Discovery Problem and Cognitive Neuropsychology
Cognitive neuropsychology is a rather young field and still cognitive neuropsychologists do not reach agreement on the proper met hodology of the field. Recently Clark Glymour (1994) argued that the problem of mental architecture is not soluble even under simplifying assumptions. If his argument is sound, this means that the status of cognitive neuropsychology as a science is threat ened. Jeffrey Bub (1994) gives elaborated counterarguments to this challenge. My purpose in this paper is to analyze Glymour and Bub's arguments. My conclusions will be two-fold. On the one hand, Glymour's argument needs modification. On the other hand, if we accept Bub's counter argument, it will be disastrous to cognitive neuropsychology.
2. Cognitive neuropsychology and Shallice's argument
In this section, I will summarize basic assumptions in cognitive neuropsychology following Shallice ( 1988).
Cognitive neuropsychology has its origin in nineteenth century diagram-makers, like Broca (Shallice 1988, 6-12). Through clinical observations of brain damaged patients, Broca claimed that the language process is localizable to a particular ar ea of brain. Other neuropsychologists found other syndromes related to other areas of brain. They tried to explain these phenomena by drawing diagrams of mental process. For example, Lichtheim assumed that language process have three centers, and Broca's aphasia and other syndromes are explained as a result of interruption of one or other connection between these centers. But the works of diagram-makers are fatally flawed in several points. First, in many cases neuropsychologists failed to localize the a rea associated to a particular syndrome. Second, their psychological concepts were not adequate to describe the inabilities found in patients. Moreover their conceptual frameworks are outdated by behaviorism and other psychological methodologies. Third, c linical evidence was too weak to support their claims. For example, often their claims depend on small number of single unusual cases, and criticized in this point.
With these difficulties, diagram-makers are forgotten until 1960s. In 1960s, cognitiv e neuropsychologists started to draw diagrams, though in more elaborate way than nineteenth century diagram-makers (Shallice 1988, 14-17). Cognitive neuropsychologists also use brain-damaged patients to reveal normal cognitive architecture. They assume th at our mental processes consist of many modules each of which has distinct function. But they are no longer interested in localize these modules in brain (213-214). They also developed methodologies to use single case studies as relevant evidence for the ir claims.
Shallice enumerates nine basic assumptions in cognitive neuropsychology (Shallice 1988, 218-219). First, there are three assumptions on the modularity. The first assumption is that "[t]he cognitive system being investigated contains a large set of isolable processing subsystem" (Shallice 1988, 218). These subsystems are often referred as "modules" (Shallice 1991, 431). Each modules may have lower level modules inside (assumption 2), and each modules have its own function (assumption 3). Nex t three assumptions are on the relation between model and performance. First, it is assumed that "[c]ognitive systems are qualitatively similar across individuals for tasks that are routinely performed in a culture" (Shallice 1988, 219) (assumption 4). Ta sk performance requires "the use of a 'procedure' --a temporary activating or inhibiting of sets of inter subsystem transmission routes" (Shallice 1988, 219) (assumption 5). For each procedure, the overall pattern of performance "depends on the amount of resource available in each subsystem required" (Shallice 1988, 219, emphasis original) (assumption 6). In a later version of the list, he adds: "task performance is monotonically related to that amount" (Shallice 1991, 431). Finally, he has three assumptions on the effect of lesions. First, to know which and how many modules are lesioned, the only evidence we have is the behaviour of the patient (assumption 7). Second, the effect of a lesion is "determined by (a) the pattern of quantitative loss of resources across the normal set of subsystems, with (b) the procedure adopted by the subject" (Shallice 1991, 431) (assumption 8). The first part of the assumption means that a lesion cannot add something to normal process. The second part says that the effect appears as an impairment of some task performance. Last of all, he assumes that the difference in resource between normal subjects is relatively small by comparison with the difference caused by such a lesion (assumption 9). These assumpti ons are not a priori, and Shallice gives supportive argument to some of them (Shallice 1988, 228-243). But we can understand them as the hard core of "research programme" (Lakatos 1970) of the field.
What is the valid method for research under these a ssumptions? By assumptions 7 and 8, we are justified to use brain damaged patients to inquire cognitive structure of normal person. But the question is how we can use the evidence to construct a theory. On this point, there are three main camps disputing with one another (Shallice 1988, 29-37). First, there are people who emphasize the importance of single case studies and dismiss group-study as irrelevant to theory construction. As we can see in assumption 7, each patient can have different lesion to dif ferent modules. And this difference between individuals can be so big that any generalization among a group of patients is dangerous. So these people think that everything we can do is to investigate what each patient can and cannot do. Shallice objects to this position because this position denies the replicability of evidence, and without replicability theoretical claims cannot be strong (31-32). Second approach is to find symptom complexes by investigating large number of patients. If some symptoms and other symptoms are always found together, we can infer from the fact that there is some relationship between two group of symptoms in cognitive architecture. Shallice again objects this group-study approach (32-34 ). The modular architecture described in the assumptions may not have no relationship to the association of symptoms. There was a cluster of symptoms called "Gerstmann syndrome." The patients of this syndrome had difficulty in calculation, right-left diso rientation and other seemingly unrelated tasks at the same time. Psychologists speculated on the relationship of these symptoms, but finally it turned out that these symptoms are not functionally related (because they are found to occur independently from one another) but that the locations on the brain for these tasks are close to each other. This example shows that the association of symptoms cannot be a solid basis for theorizing, and even a statistically high correlation may not mean a functional rela tion in cognitive architecture.
The third, and Shallice's own position is to study dissociations (Shallice 1988, 34-37). Shallice defines a dissociation as follows: "a dissociation occurs when a patient performs extremely poorly on one task -- prefera bly way outside the normal range -- and at a normal level or at least a very much better level on another task" (34). If we find a dissociation between two tasks in a patient, This means that these two tasks use different "procedure" (as is defined in ass umption 5), and we need two different routes for these tasks in cognitive process. The important thing is that if once we find a single case of dissociation, no matter how much evidence of association we have, the relevance of the evidence of dissociation does not change. In this sense, dissociation study has an advantage to the symptom complexes study. Moreover, though a single dissociation is enough to establish the existence of two different routes, we can also conduct a group study to replicate the r esult. In this sense dissociation study has an advantage to single-case study. But here is another complexity. Dissociations may be still not enough to establish the existence of two different routes, because, as is implicit in assumption 6, different two tasks operated in the same module may have different degree of difficulty, and with the given resource one task can be done normally while the resource is not enough for the other task. In this case we find dissociation though actually there is only one route involved in. To avoid this difficulty, Shallice introduces the notion of double dissociation (36). Double dissociation is the case of pair of patients "in which a second patient is found who shows the complementary dissociation, the previously spare d task being the one now impaired" (Shallice 1988, 36). In another expression, "on task I, patient A performs significantly better than patient B, but on task II, the situation is reversed" (235). If we have these two dissociations, we cannot say that the se two tasks are conducted by the same module. Thus double dissociation has the power to falsify some kind of theory (235).
Shallice's argument includes many interesting points on the methodology of cognitive neuropsychology, but I do not have the spa ce to discuss most of them. In the following sections, I will concentrate on the problem how we can construct models of cognitive process using dissociation or double dissociation. Glymour gives a negative answer to the usefulness of evidence of dissociat ion. Bub object to it. But, before we move to the next section, I would like to introduce an example of real case in which cognitive neuropsychologists constructed a diagram from dissociation data.
The example is the study of dyslexia (Shallice 1988, 68-129). Many interesting cases of reading difficulty are reported. In some cases, patients cannot read irregular words (e. g. yacht) correctly, though they can read regular words, including regular non-words (e. g. dake). Other patients hav e opposite problem, namely they can read irregular words but cannot read regular non-words. In other cases, patients who can fluently read sentences fail to answer comprehension test of written or spoken words. Other patients who understand written words have problems in reading aloud the words and substitute them with semantically related words (e. g. speak -> 'talk'). From these cases we find two dissociations, namely between repeating irregular words and repeating regular non-words, b etween understanding words and reading the words (these are, in fact, double dissociations).
Figure1 shows Morton and Patterson's earlier version of the diagram reconstructed from these dissociations (Shallice 1988, 92). Shallice introduces several cr iticisms to this diagram, and suggests several modifications of it, but for the purpose of this paper this simple version will suffice. I will use Figure 1 as a paradigm case of diagrams which cognitive neuropsychologists really make. As you can see in Fi gure 1, they explain these dissociations by assuming three routes from visual inputs to speech. One is a route via grapheme-to-phoneme conversion. This module is supposed to convert a sequence of letters into the corresponding pronunciation mechanically, so it can convert regular non-words but cannot convert irregular words. The other two routes go through visual and phonological lexicon modules. These modules can deal with an irregular word as far as it is in the lexicon, but cannot deal with a non-wor d. These two kinds of routes can explain the first dissociation. Among two routes which go through lexicon modules, one also goes through cognitive system and the other does not. According to this model, if the cognitive system or connections to it is dam aged, the patient cannot understand words, though he /she can read aloud the word. If the other route is damaged, the patient cannot pronounce the word though he/she can understand the meaning. 
3. Glymour's argument
Clark Glymour argues that the method of neuropsychology is not sufficient to construct the models of cognitive architecture. For this argument, he constructs a discovery problem for cognitive architecture under simplifying assumptions, and pro ves this discovery problem is unsolvable.
Before starting his argument, Glymour restricts the graphs he want to argue. First, he wants a more precise notion of input and output. As we saw in Figure 1, neuropsychologists use very general name for input and output ("eyes," "ears," "speech"). Glymour uses a basically same graph as Figure 1 as his example, and suggests as follows: "I want the performance whose appearance or failure (under appropriate inputs) is used in evidence to be explicitly represente d as vertices in the graphs, and I want the corresponding stimuli or inputs to be likewise distinguished" (Glymour 1994, 821). Thus, he says, instead of output labeled "speech," "I want output nodes labeled 'repeats', 'repeats with recognition', 'repeats with understanding'" (821). Second, he wants to consider only essential pathways and to ignore the existence of alternative pathways (822). He intend to simplify the problem with this second assumption. This simplification is legitimate because his aim i s to prove a negative conclusion about volubility, and if we can prove that even this simplified problem is unsolvable, then we can conclude that the same proof holds in the more complicated real problems (822).
In addition to these assumptions, Glym our has other assumptions to simplify the graphs (823-824). The reason he introduce these assumptions is similar to that for the second assumption above, namely if the discovery problem for these simplified graphs are unsolvable, then more complicated pro blems should be also unsolvable.
the simplifying assumptions
A1. The graph is acyclic, namely there is no sequence which pass one and the same module twice.
A2. The response variables take only two values, 1 or 0.
A3. All normal subjects have the same graph.
A4. A graph of an abnormal subject is a subgraph of the normal graph.
A5. The default value of all output nodes is zero.
A6. If any of passes from an input to an output is missing in an abnormal graph, the output for the inpu t is zero.
A7. Every subgraph of the normal graph will eventually occur among abnormal subjects.
Among these assumptions, A3 and A4 correspond to Shallice's assumptions 4 and 8 respectively. A2 (and maybe A5) intends to simplify Shallice's assu mption 6. A6 is saying if there are more than two routes between the input and output, this means all of the routes are necessary for the task. This "conjunctive" model (in Bub's word) needs a little analysis, so I will return this problem later. A7 is re quired to construct a discovery problem.
Glymour proposes a discovery problem under these conditions. Even with these assumptions, we still have many different conceivable graphs. Now the situation: "[w]e want out methods to be able to identify the t rue structure, no matter which graph in the collection it is, or we want our method to be able to answer some questions about the true structure, no matter which graph in the collection it is" (Glymour 1994, 824). A discovery problem is the problem to fin d such a method. Now, if we do not assume A7, the discovery problem is apparently unsolvable. What if we assume A7? "We cannot (save in special cases ) be sure at any particular time that circumstance has provided us with every possible combination of inj uries, separating all of the capacities that could possibly be separated" (825). So if we require scientists to become sure that their model is true after a finite amount of time, this is also impossible. But we can use weaker criteria for success: "the s cientist should eventually reach the right answer by a method that disposes her to stick with the right answer ever after, even though she may not know when that point has been reached" (825). Glymour's argument is that even this weak criteria cannot be met by the methods available in cognitive neuropsychology.
To see why this fails, first take a look at a successful example. Figure 2 shows six alternative graphs. Each of them has four input-output pairs (in Glymour's terminology, "capacities"). Tabl e 1 shows all possible combinations of four capacities and all possible combinations in each graph (these combinations are called "profile"). As you can see, each of six graphs has a different set of possible combinations. Therefore the following method s olves the discovery problem with these graphs:
Conjecture any normal graph whose set of normal and abnormal profiles includes all of the profiles seen in the data and having no proper subset of profiles (associated with one of the graphs) that also includes all of the profiles seen in the data. (827)
But this successful method does not work in more general cases. An easy illustration is "pinching" (827). The graph in Figure 3 is made from (3) in figure 2 by pinching the center node into two nodes. As a result, we cannot distinguish these two graphs by the capacity of patients. Thus we have no successful method to solve the discovery problem when pinching is included. Then Glymour concludes: "under the assumption A1 through A7 a good many fea tures of cognitive architecture can be distinguished from studies of individuals and the profiles of their capacity, although a graph cannot be distinguished from an alternative that has functionally redundant structure" (829). And of course, A1 through A 7 are simplifying assumptions, and the real cases have more complexity: "The assumptions made by Shallice , in particular, while substantively plausible, reduce the possibility of using abnormal data to identify properties of normal cognitive archit ecture" (829). For example, A2 simplified the problem compared with Shallice's assumption 6. If we admit partial lesions, as Shallice does, it is possible that among two tasks which go through a module one is affected by the lesion and the other is not. S hallice thinks that if we find double dissociation we can exclude this possibility. But Glymour's example shown in Figure 4 makes a counterexample. if two modules in a row have opposite tendencies in partial lesion, We get a double dissociation even thou gh the true graph for the tasks has only one route. Therefore, admitting assumption 6 of Shallice increases the underdetermination.
4. Bub's counterargument
To this Glymour's argument, Jeffrey Bub (1994) answered that if we add several other as sumptions, we can construct a solvable discovery problem.
First, Bub makes slight changes in assumptions. As I mentioned, Glymour's A6 assumes that when we have several paths between an input and an output nodes, the task need all of the routes. But t here is another way to interpret the paths. We can take each of paths is enough for the task (Bub 1994, 842). Along with this "disjunctive" instead of "conjunctive" view of task performance, Bub makes another related change in the meaning of the input and output nodes. In Glymour's graph the input and output nodes are task variables, but in Bub's graph they represent a module of functional architecture just as inner modules (844). By this change, in Bub's graphs each tasks are represented by each path, no t by the input-output pair; if there are two paths between input and output nodes, this means that there are two distinguishable tasks going through these two nodes. As both Glymour and Bub admit, the former difference (conjunctive and disjunctive interp retations of multi-route) does not make a significant difference in the result of argument (Glymour 1994, 824; Bub 1994, 842). The latter change makes a difference, however, and I will argue that later. Anyway, as you can see in Figure 1, the diagrams co gnitive neuropsychologists really make are much similar to Bub's version than Glymour's.
Next, Bub introduces two kinds of profiles, namely data profile (d-profile) and graph profile (g-profile). According to him, "d-profile for a particular patient is the total set of cognitive capacities and incapacities presented by the patient" (Bub 1994, 844) and "g-profile for a graph is a topologically possible set of intact and lesioned paths, where (initially) we understand lesioning as all or nothing" (845-84 6). This is just a change of terminology mainly due to the change of the assumptions above mentioned. The real difference comes next. The main reason Glymour got underdetermination was that he used pinching. Now, Bub agrees that if we admit pinching, we g et underdetermination (848). But we don't have to admit pinching, because "this [underdetermination by pinching] only means that we cannot tell whether modules are assembled (from more basic modules) or not" (848). The difference between pinched and unpin ched graphs is just whether lower structure is explicitly shown or not, and these two are essentially the same graph. So Bub proposes that we should not allow such a pure pinching to make an alternative graph. We can recall assumption 2 of Shallice, namel y the assumption that a module can have lower level modules inside. Bub admits a pinching with "bridging" (Figure 5 c). The difference between Figure 5 b (pure pinching) and Figure 5 c (pinching with bridging) is that in Figure 5 c, we can detect the exis tence of node 4 from the dissociation between path 135 and path 1345.
Now, the discovery problem (Bub calls it " the idealized discovery problem" because of the simplifying assumptions and prohibition of pinching) has a solution:
Conjecture any normal graph whose set of path-sets contains all the g-profiles corresponding to d-profiles seen in the data, and which has no proper subset that constitutes the set of path-sets of a graph and also contains all the g-profiles seen in the data (849-850).
The foregoing argument is under the assumption A 2, namely all outputs are assumed to be 1 or 0. Glymour showed that if we admit partial lesions the underdetermination increases. Bub thinks that this underdetermination can be avoided by the mono tonicity assumption (852). The monotonicity assumption is the assumption that each module is elementary and can be characterized by a single variable (851). Under this assumption, "performance of all tasks associated with paths through that node be gins to deteriorate at different rates relative to normal performance" (852, emphasis original). Now, this is basically implicit Shallice's assumption 6 (and made explicit in a later version I mentioned), but when used with the prohibition of pinching, t he monotonicity assumption becomes a strong one. The example Glymour gives (Figure 4 before) is made by pinching. So we should consider the intermediate two modules as lower modules, and replace them with one module. The monotonicity assumption applies t o the latter. The characterization of two modules in Glymour's argument (one is good at oval and the other is good at rectangle) contradicts with this assumption even if they are understood as submodules, because various combination of partial lesions of these two submodules make the unpinched module non-monotonic.
Then, how about pinching with bridging? Bub thinks that even though we admit partial lesion, we can distinguish Figure 5a and 5c (853-854). In Figure 5c, if a patient has a partial lesion in node 4, the task 135 is normal and task 1345 is abnormal. If a patient has a partial lesion in node 3, both of tasks are abnormal. Up to this point, the same thing can happen in Figure 5 a, assuming that the former task is easier and node 3 is partial ly lesioned. But, Bub argues, in Figure 5c, the impairments to task 1345 when the node 4 is lesioned "differ qualitatively" from those with the node 3 lesioned. This cannot happen to Figure 5a under the monotonicity assumption. Thus we can distinguish the se two graphs even if we admit partial lesions. To sum up, the discovery problem has a solution in these cases.
In this section I would like to make two points: One in favor of Bub's argument, and the other in favor of Glymour's arg ument. But the strategy used for these two arguments are similar. I think both Glymour and Bub are not just simplifying the problem, but actually altering the problem, and, therefore, their answers are irrelevant or needs modification to some extent. I wo uld like to make this point by comparing their assumptions with the actual graphs neuropsychologists make (especially with Figure 1).
Glymour claims that his assumptions are intended to simplify the problem, and since his conclusion is negative, these additional assumptions are legitimate. But in some points he seems to alter, not simplify, the graphs. First, as I mentioned before, there is a fundamental difference between Glymour's and Bub's graphs. In Glymour's argument, The input nodes and output n odes are distinguishable responses. Thus, if we recognize a new double dissociation, since this means we can distinguish two responses, we need to add another input and /or output node. On the other hand, in Bub's graph, the output nodes show the type of output (for example, "speech"). Thus, if we recognize a new double dissociation, what we should do is make another path between the input node and output node. Among these two ways, Bub's one is more truthful to the way the cognitive neuropsychologists re ally do their job. But there is another methodological point in favor of Bub's way. Let me explain with figures.
First, to make sure how Glymour's graphs are different from real cognitive neuropsychologists ones, let us rewrite the Figure 1 I took fro m Shallice's book. By the assumption A1 (the graphs should be acyclic) , we ignore the feedbacks from "cognitive system" to "visual input lexicon" and "auditory input lexicon." There are six different paths in this diagram, three from ears and three from eyes. They are distinguished by finding dissociations, so we need six input nodes if we make a diagram Glymour's way. For he requires that "the performance whose appearance of failure (under appropriate inputs) is used in evidence" and "the corresponding stimuli or inputs" should be appear as output and input nodes (Glymour 1994, 821). We can label these inputs using dissociations discussed earlier in this paper: "written irregular words," "written regular non-words," "comprehension test of written words " and counterparts of them on spoken words. On the other hand, there are at least three distinguishable outputs: "repeat irregular words" "repeat non-words" and "show understanding of the words." Glymour himself suggested following three output nodes: "re peats," "repeats with recognition," "repeats with understanding" (Glymour 1994 821). The reason I do not take his own terminology is that these are too abstract and that it is hard to identify corresponding inputs with these outputs (though Glymour himsel f required them). Moreover, "repeats with understanding is inaccurate as "performance" "used in evidence." Actually here are two performances involved, namely repeating and answering comprehension tests. With these reasons, I choose these output labels ag ainst Glymour's own words (to be truthful to Glymour's more general directions).
Now, how should we modify the graph? To know what happens, let's just add these nodes to the Figure 1 (Figure 6). This modified graph has a lot of problems, but the bigge st one is this: this graph suggests that we can have weird input-output pairs, such as from "written irregular word" (I6) to "read non-words" (O1) or "spoken non-words" (I1) to "show understanding of the words" (O3) and so on. This problem arises because several paths (especially to different outputs) share some of intermediate modules. There is nothing in Glymour's formulation of graphs which can regulate the relationship between incoming paths and outgoing paths. And from A4 (a graph of an abnormal sub ject is a subgraph of the normal graph) and A7 (every subgraph of the normal graph will eventually occur among abnormal subjects), If this graph is true, we certainly have a patient whose only intact path is the connection between I1 and O3. This does not make sense, so we need further modification. One apparent solution is to separate the graph into three independent graphs (Figure 7). In this way, different outputs have no common modules, so the nonsense relationships between inputs and outputs are avo ided. But this move seems to make Glymour's graphs too different from those of neuropsychologists. I think the main purpose of cognitive neuropsychology is to construct a model of cognitive architecture and investigate the relationships between various hu man capacities. With this point of view, the resulting graphs in Figure 7 are not what neuropsychologists look for. In this point, Glymour needs to modify one or another assumption. The easiest way is to accept Bub's recommendation and use functional modu les as input and output nodes. Moreover, if he accepts this modification, he should also accept disjunctive interpretation of multi-route. Actually there is another way to modify the assumptions. As I suggested in passing, if we allow to regulate the rela tionship between incoming connections and outgoing connections (so a particular incoming connection uses only a particular outgoing connection), he can avoid the stupidity I described. But the problem with this modification is this seems to make the disco very problem more difficult than actual one. Anyway, I think it is obvious that Glymour's argument needs some modifications.
My second argument is that Bub's counterargument has also a problem. The problem is that if we accept his two major points -- prohibition of pinching and monotonicity assumption -- it will have a disastrous effect on the research programme of neuropsychology.
To begin with, I would like to suggest a modification of his argument on the prohibition of pinching, mainly to save his conclusion. The reason he prohibits the pinching is that if we allow pinching, we get underdetermination of the graph we can accept. He also justifies it appealing to the assumption of levels of modularity. Now, he seems to think that pinching with br idging (Figure 5c) does not have underdetermination problem. But actually we can make an alternative graph which has the same g-profile as the "pinching with bridging" graph (Figure 8). The only difference between two graphs is that the path 1346 is repla ced by 136 and the path 2346 is replaced by 236. These replacements makes no new association or dissociation. For example, path 1346 and 1345 in the original graph are independent because the connection between 4 and 5 and the connection between 4 and 6 c an be lesioned independently. The same thing holds in the new graph, between the connection between 4 and 5 and the connection between 3 and 6. Thus, we have underdetermination problem between these two graphs. Fortunately, Bub can solve the problem by pr ohibiting the pinching with bridging. Let us see the Figure 9. This graph also has the same g-profile as the "pinching with bridging" graph. As you can see, however, this graph has only 5 modules, because modules 3 and 4 in the original graph get togethe r. The important thing of this graph is that we get the same graph when we put together the modules 3 and 4 in Figure 8. So the underdetermination problem disappears if we can justify the move to reduce Figure 5c into Figure 9. This move can be understood as the prohibition of pinching with bridging. Therefore, if Bub's original argument on the prohibition of pinching is valid, we can apply it to this case. Namely, the modules 3 and 4 in the "pinching with bridging" graph can be understood as submodules w hich we cannot find out from d-profiles; but we can still know the overall structure of the graph. If we accept this modification, we can get solution to the idealized discovery problem. Underdetermination is avoided.
Before I move to the next argume nt, shortly I would like to comment on a peculiar feature of the graph in Figure 9. If anyone has objection to this graph, it should be about the feature that in this graph we have two connections between the same pair of modules. It is true that it seems to be strange to assume several connections between two modules. But this is actually neuropsychologists do. For example, Shallice assumes several connections between visual word form system and phonological word form system (which correspond to the conn ection between visual input lexicon and phonological output lexicon in Figure1) (Shallice 1988, 94). The reason he introduce multi-connection is that there seems to be many different levels of connections (graphemic, sub-syllabic, syllabic and morphemic) between them. If we can admit this kind of move in real research, we should not rule out this move in simplified case especially when the ruling out make it impossible to solve the discovery problem.
The foregoing argument is generalizing the prohibiti on of pinching. But this generalized version has a problem when applied to real cases. Again, take Figure 1 as the example. We can notice there are a lot of pinchings (mainly pinching with bridging) in this graph. If we apply the prohibition to this case, how many of the module will survive? Figure 10 points out the places of pinching (the feedbacks from cognitive system to visual and auditory input lexicons are omitted in this graph because of assumption A1). I think that most of the pinching do not need explanation. So I just explain the pinching between "cognitive system" and "phonological output lexicon." This pinching is doubly bridged, so the underdetermination I argued above does not happen. But here is a different kind of underdetermination. It i s possible that both of the two arrows come out from "visual input lexicon" go into "cognitive system." This move does not change association-dissociation relationships. And as I argued above we have reason not to rule out multi-connection between two mod ules. Thus the pinching between "cognitive system" and "phonological output lexicon" also creates underdetermination. What happens if we prohibit these pinchings? the result is shown Figure 11. Just three modules two input and one out put survives the cri teria.
Actually I think that this oversimplified graph is still acceptable to neuropsychologists. We can think of the submodules inside of the three remaining modules. But if we introduce Bub's another assumption, namely the monotonicity assumption, th is will be unacceptable. For example, the upper right module in Figure 11 was formally three modules -- "orthographic analysis," "visual input lexicon" and "grapheme-to-phoneme conversion." So this module is supposed to doing three different kinds of func tions. And when this module is partially lesioned, the effect depends on which part of the module is lesioned. If it is the former "grapheme-to-phoneme conversion," the tasks which use this function will be affected and other tasks will not be affected. This is not allowed if we accept the monotonicity assumption. The upper right module should have a single function (whatever it is) and partial lesions should affect all the task which go through the module more or less. I think this too simplified model is empirically unacceptable. Neuropsychologists do find that more than three elementary functions are involved in these repeating-reading tasks, and this is exactly why they assume so many modules.
I am not sure how Bub can avoid this conclusion. If h e changes one of two assumptions, namely prohibition of pinching and the monotonicity assumption, it would be difficult to avoid underdetermination. Maybe he can add other assumptions, but I have no idea what they could be. With this difficulty, I should conclude that Bub's counterargument is not so successful as an objection to Glymour.
In this paper, first I summarized actual assumptions and methodologies in cognitive neuropsychology following Shallice. Next, I introduced Glymo ur's negative argument to the solubility of the discovery problem in cognitive neuropsychology, and I also summarized Bub's counterargument. My analysis to the debate between Glymour and Bub is basically that they altered, not simplified the problem, and that we can question the relevance of their argument to cognitive neuropsychology. But the problem I pointed out about Glymour's argument needs only a minor change, while I cannot imagine how we can modify Bub's argument to meet my criticism and still avo id underdetermination. Therefore, my temporary conclusion is that Glymour's argument makes its point though it need minor change, and that Bub's objection is not very successful.  References
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