I now argue that the two modeling ideals promoted by Marr and Craver (cf. Sects. 3 and 4) are neither incommensurate nor the same as it has sometimes been suspected in the literature. Or in other words, they are not distinct, but also not identical. I then demonstrate that the two modeling ideals by themselves do not secure fully satisfactory and complete explanations of cognitive systems. These two arguments support the basis for the formulation and justification of the MC-theory of explanation as it has already been presented in Sect. 2 and as it is discussed further in Sect. 6.
A presumed distinctness of the modeling ideals defended by Marr and Craver amounts to the claim that the two level hierarchies widely cross-classify systems and phenomena, and that the norms associated with the models do not match up in any systematic way. This was perhaps the view of Churchland and Sejnowski when they insinuated that “(...) when we measure Marr’s three levels of analysis against levels of organization [or mechanism] in the nervous system, the fit is poor an confusing at best” (1992, p. 19).
The disunity in the application of terms between the two normative ideals by Marr and Craver may be counted as evidence for this interpretation. In particular, it is not obvious that Craver (2007) makes a clear-cut distinction between the notions of a “mechanism”, a “representation”, and a “computation”. Instead, he sometimes seems to interpret computational descriptions as (preliminary versions of) mechanistic descriptions.Footnote 13 Marr, in contrast, emphasizes the relative autonomy of the computational level and the algorithmic from the implementation level,Footnote 14 and he stresses that the discovery of neural correlates to cognitive functions has contributed little to an actual understanding of cognition.Footnote 15 These points may suggest a distinctness of the level hierarchies and the normative theories associated with them.
On the other hand, the examples of neuroscientific theorizing briefly reviewed in Sects. 3 and 4 offer some reasons to believe that the hierarchies have fruitful applications in explanations of the same systems and behaviors. After all, both Marr and Craver are primarily interested in explaining the functions and dysfunctions of the human central nervous system. Moreover, the two hierarchies have at least one clear touch point, namely the “implementation states” referred to by Marr’s level 1 and Craver’s levels of mechanism. According to Marr, a satisfactory explanation of a cognitive capacity essentially involves an understanding of how the capacity or function is implemented in the processes at the neural level. This suggests that, even though the terminology of Marr’s and Craver’s level hierarchies is substantially different, the hierarchies overlap conceptually. More specifically, both theories involve descriptions of neural processes, or “mechanisms”, on at least one level.
On the opposite side of the conceptual spectrum, an identity assumption about the two normative approaches would amount to the claim that, despite initial appearance, the descriptive terms within the hierarchies simply corefer in the prototypical explanations of edge detection and other cognitive phenomena. They describe the same structures through different linguistic forms. Or in other words, they are notational variants expressing roughly the same propositions and truth conditions. Consequently, the sets of norms associated with the hierarchies overlap substantially as well. They simply demand an explication of the mechanisms constituting a phenomenon at different levels. This view is in line with an interpretation of computational descriptions as “mechanism sketches”. On this particular interpretation, the direct referents of computational descriptions are neural processes, activities, and concrete objects. They describe the latter as mechanistic descriptions do, though in less detail (cf. also Piccinini and Craver 2011; Kaplan and Craver 2011 and Sect. 6 below).
From the features summarized in Sect. 3, it is clear that Marr was skeptical about a classification of the computational level as another mechanistic level. In his view, the implementation level describing the physical mechanisms of a cognitive system is not sufficient for a full computational explanation that answers “why?”-questions on top of “what?”-questions (cf. also fn. 15 above). Craver, in contrast, points out that “lower levels” understood as sets of mechanisms are sufficient for “higher levels” either in the sense of supervenience or mereology (cf. Sect. 4).
Moreover, Marr’s computational level involves mathematical functions that require a systematic mapping onto physical states to describe a physical system (cf. Chalmers 2011).Footnote 16 Craver’s mechanistic descriptions directly describe concrete processes that causally “map” physical inputs onto physical outputs. Hence, at least from Marr’s perspective, there is a mathematical/concrete disparity between some of the levels in the two hierarchies. These observations suggest a non-identity of Marr’s and Craver’s explanatory ideals.
If the two normative models of explanation are neither distinct nor identical, the question arises whether one of the theories is more adequate and plausible than the other in light of scientific practice. I will now argue that, if taken literally, neither of the two modeling ideals actually secures satisfactory explanations of cognitive systems and of the cognitive phenomena realized by these.
As pointed out in Sect. 3, Marr believed that there are “[t]hree different levels at which an information processing device must be understood before it is understood completely”, namely on the “computational level”, the “representational and algorithmic level”, and the “hardware and implementation level” (1982, pp. 24–25). All of these levels were essential for a “complete” explanation in his view. At the same time, it appears that he saw the computational and algorithimic levels to carry the main explanatory weight (cf. Marr 1982, pp. 11–15).Footnote 17 But also Marr would probably have conceded that having understood how and why the visual system transforms values representing light intensities into edge representations, and having mapped the computational principles onto the propagation of electric signals from the retinal receptors through LGN into V1 still makes a relatively limited explanation of the phenomenon only.
First, such a mapping does not by itself answer the question why it is these regions out of all that are involved in the visual task. Second, it does not specify what the cell assemblies within V1 actually do, how they actually manage to store the relevant information, and how they communicate with other cells. Third, knowledge of such a general projection pattern in the brain in a specific task environment does not help much in predicting how the same organism will behave in different tasks or even in the same task but under the influence of certainc drugs or substances. That is simply because a coarsely grained mechanistic theory is mute about activity patterns of cell networks and singular cells. In short, a mapping of the computational level onto a coarsely grained implementation level may simply not be very informative.
These observations do not imply that the original theory is not useful. If one’s explanatory and manipulative goals are suitably modest, Marr’s three levels are often all that is required. For instance, when the explanandum is a consistent misidentification of edges of certain transparent objects by humans, or when it is a general breakdown of visual perception in a patient with severe lesions in the thalamus, Marr’s model may constitute a satisfactory explanans. It offers correct predictions about both cases, and it scores high on simplicity.
Notwithstanding, rigorous explanation in science is usually expected to aim, among other things, at a high predictive accuracy and a broad generalizability of the selected model (cf. Forster 2000). As Craver and others have long emphasized, there is an important asymmetry between explanation and prediction (cf.Craver 2007, ch. 2.4). At the same time, Craver’s expectation has been that detailed mechanistic models will allow for better predictions in novel circumstances than purely functional models designed to fit a set of past observations.
Consequently, even if Marr gets the predictions right in some contexts, in many other contexts his three-level computational model of edge detection is likely to fall behind models that dive deeper into the mechanistic hierarchy. The reason is that the latter models usually offer more accurate predictions about the visual system in more circumstances and that they allow more successful generalizations to similar systems and their visual capacities.Footnote 18 In particular, detailed information about the conversion of light quanta into electric signals in the photoreceptor layer of the retina allows making predictions about the impact of certain genetic defects, lesions, drug infusion etc. on edge detection in human vision. Morever, the model can serve to generalize to the computational capacities of other parts of the brain, or even other kinds of brains, that happen to display the same kind of mechanistic structure. It is due to this increase in predictability and generalizability that the model specifying the mechanisms underlying the propagation of electric signals from the retinal receptors through LGN into V1 etc. typically offers a more satisfactory explanation of human vision.
In the opposite direction, it is questionable that neuroscience is primarily about a specification and modeling of mechanistic levels, and that computational descriptions have a secondary or merely preliminary role to play in the discovery of full-fledged mechanistic descriptions. Marr’s theory of edge detection is an example in support of this claim. Knowing which brain regions are involved in the completion of a certain cognitive task, and how the various mechanisms underlying this activity look like, is certainly interesting and informative to some extent.
For instance, knowledge about the propagation of electric signals from the retinal receptors through LGN into V1 in the case of edge detection enables researchers to make certain general predictions about the effect of certain brain lesions in V1 onto vision. Moreover, it allows researchers to make predictions about the brain activity of other mammals in comparable tasks. However, knowing where visual information is processed in the brain provides almost no understanding of the kinds of information that are being processed, of how the information is transformed, and of how aspects of the visual environment are actually represented in the brain.
As Shagrir (2001) has shown, a physical system with cognitive capacities can sometimes be “carved up” in various incompatible ways, such that different aspects of the system become the vehicles of computation and the system as a whole computes different functions. Only when the task that the system completes is specified, it becomes possible to determine which of these different functions the system actually computes. In this sense, satisfactory explanations in neuroscience usually go beyond a purely mechanistic model of explanation.
To be sure, this demand for a computational dimension in certain explanations does not imply that all explanation should involve computational descriptions. For some systems, a full mechanistic description seems to be sufficiently explanatory. For instance, an explanation of the human heart might be complete once the heart’s pumping mechanism is explicated in detail and its place in the organism (its “causal function”) is specified.Footnote 19 In contrast, to fully explain the working of a cognitive system, it does not suffice to describe its physiological structure and its causal-mechanistic connections. Without a specification of the system’s representations and information processing strategies, it remains unclear why nature has equipped the system with these mechanisms and not others. The mechanistic description can only identify what is there; it cannot explain why it is there. Only when it is shown which tasks the system has to solve within its specific environment and what role its representations play in this respect, this important piece of information about the system becomes available.
As an example, consider the conversion of an array of light quanta of different intensities (the input of the mechanism) into a cascade of action potentials passing through LGN into the primary visual cortex (V1), which is locatable and describable in purely mechanistic or physiological terms, at least in principle. Such a mechanistic description does not help to understand what the system actually does, namely identifying edges of objects in its environment. It is not even clear which of the various outputs of the retina are actually relevant for the case of vision. Only a computational theory involving semantical and computational descriptions achieves such. In contrast, it seems much more plausible that the comparable mechanistic description would hep to understand what the heart does: it pumps blood.
To conclude, the MC-picture emphasizes the non-redundancy of computational descriptions, and it embraces Marr’s distinction between computational entities such as functions, variables, values, algorithms etc., and implementation states (cf. Sect. 3). Neural mechanisms are considered as ontologically different from computations. Moreover, the mechanistic processes as such are described as insufficient for the implementation of a specific computational level description including the algorithm, the computed function, and the “why?”-element. At the same time, Craver’s metaphysical hypothesis about the objective existence of a hierarchy of mechanistic levels and the normatively proclaimed integration from different fields into any complete explanation of a given cognitive phenomenon (cf. Sect. 4) are integrated into the MC-hypothesis. Moreover, within this framework, Craver’s claim about the sufficiency of lower mechanistic levels for higher levels is consistent with Marr’s denial of an intrinsicness of computational levels. It may actually come as a natural extension of Craver’s framework that, according to the MC-hypothesis, computational functions can be sensibly associated with many mechanistic levels. There is not the computational level even within a single theory of a particular cognitive task such as edge detection. Rather, there are several, and potentially nested, ones. Neither is there the implementation, or mechanistic, level underlying a given computational task. Rather, there are several hierarchically ordered levels. Also Craver’s definition of the constitution relation between mechanistic levels fits well with the MC-framework and the explanatory norms associated with it.
As a potential objection to the MC-ideal, one might worry that the unification of Marr’s and Craver’s views creates a tension between what the authors have said about the completeness of explanations in neuroscience respectively. Marr was quoted above as suggesting that a “complete” (cf. Marr 1982, p. 24) explanation specifies the computational function, the algorithm, and the implementation. Hence, in some of his works he seems to suggest that the specification of one or perhaps two such implementation level(s) at some grain is sufficient to complete the explanation and nothing more is required.Footnote 20
Craver’s focus on mechanistic levels, on the other hand, could be interpreted as implying that a full description of the physical entities and their physical activities is sufficient for attaining a satisfactory explanation for cognitive phenomena. No specification of computed functions and “why?”-elements seems to be required for the explanation in his view.Footnote 21
These more or less explicit “and that is all what is required” claims found in Marr and Craver cannot be upheld if the norms of explanation associated with the two level frameworks respectively are united. The unified ideal, in contrast, demands that complete explanations of cognitive phenomena in the human brain ought to ascribe information-processing tasks not only to macro-systems, but to various kinds of subsystems of the brain. Only when this complex picture of the originally to-be-explained cognitive phenomenon can be laid out, the explanation becomes adequate and satisfactory. In this sense, not all of what Marr and Craver have said about explanation in neuroscience is consistent with the MC-framework.
A second potential objection may challenge the need for computational explanations on top of mechanistic explanations by pointing out that physical mechanisms are often already characterized mathematically. For instance, the mechanism of stochastic resonance (cf. Benzi et al. 1981), the mechanism of heat transfer in metals (cf. Qiu and Tien 1993), and the mechanism of gene expression (cf. Chen et al. 1999) have all been modeled with differential equations. Hence, it may seem as though computational explanations of mechanistically modeled physical systems are often simply redundant. Arguments of this kind neglect the fact that not every mathematical model is a computational model. The latter, in contrast to the former, essentially involves an interpretation of the arguments and values of a mathematical function as units of information, as well as a specification of a task that the modeled system is taken to perform in its environment. The unsupplemented mathematical models of stochastic resonance, of heat transfer in metals, and of gene expression do not fulfill these broader requirements. In this sense, not every mathematical model of a given mechanism satisfies the MC-ideal of modeling in cognitive science.
A third objection may point out that a non-computational system can also perform a task. For instance, a vacuum cleaner has been designed to complete the task of cleaning floors and carpets. This is entirely correct, of course. But it does not challenge the claim that, in order to explain a cognitive system, it suffices to model its mechanisms only. Whether a vacuum cleaner can be explained in a satisfactory way by a description of its physical structure only (and without reference to its sociological and hygenic function) is a question I will not go into here.
A fourth objection could perhaps add that a vacuum cleaner could be a computing system also, according to the MC-model. In particular, it could be that it is a random number generator, where the random numbers are encoded by the configuration of dust particles. From the view point of the MC-model, this is much less absurd than it might first seem. If the generation of random numbers in a certain context serves to solve a task, a vacuum cleaner can well be a cognitive system.