Charles Wallis (1992) Asymmetric Dependence and Mental Representation. Psycoloquy: 3(70) Fodor Representation (1)

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Psycoloquy 3(70): Asymmetric Dependence and Mental Representation

Target Article on Fodor-Representation

Charles Wallis
Department of Philosophy
University of Rochester
Rochester, NY 14627


Fodor's theory of representation cannot account for obvious cases of misrepresentation as understood by contemporary theories of psychophysical transduction, feature detection, and object recognition. Drawing upon Fodor's larger theoretical views and additional hypotheses makes Fodor's theory even less plausible.


color vision, Fodor, mind/body problem, perception, representation, semantics, sensory transduction, verificationism
1.1 Philosophy's search for a theory of mental representation has two goals: to deepen our understanding of explanation in cognitive science and to solve the mind/body problem (the clash between physicalism and pretheoretical intuitions about mental concepts). Philosophers try to understand how a physical system could have mental properties.

1.2 Although philosophers disagree on specifics, they agree on two criteria for a successful theory of representation: (i) It must be a "naturalized" theory (i.e., it must describe conditions for representation in nonintentional and nonsemantic terms). (ii) It must prove consistent with findings of cognitive science.

1.3 A theory of representation satisfying (i) and (ii) would clarify the representation relation and its role in explanation in cognitive science and would make an important contribution to solving the mind/ body problem. Philosophers consider contemporary work in cognitive science to be committed to versions of the representational theory of mind (RTM), according to which mental systems are specified functionally and operate in a law-like manner on representational structures. According to the RTM, certain mental properties are the representational properties of a physical system. A naturalized theory of representation would provide a physicalistic explanation of mental representation and of how some mental properties could be physical properties.


2.1 Fodor's (1990) theory of representation specifies a set of sufficient conditions for a mental state, Sb, to represent an object, B, as an instance of type-B objects. Fodor claims that tokenings (instances) of Sb represent Bs as Bs when the following conditions hold (Fodor 1990, pp. 121-2):

(1) Tokenings of Sb by B are subsumed under natural laws.

(2) Bs in fact cause tokenings of Sb.

(3) Tokenings of Sb are robust, and tokenings of Sb not caused by B (let us call them the F-caused tokenings) "depend asymmetrically" upon B-caused tokenings of Sb.

2.2 Fodor's third condition requires explication: Tokenings of Sb count as "robust" if they have more than one cause (p. 118). F-caused tokenings of Sb depend asymmetrically upon B-caused tokenings if and only if breaking the B to Sb connection breaks the F to Sb connection but breaking the F to Sb connection will not break the B to Sb connection (p. 113)

2.3 I deal with interpretations of asymmetric dependence in section 6. I now want to note that Fodor's conditions exclude a class of representational states he considers important. In 1986 Fodor wrote:

     "Unlike paramecia, we [humans] are frequently implicated in primal
     scenes in which the behaviorally efficacious stimulus property... is
     nonnomic [not natural-law-dictated]. ...the difference between
     paramecia and us is that we can `respond selectively' to nonnomic
     stimulus properties and they can't" (p. 11).

2.4 For Fodor, the human ability to respond selectively to nonnomic properties is what makes humans candidates for having mental states. He claims that systems must respond selectively to at least one nonnomic property to have a mind (1986, p.13). Yet Fodor's conditions for representation do not explain a human's ability to represent and respond to nonnomic properties: Tokenings of a state by a nonnomic property are not subsumed under natural laws, violating condition 1. Moreover, as no nomic correlations exist (according to stipulation) between states and nonnomic properties, correlations between states and nonnomic properties must depend asymmetrically upon other connections, thereby violating Fodor's condition (3).

2.5 Fodor's sufficient conditions for representation cannot explain how humans represent and respond to nonnomic properties -- i.e., how they do what makes them cognitive creatures. This failure to account for the human ability to represent and respond to nonnomic properties underlines the problems with Fodor's search for sufficient conditions for representation. After all, sufficient conditions are not necessarily unique. Several sets of sufficient conditions for mental representation might exist. Some other set of sufficient conditions might explain mentality. That is the problem with sufficient conditions: They often prove uninteresting.

2.6 In the sections that follow I examine how interesting (or uninteresting) Fodor's conditions for representation prove when applied to real theories of transduction and visual task performance. Traveling down the main visual pathway, I argue at each stop that Fodor's theory fails to account for the representational properties required to explain vision.


3.1 Current theories of visual task performance share the same gross structure: Task performance starts with the transduction of simple properties (the conversion of external stimuli into representations of those stimuli: e.g., light into arrays of more or less excited rods and cones). Systems then enter into a series of low-level inferences, inferring higher-order properties from the representational output of transducers (Marr 1982 and Biederman 1987). In this section, I consider whether Fodor's conditions capture sufficient conditions for representation as regards the products of transduction. My answer is simple; Fodor's conditions prove unilluminating. Rods and cones are typical transducers. Researchers can and do construe their outputs as representing the intensity or wavelength of light reflected by an object. Rod and cone firings nevertheless fail to satisfy Fodor's asymmetric dependence condition.

3.2 Rods can exhibit remarkable sensitivity to light. A single photon can cause a rod to fire (Baylor et al 1984; Gouras 1984). Light causes a rod to fire because rods are packed with rhodopsin molecules. Rhodopsin has two components, 11-cis-retinal and opsin, a protein. Absorption of the light-energy of a photon by the 11-cis-retinal in a rhodopsin molecule triggers enzymatic action by the opsin component, eventually triggering an electrical discharge at the rod's synaptic terminal (transduced light). Psychophysicists theorize that rods receive the light reflected from objects and transduce it into electrical discharges. In other words, rod firings represent reflected light. Fodor's theory would deny that rod firings represent reflected light. Let us see how Fodor's theory fails:

3.3 The connection between rod firings and reflected light is subsumed under natural laws (condition 1). Light reflected from objects causes rod firings (condition 2). The kinetic energy of one's body temperature causes rods to fire, so rod firings have more than one cause. Hence, rod firings are robust (half of condition 3). However, heat-triggered rod firings (what I call "phantom photons") are not asymmetrically dependent upon reflected light firings.

3.4 The relevant cases involve breaking the light-to-firing connection and the kinetic-energy-to-firing connection. One can break such connections in two ways; one can change (1) the system's principles of operation (i.e., the physiology) or (2) its typical environmental interactions. Let us consider (1) first.

3.5 Suppose one breaks the photon-to-firing connection. The rhodopsin molecule triggers firing because the 11-cis-retinal component absorbs a photon's energy. If one alters the rhodopsin molecule so that it has no 11-cis-retinal to absorb a photon, then kinetic energy will not cause firings. But if one alters the rhodopsin molecule so that kinetic energy does not cause firings (i.e., if one removes the 11-cis-retinal component), then photon energy will not cause firings. In short, phantom photons do not depend asymmetrically upon photon firings. The relevant covering laws explain both cases of firing; breaking one connection breaks both connections. In the case of phantom photons, then, there really is a ghost in the machine.

3.6 What if one breaks the photon-to-firing connection by altering the system's typical environmental interactions? One can shield the rods from light or transfer rod populations to environments not having light in the rod's sensitivity curve (roughly between 400nm and 650nm). Kinetic energy still causes rod firings. Likewise, lowering the system's temperature will not break the light to rod firing connection.

3.7 How do rods manage to operate, given this lack of asymmetric dependence? The answer is straightforward: There are about 100,000,000 rods and phantom photons are extremely infrequent. One misfiring cell out of 100,000,000 does not introduce much equivocation. Moreover, a rhodopsin molecule registers a phantom photon about once every 840 to 1,000 years. The probability of a cell's registering a phantom in any particular second is on the order of 6.7 x 10-1.

3.8 Turning to cones: Cones and rods operate in a manner similar to rods. Each cone has molecules with an 11-cis-retinal component and a cone opsin. Each of the three cone types has a different protein (type of opsin). The proteins native to each cone type act to make the cone more likely to fire or to fire most strongly if the photon is of a particular wavelength. Some cones are more likely to fire or will fire strongest if the light is around 419 nanometers (blue), others at 531nm (green), others at 559nm (red). [I use Lennie's (1984) numbers; Schnapf and Baylor (1987) use 430, 530, and 560.] The selective sensitivity of the various types of cones plays an important role in color vision -- a role not explained by Fodor.

3.9 Though red cones are more likely to fire or will fire most strongly for red light, they also fire for light of other wavelengths; green, for instance. When one looks for asymmetric dependence, none appears. Starting with changes in physiology, one could break, for example, the red cone's red to red-firing connection by removing the protein (opsin) or by fine tuning the opsin so that red light does not cause firing (by switching the opsin's amino acid sequence). But breaking the red to red-firing connection breaks the green to green-firing connection. Likewise, the sensitivities overlap so substantially that altering the opsin so that green light does not cause firings prevents red light from causing firings. Moreover, fine tuning only moves the location of the sensitivity curve on the light spectrum. Actual reductions in the range of sensitivity result in losses in sensitivity (Gouras 1984, pp. 230-231).

3.10 Suppose one tries to break the red to red-firing connection by changing the system's typical interactions with its environment. Suppose one alters the composition of the light to exclude red light. Green light will still cause firings. Likewise, altering the light composition by removing green light does not prevent red light from causing firings.

3.11 How, then, does the eye detect colors, given this symmetric dependence? From the standpoint of vision, one is after surface reflectance in color vision. Detecting the humanly discriminable surface reflectances requires detectors for three distinct wavelengths of light: red, green, and blue. Tuning detectors (cones) to particular wavelengths of reflected light -- but not limiting them to those frequencies -- allows one to detect surface reflectance even as light intensity and composition varies (within limitats). This strategy for extending the range of surface reflectance detection introduces the possibility of equivocation. Yet one generally runs into few problems in determining surface reflectance because other mechanisms act to control equivocation. First, mechanisms of "adaptation" based largely in the cones act to desensitize the cones in increased light intensity. Second, the brain can rely upon the ratio of the firings of the three type of cones to determine color given the large sample size (6,000,000). Third, the eye pools the signals of several individual cells, a process often called "simultaneous contrast." Fourth, the eye constantly moves around the visual field in both short, quick flicks and slow meanderings. These movements act to change the areas of the visual field covered by the most discriminative areas of the retina. This process of movement is often called "successive contrast." Gouras describes its functioning "as a hand which rubs across contours in order to enhance their contrast" (1984, p. 229).

3.12 I conclude that Fodor's theory, having batted 0 for 2, will not help us understand transduction. Fodor may capture a set of sufficient conditions for mental representation; in the case of transduction, however, he has not captured a set of sufficient conditions that will interest the vision researcher.


4.1 Perhaps Fodor's failure results from looking too far forward along the primary visual pathway. Moving farther down the visual pathway one comes to the simple cells of the striate (visual) cortex. Simple cells respond best to bars of light at particular orientations. One would like to say that excited arrangements of simple cells represent edge patterns. That is what one would like to say, but consider what Fodor's theory allows one to say:

4.2 The connection between simple cell firings and bar orientations is subsumed under natural laws (condition 1). (I will not question the satisfaction of condition 1 in this and future cases, although as one moves towards higher-order features, it looks less and less likely that the connection is law-like.) Bars of specific orientation cause simple cell firings (condition 2). Like the responses of rods and cones, simple cells exhibit an orientation tuning curve. That is, simple cells fire for bars at other orientations, though at lesser rates for the same intensity value. The tuning curves of simple cells result in a simple cell's responding with the same firing rate for an infinite number of different orientation and intensity combinations. Hence, other bar orientation/intensity combinations cause simple cell firings, making simple cell firings robust (half of condition 3). However, tilted firings do not depend asymmetrically upon nontilted firings.

4.3 One can demonstrate a lack of symmetric dependence by breaking the connections in two ways: (1) One can change the system's principles of operation (i.e., the physiology). (2) One can alter the system's typical environmental interactions. Consider the former option first: One has good reason to suppose that breaking the tilted bar to firing connection would break down the visual system. Each simple cell's receptive field has an "on" area sandwiched between two "off" areas. Stimulation in the on area excites the cell whereas in the off areas its effect is inhibitory. Fine tuning the responses of a simple cell by compressing the on area in a simple cell's receptive field and enhancing the inhibitory effects of the off area will narrow the orientation tuning curve. Narrowing the tuning curve, however, will have a dramatic effect upon the visual system's graceful degradation: By narrowing the range of orientations to which the cell responds, one turns the cell into a template matcher. Although the environment will continue to manifest examples of bars that violate the cell's preferred orientation by slight degrees, the cell's ability to function in these cases diminishes as one fine tunes its responses. Similar problems would occur as one moved one's head.

4.4 It is likewise implausible that one can change the system's typical environmental interactions so as to eliminate tilted bar stimuli. As with the internal case, breaking the tilted bar to firing connection seems uninteresting. Systems in worlds in which the connections are broken manifest processing properties radically different from our own.

4.6 The visual system generally handles equivocation at the level of simple cells by considering the firing patterns of populations of simple cells (Kersten 1990 and Movshon et al 1985). Again, as with rods and cones, the visual system deals with -- even introduces -- the equivocation necessary to robust functioning by higher-order processing. The system's higher-order processing does not eliminate equivocation; it merely makes false signals very improbable.


5.1 One might claim that Fodor developed his theory for object recognition, not transduction or feature detection. I find the no-representation-with-transduction line an unconvincing interpretation of Fodor. Fodor spends a great deal of time in Psychosemantics (the book) and "Psychosemantics" (the paper) arguing that one should think of object recognition in terms of the detection of simple low level features:

     "Psychophysics gives us a naturalization of a certain set of
     concepts; ... Perhaps we've under estimated the number of concepts
     that can be treated as psychophysical. Perhaps that treatment can
     be extended, if not to PROTON, then at least to an indefinite
     variety of concepts that subtend 'middlesized' objects." (Fodor
     1988, p. 115)

Likewise, in "Why Paramecia Don't Have Mental Representations," Fodor claims only that systems that do nothing but transduce or detect simple features do not represent.

5.2 Fodor seems committed to developing a concept of representation for transduction and feature detection. Regardless of whether Fodor has such interests, however, vision researchers do have such interests. Nevertheless, one should look at object recognition, if only to see that Fodor's theory fares no better for cases of object recognition than it does for cases of transduction or feature detection.

5.3 I use a slightly modified version of Irving Biederman's (1987) "Recognition By Components" theory of object recognition and an example to serve as a background for discussion. I will not try to catalogue all the virtues or weaknesses of Biederman's theory, noting only that it is well documented, and has a connectionist model that can do object recognition in real time (about 100 msec). (Biederman's model presupposes the solution to several problems of perception, viz., the model assumes a solution to the problem of distinguishing figures from background.) While the theory may not represent the end solution to the problem of human object recognition, it does present a concrete model representative of how researchers think about object recognition.

5.4 Biederman supposes that the striate cortex codes sufficient information to detect certain types of volumetric primitives, which he calls "geons," and certain primitive spatial relations, such as "above." Geons have the desirable property of being recognizable in almost any orientation and in many cases of partial occlusion. By assuming that object representations are computed by first computing geons and relations, Biederman's theory also has the nice feature that the number of detectable object/orientations is very large practically and infinite in the abstract.

5.5 As an example, suppose I know that large red buildings having extended rectangular bodies and extended triangular roofs are barns. This knowledge proves important. In the terms of my Biederman-inspired object recognition system: I have a barn representation, Sb. I token my barn representation when I see a red building having a rectangular body and a triangular roof. (Biederman's theory lacks color primitives, though adding them does not look problematic.) Specifically, Sb gets tokened every time my extended rectangle and extended triangle geons get tokened along with my red and above (triangle above rectangle).

5.6 When I go to the country I token my rectangle and triangle geons along with my red and above. I token an Sb. Unbeknownst to me, however, my evil twin (one must get twins in these cases somehow) has made a red papiermache barn-facsimile to make me look foolish. There is a nomic (lawful) connection between barns and Sb (condition 1). Barns cause tokenings of Sb (condition 2). Tokenings of Sb are robust since barn-facsimiles also cause tokenings of Sb (half of condition 3). However, the counterfactuals do not reveal asymmetric dependence.

5.7 Consider the internal and external ways of breaking the barn to Sb connection: Breaking the barn to Sb connection, say, by breaking the rectangle-triangle-red-above to Sb connection, one also breaks the barn-facsimile to Sb connection. Breaking the barn-facsimile to Sb connection by breaking the rectangle-triangle-red-above to Sb connection also breaks the barn to Sb connection. On the other hand, suppose that one breaks the barn to Sb by stipulating that one must paint barns green and barn facsimiles red. The facsimiles still trigger Sb. The same is true if one reverses the story: Suppose that one must paint barns red and facsimiles green. Barns cause Sbs while facsimiles no longer cause Sbs.

5.8 According to Fodor's set of sufficient conditions, I fail to represent barns. Fodor in fact renders such a verdict in considering cases that parallel the barn case exactly (1990, pp. 117-9). He must therefore either discount visual object recognition (in which case I have no idea what counts as the really important cognitive processes), or find a way to reassert an asymmetric dependence of barn-facsimile-caused Sb tokens upon barn-caused Sb tokens. I devote the next section to showing Fodor's various lines of retreat to be ineffective.


6.1 One line of retreat revives asymmetric dependence by looking to asymmetries in the history/environment of the system. Historic/environmental accounts of representation have several weaknesses. First, and most important, such asymmetries do not support counterfactuals. One can, as a result, circumvent the asymmetry without altering the salient features of the case. Second, one must leave behind Biederman's theory of object recognition to set out on such a retreat. It is never a good thing if the history/environment of the system, and not the theory of object recognition, tells one why the theory of object recognition works. Still, I consider a few examples of the historic/environmental line of retreat.

6.2 Version 1: If barns did not exist, then the barn-facsimile would not exist, as facsimiles are facsimiles of something. One can circumvent this asymmetry as follows: My evil twin did not make the facsimile. It was actually made as a facsimile of red army headquarters for NATO's latest war games. The existence of the facsimile therefore does not depend upon barns having existed at all.

6.3 Version 2: You would never have acquired the rectangle-triangle- red-above to Sb connection had no barns existed. Suppose that my mother told me as a child about these things on farms called barns. Though she did not know that barns existed, she told me that they looked like rectangles with triangles on top of them, and that they were often red. My rectangle-triangle-red-above to Sb connection resulted from my mother's whimsy. When I came to the United States, however, the country was full of red barns. I fit in perfectly. One should note that Fodor does, and must, allow for such stories in order to account for concepts of uninstantiated objects, like unicorns and round-squares (1990, pp. 100-101).

6.4 Two versions are sufficient to demonstrate that the historical/environmental line of retreat leads nowhere. Now, consider what I call "the asymmetry cum verificationist" line of retreat. This retreat interprets asymmetric dependence in light of Fodor's claim that the gist of asymmetric dependence is that

     "You cannot have a symbol (/concept) which expresses property X
     unless it is nomologically possible for you to distinguish
     X-instantiations from instantiations of any other property"
     (Fodor 1990, p. 119).

The idea here is that one cannot represent an object's having some property unless one could verify that it was that property and not some other property.

6.5 Fodor takes the "asymmetry cum verificationist" line in passages like the following:

     "The relevant consideration isn't, however, just that frogs go for
     bee-bees; it's that they are prepared to go on going for bee-bees
     forever. ... Sometimes Macbeth starts at mere dagger appearances;
     but most of the time he starts only if there's a dagger" (Fodor
     1990, p.  107).

Actually, the important quotation appears in Fodor's footnote:

     "Is this a dagger which I see before me.... let me clutch thee.
     I have thee not, and yet I see thee still. Art thou not, fatal
     vision sensible to feeling as to sight? Or art thou but a dagger
     of the mind" (1990, p. 134).

Macbeth discovers the deceptive nature of his appearances by reasoning. Reasoning occurs when one has epistemic liaisons (causal relationships between states that subserve reasoning). According to functional role semantics, the epistemic liaisons of tokens determine their content. But Fodor openly and often proclaims functional-role semantics false. He begins A Theory of Content and Other Essays by stating that "finding alternatives to functionalist accounts of mental content is a major concern in these studies" (1990, p. x). So, in appealing to epistemic liaisons, Fodor advocates an alternative theory of representation that implicitly relies upon the theory of representation that his would replace!

6.6 Another problem for the approach is that appeals to background knowledge do not actually break the dagger-appearance to DAGGER and the barn-facsimile to Sb connection. The system still tokens the state; it simply disregards it at a latter time. Appeals to background knowledge do not show that one can break the barn-facsimile to Sb connection without breaking the barn to Sb. Rather, they show that one can recover from a barn-facsimile to Sb tokening assuming one is able or inclined to access the relevant background knowledge.

6.7 In addition, the verificationist interpretation again reaches beyond Biederman's theory for an account of why that theory works. One does not have time to consult theory or perform experiments in 100 msec. Moreover, if anyone in the philosophy of psychology must be held to Biederman's theory in explaining Biederman's theory, it is Fodor. Fodor holds that inputs systems are modular. That is, input systems do not have access to everything that the system knows.

     "when you voluntarily move your eyeball with your finger, you
     certainly are possessed of the information that it's your eye (and
     not the visual scene) that is moving. This knowledge is absolutely
     explicit; ... But this explicit information, available to you for
     (e.g.) report, is not available to the analyzer in charge of the
     perceptual integration of your retinal stimulations. That system
     has access to corollary discharges from the motor center and to no
     other information that you possess. Modularity with a vengeance"
     (Fodor 1983, p. 67).

It would be odd if Fodor had to explain the functioning of modular input systems by appealing to information to which those systems have no access.

6.8 Fodor cannot understand asymmetric dependence through the execution of experiments, the accessing of background knowledge, etc. These ways of distinguishing barn-caused tokenings of Sb from barn-facsimile-caused tokenings involve relying upon epistemic liaisons and functional-role semantics.

6.9 One might object that in Psychosemantics, Fodor allows inferences to determine meaning. I have three responses to this objection. But first, one must understand Fodor's preface to the discussion in Psychosemantics. Fodor starts the discussion with "Here is where the cheating starts" (Fodor 1988, p.120).

6.10 Fodor claims that a theory written in observable terms can mediate covariance between abstract theoretic terms and their objects because one already has a theory of representation for observable terms. The requisite theory is represented by tokens, the representational properties of which one already (naturalistically) understands through Fodor's theory. One can state how theory mediates covariance by referring only to the causal connections: "all that requires is that the computer output 'proton' when its inputs are tokenings of psychophysical concepts for which protons are in fact causally responsible" (1988, p. 123).

6.11 First, the above move does not work for psychologically basic concepts like barn: One has no more basic states in which to write one's theory! Without the basic observables, one cannot write the theory by which the system maintains covariance (see Cummins 1989, pp.47-49, 62-66). Second, the move might show how one can naturalize a theory of representation yet rely upon inferential roles to fix the contents of some states. The move will not show one how to fix the contents states independent of inferential roles. Fodor never mentions functional-role semanticists in the discussion in Psychosemantics. The Psychosemantics move is a partial concession to functional-role semantics. In the context of Biederman's theory, the move would be a complete concession.

6.12 So Fodor cheats when he claims that "The unit of meaning is not the theory; it's the world/symbol correlation however mediated" (1988, p. 125). If epistemic liaisons (inferential roles) mediate covariance, then epistemic liaisons determine, in part, the content of the state. Asserting that only those roles that lead to the eventual retraction of a tokening are relevant to content is an attempt to stave off meaning holism (the position that all causal roles, no matter how distant, are determinants of content), not a means of eliminating epistemic liaisons in determining content. In fact, Fodor ends his discussion with meaning holism.

6.13 Third, Fodor also cheats in claiming that restricting the role to the epistemic liaisons that mediate covariance allows for inference without holism. Since Fodor holds that one cannot have an analytic/synthetic distinction, he holds that every epistemic liaison could mediate covariance. So every epistemic liaison determines representational content. After all, Fodor uses such an argument to reject functional-role semantics:

     "Quine was right; you can't have an analytic/synthetic
     distinction. ...this means that you can't have a principled
     distinction between the kinds of causal relations among mental
     states that determine content and the kind of causal relations
     among mental states that don't. The immediate consequence is
     that... there can be no such thing as psychological explanation
     by subsumption under intentional law" (Fodor 1990, p. x).


7.1 None of the lines of retreat mentioned in the last section save Fodor. His conditions for representation prove inadequate to handle Biederman's theory of object recognition. Fodor's theory of representation has batted 0 for 4 across three different levels of psychological explanation. I conclude that Fodor's set of sufficient conditions for representation are uninteresting to cognitive psychology.


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