategic choice of cognitive model modelers in favor of generality is related to certain ideas concerning the status of functional kinds. Particularly, the maximization of generality is linked with the (perhaps implicit) acceptance of the multiple realizability of functional kinds. The mechanists themselves acknowledge that the same psychological capacity is fulfilled at different times by entirely different configurations of neural structures (Piccinini and Craver 2011). But more relevant for our purposes is the purported fact that one psychological capacity can be realized in multiple neurobiological
Considered from the mechanist point of view, the compound eye of the horseshoe crab and the camera eye of some vertebrates are as different as two kinds of neurobiological mechanisms can be. The lateral eyes of the horseshoe crab are composed of simple structures known as ommatidia. Each of these ommatidia contains photoreceptive cells that can activate a central eccentric cell. This central cell is connected to adjacent ommatidia, constituting the “lateral plexus”. These ommatidia are organized in such a way that the activity of one ommatidium can be inhibited by the depolarization of adjacent ones. In contrast with this relatively simple structure of the lateral plexus of the crab, the retina of the vertebrate eye is extremely complex. It is organized into several layers, and there is a greater range of cell types with highly specific connectivity patterns. Since these mechanisms differ in the number and complexity of their parts, in the nature of their activities, and in the dynamical organization of those parts and activities, it is not bold to infer that they are two distinct mechanisms. Despite having different neurobiological properties, however, both mechanisms can produce the same phenomenon of lateral inhibition. In this phenomenon, the activity in one kind of photoreceptor inhibits activity in other receptors. This pattern of activation may produce a particular experience known as Mach bands, the appearance of light or dark stripes after the end of a brightness gradient (Weiskopf 2011b).
What this example illustrates is that the same functional property (lateral inhibition between receptors) that accounts for a phenomenon (the perception of Mach bands) is realized in significantly distinct neurobiological mechanisms across different species (the relatively simple compound eye of the horseshoe crab and the complex mammalian camera eye). A very detailed and/or precise model of the horseshoe crab’s compound eyes would fail to capture the causal superstructure that those eyes share with vertebrate eyes, namely lateral inhibition, a functional property that accounts for some relevant phenomena, such as the formation of Mach bands. Consequently, it would be rational for a modeler interested in capturing that causal superstructure common to different neurobiological structures to choose a modeling strategy that increases the model’s generality. Such a strategy would trade neurobiological precision for explanatory scope.
Therefore, even if a functional model aims to represent the same interlevel mechanism as other mechanistic models, and even if the functional model sacrifices neurobiological precision, it could be the case that the modeler’s choice of maximizing generality results in an increase of explanatory scope. The mechanists’ choice to maximize precision is not justified
We have seen that even when both FA and ME intend to offer model explanations (section 2), they seem to adopt different strategies in the context of the idealization approach to complex system modeling (section 3). While FA tends to maximize generality at the expense of structural precision or detail, ME tends to maximize precision at the expense of generality. The same point can be formulated as a problem for the mechanist image of the relationships between FA and ME. The relevant question is: does ME endorse generality as a representational or explanatory goal? I have already mentioned that generality is a common ideal for most models in the idealization approach, but the mechanist emphasis on complete descriptions of mechanisms suggests that perhaps the mechanist conception does not adopt the idealization approach, but rather the brute-force approach. If the latter were the case, then the mechanist stance would drop generality as a
I believe that Bokulich is correct in her diagnosis of Craver’s proposal. However, the argument I want to formulate against the mechanist conception of FA does not require considering the mechanist conception as an instance of the brute-force approach. The objection runs as follows: either the mechanistic pattern of explanation presupposes P-generality as a legitimate representational/explanatory ideal for model building, or it does not. If P-generality is a valuable attribute for mechanist modelers, then they ought to admit that there are relevant modeling scenarios in which adopting a FA can be genuinely explanatory in spite of its lack of structural detail. In that case, it would be false of functional analyses that they are faulty models of mechanisms. It would likewise be false that “explanations that capture these mechanistic details are deeper that those that do not” and that “full-blown mechanistic models are to be preferred” (Piccinini and Craver 2011, p. 307). If P-generality is not a valuable attribute for mechanist modelers, then there is no reason to believe that functional analyses are elliptical kinds of mechanistic explanations. It is important to remember that the best construal of
There are many promissory notes concerning the direction that such an amendment should take. Despite the emphasis that mechanists put on the precision
Craver (2009) exemplifies this issue with different schemata of the hippocampus. First, we have Ramon y Cajal’s schemas of particular hippocampal specimens. These schemas exhibit the precise and detailed locations, shapes, and orientations of the constituent neurons. Next, we have the textbook diagrams of the hippocampal trisynaptic circuit, which are relatively more abstract. These schemata capture the spatial organization of excitatory synapses, but they omit other details concerning inhibitory neurons, support cells, etc. Finally, we have the diagrams in computational models of the hippocampus. These computational models abstract away from most structural details and represent the abstract functional organization among sub-regions of the hippocampus. Each region is represented as performing different functions. This last schema need not be applied only to biological organisms; it could apply to any system that shares its abstract functional superstructure (Craver 2009). In this context, Craver happily accepts that the computational model of the hippocampus, even if it is abstract in regard to almost every neurobiological detail, can offer a genuine explanatory step relative to other, more concrete, scientific representations.
It is evident that mechanists should accept that generality constitutes an important and desirable feature of mechanistic models. The consequence of such an endorsement is that functional models (the kind of models that are legion in cognitive psychology) should not be considered to be faulty or inadequate models of mechanisms. They may be maximizing a legitimate
4It could be maintained that the argument about generality and precision tradeoff (in section 4) could have been made without the No Distinctness. component (in section 2). However, as far as I can see, it is a non-trivial premise of the tradeoff argument that FA and ME belong to the same general class of model explanations. Otherwise, it would not be mandatory for FA and ME to be constrained by (at least some of) the representational ideals that govern model-based science in general.
Piccinini and Craver (2011) maintain three different theses. First, functional analyses and mechanistic explanations are explanations of the same kind. Second, FA is a kind of ME because they share the same representational/ explanatory ideals. Third, FA offers, at best, a faulty or inadequate explanation of a given phenomenon, because it fails to satisfy the ideal of precision. In this paper, I have argued that these three theses cannot be maintained simultaneously. In section 2, I argued that FA and ME are subkinds of model explanation. This minimal assertion denies
Piccinini and Craver (2011) exacerbate the centrality of precision in detriment of generality in model building, but there are reasons to believe that there are contexts in which the alternative strategy is preferable in order to obtain an acceptable explanation of the