2.1. The Levels Problem

The first major critique concerns what level PDP models are intended to occupy. Broadbent argues that McClelland and Rumelhart (Reference McClelland and Rumelhart1985) inappropriately cast their distributed memory system as having “implications at the psychological and not merely at the physiological level” (Broadbent Reference Broadbent1985, 189). Broadbent’s appeal to levels refers to Marr (Reference Marr1982), with the implication that cognition ought to be independent of implementation.

Fodor and Pylyshyn (Reference Fodor and Pylyshyn1988) pose Broadbent’s challenge as a dilemma: either connectionist models are “mere implementations” of symbolic models, or they fail to adequately capture cognition. If PDP models are psychological models, then neural details should be irrelevant and afford no advantage. If PDP models are implementation level models, they might be interesting to neuroscientists but are not cognitive science.

It would require many pages to list all the variations of this reaction. Suffice it to say that the Stanford Encyclopedia of Philosophy has set it down as received opinion that there are two kinds of connectionist: implementational and radical. Implementational connectionists “hold that the brain’s net implements a symbolic processor,” while radical connectionists “claim that symbolic processing was a bad guess about how the mind works” (Garson Reference Garson and Zalta2015). Some connectionist projects, such as the articles in Hinton (Reference Hinton1990), show that PDP models are capable of structured representations and serial processing (i.e., implementational connectionism). Other connectionist projects, such as Plaut (Reference Plaut1995), show that what looks like serial processing on the surface might be better explained in terms of network-level details (i.e., radical connectionism). A not-so-radical connectionism claiming that symbolic processing is a bad guess at how some mental functions work is closer to what most connectionists believe.

Either way, connectionists do not generally accept that their models are mere implementations. Rumelhart and McClelland (Reference Rumelhart and McClelland1985) object that much of what concerns cognitive psychologists is at the algorithmic rather than the computational level.Footnote ⁵ Smolensky (Reference Smolensky1988a, Reference Smolensky1988b) describes connectionist models as being at the “sub-symbolic level” and says that the goal of connectionist research is a “middle ground between implementing symbolic computation and ignoring structure” (Smolensky Reference Smolensky1988a, 152). What this middle ground is exactly is unclear.

2.2. The Neural Detail Problem

Another well-rehearsed challenge is that connectionist models are unlike brains in their details. The backpropagation algorithm is infamous for being neurally implausible; error signals cannot in general be propagated backward through a network of neural connections, as the algorithm requires. Likewise, nodes in connectionist models typically have deterministic activation functions, whereas real action potentials are stochastic.

A key example of the neural detail problem is the flexibility in how to interpret single units. In networks with local representations, units are assigned specific meanings, such as the names, occupations, and ages of members of the Jets and Sharks in McClelland (Reference McClelland1981). In networks with distributed representations, “each entity is represented by a pattern of activity distributed over many computing elements, and each computing element is involved in representing many different entities” (Hinton Reference Hinton1984, 1). Far too few units are used in most connectionist models to be realistic brain models. In some connectionist networks, units explicitly stand in for whole populations of neurons, with the activation of the unit representing a population vector.Footnote ⁶ There is thus considerable diversity in what a unit is meant to correspond to.

One of the most debated examples is the past-tense learner (Rumelhart and McClelland Reference Rumelhart and McClelland1986a). This network takes English verbs as inputs and learns to output their past tenses. It is trained using a series of examples, including both regular verbs (add “ed”) and irregular verbs (went, swam). The past-tense learner’s success in learning to conjugate past tenses without any explicit set of rules separating regular and irregular verbs was, as Boden puts it, “theoretical dynamite” (Reference Boden2006, 956). However, the past-tense learner was also vigorously criticized for its failure to simulate physiological detail. The encoding of its input and output verbs, as phonetic triples called “Wickelfeatures” is perhaps the least plausible detail.

Critics of connectionism treat these disanalogies as mistakes, but the PDP group was well aware that the “physiological” flavor stopped short of realistic detail. Volume 2, chapter 20 of the PDP bible describes the ways in which artificial neural networks are not like real brains. The introduction also hedges on whether physiological plausibility is the goal: “Though the appeal of PDP models is definitely enhanced by their physiological plausibility and neural inspiration, these are not the primary bases for their appeal to us. … PDP models appeal to us for psychological and computational reasons” (McClelland and Rumelhart Reference McClelland and Rumelhart1986, 11). Lack of realistic neural detail was, apparently, a design feature.

Part of what is going on is that practical concerns require that models not be too complex. That putting too much detail into a model is a mistake is a common refrain among connectionists: “It’s not necessary to put in the kitchen sink to get insight. … Just to simulate the hell out of populations of everything in the model is mindless” (J. D. Cowan, quoted in Anderson and Rosenfeld Reference Anderson and Rosenfeld2000, 123). McClelland (Reference McClelland2009) argues that while there is a cost to making simplifications in modeling, it is necessary to simplify to achieve understanding. But the implausibility seems to run deeper than just pragmatism.

2.3. The Abstraction Problem

Another puzzle is that connectionists sometimes describe their models in mathematical terms. Smolensky (Reference Smolensky, Loewer and Rey1991) claims that connectionism explores what continuous (rather than discrete) mathematics can reveal about the nature of cognition. Thomas and McClelland call connectionist models “a subclass of statistical models involved in universal function approximation” (Reference Thomas, McClelland and Sun2008, 23).

An example of this is Touretzky and Hinton (Reference Touretzky and Hinton1988), who show how distributed representations can be used to “construct a working memory that requires far fewer units than the number of different facts that can potentially be stored” (423). Here no effort is made to re-create neural details beyond general structural features. The point is to demonstrate a property such networks have no matter what the units represent, yet at the same time, the model is clearly meant as an investigation of working memory. One might wonder how it can do both.

2.4. The Explanation Problem

The final challenge concerns the status of PDP models as explanations. Green worries that “if connectionist models are NOT to be considered THEORIES of cognition, in the traditional scientific sense of the word, then the question arises as to what exactly they are, and why we should pay attention to them” (Reference Green1998). According to Green, the only interpretation of connectionist networks as theories is one in which they are “literal models of the brain activity that underpins cognition.” But this is undermined by the implausibility of connectionist models.

In classical AI, a computer program that produces output comparable to human performance on a cognitive task is considered a theory of that cognitive task. In calling their programs theories, Newell and Simon (Reference Newell and Simon1961, Reference Newell and Simon1976) have in mind the deductive-nomological (DN) account (Hempel Reference Hempel1958): “A computer program used as a theory has the same epistemological status as a set of differential equations or difference equations used as a theory” (Newell and Simon Reference Newell and Simon1961, 2013). The logical calculus in the program has the same status as the law and observation statements that constitute a theory in the physical sciences.

Connectionist models are not theories in the DN sense; they do not logically deduce behavior or encode law-like regularities. By the late 1980s the DN account was no longer the received view of scientific explanation, but the lack of consensus on what should take its place left it open what sort of explanations connectionist models provide.

3.1. Mechanistic Explanation

The mechanistic view of explanation has largely supplanted the DN account in the biological sciences. The levels connectionists are concerned with can be thought of as mechanistic levels (Craver Reference Craver2007). Mechanistic explanation situates a phenomenon within a multilevel system of mechanisms, where each level constrains and is constrained by its neighboring levels. A mechanistic explanation involves showing how component entities and their activities are organized to bring about a phenomenon and identifying the mechanism’s role in higher-level phenomena.

The suggestion that connectionist models can be understood in terms of mechanistic explanation is raised in Miłkowski (Reference Miłkowski2013) and expanded on in Stinson (Reference Stinson, Colombo and Sprevak2018). This insight is in tune with the PDP group’s stated motivations. Rather than seeing physiology and cognition as independent, connectionists explore the ways in which the physiological microstructure constrains cognition. The PDP bible lists the constraints they take from neuroscience, including “there is a very large number of neurons. … Neurons receive inputs from a large number of other neurons. … Learning involves modifying connections. … Neurons communicate by sending activation or inhibition through connections” (Rumelhart and McClelland Reference Rumelhart and McClelland1986c, 130–32).

That mechanistic explanations have no privileged level helps explain why units can correspond to single neurons, populations of neurons, or higher-level entities like phonetic representations. Connectionist models can investigate any number of locations in a system of mechanisms. As Churchland and Sejnowski put it, “Network models … depend in important ways on constraints from all levels of analysis. … Since the networks are meant to reflect principles at entirely different levels of organization, their implementations will also be at different scales in the nervous system” (Reference Churchland and Sejnowski1990, 368–69).

3.2. Abstraction

Simplicity is essential not only for getting models to work but also for explanation. The cost of simplification is that when you draw an inference from a simplified model, it may be that the interesting properties of the model result from aspects of the model that differ from the target rather than from what the model and target have in common. Connectionist models are different from brains in many ways, so one might expect them to behave differently. This is an instance of a very general worry about scientific models, namely, which details need to be captured accurately for a model to inform us about the target system and which can be safely altered. This problem has been the subject of much work in philosophy of science.

One kind of simplification is what Cartwright (Reference Cartwright, Kitcher and Salmon1989) calls abstraction. Abstract models remove details so that the effects of a small number of variables can more easily be investigated on their own. Abstracting away too many details can lead to error when there are complex relationships between variables, such that investigating each in isolation is not straightforwardly informative about the combined picture. Nevertheless, quite often it is perfectly legitimate. A comparison can be made to how experiments need to control variables in order to be interpretable. There is a trade-off to be made between naturalistic field experiments with many uncontrolled variables and lab experiments that are more readily interpretable but have less external validity.

The trick is to figure out which details matter. Morgan (Reference Morgan, Magnani and Nersessian2002, Reference Morgan and Radder2003) argues for the importance of materiality: sharing the same materials lends experiments closer access to their targets than models, which makes experimental systems more likely to share the properties that are relevant. Parker objects to assessments of computer simulations as “just mathematical modeling exercises” (Parker Reference Parker2009, 491), arguing that simulations are physical models. She points out that, in weather forecasting, modelers are better able to set up the relevant initial conditions in a computer simulation than in a laboratory model that uses the same materials as real weather systems. Simulations are thus better able to predict the weather than “same stuff” laboratory models, and the key is “whether the experimental and target systems were actually similar in the ways that are relevant, given the particular question to be answered about the target system” (493). In another meteorological model, sizable volumes of atmosphere are treated as homogeneous points in a grid, while measurements of the complex dynamics at a scale lower than the grid resolution are approximated with a single parameter value. Ignoring the known details at a finer grain of resolution leads to more accurate weather predictions than if those details were included in the model (Norton and Suppes Reference Norton, Suppe, Miller and Edwards2001, 95–96; see also Küppers and Lenhard Reference Günter, Lenhard and Horton2004).

Likewise in cognitive modeling, when the goal is to predict the behavior of a cognitive agent, pragmatic concerns like maximizing accuracy take precedence over modeling the finer details of the system. This can be seen in the popularity of support vector machines, which make little to no effort to mimic human visual processing, in the ImageNET image recognition challenge (Russakovsky et al. Reference Russakovsky, Deng, Su, Krause, Satheesh, Ma, Huang, Karpathy, Khosla, Bernstein, Berg and Fei-Fei2015).

Giere (Reference Giere2004) and Godfrey-Smith (Reference Godfrey-Smith2006) focus on the representational role of models and likewise argue that models and targets being similar in the relevant respects is what justifies inferences from the one to the other. Which similarities are relevant depends on the context: “scientists use continuous fluid models to represent water for the purpose of studying fluid flow and also use molecular models for the purpose of representing water for the study of Brownian motion” (Giere Reference Giere2004, 750).

If the point of the past-tense learner had been to model how verbs are represented in the brain, or to simulate conjugation in detail, then the manner of encoding input and output verbs would have been relevant, and using Wickelfeatures would have been inappropriate. But Rumelhart and McClelland wanted to see whether what appeared to be a structured rule-following behavior could be achieved without building that structure in. The way the verbs are represented was bracketed off as irrelevant, given that goal.

Winsberg highlights the importance of arguments, to demonstrate that the results scientists get “from manipulating their respective pieces of equipment are appropriately probative concerning the class of systems that interest them” (Reference Winsberg2009, 577). Those arguments are based not just on similarity but also on having knowledge about how to build good models, which comes from past successes using the same bag of modeling tricks.

Batterman (Reference Batterman2001, Reference Batterman2002) describes how the use of mathematical tools like renormalization groups depends on paring down particular problems to minimal models. What Batterman calls “asymptotic” methods are able to explain the universal, stable phenomenologies that are shared by, for example, microstructurally diverse fluids near the critical point in phase transitions, as well as magnets transitioning between ferro- and paramagnetic states (Reference Batterman2001, 38). These methods not only offer explanations of these universal phenomena, but by “telling us what (and why) various details are irrelevant for the behavior of interest, this same analysis also identifies those physical properties that are relevant for the universal behavior being investigated” (42).

Something like asymptotic explanation appears in Fuhs and Touretzky’s (Reference Fuhs and Touretzky2006) model of path integration in spatial memory. Their model seeks to explain how rats navigating mazes are able to find efficient paths to goal locations regardless of the paths they have previously traveled, as well as the peculiar hexagonal patterns found in grid cells’ firing fields. As a possible explanation of the hexagonal patterns, Fuhs and Touretzky showed that “hexagonally spaced activity bumps can arise spontaneously on a sheet of neurons in a spin glass-type neural network model” (4266). In spin glass models, each unit is connected to its closest neighbors in a multidimensional grid. This network structure is loosely based on the local structure in entorhinal cortex, where grid cells are found, on the assumption that dendrites are closely packed. When circles or cylinders of uniform size are closely packed together, the highest density arrangement is a hexagonal pattern. This is true regardless of whether they are telecommunication cables or dendrites running through nerve tracts. Fuhs and Touretzky (Reference Fuhs and Touretzky2006) justify arranging the units in their connectionist model of grid cells in a hexagonal pattern based on this fact about close packing, even though real dendrites are neither perfectly cylindrical nor uniform in size. Their explanation depends on not using a more accurate, detailed model, because without the assumption that the dendrites are uniform cylinders, the geometric fact about close packing could not have been applied.

3.3. Idealization

On Cartwright’s (Reference Cartwright, Kitcher and Salmon1989) definition, idealization adds or changes details, such that the idealized model has properties not present in the target system. In lab experiments, idealizations might substitute more convenient materials or assign implausible values to variables for ease of calculation. Backpropagation and deterministic activation functions are the clearest cases of idealization in connectionist modeling. At first blush, it seems like putting the wrong details in, as opposed to merely removing irrelevant details, should make for a worse model, but this is not generally the case.

A number of authors have compared idealizations to fictions and suggested that models are interpreted in much the same way as we interpret literature. Mäki’s (Reference Mäki, Humphreys and Imbert2012) analysis goes in a different direction. Mäki argues that apparently false idealizations can be interpreted as true in several distinct ways. Leaving out some factors can be intended as a “negligibility assumption”; that is, those factors have a negligible effect, given the intended purposes and audience of the model (222). “Applicability assumptions” restrict the intended use of a model to domains where the factors left out have negligible effects (225). Other kinds of assumptions might defend the use of an idealized model on the grounds that the idealization makes the model more tractable or more suitable for pedagogical purposes (228–30). These assumptions are not always spelled out explicitly.

In some cases, the use of backpropagation in connectionist models could be justified with a tractability assumption, since it was for a time the only known method of updating weights that was guaranteed to converge. In other cases backpropagation can be justified with a negligibility assumption. For example, in NETtalk (Sejnowski and Rosenberg Reference Sejnowski and Rosenberg1986) backpropagation is unproblematic given the purpose of the model, because their goal is to show that a system capable of pronouncing English words need not encode a complicated set of rules. For that purpose, it is fair to simply assume that the brain has some way of propagating error signals, without worrying about how exactly that happens. The particular pathways the error signals take do not make a difference to what they are investigating. In contrast, Suri and Schultz (Reference Suri and Schultz2001) develop a model of learning mechanisms, so the way error signals are propagated is highly relevant. In their model, backpropagation is not used; instead the anatomy of the basal ganglia is reproduced in some detail, including only pathways that exist in the brain and through which feedback is known to actually travel.

The curious phrase “‘physiological’ flavor” might be interpreted to mean that connectionist models are idealized models of cognitive mechanisms. If you take away irrelevant details, and idealize others, cortex is an interconnected network of simple learning units.

3.4. Discovery

Models serve many different purposes in science, and many different strategies may be employed in the search for mechanisms. Anderson and Rosenfeld’s (Reference Anderson and Rosenfeld2000) history of connectionism demonstrates that among connectionist modelers there have always been widely differing approaches in terms of how much physiological detail to include and what the goals are. These goals include engineering, mathematical, psychological, and neuroscientific questions. Models intended for different epistemic roles require different characteristics.

Steinle (Reference Steinle1997, Reference Steinle2002) argues that experiments at different stages in a research project tend to have different epistemic goals, which means that different sorts of experiments are performed. For example, earlier exploratory experiments tend to try out many more combinations of parameter values in a search for potentially meaningful correlations, while later “theory-driven” experiments use high-precision equipment and “are typically done with quite specific expectations of the various possible outcomes” (Steinle Reference Steinle1997, S70).

Steinle’s analysis also holds for models. Models used at different stages in a research project tend to have different epistemic goals and correspondingly may vary in terms of how idealized or specific they should be in order to meet those goals. This difference in epistemic goals is reflected in the difference in detail in the learning mechanisms used in NETtalk compared to models of the basal ganglia.

4.1. Overview

This section continues in the spirit of Irvine (Reference Irvine2014), where considering computational modeling practices from cognitive neuroscience problematized and revised claims from the models and simulations literature. Other examples of work on computational modeling in the neurocognitive sciences are Kaplan (Reference Kaplan2011), who argues that computational explanations in neuroscience are mechanistic explanations; Chirimuuta (Reference Chirimuuta2018, 851), who argues that there are “numerous instances of distinctively mathematical, non-causal explanation” in computational neuroscience; and Stinson (Reference Stinson, Colombo and Sprevak2018), where I argue that connectionist cognitive models explain using a logic of tendencies in contrast to classical AI’s use of inference to the best explanation.

What these examples share is a concern with questions about causation and ontology, quite unlike the focus on representations characteristic of the models and simulations literature (see Suárez Reference Suárez2003; Giere Reference Giere2004; Weisberg Reference Weisberg2012; Frigg and Nguyen Reference Frigg and Nguyen2016). Perhaps the reason is that cognitive scientists have learned to regard with some suspicion appeals to representations as explanations and tend to worry about how putative representations acquire and transmit their contents. This more critical take on representation and causal-mechanistic bent could be helpfully applied to the models and simulations literature.

Three open questions in that literature are how relevant similarity ought to be judged, how inferences from models to targets are justified, and what the metaphysical status of models is. On the first two questions, the state of the art seems to be that which similarities are relevant has to be decided on a case-by-case basis (Parker Reference Parker2009) and that we have to provide arguments to justify our modeling choices (Winsberg Reference Winsberg2009). A deeper analysis of the criteria modelers use in making these judgments is needed.

Godfrey-Smith (Reference Godfrey-Smith2009) lays out the problem of the metaphysical status of models. He notes that model systems are “in a sense, of the same kind as the target systems that the models are used to help us understand” (104) but rejects what scientists say about planets, populations, or economies being “inside the computer” (106) even in a loose sense. He resists attributing computational models object-hood such that they are taken as “shadowy additional graspable thing[s]” (108) and endorses the comment attributed to Deena Weisberg that the Platonism of mathematicians is a “folk ontology” (107). Godfrey-Smith describes the Platonist view as taking the model to be an abstract entity that can be investigated mathematically, then requiring a mapping of abstract properties to the physical properties of the target.

The Platonist view is implicitly rejected because it runs into the Third Man problem, by assuming the independent reality of abstract objects. But, if models are not objects that can be directly compared to targets, the question remains how they can inform us about concrete things. Representations and fictions are overly flexible; anything can happen in fiction, so it does not adequately constrain inferences to real world targets. As Frigg and Nguyen argue, “One can imagine almost anything about almost any object, but unless there are criteria telling us which of these imaginings should be regarded as true of the target, these imaginings don’t licence any surrogative reasoning” (Reference Frigg and Nguyen2016, 233). The metaphysical problem and the inference problem are thus in tension with one another.

Winsberg likewise notes that “practitioners of simulation” favor the idea that simulations literally mimic their target systems, such that a simulation of fluid dynamics can be viewed as an experiment in a “virtual wind tunnel” (Reference Winsberg2010, 35). But Winsberg raises the problem of “whether or not, to what extent, and under what conditions a simulation reliably mimics the physical system of interest” (37).

A common assumption in representational accounts of models is that the relation between model and world is one of similarity, following Giere’s (Reference Giere1988) diagram, reproduced here in figure 1. Winsberg notes that the relation between models and targets has to be something “far more complicated than mimicry” (Reference Winsberg2010, 39). What this more complicated relation might be is key to all three questions at hand.

Figure 1.

Relations between theory, model, and reality, reproduced from Giere (Reference Giere1988, 83).

Frigg and Nguyen offer a more complicated candidate relation in their DEKI account. According to DEKI, models are interpreted as exemplifying a set of properties of interest, which are mapped to properties imputed to the target. The addition of more stations along the way between model and target solves a number of problems with direct representation accounts (see Frigg and Nguyen Reference Frigg and Nguyen2016) but retains the main weakness of representational accounts, since a mapping between sets of properties does little to ensure that one reliably mimics the other.

4.2. An Alternative to Representational Accounts of Models

My analysis of inference in connectionist modeling from Stinson (Reference Stinson, Colombo and Sprevak2018) can be extended into an alternative account of models. This account provides a more robust connection between properties of models and targets and legitimizes scientists’ views about the ontology of models. I argue that inferences are drawn from connectionist models to their targets indirectly via kinds that both the model and target exemplify. A diagram illustrating this set of relations is given in figure 2.

Figure 2.

Relations between model, target, and kind.

On this account, the inferences modelers draw from models to targets have the following structure:

In the case of connectionist models, T is the brain or cognitive system being investigated, and M is the connectionist model.

This extra step of associating the model first with a kind then that kind with the target is promising for several reasons. One is that it makes better sense of idealization than representational accounts of modeling do. A good model is often very minimal, including only the properties of interest and few other details. If similarity were the criterion for model target relations, more details would be better, not fewer. But if capturing the characteristic properties of a kind is the goal, then idealized models are exactly what one ought to aim for. Similarity is what we want to infer as a conclusion, not what we aim for in model building.

Second is that it can provide needed guidance about which similarities are the relevant ones to capture in a model. The properties that a model should mimic from the target are the ones that are characteristic of the kind they both belong to. As long as we have a way of picking out kinds, this gives specific guidance about what the relevant similarities are: something representational accounts were unable to do.

The account also has other nice properties. It fits well with Godfrey-Smith’s (Reference Godfrey-Smith2009) observation that models sometimes describe one case of a target phenomenon, then act as a hub, anchoring all the “actual-world” cases (107). The hub is the kind captured by the model. Models with no target are likewise accounted for by treating the kind as a generalized target.

What is still wanting in this account is a way of delineating kinds, telling which kinds a target belongs to, and a workaround to the problem of universals. One missing piece can be provided by Khalidi’s (Reference Khalidi1998, Reference Khalidi2013) broad view of kinds. Khalidi argues that scientific kinds like parasite, liquid, or schizophrenia should be considered “real kinds” because “we discovered things about them which were by no means implied when they were first introduced” (Khalidi Reference Khalidi1998, 42).Footnote ⁷ This account of kinds assumes neither essential natures nor strictly hierarchical relationships between kinds. As such, it is promiscuous enough to accommodate most any phenomena that one might want to model. But because members of kinds have nonarbitrary things in common, kinds provide a basis for inferring that members likely have the properties characteristic of the kind in common with each other.

Khalidi’s kinds might be made more robust by connecting them to Andersen’s (Reference Andersen2017) information-theoretic update to Dennett’s (Reference Dennett1991) “real patterns.” A real pattern is one that “can be reliably picked out and tracked through time … and which allows one to make predictions that are better than chance” (Andersen Reference Andersen2017, 603). A collection of phenomena that manifest a real pattern according to Andersen would count as the members of a real kind according to Khalidi.

Andersen comments on the “profligacy” of patterns, saying that “there could be a vast number of different ways of picking out such patterns that give us predictive grasp on the system” (Reference Andersen2017, 603), but just as the promiscuity of Khalidi’s kinds should not be troubling given that they do not assume anything about essences or hierarchies of kinds, the profligacy of Andersen’s patterns should not be troubling because “the degree of realism is very, very minimal” (603). Both Khalidi and Andersen argue that the concern that this allows for too many kinds or patterns is overblown. The criteria that kinds or patterns can be reliably picked out, tracked, and make useful predictions are not met by jerry-rigged kinds.

Against the worry that patterns are epiphenomenal, Andersen claims “the overwhelming majority of patterns are counterfactually robust, in that they could have differed in their microphysical details in each token instantiation without thereby altering the relatum’s causal profile” (Reference Andersen2017, 594). That idealized and simplified models of causal processes are often most useful for figuring out how those processes work would be mysterious, were it not the case that these patterns are real in some sense that goes beyond the reality of their microphysical details.Footnote ⁸

Both Khalidi and Andersen claim at least a minimal reality for their kinds/patterns. On Andersen’s account, patterns are part of the causal nexus, and “higher-level causes are just as real as lower-level causes” (Reference Andersen2017, 619). Her deke around the problem of universals is that what is real is “the causal nexus and patterns instantiated in it, which are informationally structured, but where the information itself is a structure of something else, not a reified extra substance” (619).

One can go a step further in endorsing the folk ontology of scientists and interpret these reality claims as implicating additional shadowy things of a sort. But before the knee-jerk reaction that this runs into the problem of universals kicks in, let us look at some recent developments in metaphysics, where respectable options are available for considering universals as concrete in some sense.

Hennig (Reference Hennig2015) offers a possible solution to the problem of universals, based on Baxter (Reference Baxter2001), wherein kinds have concrete aspects, making them in a sense “the same as” instances of the kind. Hennig summarizes the account in the following way: “that Socrates instantiates the kind seated thing means that there is an aspect of Socrates that is also an aspect of the kind seated thing. This aspect can be described in two ways: (1) as Socrates qua seated thing or (2) as seated thing qua instantiated by Socrates” (Reference Hennig2015, 5). Hennig clarifies as follows: “That Socrates instantiates the kind seated thing means that there is a seated thing that is the same as Socrates. This thing is one of his aspects. Socrates is an instance of seated thing, and seated thing is an aspect of Socrates. The aspect is not a third entity mediating between Socrates and the universal ‘being seated’; there are only two things: Socrates and the aspect” (Hennig, pers. comm., April 12, 2019). Aspects, unlike Platonic universals, are concrete and in the world. The aspect ‘Socrates qua human’ has flesh and bones.

This brief detour into contemporary metaphysics shows that there are respectable options available that allow us to take seriously the views of scientists about the reality of models. Putting these pieces together, the relation between kind and target can be understood as the relation between aspect and instance, and the relation of model to target as between two instances of the same aspect. It is tempting to think of models as though there are two of them, the ideal one and the instantiated one. The ideal one is what scientists think is really in the target system and really in the computer. The instantiated model is the tool we use to get at the ideal. The former is the aspect. The latter is an instance.

The practice of modeling picks out an aspect of the target to investigate and then constructs an instance of that aspect that can be manipulated conveniently. A mathematical model like the Hodkin-Huxley equation comes pretty close to being the aspect under investigation, while models that substitute another material for the material in the target (like architectural models, model organisms, and analog models) are instances that have additional aspects not characteristic of the kind in question.

I am seated right now as I write, making me an instance of ‘seated thing’. In virtue of being seated, I could act as a model of ‘Socrates qua seated thing’. Using this model, I could speculate that Socrates’s toes might also have been prone to falling asleep after sitting too long on a hard chair. But I also have other aspects that are not shared with Socrates. It would not be wise to conclude that Socrates too would usually be drinking tea and overhearing conversations in English while sitting on a hard chair. The instances of ‘seated thing’ near me do share some of those aspects, but they share them in virtue of being instances of ‘person working at Propeller Coffee’. A better model of ‘seated thing’ would be isolated from noises and hot beverages.

The status of computational models is a bit subtler. In some ways they are like mathematical models in that they are close to being pure aspects. But as Parker argues, computational models are also physical models with properties of their own (like being made with transistors). Within a range of conditions those other aspects can be made irrelevant, but in the presence of large magnets or when submerged in water, computational models will show their colors as electronic devices. A computational model qua made with transistors may not be informative about cognition, but a computational model qua connectionist network ought to be.

What makes computers so useful in modeling is that they are designed to have the capacity to explore the aspect of your choice, while isolating that aspect from their other aspects (made with transistors, notebook sized, manufactured in China, etc.). If you consider only particular output streams, like images, printouts, or certain files (as opposed to measuring the CPU’s temperature or seeing what happens when you whack it with a hammer), and assume a translation code that interprets that output, a programmer can make a computer be an instance of a wide variety of aspects. Other kinds of models, like fruit flies in genetics, are likewise chosen because they make the investigation of a given aspect more feasible (faster, cheaper, more ethical) than it would be to investigate that aspect in the target itself. For a model to be minimally appropriate it has to be an instance of the aspect of interest. That the model and target are the same in the sense of sharing an aspect is what sanctions inferences from one to the other.

The starting point in building a model is identifying a kind K that the system of interest belongs to and that the model will be designed to investigate. One factor that affects the strength of the inference is whether K is a real, robust kind capable of sustaining generalizations. For the most generic Ks in connectionist modeling, the choice of model amounts to the wager that some of the generalizations that are relevant to cognition operate at the network level. Another factor is whether M is a representative instance of K. Models with a minimum of properties that are not typical of Ks are more representative. Finally, the inference depends on T also being of kind K. If K is a real kind, and M is a minimal instance of K, whatever one finds out about the kind K by investigating M should, all else being equal, also be true of T, assuming T belongs to K. It may still happen that T is atypical in relevant respects and so fails to have the same properties as M despite belonging to the same kind K.

Considering models in the neurocognitive sciences has motivated the need for a more complex account of the model-target relation, better answers to questions about relevant similarity, and more detail about the metaphysics of models. The bare outlines of a novel epistemology and metaphysics of models has been drawn here from an analysis of inference in connectionist modeling.