3 Using Functional Analysis to Explain Cognition

3.1 Competing Notions of Explanation

Cognitive psychology’s pioneers trained as behaviorists (Miller, 2003). In his first book, Miller (1951) adopted a behaviorist perspective that he would soon abandon. “In 1951, I apparently still hoped to gain scientific respectability by swearing allegiance to behaviorism. Five years later, inspired by such colleagues as Noam Chomsky and Jerry Bruner, I had stopped pretending to be a behaviorist” (Miller, 2003, p. 141). Pioneering cognitive psychologists discarded behaviorism because it limited what could be studied. Behaviorists argued that psychology must eliminate mental terms from its vocabulary (Watson, 1913). Cognitive psychologists fiercely rejected behaviorism’s stance against mentalism (Bruner, 1990; Sperry, 1993).

Replacing behaviorism did not merely change the topics that psychologists could study. The cognitive revolution involved “discovering an alternative logic by which to refute the seemingly incontestable reasoning that heretofore required science to ostracize mind and consciousness” (Sperry, 1993, p. 881). Cognitive psychologists aimed to replace behaviorist theories with a new approach, an approach both mentalistic and scientific.

Chapter 1 introduced the inspiration for an alternative form of explanation, the computer. Computer scientists explain how computers work by appealing to the functional properties of computer programs. Chapter 2 illustrated how cognitive psychologists collect data to support similar accounts of human cognition. Like behaviorists, cognitive psychologists observe behaviour. Unlike behaviorists, cognitive psychologists use observations to infer information processes that cannot be observed directly.

Chapter 1 related cognitive psychology to computer science, and Chapter 2 related cognitive psychology to experimental psychology. Chapter 3 now relates cognitive psychology to the philosophy of science. Cognitive psychology uses explanations very different from those of behaviorism. Cognitive psychology’s theories arise from a philosophical approach called functional analysis. In Chapter 3, I introduce functional analysis and explore how it shapes the practice of cognitive psychology.

3.2 Functionalism, Hierarchies, and Functional Decomposition

Cybernetics explained behaviour by appealing to the feedback loop (Ashby, 1956, 1960; Wiener, 1948, 1950). Feedback measures the distance between an agent’s current state and a goal state that the agent desires. The agent acts on the world to decrease the distance between the current state and the desired state. A feedback loop cycles back and forth between an agent’s actions and environmental changes, constantly measuring the distance from a desired goal to alter or guide the agent’s future actions.

Cybernetics played an important role in founding cognitive psychology (Conway & Siegelman, 2005). For instance, one pioneering book on cognition, Plans and the Structure of Behavior (Miller et al., 1960), explored the relevance of cybernetics to psychology. Miller et al. proposed the feedback loop as behaviour’s fundamental building block by introducing the TOTE unit (Figure 3-1). TOTE stood for “Test-Operate-Test-Exit.” One component, “Test,” provides feedback to the unit. “Test” compares the world’s current state to a desired state. If the desired state is true, then the unit “Exits,” passing control elsewhere. However, if the desired state is false, then the TOTE unit passes control to the second component, “Operate.”

“Operate” acts on the world to help achieve the desired state. “Operate” changes the world, making it more similar to the desired state. After “Operate” performs the action, control again returns to “Test” to determine whether the action achieved the goal. If not, then “Test” passes control back to “Operate.” Thus, the TOTE unit repeatedly moves back and forth between testing and operating until achieving the desired state.

The TOTE unit illustrates one core assumption of cognitive psychology, functionalism (Polger, 2012). Functionalism explains how a system works by describing what its components do rather than by describing their physical properties. I describe TOTE units functionally, not physically, as detailed below.

Functionalism arises from a many-to-one relationship (introduced in Chapter 1). Functionalists realize that physically different components can serve the same function. For instance, the total artificial heart (Mollon, 1982) performs the same function as the human heart but is built from different physical materials. Miller et al. (1960) treat TOTE units functionally, not physically. First, they describe TOTE units as transmitting control, not as transmitting energy or neural pulses. Their proposal is deliberately abstract and non-mechanistic. Second, Miller et al. recognize that TOTE units can be studied with computer simulations, arguing that a valid simulation need only emulate a theory’s functional characteristics. “A successful model does not have to look like the organism it simulates” (p. 48). Third, Miller et al. spend 13 chapters developing their functional theory before mentioning the brain. A final chapter, entitled “Some Neuropsychological Speculations,” has only fourteen pages. Cognitive psychologists typically develop a functional theory first and only later relate the theory to the brain.

The TOTE unit was but one of the pioneering ideas of Miller et al. (1960). They also proposed a hierarchical organization for TOTE units. The foundational concept of their book, the “Plan,” appeals to hierarchy: “A Plan is any hierarchical process in the organism that can control the order in which a sequence of operations is to be performed” (p. 16). Importantly, they also treated hierarchical organization functionally.

Miller et al. (1960) hierarchically organize TOTE units by decomposing a TOTE unit’s “Operate” component into organized sub-functions; each sub-function is another TOTE unit. We call recasting one function as an organized system of sub-functions functional decomposition. Figure 3-2 illustrates Miller et al.’s functional decomposition using a TOTE unit for sawing a wooden board into two. In Figure 3-2, the higher-level “Operate” component “Saw the Wood” is decomposed into two linked TOTE units, one for pulling a straight arm backward, the other for pushing a bent arm forward. Note that the second sub-component “Exit” passes control back to the upper-level “Test” “Is the Wood in Two Pieces?”

Figure 3-2 permits further functional decomposition. We could decompose both the “Pull Arm Backward” and “Push Arm Forward” operations into new TOTE units—sub-sub-functions—to ensure that “Saw the Wood” proceeds as desired.

Miller et al. (1960) use functional decomposition to explain how we perform operations. They realize that some operations (e.g., “Saw the Wood”), too complex to build directly into a device, must instead be created from simpler processes. Thus, they explain a complex operation by decomposing it into an organized system of simpler operations. However, such decomposition adds new TOTE units. Can we explain one functional component by decomposing it into other functions that also require explanation? Cognitive psychology must answer this question and does so using an approach outlined below.

3.3 Ryle’s Regress

Behaviorists argued that mental terms did not carry any explanatory value. A theory including mental states could not explain because it incorporated unexplained components. “When we attribute behavior to a neural or mental event, real or conceptual, we are likely to forget that we still have the task of accounting for the neural or mental event” (Skinner, 1950, p. 194). Miller et al. (1960, p. 9) understood Skinner’s concern: “The criticism is that the cognitive processes Tolman and others have postulated are not, in fact, sufficient to do the job they were supposed to do. Even if you admit these ghostly inner somethings, say the critics, you will not have explained anything about the animal’s behavior.”

Gilbert Ryle (1949) provided the philosophical foundations for Skinner’s criticism. He opposed what he called the intellectualist legend, which requires intelligence to be produced by mental rules. Ryle argued that such accounts produce an infinite regress of mental state terms. To explain one cognitive process, cognitive psychologists decompose it into other cognitive processes. However, new cognitive processes themselves require explanation. If we use the intellectualist legend to explain new cognitive processes, then we perform further functional decomposition.

As a result, Ryle argued that functional decomposition creates an infinite regress of mental state terms. This infinite proliferation of unexplained functions is called Ryle’s regress. If a cognitive psychologist is trapped in Ryle’s regress, then her theories merely describe and do not explain.

Cognitive psychology’s functionalism seems to lead into Ryle’s regress. Consider the modal memory model (Figure 2-5). Cognitive psychologists began with the task of explaining human memory. However, they decomposed a general function—memory—into an organized system of sub-functions (e.g., sensory registers, primary memory, secondary memory, etc.). However, each new sub-function also requires explanation. But if we explain a new sub-function using functional decomposition, we produce new to-be-explained sub-sub-functions. Given Ryle’s regress, how did cognitivism replace behaviorism? Cognitive psychologists adopted an explanatory approach to escape Ryle’s infinite regress, which I consider in the next section.

3.4 Functional Analysis

In science, explanations typically appeal to causal laws or transition laws (Cummins, 1983). For instance, physicists explain the transition from one physical state to another by citing a law that “explains an effect by citing its cause” (Cummins, 1983, p. 4).

Behaviorists used physics to inspire their psychology (Köhler, 1947). As a result, in addition to focusing on observables (stimuli and responses), behaviorists appealed to transition laws. Behaviorist explanations cite causal laws: a stimulus causes a response. “In a system of psychology completely worked out, given the response the stimuli can be predicted; given the stimuli the response can be predicted” (Watson, 1913, p. 167). However, philosophy proposes other explanatory approaches. Scientists choose the approach that they prefer; their choice depends on beliefs about what constitutes good science (Osbeck, 2019).

When reacting to behaviorism, cognitive psychologists chose an alternative kind of explanation: functional analysis (Cummins, 1975, 1983). Functional analysis explains complicated systems by breaking them down into simpler subsystems and requires three general steps.

First, functional analysis specifies the function to be explained. This step is very general because it specifies only some regularity to convert stimuli into responses (Ashby, 1956), relating this step to the computational level of analysis (Section 1.7). At the computational level, a researcher specifies which information processing problem is being solved, equivalent to indicating the overall input-output mapping—the function—performed by the system.

Second, functional analysis performs the analytic strategy. With this step, a researcher analyzes the function into an organized set of sub-functions, a practice called reverse engineering. When a cognitive psychologist engages in functional decomposition, she adopts the analytic strategy. We conduct the analytic strategy iteratively; once we propose some sub-function, we might decompose it further into simpler sub-sub-functions. Analysis can continue again and again. We stay in Ryle’s regress if we cannot stop applying the analytic strategy.

Importantly, any new sub-functions proposed during the analytic strategy must be simpler than the functions from which they were derived for cognitive psychologists to escape Ryle’s regress. Functional analysis decomposes a system into functional components simple enough to be explained using causal laws.

Figure 3-3 illustrates the first two steps of functional analysis. The figure’s top part defines some function to explain, a mapping between the input and the output indicated by the two arrows. The figure’s middle part shows the first functional decomposition of the top function into two sub-functions. The figure’s bottom part decomposes the two sub-functions into various sub-sub-functions.

Figure 3-3 portrays two additional characteristics of the analytic strategy. First, we decompose functions into simpler sub-functions, illustrated by making the boxes for sub-functions smaller than the boxes for functions. Second, we decompose a function into an organized set of sub-functions, reflecting the idea that information processing occurs in stages. First one sub-function manipulates symbols; then the sub-function passes results to another sub-function. The arrows in Figure 3-3 indicate how information moves from one function to another. These two ideas reflect a very powerful insight: when simple functions form an organized system, that system can perform a more complex function.

However, Figure 3-3 does not show how to escape Ryle’s regress. We need to explain some simple function without further decomposing that function into further sub-functions. If (infinite) functional decomposition somehow stops, then we escape Ryle’s regress. The final step in Cummins’s (1983) functional analysis stops functional decomposition. The subsumption strategy describes how physical mechanisms instantiate functions. We explain an instantiated function by appealing to a causal law. Cummins calls such an appeal causal subsumption.

Causal subsumption explains some function’s input-output regularity with a (physical) transition law. We subsume a function by explaining how we can replace the function with a physical device to perform the same input-output mapping. We do not explain the device via further functional decomposition because of the physical nature of the device. Instead, we explain the device by appealing to causal law, ending Ryle’s infinite regress.

Cummins’s functional analysis provides an alternative scientific explanation. Unlike behaviorist explanations, functional analysis appeals to internal functions that we cannot observe directly. However, Cummins, sensitive to Ryle’s regress, requires functional analysis to reach a set of final, instantiated, functions. Only then will a functional analysis explain. “Analysis of the disposition (or any other property) is only a first step; instantiation is the second” (Cummins, 1983, p. 31). Miller et al. (1960, p. 42) promoted testing theories with computer simulations by interpreting simulations as instantiations: “The reflex theorist is no longer the only psychologist who can summon up a tangible mechanism to make his claims sound more reasonable.”

Cognitive psychologists assume that cognition is computation: rule-governed symbol manipulation. As a result, they must explain cognition by appealing to processes that they cannot observe directly. Cognitive psychologists must adopt a philosophy of science different from that of behaviorism. Behaviorists criticized the cognitive approach as being non-scientific because behaviorists believe that functional decompositions do not explain. In response, cognitive psychologists adopt a different approach to explanation, one no less scientific than the approach used by behaviorists.

Cognitive psychologists explain cognition by performing functional analysis, which proceeds in three basic steps: (1) defining a to-be-explained function; (2) iteratively decomposing this function into organized sub-functions; and (3) ending this decomposition by causally subsuming the final functions. The final step converts a functional analysis from a description into an explanation.

3.5 The Architecture of Cognition

We can explain a computer by describing its architecture: detailing the computer’s basic symbols, rules, and control. When psychologists assume that cognition is information processing, they also claim that we can explain cognition in the same way, with an architectural account (Anderson, 1983; Newell, 1990; Pylyshyn, 1984).

Computers process information by executing a program, a sequence of processes for manipulating symbols to accomplish a goal. A program ultimately uses the computer’s most basic operations. Basic operations are literally built into the machine and are called primitives. We explain a primitive function’s operation by appealing to physical properties or to causal laws. A primitive is not explained by further decomposition into functional sub-components.

A computer’s primitives define its functional architecture. “Specifying the functional architecture of a system is like providing a manual that defines some programming language” (Pylyshyn, 1984, p. 92). Functional analysis escapes Ryle’s regress by causally subsuming basic functions, explaining functions via causal laws. The final stage of a functional analysis of human cognition must specify the primitives, the functional architecture of cognition. “Theories of human cognition are ultimately theories of physical, biological systems” (Newell, 1990, p. 42).

Cognitive psychologists must discover the architecture to convert functional descriptions into explanations. We sometimes call the cognitive architecture the language of thought (Fodor, 1975), realizing that language of thought refers to a programming language. How do we determine the language of thought? We do so with a complete functional analysis of human cognition. Higher-order functions in such an analysis describe the general information processing being carried out. Lowest-order functions are physically instantiated and therefore represent the cognitive architecture.

In short, then, determining the language of thought requires researchers to conduct a complete functional analysis, which includes collecting evidence for claiming that certain functions are primitive. The primitive functions define the language of thought. Therefore, cognitive psychologists aim to identify the architecture of cognition.

3.6 Functional Analysis of Colour Perception

To illustrate functional analysis, consider the trichromatic theory of colour perception (Wasserman, 1978), which begins with Sir Isaac Newton’s 17th-century experiments using prisms. Newton found that a prism refracts sunlight into the rainbow’s full spectrum. A second prism recombines the rainbow back into white light. Newton hypothesized that we can describe any perceived colour as a weighted combination of seven different primary colours (red, orange, yellow, green, blue, indigo, and violet).

Newton’s theory inspired several competitors. The German poet Johann Wolfgang von Goethe proposed his own two-colour theory (based upon yellow and blue) in 1810. Thomas Young proposed a three-colour theory in 1801. Others proposed four-colour theories (Karl Hering in 1874 and Christine Ladd-Franklin in 1893). Physicist James Clerk Maxwell resolved the debate about the minimum number of primary colours for colour perception in 1856. He proved that we can express any perceived colour using no more than three primary colours.

Maxwell’s proof provides the computational foundation for the trichromatic theory of human colour perception. That theory is also known as the Young-Helmholtz theory because physiologist Hermann von Helmholtz (1868/1968) popularized Young’s theory in biological terms at the dawn of experimental psychology. Helmholtz hypothesized that colour vision uses three different “nerve fibres,” each sensitive to a different colour (red, green, or blue). A perceived colour results from combining the different fibre activities. Equal (and maximum) stimulation of all three fibres causes us to experience the colour white. Otherwise, the three fibres produce the sensation of some other colour. Helmholtz refined Young’s theory by proposing that the three fibres had overlapping colour sensitivities to explain why we might fail to match some spectral colour by mixing the three primary colours in the Young-Helmholtz theory.

How do we relate the trichromatic theory to functional analysis? Helmholtz’s theory was functional, not physical: “It must be confessed that both in men and in quadrupeds we have at present no anatomical basis for this theory of colors” (Helmholtz, 1868/1968, p. 95). Given the functional nature of the theory, why was it so influential?

First, the trichromatic theory predicted many observations about colour perception. From the early 18th century on, artists knew that we could use trichromatic techniques to produce diverse colours (Mollon, 1982). More precise colour-mixing experiments performed by Helmholtz and Maxwell provided strong support for the theory and could explain colour blindness. In other words, the trichromatic theory’s predictive power led to its wide acceptance without being causally subsumed. Even though the theory’s red, blue, and green detectors were not linked to biology, there was no evidence to weaken the claim that the three detectors were primitives.

Causal subsumption of the Young-Helmholtz theory required 20th-century methodologies. We now know that Helmholtz’s nerve fibres are instantiated as different retinal cone receptors. Different receptors contain different photo-pigments. Microspectrophotometry reveals that each photo-pigment generates maximum responses to different light wavelengths, the wavelengths required by Helmholtz’s theory (Dartnall et al., 1983). Measures of action potentials from cone cells support Helmholtz’s hypothesis that different channels have overlapping sensitivities (Schnapf et al., 1990). Mechanical principles explain how detected light generates an action potential. When a photo-pigment molecule absorbs light, the molecule’s shape changes. The molecular shape change causes the receptor containing the photo-pigment to initiate a neural response (Nicholls et al., 1992). The trichromatic theory is a subsumed functional analysis.

3.7 The Cognitive Approach

Ulric Neisser (1967) tried to define cognitive psychology by the topics studied. He listed sensation, perception, imagery, retention, recall, problem solving, and thinking. But Neisser realized that his list did not separate cognitive psychology from other approaches: “It is apparent that cognition is involved in everything a human being might possibly do; that every psychological phenomenon is a cognitive phenomenon” (p. 4).

If we cannot define cognitive psychology via its topics, then perhaps we can define it via its research methods. However, we encounter problems. Modern textbooks show that cognitive psychologists use a staggering diversity of methods (Anderson, 2015; Goldstein, 2011; Sinnett et al., 2016). Many methods have long histories, and cognitive psychologists have borrowed and adapted them from other schools of experimental psychology. Hence, research methods do not uniquely define cognitive psychology.

Neisser (1967) finally adopted a broader perspective to define cognitive psychology. For him, cognitive psychology uniquely adopts the cognitive approach. That approach assumes a strong analogy between a computer program and human cognition. Neisser noted that a computer program is “a device for selecting, storing, recovering, combining, outputting and generally manipulating [information]” (p. 8). The cognitive approach aims to provide a similar account of human cognition. Importantly, functional analysis provides exactly the sort of theory required by Neisser’s cognitive approach. Functional analyses can take the form of computer programs.

Consider one approach to computer programming, creating a flow diagram. A flow diagram illustrates a program’s logical structure, defining what happens at different program stages. We can create a flow diagram without expressing how functions actually operate. Flow diagrams for computer programming appeared just after the Second World War (Goldstine & von Neumann, 1947). By the time of psychology’s cognitive revolution, students learning to program first learned how to make flow diagrams (Farina, 1970; Schriber, 1969).

Crucially, we can represent both cognitive theories and computer programs as flow diagrams. Cognitive psychology’s first flow diagram appeared in 1958 (Benjamin, 2019) to describe attentional filters (Broadbent, 1958). Using flow diagrams to represent cognitive theories rapidly grew in popularity. I discussed two examples earlier, the modal memory model (Figure 2-5) and hierarchical TOTE units (Figure 3-3). Modern cognitive psychology textbooks use many flow diagrams. Their use proliferated because cognitive psychologists employ functional analysis. When we explain some function by decomposing it into an organized system of sub-functions, we can easily express the explanation as a flow diagram (see Figure 3-3).

Although we can express cognitive theories as flow diagrams, and we can convert flow diagrams into computer programs, we need not always frame cognitive theories as working computer simulations. Neisser himself counselled against using simulations, arguing that “none of them does even remote justice to the complexity of human mental processes” (1967, p. 9). He believed instead that the cognitive approach generates testable hypotheses about whether computer programming ideas also apply to human cognition.

The usefulness of functional analysis comes from producing information processing accounts to generate testable hypotheses about human cognition. We need not convert a functional analysis into a working simulation to generate hypotheses. Instead, we can think through the flow diagram to make predictions (Braitenberg, 1984). Nevertheless, cognitive psychology has a long history of converting theories into working computer models (Dutton & Starbuck, 1971; Feigenbaum & Feldman, 1963; Lewandowsky, 1993; Newell, 1990; Newell & Simon, 1961; Simon, 1979). Creating such models offers many benefits (Lewandowsky, 1993). For instance, the computer simulation’s behaviour provides testable predictions about human behaviour.

Cognitive psychology works to validate functional analyses by comparing behaviour predicted by functional analyses to behaviour observed in human participants. Have we decomposed the system into the correct set of sub-functions? Have the sub-functions been organized correctly? Do we have evidence of the causal subsumption of any sub-function? I now relate such questions to methods used by cognitive psychologists.

3.8 Seeking Strong Equivalence

Cognitive psychologists perform functional analysis to develop theories analogous to computer programs, theories for generating testable hypotheses about human cognition. Cognitive psychologists conduct experiments either to support or to reject a particular functional analysis by comparing the behaviour predicted by the theory to the behaviour observed in human participants. How do cognitive psychologists compare theories to data? Let us start by relating the comparison to a task from computer science: deciding about a computer program’s intelligence.

Alan Turing (1950) proposed a method, now known as the Turing test, to determine whether a machine had achieved intelligence. He believed that we require intelligence to carry on meaningful conversations. In the Turing test, a human judge converses with different agents, some human, others computer programs. Turing argued that, if the judge cannot correctly distinguish humans from a program, then the computer program must be intelligent.

For example, consider testing a computer simulation of paranoid schizophrenia, PARRY, which participated in conversations, but its contributions became more paranoid over time. Colby et al. (1972) evaluated PARRY by having psychiatrists compare its conversations with conversations with human paranoids. The psychiatrists could not reliably determine whether a conversation was generated by a human or by PARRY. PARRY had passed the Turing test.

Unfortunately, the Turing test can be passed for the wrong reasons, as shown by another conversation-making program called ELIZA (Weizenbaum, 1966, 1976). ELIZA mimicked a humanistic psychologist’s conversational style and generated extremely compelling conversations. “Some subjects have been very hard to convince that ELIZA is not human. This is a striking form of Turing’s test” (Weizenbaum, 1966, p. 42). However, Weizenbaum did not create ELIZA to model natural language understanding. Instead, ELIZA used some programming tricks to parse incoming sentences into templates for creating convincing responses. “A large part of whatever elegance may be credited to ELIZA lies in the fact that ELIZA maintains the illusion of understanding with so little machinery” (Weizenbaum, 1966, p. 43).

ELIZA is simply a procedure—a flow diagram—for converting stimuli into responses. Let us consider the human with whom ELIZA converses as another flow diagram. When ELIZA and a human produce a convincing conversation, both flow diagrams generate appropriate outputs to inputs. We call two different systems generating the same input-output behaviour weakly equivalent systems (Pylyshyn, 1984).

We call input-output equivalence weak equivalence because two very different procedures can produce the same input-output mapping. Weak equivalence therefore illustrates another many-to-one relationship. For example, ELIZA uses the programming tricks invented by Weizenbaum, who intended ELIZA not to understand language. In contrast, humans use very different methods, methods for actually understanding sentences.

Weak equivalence affects our validation of functional analyses. A cognitive psychologist wants to claim that her functional analysis correctly explains some cognitive phenomenon. But weak equivalence means that methods only examining input-output mappings—like the Turing test—cannot validate a cognitive theory.

Cognitive psychologists do not want to propose weakly equivalent theories about human cognition. Instead, they want to propose strongly equivalent theories about cognition. Strong equivalence exists when two systems use the same procedures to generate the same input-output mapping (Pylyshyn, 1984). Strongly equivalent systems (1) generate the same input-output mapping, (2) use the same program or algorithm to produce the mapping, and (3) use the same architecture or programming language to bring the algorithm to life. In other words, both systems use the same flow diagram, which in turn uses the same primitive functions.

To establish the strong equivalence of a functional analysis to human cognition, cognitive psychologists must go beyond the Turing test and examine additional evidence. They must observe behaviours, produced as unintended consequences of information processing, that reveal the nature of internal processing. We call such unintended behaviours second-order effects (Newell & Simon, 1972). Pylyshyn (1984) argues that we can study second-order effects using three different measures: relative complexity evidence, error evidence, and intermediate state evidence. In the next sections, I consider second-order effects in more detail.

3.9 Relative Complexity Evidence

In the 19th century, Dutch physiologist Franciscus Donders (1869/1969) launched mental chronometry to measure the duration of mental processes. Prior to Donders, researchers used the simple reaction time task to measure nerve impulse latency. Researchers presented a stimulus (e.g., a mild shock to the foot) to a participant, who pressed a response key as soon as he felt the shock, and measured the time elapsed between presenting the stimulus and pressing the key.

Donders added a condition that required participants to decide before responding; we call his method the choice reaction time task. For instance, Donders could deliver a shock to either foot; the participant would then press one key if he felt a shock in the left foot or a different key if he felt a shock in the right foot. Participants decided which key to press. Donders reasoned that participants would take longer to respond by having to decide (about shock location) in addition to performing the other actions required by the simple reaction time task. Figure 3-4 illustrates the differences that he assumed to exist between the two reaction time tasks.

Donders believed that the differences between the two tasks permitted him to measure the duration of mental processes. He argued that we can measure the time required to decide by subtracting the response time for the simple reaction task from the response time for the choice reaction time task, because the only difference between the two tasks is the decision-making stage. We call his technique the subtractive method.

The subtractive method requires two assumptions. First, a processing stage must start only after the preceding stage finishes. Second, adding a new processing stage must not affect the other stages—the assumption of pure insertion (Sternberg, 1969b). The subtractive method fell out of favour in the 19th century when some researchers questioned these two assumptions (Külpe & Titchener, 1895). However, by the 1960s, cognitive psychologists altered the method established by Donders to address such concerns.

One variation was the additive factors method (Sternberg, 1969a, 1969b). This method holds the number of processing stages constant across conditions but manipulates processing steps within a processing stage. For instance, consider Sternberg’s (1969b) landmark memory scanning task. In that task, participants remember a list of items (in primary memory). When presented with a probe item, they decide as quickly and accurately as possible whether the probe item belongs to the remembered list.

The additive factors method manipulates processing within a particular stage. For instance, Sternberg (1969b) varied the number of items remembered in the list. By increasing the length of a list, Sternberg influenced processing times within the stage in which memorized items compared with the probe. Sternberg generated different hypotheses about how manipulating list length would affect reaction time; different hypotheses assumed that memory scanning uses different search processes.

For instance, Sternberg hypothesized that an exhaustive search scans the memory. An exhaustive search scans every item (in order) before responding. If scanning each item requires constant time, then speed in responding to the presence of the probe will increase as the list increases. Furthermore, an exhaustive search should produce no differences in response time for trials in which the probe belongs to the list versus trials in which the probe does not belong to it (Figure 3-5, left panel).

Sternberg made different predictions if a serial self-terminating search scanned memory. This search moves from the first item to the last item on the list but stops when it discovers the probe item. The serial self-terminating search hypothesis predicts the same reaction time function as that predicted by an exhaustive search for trials in which the probe does not belong to the list, because both processes scan all items. However, when the probe belongs to the list, the reaction time function will have a shallower slope (in fact, half of the slope found when the probe does not belong to the list; Figure 3-5, right panel). When the probe belongs to the list, the scan will only process, on average, half of the items before finding the probe. “Yes” responses with a serial self-terminating search require half of the scanning compared with “No” responses, halving the slope of the reaction time function.

Sternberg (1969b) found that human participants in the memory scanning experiment produced reaction time functions consistent with the exhaustive search hypothesis and proposed a memory scanning model for which an exhaustive search provided more efficiency than a serial self-terminating search.

Sternberg’s use of reaction time to evaluate memory scanning illustrates what Pylyshyn (1980, 1984) calls relative complexity evidence, which recognizes that some problems are more challenging, and require more processing, than others. A valid cognitive theory will produce relative complexity rankings of problems identical to rankings based upon human performance. Both the model and the participant will find the same problems “easy”; both the model and the participant will find the same problems “hard.”

Reaction time provides relative complexity evidence, because harder problems presumably require more processing time than do easier problems. Sternberg’s predicted reaction time functions (Figure 3-5) illustrate the relative complexity of different memory scan techniques. The number of items in memory, and whether the probe belongs to the list, affect Sternberg’s techniques differently. Sternberg supported exhaustive search over serial self-terminating search by comparing modelled reaction time functions to functions obtained from human participants.

Relative complexity evidence informs functional analysis. Researchers frequently use visual search tasks to study visual cognition. In a visual search task, a participant sees several displayed objects and must decide whether one object (the target) is unique compared with the others (the distractors). The dependent measure is reaction time, and the independent variables include the number of distractors and the features used to define objects.

Visual search tasks reveal the pop-out effect. Some targets immediately “pop out” from the display, so the number of distractors does not influence the time to detect the presence of the target (Treisman & Gelade, 1980). A target that pops out possesses a unique visual feature (e.g., a unique colour, orientation, contrast, or motion). For example, a red object pops out from a display in which all distractors are green.

However, other unique targets do not pop out from a display. These targets are unique feature combinations, such as a red circle among distractors that are either red squares or green circles. The time to detect unique feature combinations increases with an increase in the number of distractors.

Visual search results inspired Treisman’s feature integration theory (Treisman, 1985, 1986, 1988; Treisman & Gelade, 1980; Treisman & Gormican, 1988; Treisman et al., 1977). In feature integration theory’s early processing stages, different detectors register the locations of different, basic, visual features. Unique basic features produce pop out. A different feature map represents locations of different features (different colours, orientations, movements, etc.). A target possessing a unique feature will be the only active location in one feature map and will pop out.

However, targets created from unique feature combinations do not produce unique activity in a single feature map and therefore do not pop out. Instead, detecting such targets requires additional processing. The additional processing aligns different feature maps using a master map of locations. The master map indicates which feature combinations exist at each location. An attentional spotlight performs a serial self-terminating scan of the master map. Attention scans from one location to the next until discovering a unique target. With such a serial search from location to location, the reaction time for detecting a unique combination of features increases as the number of distractors increases.

Feature integration theory explained why some unique targets pop out, but others do not. Reaction time data motivated a particular functional decomposition. However, reaction times can provide relative complexity evidence for evaluating competing functional analyses. For instance, guided search theory arose from concerns about feature integration theory (Wolfe, 1994; Wolfe et al., 1989; Wolfe et al., 1988). Wolfe worried that feature integration theory did not use results from early feature processing stages to direct the attentional spotlight. In contrast, guided search theory informs the search with both early feature processing and attentional processing. Early feature processing directs attention to visual objects that differ from their neighbours; higher-order processes direct attention to objects possessing target features. Thus, the two processes produce an efficient search by directing attention to locations likely to hold the target.

3.10 Error Evidence

Relative complexity evidence uses problem difficulty to rank order problems for comparing two systems (e.g., a functional analysis and a human participant). A valid functional analysis should match a human participant when we order problems from the easiest to the hardest. Section 3.9 related relative complexity evidence to measuring reaction time, because more challenging tasks should take longer to perform than less challenging tasks. However, relative complexity evidence can come from other sources, such as measuring performance accuracy. Harder problems cause more errors than easier problems.

A recent study gives an example of using errors to provide relative complexity evidence (Dawson, 2022). In this study, cue combinations signalled reward probability. The logical structure of cue combinations was manipulated; the interaction was either the AND of two cues (signalling a reward if both cues were present) or the XOR of two cues (signalling a reward if only one cue was present). The reward probability signalled by the cue interactions was also manipulated (high versus low probability) to alter the interaction’s size as measured by a probabilistic value called conditional dependence.

Dawson (2022) trained very simple artificial neural networks called perceptrons (Rosenblatt, 1958) to predict the reward probability signalled by cues. He found an interaction between the manipulations of the logical structure and of reward size associated with the cue interaction. As a result, the networks were very poor at estimating reward probability for the XOR/low-probability condition compared with the other conditions.

Dawson (2022) then ran an experiment in which human participants learned to estimate probabilities signalled by stimuli defined by different cue patterns. He discovered higher accuracy for participants in conditions for which the perceptrons also performed well and lower accuracy for participants in conditions for which the perceptrons also performed less well. Dawson proposed the perceptron as a plausible model of human probability learning.

The example provided by Dawson (2022) illustrates how accuracy measures can provide relative complexity evidence. However, the errors made by models or by participants can also provide additional information. A system’s mistakes can reveal information about internal processing, information called error evidence (Pylyshyn, 1984).

Cognitive psychology frequently examines error evidence. We saw in Chapter 2 that Conrad’s (1964) analysis of letter confusion provided evidence for acoustic, not visual, representations in primary memory. Similar results emerge when using words as stimuli (Baddeley, 1966). Baddeley found more confusion between memories of similar-sounding words, even when he presented words visually. The semantic similarity between words held in primary memory interferes far less with recall.

In contrast, semantic similarity produces more recall errors from secondary memory (Baddeley & Dale, 1966). For instance, for two semantically similar word lists, learning the second list of words interfered with memory of the first list. However, primary memory did not produce the same effect. Such error evidence indicates that secondary memory encodes concept meanings. Encoding meanings causes other memory errors. For instance, human participants will mistakenly recognize a sentence as having been seen before provided that the sentence conveys the same meaning as that provided by previously presented material (Bransford et al., 1972).

Error evidence also provides insight into finer details. One study used multivariate statistics to explore letter confusion in iconic memory (Dawson & Harshman, 1986). The study found more likely confusion between letters with many features and letters built from a subset of the features than vice versa. For example, confusion between E and F or between E and L occurred more frequently than confusion between F and E or between L and E. Dawson and Harshman argued that such error evidence supports a letter recognition model involving feature accumulation. For instance, such a model would accumulate a vertical line and three horizontal lines as the features of E. Mistakes occur when not all features are correctly detected. For instance, a failure to detect one of the horizontal lines in E could incorrectly register F, and a failure to register two of these lines could incorrectly register L. Confusion asymmetries—E is more likely to be confused with L than L is with E—emerge naturally from feature accumulation failures.

3.11 Intermediate State Evidence

Cognitive psychologists also use intermediate state evidence to validate a functional analysis (Pylyshyn, 1984). Such evidence concerns the intermediate knowledge states that a system passes through during information processing. If a functional analysis is strongly equivalent to a modelled system, then both proceed through identical intermediate states.

Intermediate state evidence plays a central role in studying human problem solving. Newell and Simon’s classic 1972 book Human Problem Solving summarized 20 years of studying how humans solved problems. Their explanations took the form of working computer simulations; they evaluated simulations by comparing their intermediate states to those of human problem solvers.

Newell and Simon (1972) used a core methodology called protocol analysis (Ericsson & Simon, 1984). Protocol analysis begins by collecting verbal protocols from participants solving problems. A verbal protocol records what participants say as they “think out loud” while solving a problem. The problems that Newell and Simon studied—problems in cryptarithmetic, logic, and chess—were difficult enough to ensure that participants engaged in problem-solving behaviour but not so difficult that the problem could not be solved in a reasonable time, or the problem would produce a verbal protocol too long for later analysis.

Protocol analysis proceeds in several steps. First, a single participant solves a problem, speaking aloud at all times. Participants have been trained to think out loud and are encouraged to think out loud by the experimenter if they stop talking during a session. The session is tape-recorded, providing the raw data for the analysis.

Second, the recorded protocol is transcribed, breaking the transcription into short phrases labelled for later reference. The labelling is a form of data preprocessing because each labelled phrase is assumed to represent a single problem-solving state. However, there is very little additional editing of the protocol.

Third, the transcribed problem is used to infer the participant’s problem space. A problem space defines the different knowledge states used to represent a problem during its solution. A particular knowledge state can be thought of as a set of symbols that represents a problem’s current condition. To move from one state to the next is to apply some rule to manipulate symbols in order to change the knowledge state. A participant was presumed to “encode these problem components—defining goals, rules, and other aspects of the situation—in some kind of space that represents the initial situation presented to him, the desired goal situation, various intermediate states, imagined or experienced, as well as any concepts he uses to describe these situations to himself” (Newell & Simon, 1972, p. 59). The problem space makes explicit such encoded properties.

Fourth, a participant’s problem space is converted into a problem behaviour graph. This graph is a set of connected nodes. Each node represents a knowledge state about the problem. Each link represents a rule in the problem space that, when applied to a knowledge state, produces the next knowledge state in the graph. Typically, nodes are linked from left to right to illustrate the process of solving a problem.

However, a problem behaviour graph can also represent a participant’s changing approach to a problem. Sometimes in pursuing a train of thought a participant reaches a dead end and backtracks to some earlier point in her reasoning. A problem behaviour graph represents such backtracking by going back to the knowledge state to which the participant has returned, drawing a link downward, and duplicating the returned-to knowledge state. Thus, the problem behaviour graph illustrates both progress on a problem (by growing outward from left to right) and backtracking to previous knowledge states (by growing downward from top to bottom).

Fifth, a production system is used to create a working computer simulation to solve the problem. A production system’s basic operations are derived from the problem behaviour graph by inferring potential rules that describe the links between states. Intermediate state evidence evaluates how well the production system emulates human performance by comparing the production system’s problem behaviour graph to the participant’s.

Newell and Simon (1972) proposed the production system as the cognitive architecture. A production system consists of a set of operators. Each operator is a condition-action rule. A simulation begins with each operator scanning memory simultaneously, searching for its condition (i.e., a particular string of symbols). When one operator finds its condition, it temporarily inhibits the other operators and performs its action. A production’s action involves manipulating the symbols in memory. Once symbol manipulation finishes symbols, the production releases control, and the system returns to the state in which all operators scan memory in search of their conditions.

Note that a production system like the one described above generates all of the information required to create a problem behaviour graph for the simulation. At any moment in time, the current knowledge state for the production system is the set of symbols being held in memory. To move from this state to the next, a particular production captures control and manipulates the symbols in memory. Thus, a link between knowledge states indicates which production was used. The fact that a production system can generate its own problem behaviour graph means that we can compare the production system graph to the problem behaviour graph created from a participant’s example.

For instance, Newell and Simon (1972) studied the cryptarithmetic problem DONALD + GERALD = ROBERT. A participant is presented with this statement and told that D = 5. The task is to determine the integer represented by each remaining letter. Newell and Simon’s protocol analysis of one participant’s work on this problem generated a problem behaviour graph consisting of 238 nodes. Newell and Simon used this graph to find evidence for 14 separate productions and used them to create a working production system. They found that the production system accounted for approximately 80% of the subject’s problem behaviour graph. This is a striking correspondence between the intermediate states measured for a human participant and those created by a computer simulation of his thought processes.

3.12 The Cognitive Impenetrability Criterion

Cognitive psychology seeks strong equivalence between systems. Strongly equivalent systems generate the same input-output mapping by using the same information processing steps. Three different sources of information can establish whether two systems use the same algorithm: relative complexity evidence, error evidence, and intermediate state evidence.

However, strong equivalence requires that two systems not only run the same program but also use the same programming language, the same information processing primitives, and the same functional architecture (Section 3.5). “Devices with different functional architectures cannot, in general, directly execute identical algorithms” (Pylyshyn, 1984, p. 96).

In many cases, supporting the claim that a function is a primitive involves appealing to findings collected from outside cognitive psychology, such as evidence from neuroscience. For instance, discovering that the surgical removal of part of the human brain disrupted primary memory, but not secondary memory (Scoville & Milner, 1957), provided anatomical evidence for the modal memory model (Squire, 2009). Similarly, evidence from visual neuroscience (Livingstone & Hubel, 1988) supports the existence of the various feature maps proposed as the early stages of feature integration theory (Treisman, 1986; Treisman & Gelade, 1980).

In other cases, a functional theory becomes widely accepted by explaining experimental results. Such success permits the theory to flourish while awaiting its subsumption, as illustrated earlier by the trichromatic theory, which provided the dominant account of colour perception, a century before being subsumed.

Given the importance of discovering primitive functions, can cognitive psychologists do so by collecting data from within their own discipline? Can the results of a cognitive psychology experiment help to subsume causally a functional analysis? Pylyshyn (1980, 1981b, 1984) proposes the cognitive penetrability criterion as one approach that cognitive psychologists can use to examine whether a function is primitive. If we can change a function’s behaviour by altering a participant’s beliefs, then we call the function cognitively penetrable. Cognitively penetrable functions are not primitive.

In contrast, if a wide variety of relevant belief changes do not affect the function, then we call the function cognitively impenetrable. Primitive functions must be cognitively impenetrable. The cognitive penetrability criterion “allows us to drive a wedge between cognitive processes and the part of the cognitive system fixed with respect to cognitive or semantic influences” (Pylyshyn, 1984, p. 139).

The cognitive penetrability criterion’s logic begins by assuming that human information processing is instantiated by brain function. As we learn about the world, our brain structure changes (Doidge, 2007; Kolb, 1995). Knowledge must be stored by modifying neural connections. However, some brain features must be less modifiable than others (Newell, 1990). Newell argued that the brain has some structures, called fixed structures, that change relatively slowly. Fixed structures provide the architecture of cognition and differ from other structures that change much more rapidly because they store information.

An architecture associated with fixed brain structures will not change as new information is acquired. Adding new mental contents will not change the mechanisms for manipulating information. “An architecture provides a boundary that separates structure from content. Behavior is determined by variable content being processed according to the fixed processing structure, which is the architecture” (Newell, 1990, p. 82). Therefore, we can test whether a particular function belongs to the architecture by changing mental contents. If changes in contents alter the function’s operation, then the function is not part of the architecture. If the function belongs to the architecture, then it is fixed and should not be affected by content manipulations.

Pylyshyn’s cognitive penetrability criterion follows directly from this logic. Pylyshyn’s method proceeds by first measuring some function of interest. Then a participant’s beliefs are changed in a fashion related meaningfully to the function. Finally, the function is measured again after manipulating mental content. If the function changes in a way related to the changed belief, then it is cognitively penetrable and does not belong to the architecture. The cognitive penetrability criterion plays an important role in the debate about whether the spatial properties of mental images belong to the architecture.

We experience mental images as “pictures in the head” when we solve spatial problems. Many experiments study the properties of mental images (Kosslyn, 1980; Shepard & Cooper, 1982). These experiments reveal that mental images have spatial properties. Mental images have a spatial layout, so we require time to scan from one image location to another. Similarly, the time to rotate mental images to a new orientation increases with the amount of rotation required. The imagery debate examines whether the spatial properties of mental images belong to the cognitive architecture (Block, 1981; Pylyshyn, 1973). Some evidence in the imagery debate shows cognitive penetrability of spatial properties of mental images; such properties do not belong to the architecture.

To illustrate using such evidence, consider the image scanning task (e.g., Kosslyn, 1980, pp. 36–52). In a typical scanning experiment, participants create a mental image of a memorized map. Then they use the image to answer questions. For instance, Kosslyn asked participants to focus their attention on one location, and then Kosslyn named another location. Participants scanned the image from the first location to the second one. Kosslyn manipulated the distance between the two locations and found that a participant’s response time increases with increases in the distance between the two locations.

Kosslyn (1980) presumed that the linear relation between distance and response time arose because a mental image’s spatial extent belonged to the architecture. If so, then changing a participant’s beliefs about the task should not alter the relationship between distance and scanning time. However, some evidence indicates that belief changes alter scanning times, meaning that image scanning is cognitively penetrable.

For instance, Liam Bannon first replicated the linear relationship between image distance and reaction time (Pylyshyn, 1981b, pp. 242–243). However, Bannon hypothesized that task instructions led participants to believe that scanning should take time, because they were told to press a response button “when they arrived” at the second location. To test his possibility, Bannon altered the instructions to change participants’ beliefs about the task. “The instructions specified merely that subjects give the compass bearing of the second place—that is, to state whether the second place was north, northeast, east, southeast, and so on of the first” (Pylyshyn, 1981b, p. 243). With these instructions, Bannon discovered that there was no relation between distance and reaction time; this result has been replicated by other researchers (e.g., Finke & Pinker, 1982). Thus, the map-scanning results are not caused by a primitive property of imagery, because results change when participants change beliefs about the task.

Cognitive psychologists must causally subsume their functional analyses and usually do so by appealing to evidence from other disciplines, such as neuroscience (Dawson, 2013). However, some results from experimental psychology can determine whether functional properties are primitives. The cognitive penetrability criterion, as illustrated in the imagery debate, shows how cognitive psychologists can explore architectural issues.

3.13 Cognitive Psychology in Principle and in Practice

In principle, cognitive psychology proceeds by conducting functional analysis, an approach inspired by the computer metaphor. In general, cognitive psychologists analyze cognition into components that we can describe as information processing functions. Such functions use rules to manipulate symbols. Furthermore, strong similarities exist between functional analyses and programs or algorithms. Explaining human cognition with functional analysis uses techniques similar to the methods used to explain a computer’s behaviour. A functional analysis rests on the results of psychological experiments. Experimental observations of human behaviour motivate carving a complex process into an organized system of simpler sub-processes (see Chapter 2).

If, in principle, cognitive psychologists conduct functional analysis, then we expect, over time, that they will produce theories that include organized systems of larger numbers of sub-functions. For example, by the mid-1960s, cognitive psychology’s crowning achievement was the modal memory model (Figure 2-5). Since then, both primary memory and secondary memory have been further analyzed into sub-components.

For instance, cognitive psychologists have decomposed primary memory into a more complex system known as working memory (Baddeley, 1986, 1990). Working memory consists of three sub-functions. The central executive operates on symbols stored in buffers and determines how attention is allocated across simultaneously ongoing tasks. The visuospatial buffer stores visual information. The phonological loop stores verbal information and itself has been further analyzed into sub-functions that include a phonological store for holding symbols and a rehearsal process for preserving items in the phonological store. Similarly, cognitive psychologists have decomposed secondary memory into distinct functional sub-components, including declarative versus non-declarative memory (Squire, 1992), semantic versus episodic memory (Tulving, 1983), and memory for words versus memory for images (Paivio, 1971, 1986).

Cognitive psychologists do not only use experimental results to decompose functions into sub-functions. They also use special observations—relative complexity evidence, error evidence, and intermediate state evidence—to validate a particular functional analysis. Furthermore, the cognitive penetrability criterion can determine if a function is primitive.

In practice, when cognitive psychologists conduct functional analysis, they do not produce unified accounts of human cognition. Instead, they generate diverse, competing theories. Validating a functional analysis not only establishes strong equivalence but also finds support to counter competing theories. For example, in Chapter 2 I briefly reviewed experimental results from studying human memory and used these results to motivate the modal memory model. Chapter 2 implies that all cognitive psychologists accepted the modal memory model. However, other theories offer very different explanations of the same results.

The levels of processing theory provides one example (Cermak & Craik, 1979; Craik & Lockhart, 1972). This theory emphasizes different kinds of processing instead of different kinds of memory stores. According to levels of processing, we retain items receiving deeper or more semantic processing better and longer than we retain items receiving shallower or less semantic processing. Levels of processing deliberately opposed the multi-store approach introduced in Chapter 2. “While multistore models have played a useful role, we suggest that they are often taken too literally, and that more fruitful questions are generated by the [levels of processing] formulation” (Craik & Lockhart, 1972, p. 681).

Because competing memory theories exist, cognitive psychologists who study memory must design experiments to determine whether to prefer one account (e.g., levels of processing) over another (e.g., multi-store models). The kinds of evidence introduced in Chapter 3 can evaluate competing functional analyses of the same cognitive phenomenon. Such evaluation is not limited to studying memory. For instance, earlier we saw different functional analyses exist for a visual search (i.e., feature integration theory versus guided search). Most topics in cognitive psychology have inspired competing theories.

Cognitive psychology’s diversity arises from an evolving notion of what “information processing” means. In the mid-20th century, the digital computer provided the only notion of information processing available to cognitive psychology. Since then, new ideas about information processing have inspired competing cognitivist positions (Dawson, 1998, 2013). Connectionism arose from the belief that biological brains do not process information in the same way that digital computers do, leading to theories that abandon the explicit distinction between symbols and rules (Bechtel & Abrahamsen, 2002; Clark, 1989, 1993; Horgan & Tienson, 1996; McClelland & Rumelhart, 1986; Rumelhart & McClelland, 1986b). Embodied cognition arose from a rekindling of cyberneticists’ interest in the interactions between agents and environments (Shapiro, 2011, 2014). Embodied theories propose that complex behaviours emerge from the interactions between simple agents and complicated environments (Braitenberg, 1984; Clark, 1997, 2003, 2008, 2016; Dawson et al., 2010; Noë, 2004, 2009). Many embodied cognitivists believe that the mind extends from inside the skull to include the surrounding environment (Clark & Chalmers, 1998).

Different ideas about information processing also inspire a diversity of proposed cognitive architectures. For instance, Dawson (1998, Table 6-1) lists 24 different proposals for the language of thought. We should not be surprised that many competing theories, and many competing architectures, exist in cognitive psychology. All psychological schools of thought have exhibited similar diversity (Heidbreder, 1933). Earlier schools began not by organizing pre-existing facts but by investigating general notions of the mind, collecting new facts along the way. A school’s general ideas about the mind “can best be understood not as statements of scientific fact, not as summaries of existing knowledge, but as ways and means of arriving at knowledge, as temporary but necessary stages in the development of a science” (Heidbreder, 1933, pp. 16–17).

Cognitive psychology provides a modern illustration of Heidbreder’s point. Cognitive psychology begins by asserting that cognition is computation and then develops new methodologies to collect evidence to permit cognitive psychologists to explain human cognition in the same way that computer scientists explain the operations of a computer.

Neisser’s cognitive approach requires evaluating competing functional theories and competing architectural proposals. We cannot define cognitive psychology by which facts it collects or by which theories it considers. Instead, we must define it by using its primary method, functional analysis, as well as the directions in which functional analysis leads cognitive psychologists. “Science does not proceed in the light of reason alone, but like other human enterprises is a muddled adventure working itself out” (Heidbreder, 1933, p. 17). Cognitive psychology’s diversity illustrates its unique “muddled adventure.”

3.14 Chapter Summary

Chapter 1 related cognitive psychology to computer science, arguing that cognitive psychologists assume that human cognition is similar to the processing used by digital computers. Chapter 2 related cognitive psychology to general experimental psychology by illustrating how cognitive psychologists infer human information processing because we cannot directly observe it. Chapter 3 related cognitive psychology to the philosophy of science by arguing that cognitive psychologists analyze complex phenomena into organized systems of simpler sub-functions, an approach called functional analysis.

However, cognitive psychologists appear to explain one function by decomposing it into further, unexplained, sub-functions, leading to Ryle’s regress. Cognitive psychologists must escape Ryle’s regress if their functional descriptions are to achieve the status of scientific explanations. They escape Ryle’s regress by discovering sub-functions simple enough to be explained by physical causes: causally subsumed functions. We do not explain a causally subsumed function by decomposing it into further functions.

Cognitive psychology aims to show strong equivalence between a functional analysis and human cognition. Chapter 3 introduced three kinds of evidence for establishing strong equivalence: relative complexity evidence, error evidence, and intermediate state evidence. The chapter also introduced the cognitive penetrability criterion for testing whether a function belongs to the architecture.