DATE: February 26, 1997

FILE: reading.doc


            The Explanation of Cognition

                  By John R. Searle .

                  I. The Problem

      What sorts of systematic explanations should we and can we seek in  cognitive science for perception,  language comprehension, rational action, and other forms of cognition? In broad outline I think the answer is reasonably clear: We are looking for causal  explanations, and our subject matter is certain functions of a biological organ, the human and animal brain. 

      As with any other natural science there are certain assumptions we have to make and certain conditions that our explanations have to  meet.  Specifically we have to suppose that there exists a reality totally independent of our representations of it (in a healthier intellectual era it would not be necessary to say that) and we have to suppose that the elements of that reality that we cite in our explanations genuinely function causally. 

      Not all functions of the brain are relevant to cognition, so we have to be careful to restrict the range of brain functions we are discussing.  Cognitive science is about the  cognitive    functioning of the brain and its relation to the rest of the organism and to the rest of the  world in the way that nutrition science  is about the digestive functioning of the digestive system and its relation to the  rest of the organism and the rest of the world.   Like other organs, and indeed like other physical systems, the brain has different levels of description and cognitive science is appropriately concerned with any level of description of the brain that is relevant to the causal explanation of cognition.   These can range from conscious processes of decision making, at the top level, to  the molecular structure of  neurotransmitters, at the bottom.

      Typically, the higher levels will be causally emergent properties of the behavior and organization of the elements of the brain at the lower levels.  Consider an obvious, common sense example of an  explanation at one of these higher levels.  If I explain my  driving behavior in Britain by saying I am  following the rule, "Drive on the left" I have given a genuine  causal explanation by citing a mental process. The operation of the rule is itself caused by lower level neuronal events in the brain and is realized in the brain at  a level higher than that of individual neurons.  In what I hope is an unmysterious sense of "emergent property" the operation of the rule in producing my behavior is a causally emergent property of the brain system. Another way to put this same point is to say: we can give genuine causal explanations that are not at the bottom level, not at the level of neurons, etc., because the  higher levels of explanation are also real levels. Talk of them is not just a manner of  speaking or a metaphor. In order to be a real level, a putative causal level  has to be appropriately related to the more fundamental levels, for  example by being a causally emergent property of those levels.  Let us call this constraint, namely that in explaining cognition we have to cite real features of the real world which function causally, the  causal reality constraint.  

  So, just to summarize these constraints, we are seeking  causal explanations   of brain  functioning    at different  levels of description.   We allow ourselves complete freedom in talking about different levels of description, but that  freedom is constrained by the requirement that the levels be causally real.

      The claim I want to defend in this talk is that some, though of course not all, of  the explanatory models in cognitive science fail to meet the causal reality constraint.  I will also suggest  some revisions that will enable the explanations  to  meet that constraint.


      II. Marr's Version of the Information Processing Model

      My dog, Ludwig, is very good at catching tennis balls. For example, if you bounce a tennis ball off a wall, he is usually able to leap up and put his mouth at precisely the point the ball reaches as he grasps it in his teeth.  He doesn't always succeed, but he is pretty good at it. How does he do it? 

     According to the current explanatory models in cognitive science, Ludwig performs  an information processing task of enormous complexity. He takes in information in the form of a 2D pattern on his retina, processes it through the  visual system until he produces a 3D representation of the external world, and inputs that representation into the motor output system.  The computation he is performing, even for the motor output module,  is no trivial matter.  Here is a candidate for the first formulation of the algorithm. Ludwig is unconsciously following the rule: Jump in such a way that the plane of the angle of reflection of the ball is exactly equal to the plane of the angle of incidence of impact, and put your mouth at a point where the ball is in a parabolic arc, the flatness of whose trajectory and whose velocity is a function of impact velocity times the coefficient of  elasticity of the tennis ball, minus a certain loss due to air friction.   That is, on the standard computational model of cognition, Ludwig unconsciously computes a large number  of such functions by  unconsciously doing a lot of mathematics.  

      In form, the explanation of his behavior is just like that of  the person who follows the rule "drive on the left"  except for the fact that there is no way even in principle that he could become consciously aware of the operation of the rule.  The rules are not just not present to consciousness in fact, they are not even the sort of rules he could become aware of following. They are what I have called "deep unconscious" rules.[1]

      I have never been completely satisfied with this mode of  explanation. The problem is not just that it attributes an awful lot of  unconscious mathematical knowledge to Ludwig's doggy brain,  but more importantly, it leaves out the crucial element that Ludwig is  a conscious rational agent trying to do something.  The  explanatory model  seems more appropriate for someone building a machine, a robot canine, that would catch tennis balls. I think in fact that the intuitive appeal of the approach is that it would predict Ludwig's behavior and it is the sort of information we would put into a robot if we were building a robot to simulate  his behavior.

      So let us probe a bit deeper into the assumptions behind this  approach.

      The classic statement of this version of the cognitive science  explanatory paradigm is due to David Marr[1], but  there are equivalent views in  other authors. On this paradigm cognitive science is a special kind of  information processing science. We are interested in how the brain and other functionally equivalent systems, such as certain kinds of computers, process information.  There are three levels of explanation. The highest is the computational level, and this Marr defines as "the informational constraints available for mapping input information to output information."[1]     In Ludwig's case the computational task of his brain is to take in information about a two dimensional visual array and output representations of  muscle contractions that will get his mouth and the tennis ball at the same place at the same time.

      Intuitively I think Marr's idea  of the computational level is clear.  If you were instructing a computer programmer to design a program the first thing you  would tell him is what job you want the program to do. And the statement of that job is a statement of the computational task to be performed at the computational level. 

      How is it done? Well that leads to the second level, which Marr calls the algorithmic level. The idea is this. Any computational task can be performed in different ways. The  intuitive idea is that the algorithmic level determines how  the computational task is performed by  a specific algorithm.   In a computer we would think of the algorithmic level as the level of the program. 

      One puzzling feature of cognitive science versions of this level is the doctrine of recursive decomposition. Complex levels decompose into simpler levels until the bottom level is reached and at that  level it is all a matter of zeroes and ones, or some other binary symbols.  That is, there is not really a single intermediate algorithmic  level but rather a series of nested levels that bottom out in primitive processors, and these are binary symbols. And the bottom level is he only one that is real. All the others are reducible to it. But even  it has no physical reality. It is implemented in the physics as we will see, but  the alogorithmic level makes no reference to physical processes  .

      I used to think that the computation I gave for Ludwig might be his algorithm, but not so on this model. All Ludwig is really doing is manipulating zeroes and ones.  All the rest is mere appearance.

      The bottom level for Marr is the level of implementation, how the  algorithm is actually implemented in specific hardware. The same program, the same algorithm, can be implemented in an indefinite range of different hardwares, and it is quite possible, for  example,  that  a program implemented in Ludwig's brain might also be implemented on  a commercial computer. 

      So, on Marr's tripartite model you  get the following picture. Cognitive science is essentially the  science of information processing and it is primarily concerned with  explaining the top level by the algorithmic level.  What matters for cognitive science explanation is the intermediate level. Why?  Why should we explain brains at the intermediate level and not at  the hardware level? The answer is given by  my initial characterization of  the brain as a  functional    system. Where other functional  systems are concerned, such as cars, thermostats, clocks, and  carburetors we are interested in how the function is performed at the level of function,  not at the level of microstructure. Thus in explaining a car engine we speak of pistons and cylinders and not of the subatomic particles of which the engine is composed; because,  roughly speaking, any old subatomic particles will do as  long as they implement the pistons and the cylinders.  In Ludwig's case we are interested in the unconscious rule he is  actually following and not in the neuronal implementation of that rule following behavior. And the rule he is actually following must be statable entirely in  terms of zeroes and ones, because that is all that is really going on. So on this conception my earlier characterization of cognitive science as a science of  brain function at a certain level or levels of description was misleading.  Cognitive science is a science of information  processing, which happens to be implemented in the brain but which  could equally well be implemented in  an indefinite range of other  hardwares. Cognitive science explains the top level in terms of  the intermediate level but is not really concerned with the bottom level except insofar as it implements the intermediate level.


      One problem with Marr's tripartite analysis of cognitive functionalism is that just about any system will admit of a  this style of analysis. And the point is not just that clocks, carburetors, and thermostats admit of the three level analysis, (this is welcomed by adherents of the classical model as showing that cognition admits of a functional analysis similar to that of clocks,  etc.)  The problem is that any system of any complexity at all admits  of an information processing analysis.

      Consider a stone falling off the top of a cliff. The "system", if I may so describe it, has three levels of analysis.  The computational task for the stone is to figure  out a way to  get to the ground in a certain amount of time. It has to compute the  function S=1/2 gt\u2\d. At the intermediate level there is an algorithm that carries out the task. The algorithm  instructs the system as to what steps to go through to match time and space in the right way.  And there is the familiar hardware implementation  in terms of masses of rock, earth and intervening air.  So why isn't the falling stone an information processing system? But if the stone is, then everything is.

      This is a crucial question for cognitive science and several  authors have answered it.  According to them, we need to distinguish between a system being describable by a  computation and one actually carrying out the computation.  The system just mentioned is  describable   by a computable  function, but it does not  carry out   that computation because (a) there are no representations for the computation to operate  over and (b)   a fortiori   there is no information encoded in  the representations. A genuine science of cognition, an  information processing science requires computations performed  over symbols or other syntactical elements, and these are the representations which encode information which is processed by  the algorithm. These conditions are not met  by a falling rock, even though the rock is computationally describable. 

    If we are going to make this reply stick,  we will need a satisfactory definition or account of "information", "representation".  "symbol", "syntax" ,not to mention "computation" and "algorithm". And these accounts must enable us to explain how information,  representation, etc., gets into the system in such a way as to satisfy the causal reality constraint.  The account will have to show how information gets into the system in some intrinsic form in the first place,  and then retains its character as information throughout the processing.  Furthermore the account would have to show how the real information processing level is an emergent property of the more fundamental micro-levels. To nail this down to specific cases, it is not going to be enough to say, as Marr did, that there is a two dimensional visual array on the retina as an input to the system, we now have to say  what fact about that visual array makes it information, and what exactly the content of the information is. 

      I have looked at a lot of the literature on this issue, and I cannot find a satisfactory definition of representation and  information and the other notions that will solve our problems. To their credit, Palmer and Kimchi[1] admit that they have not the faintest  idea what information, in their sense, might be. I want to explore the notion of information a little more fully. The basic question of this paper is: can we give any empirical sense to the basic concepts of the  information processing  model that would  make the information processing version of cognitive science a  legitimate empirical discipline?



                      III. Following a Rule.


      If we are going to be clear about the claim that the cognitive agent is following unconscious rules we first have to understand what is involved in  rule following behavior in the first place.  Consider a case  where it seems  clear and unproblematic that the agent is  following a rule. When I drive in England, I follow the  rule:  Drive on the left hand side of the road.   And if  I stay in England for any length of time, I find that I get used to driving on the left and I don't have to think consciously of the rule.  But it seems natural to say that I am still following the rule even when I am not thinking about it. Such an explanation meets the causal reality constraint. When I say that  I am following a rule I am saying that there is an intrinsic intentional content in me, the semantic content of the rule, that  is functioning causally to produce my behavior. That intentional content is at an emergent level of brain processing. The rule has the  world-to-rule direction of fit and the rule-to-world direction of  causation.

      I want to explore some of the features of this type of explanation to see whether they can be preserved in information processing  cognitive science. I will simply list what seem to me the most important features of  rule following behavior:

 1. The most important feature is the one I just mentioned. The  intentional content of the rule must function causally in the production of the behavior in question. To do this it must be an emergent level of brain functioning. This is what I have been calling the causal reality constraint. Any rule following explanation in cognitive science has to  meet that constraint. 

 2. Rule following is normative from the point of view of the  agent. The content of the rule determines for the agent what  counts as right and wrong, as succeeding or failing.

 3. The next feature is a consequence of the first.  The rule must have a certain aspectual shape, what Frege called the mode of presentation. This is why extensionally equivalent rules can differ in their explanatory force. I can be following one rule and not another, even though the observable behavior is the same for  both cases. For this reason, that rule explanation must employ to specific aspectual shapes, rule explanations are intensional with an s.  For example, the rule "Drive on the left on two lane roads" Is extensionally equivalent to the rule "Drive so that the steering wheel is nearest to the center line of the road", given the structure of British cars, but in Britain I follow the first rule and not the  second, even though each would equally well predict my behavior.

 4. In ordinary rule governed behavior the rules are either conscious or accessible to consciousness.  Even when I am following the rule  unthinkingly, still I could think about it. I am not always conscious of the rule, but  I can easily become conscious of it.   Even if the role is so engrained in my unconscious that I cannot  think of it, still it must be the sort of thing that could be conscious.

 5. Accessibility to consciousness implies a fifth  requirement.  The terms in which the rule is stated, must be terms that are in the cognitive repertoire of the agent in question.   It is a general characteristic of intentionalistic explanations, of which rule explanations are a special case, that the apparatus appealed to by the rule must be one that the agent is in possession of.  If I wish to explain why Hitler invaded Russia, I have to use terms that are part of Hitler's conceptual repertoire.  If I postulate some mathematical formula that Hitler never heard of and couldn't have mastered, and couldn't have been aware of, then the explanation cannot be an intentionalistic explanation. It is a peculiarity of cognition, often remarked on by  people who discuss the special features of historical  explanation, that the explanation must employ concepts  available to the agent.  

 6. The next feature is seldom remarked on: Rule following is normally a form of voluntary behavior. It  is up to me whether I follow the rule or break it. The rule does indeed function causally but the rule as cause, even the rule together with a desire to follow the rule do not  give causally sufficient conditions. 

      This is typical of rational explanations of behavior. It is  often said that actions are caused by beliefs and desires, but if we take that to be a claim about causally sufficient conditions, it is false. A test of the rationality of the behavior is that there is a gap between the intentional contents - beliefs desires, awareness of rules etc. and the actual action. You still have to  haul off and do the thing you have decided to do, even in cases  where the rule requires you to do it. I am going to call this gap between the rule and other intentional phenomena which are the  causes and the  action which is their effect, the "gap of voluntary action" or simply "the gap".

 7. A feature, related to the gap, is that rules are always subject to interpretation and to interference by other rational considerations. So, for example, I don't follow the rule, drive on the lefthand side of the road, blindly.  If there is  a pothole, or a car parked blocking the road, I will swing around it. Such rules are in this sense ceteris paribus rules. 

 8.  The final feature is that the rule must operate in real time. For actual rule governed behavior, the rule explanation requires  that the time of the application of the rule  and the time of the  causal functioning are co-extensive. 

 Just to summarize, then, we have eight features of intentionalistic rule explanations.   First, the intentional content of the rule must function causally;  second, the rule sets a normative standard for the agent. Third, rules have aspectual shape and so rule explanations are  intensional-with-an-s. Fourth, the rule must be either conscious or accessible to consciousness, Fifth, rules must have semantic contents in the cognitive repertoire of the agent.  Sixth, rule governed behavior is voluntary, so the rule explanation does not give a causally sufficient conditions.  Seventh, rules are subject to interpretation and to interference by other considerations. And finally, eighth, the rule must operate in real time.

      Let's compare this with Marr style cognitivist forms of explanation.  In such explanations only features 1 and 3 are unambiguously present. Now one problem with the causal reality constraint on cognitive science explanations is that it is not clear how you can have  those two without any of the other six. It is no accident that these features hang together, because rule following explanations are typical of intentionalistic explanations of rational behavior. How can it be literally the case that Ludwig is following a rule with a specific semantic content, if that rule is not  normative for him, is not accessible to his consciousness even in principle, has concepts totally outside his repertoire, is not voluntarily applicable,  and is not subject to interpretation and appears to operate  instantaneously rather than in real time?

         IV. Some Preliminary Distinctions.


      In this section I want to remind you of certain fundamental distinctions. First we need to recall the familiar distinction between   rule  governed or rule guided   behavior, on the one hand,  and  rule described behavior,[1] on the other. When I follow a rule, such as the rule of the road in England, drive on the left hand side, the  actual semantic content of the rule plays a causal role in  my behavior. The rule does more than predict my behavior, rather it is part of the cause of my behavior. In this respect it differs from  the laws of nature which describe my behavior including its causes,  but the laws of nature do not cause the behavior they describe. The distinction between rule guided and rule described can be generalized as a distinction between  intentionality guided and  intentionality described  . All descriptions have intentionality, but the peculiarity of intentionalistic explanations of human  cognition  is that the intentional content of the explanation functions causally in the production of the explanandum.  If I say, ``Sally drank because she was thirsty''  the thirst functions causally in the production of the behavior. It is important to remind ourselves of this distinction because if an information processing cognitive science is to meet the  constraint, the intentionality of the information must not merely describe but must function causally in the production of  the cognition that the information processing explains. Otherwise there is no causal explanation. To meet the causal reality constraint, the algorithmic level must function causally.

      I believe that the standard cognitive science accounts acknowledge this point when they distinguish between being describable by a  function and actually computing a function. This a special case of  the general distinction between rule described and rule guided. 

      The second important distinction is between observer-relative and observer-independent features of reality. Basic to our whole scientific world view is the distinction between those features that exist independently of any observer, designer or other intentionalistic agent and those that are dependent on observers, users, etc.  Often the same object will have both sorts of features. The objects  in my pocket have such observer independent features as a certain mass and a certain chemical composition, but they  also have observer relative features: For example,  one is a  British  Ten Pound Note and another is a Swiss Army knife. I want to label this the  distinction  between features of the world that are observer (or intentionality) relative, and  features that are observer  (or intentionality) independent.  Money, property, marriage,  government and correct English pronunciation as well as knives, bathtubs and motor cars are observer relative; force, mass, and gravitational attraction are observer independent.

      "Observer relative" does not mean arbitrary or unreal. The fact that something is a knife or a chair or a nice day for a picnic is observer relative but it is not arbitrary. You can't use just anything as a knife or a chair or a nice day for a picnic. The point about observer  relativity is that observer relative features,   under those descriptions, only  exist relative to human observers.  The fact that this object in my hand has a certain mass is not observer relative but observer independent. That the same object is a knife is relative to the fact that human agents have designed it,  sold it,  used it, etc. as  a knife. Same object, different features: some features observer  independent, some observer relative.

      It is characteristic of the natural sciences that they deal with observer independent features -- such as force, mass, the chemical bond, etc. -- and it is  characteristic of the social sciences that they deal with  observer relative features, such as money, property, marriage and government.  As usual, psychology falls in the middle.  Some parts of psychology deal with observer relative features, but cognitive psychology, the part that is the core of cognitive science, deals with observer independent features such as perception and memory.

       Wherever there is an observer relative feature, such as being a knife or  being money, there must be some agents who use or treat the entities in  question as a knives or as money.  Now, and this is an important point, though money and knives are observer relative,  the fact that observers treat certain objects as money or knives is not observer  relative, it is observer independent. It is an intrinsic fact about me that I treat this object is a knife, even though the fact that this object is  a knife only exists relative to me and other observers.  The attitudes of observers relative to which entities satisfy observer  relative descriptions are not themselves observer relative. 

 This is why social science explanations can  satisfy the causal reality constraint even though the features appealed to are observer relative features.   So for example, if I say "The rise in American interest rates caused a rise in the exchange value of the dollar against the pound" that is a perfectly legitimate  causal   explanation, even though pounds, dollars and interest rates are all observer relative. The causal mechanisms work in such an explanation even though they work through the attitudes of investors, bankers, money changers, speculators, etc. In that respect the rise in the value of the dollar is not like the rise in the pressure of a gas when heated.  The rise in pressure of a gas is observer independent, the rise in  the value of the dollar is observer dependent. But the explanation  in both cases can be a causal explanation. The difference comes out  in the fact that the explanation of the observer relative phenomena makes implicit reference to human agents. 

      The third distinction is an application of the second.  It is the distinction between intrinsic or original intentionality and derived intentionality.  If I am currently in a state of thirst or hunger, the intentionality of my state is intrinsic to those states---both involve desires.  If I report these states in the utterances of sentences such as ``I am thirsty'' or ``I am hungry'' the sentences are also intentional because they have truth conditions.  But the intentionality of the sentences is not intrinsic to them as syntactical sequences.  Those sentences derive their meaning  from the intentionality of English speakers.  Mental states such as beliefs, desires, emotions, perceptions, etc., have intrinsic intentionality;  but sentences, maps, pictures and books have only derived intentionality.   In both cases, the intentionality is real and literally ascribed, but the derived intentionality has to be derived from the original or intrinsic intentionality of actual human or animal agents.

      I want this distinction to sound obvious, because I believe it is. And I also believe it is a special case of the equally obvious distinction between observer relativity and observer independence. Derived intentionality is observer relative, intrinsic intentionality is observer independent. 

      There are, furthermore, intentional ascriptions that do not ascribe either. These are typically metaphorical or as-if ascriptions. We say such things as ``My lawn is thirsty because we are in a drought,'' or ``My car is thirsty because it consumes so much gasoline.'' I take it that these are harmless metaphorical claims of little philosophical interest. They mean, roughly, my lawn or my car is in a situation similar to and behaves like an organism that is literally thirsty. 

      Derived intentionality should not be confused with as-if  intentionality. Derived intentionality is genuine intentionality all right but it is derived from the intrinsic intentionality of actual  intentional agents such as speakers of a language. Hence, it is observer relative. But as-if intentionality is not intentionality at all. When I say of  a system that it has as-if intentionality, that does not attribute intentionality to it. It merely says that the system behaves as  if it had intentionality, even though it does not in fact. 

      To summarize these distinctions, we need to distinguish between rule guided and rule described behavior. We need to distinguish observer independent features from observer relative features. Furthermore, we  need to distinguish observer independent (or intrinsic) intentionality, from  both   observer dependent (derived) intentionality and as-if  intentionality. .

       V. Information and Interpretation    


      I now want to apply these distinctions to the information  processing model of cognitive explanation.  I will argue that if the Marr style model is to have explanatory force, the behavior to be explained by the information processing rules must be rule guided and not just rule described. It can only  meet that condition if the information is intrinsic or  observer independent.  To make the distinction between Ludwig and the falling rock, we have to show that Ludwig is actually following a rule and he  can only  do that because he  has an appropriate intrinsic intentional content. The difficulty with the classical model  can now be stated in a preliminary form. Every key notion in the  model is observer relative:  information, representation, syntax,  symbol  , and  computation   as used in cognitive science are all observer relative notions. This has the consequence that the classical model in its present form cannot meet  the causal reality constraint.  I will try  to state this more precisely in what follows. 

      Let us go through these notions, starting with "symbols" and "syntax". I take it as obvious that a mark or a shape or a sound is a symbol or a sentence or other syntactical device only exists as such relative to some agents who assign a syntactical interpretation to it.  And indeed, though this is less obvious, I think it is also true that an  entity can only have a syntactical interpretation if it also has a semantic interpretation, because the symbols and marks are syntactical elements only relative  to the meaning they have. Symbols have  to  symbolize something and sentences have to mean something. Symbols and sentences are indeed syntactical entities but the  syntactical interpretation requires a semantics.     

      When we get to "representation" the situation is little bit trickier. A representation can be either observer relative or observer  independent. Thus maps, diagrams, pictures and sentences are all representations and they are all observer relative. Beliefs and  desires are mental representations and they are observer independent. Furthermore an animal can have such mental representation as beliefs or desires without having any syntactical or symbolic entities at all. When Ludwig wants to eat or wants to drink, for example, he need not use any symbols or sentences at all to have his canine desires.  He just feels hungry or thirsty.  The tricky part comes from the fact that  sometimes observer independent  beliefs and desires make use of sentences, etc. which are observer relative.    

 Indeed some philosophers have said that all beliefs and desires are "propositional attitudes" in the sense of being attitudes towards propositions or sentences or some other form of representation. I used to think this was a harmless mistake, but it is not. If I believe that  Clinton is President of the U.S. I do indeed have an attitude toward Clinton, but not toward a sentence or a proposition. The sentence  "Clinton is President of the U.S." is used to express my belief and the  proposition that Clinton is President of the U.S. is the content of my belief. But I have no attitudes  toward the sentence or proposition.  Indeed, the proposition construed as believed just is  identical with my belief. It is not the object of the belief.

      The doctrine of propositional attitudes is a harmful mistake because it leads people to postulate a set of entities in the head, mental representations, and having a belief or desire is supposed to be  having an attitude toward one of these symbolic, sentence like  entities. The point for present purposes is that intrinsic mental representations such as beliefs and desires (intentional states, as I prefer to call them) do not require some representing device, some syntactical device, in order that they exist. And where there is  a syntactical device, the syntactical device being observer dependent inherits its status as  syntactical and semantic from the intrinsic intentional content of the  mind and not conversely. The crucial point for the present discussion is that all syntactical entities are observer relative.

      This distinction between observer independent and observer dependent applies to information. Information is clearly  an intentionalistic notion, because information is always information  about   something and typically the information is: that such and such is the case.  Aboutness in this sense is the defining quality of intentionality, and intentional content of this propositional sort is typical of intentionality.  So it should not be surprising that the   distinctions between the different kinds of  intentional ascriptions will apply to information. Thus if I say, "I know the way to San Jose", I ascribe to myself information which does not depend on any observer. It is intrinsic or observer independent. If I say "This book contains information about how to  get to San Jose", the book literally contains information, but the  interpretation of the inscriptions in the book as information depends on interpretors.  The information is observer dependent. 

      There are also as-if ascriptions of  information. If I say ``These tree rings contain information about  the age of the tree,'' that is not a literal ascription of intentionality. There is no propositional content expressed by the wood. What I am actually saying, stated literally, is that a knowledgeable person can infer the age of the tree from the number of rings, because there is an exact covariance between the number of the tree's rings and its age in years. I think that with the widespread use of the notion of "information", particularly as a result of information theory, many people would now say that the stump literally contains information. I think they think they are speaking literally when they say that DNA contains information.  This is perfectly  reasonable, but it is a different meaning  of "information". It is a meaning that separates information from intentionality. There is no psychological reality to the  "information" in the tree rings or the DNA. They have neither propositional content nor intentionality in  the sense in which the thoughts in my head have  original intentionality and the  sentences in the book have derived intentionality.  

      Of these three types of intentional ascription only intrinsic information is  observer independent.

      Which type of information is appealed to in cognitive science  information processing theories? Well, "as-if" information won't do. If the explanation is to satisfy the causal reality constraint  some actual informational fact must be appealed to.  Why won't derived information satisfy the reality constraint? After all we can give genuine scientific accounts of the flow of  money in the economy, why not scientific accounts of the flow of  information in the cognitive system, even though the information, like the money, is an observer relative phenomenon. The brief answer to that is that  in the case of economics the agents who treat such and such  physical phenomena as money are parts of the subject matter we  are studying. But in cognitive science, if we say we are  giving an information  processing explanation of the agent's cognitive processes we cannot accept an  explanation in which the agent's information processing only  exists relative to his intentionality, because we then have not  explained the intentionality on which all of his cognitive  processes depend. We will in short have committed   the homunculus fallacy.  If, on the other hand, we think of the information as existing relative only to us---the observer---then we have not satisfied the causal reality constraint because we have not identified a fact independent of the theory which explains the data that the theory is supposed to explain. So if  cognitive science explanations are going to satisfy the causal reality constraint they  are going to have to appeal to   information which is intrinsic in the agent, information  that is observer  independent. 

         VI. Computation and Interpretation.


       Well why must the requirement be so strong? Why can't we just say that the brain behaves like any other computer?  We give causal explanations of ordinary computers, explanations which meet the causal reality constraint but which do not force us to postulate intrinsic intentionality in the computer.    

      The answer is that the distinction between observer independent  and observer relative applies to computation as well.  When I  add 2 plus 2 and get 4 the arithmetical calculation is intrinsic to me. It is observer independent. When I punch out "2  + 2" and get "4" on my computer, the computation is observer relative. The electrical state transitions are just electrical state transitions until an interpreter interprets them as a   computation. The computation is not intrinsic  to the silicon nor to the electric charges. I, and others like me, are the computer's homunculi. So if  we say that the brain is doing computation we need to say whether the computation is observer relative or observer independent. If it is  observer independent then we have to postulate a homunculus inside the brain who is  actually manipulating the symbols so as to carry out the computation, just as I am consciously manipulating arabic numerals when I add 2 plus 2 to get 4. If we say it is observer relative then we are supposing that some outside observer is assigning  a computational interpretation to the neuron firings.

      I think this last point is clear if you think about it,  but not everyone finds it so and I will therefore explore it a bit further. We are blinded to the observer-relativity of computational  ascription because we think that since computation is typically mathematical and since we also think that the world satisfies certain mathematical descriptions in an observer-independent fashion, that somehow it must follow that the computation is observer-independent.   However, there is a subtle but still important distinction between the observer independence of certain mathematically described facts and the observer relativity of computation exploiting those facts. Consider the example I gave earlier of a rock falling off a cliff. The rock satisfies the law S=1/2gt\u2\d, and that fact is  observer independent. But notice, we can treat the rock as a computer if we like. Suppose we want to compute the height of the cliff. We know the rule and we know the gravitational constant. All  we need is a stop watch. And we can then use the rock as simple analog computer to compute the height of the cliff. 

      So what is the difference between the first case where the rock is just a rock and  is rule described and the second case where the rock is a computer carrying out a computation implementing exactly the same rule? I think the answer is obvious. In the second case we have assigned -- that is there is an observer relative assignment of -- a computational interpretation.  But what is true of the rock is true of every computer. What is special about the rock is that the law of nature and  the implemented algorithm are the same. In  a commercial computer we exploit the laws of nature to assign other algorithms, for addition, subtraction, word processing, etc. But the general  principle is this: We cannot appeal to the analogy between  the computer and the brain to justify the special character of  the tripartite model as applied to the brain because something is a  computer only relative to a computational interpretation. 

      What I have tried to show with  the parable of the falling rock, is that one and the same mathematical description can be treated both as a description of an observer-independent process, and as an observer relative computation. It is just a fact about the stone that it falls in accordance with the laws of physics.  There is nothing observer-relative about that. But we can use this

Fact of physics for our own computational purposes. If we treat that  fact computationally, if we use the stone to carry out a computation, then that computation only exists relative to us just as the computation exists relative to us when we use a pocket calculator.  

      I think that you can see this point if I give you  a simpler example.  If it is a fact that there are three cows in one field and two cows in the next field, both  are observer-independent facts.  But if I then decide to use these facts in order to perform a mathematical calculation, and I add three plus two to get five by counting the cows, the computational process of addition is not something that is intrinsic to the cows in the field.  The process of addition is a process that I perform using the cows as my adding machine.

      Now, what is true of the rock and the  cows in the field is true of computation, generally.  If I am consciously doing arithmetic, that computation is intrinsic.  If a pocket adding machine is doing arithmetic, that is observer relative. It is worth pointing out, by the way, that over the years the word ``computer'' has changed its meaning. When Turing wrote his famous 1950 article, the word ``computer'' meant ``person who computes.'' That is why Turing called the article ``Computing Machinery, and Intelligence" not  "Computers and Intelligence".  Computers meant ``people who compute.'' Nowadays, the word ``computers'' has changed its meaning from observer-independent to an observer-relative phenomenon.  ``Computer'' now refers to a class of artifacts.  

       VII. Information Processing in the Brain.


      The crucial question for the classical model can now be stated with more precision.  What fact exactly corresponds to the claim that there is an  algorithmic level of information processing in the brain?  And what fact exactly corresponds to the claim that everything going on at this level reduces to a level of primitive processing which consists entirely in the manipulation of binary symbols. And are these  computational information  processes observer independent or observer relative?

      As a first step lets ask how the proponents of the model think of it themselves. The answer to that question is not as clear as it ought to be but I think the answer is something like this. At this level, the brain  works like an ordinary commercial computer. Just as there are symbols in the computer which are information bearing, so there are sentences in the head and they too are information bearing. Just as the  commercial computer is an information processing device so is the  brain. 

     This answer is unacceptable. As we have already seen, in the commercial computer the symbols, sentences, representation, information and computation are  all observer relative.  They exist as symbols, etc.,  only relative to us. Intrinsically speaking the commercial computer is just a complicated electronic circuit. For the commercial computer to meet the causal reality constraint we have to appeal to the outside programmers, designers and users who assign an interpretation to the input, to the processes in between, and to the output. For the commercial computer, we are the homunculi who make sense of the whole operation.     

       This sort of answer can never work for Ludwig because whatever else he is, he is a conscious intentional agent trying to do something,  trying to catch a tennis ball; and all of that is intrinsic to him, none of it is observer relative. We want to know how he himself really works, what his intrinsic mechanisms are, and not just what sorts of stances we might adopt toward him or what  computational interpretations we might impose on him.

     Well, why can't Ludwig be computing intrinsically,  why can't he be carrying out algorithms unconsciously the way I  carry out algorithm for long division consciously? We can say that, but if we do we  have abandoned the model, because now the  explanatory mechanism is not the algorithm, but the mental agent inside who is  intentionally  going through the steps of the algorithm. This  answer, in short, commits the homunculus fallacy. We don't explain Ludwig's intentionally-trying-to-catch-the-ball  behavior by an algorithm if we have to appeal to his intentionally-carrying-out-the-parabolic-trajectory-computation behavior and then explain that in turn by his intentionally-going -through-millions-of-binary-steps-behavior. The explanatory mechanism of his system is his irreducible intentionality. The idea of the model was that the information in the system is carried along by the computational operations over the syntax. The  semantics just goes along for the ride.  But on this analysis it is the syntax that is going along for  the ride. The intrinsic intentionality of the agent is doing all the work. To see this point notice that the  psychological   explanation of my doing long division is not the algorithm, but my  mastery   of the algorithm and my  intentionally   going through the steps of the algorithm.

      The upshot can be stated in the form of a dilemma for the classical model: either the crucial notions are taken in an observer relative or in an observer independent sense.  If observer relative then the explanation fails because it fails to meet the causal reality constraint. If observer independent then it fails because of the homunculus fallacy. The homunculus is doing the work. You get a choice between an outside  homunculus (observer relative) or an  inside homunculus (observer independent). Neither option is acceptable.    


        VIII. Deep Unconscious Rule Following.  

     I think one way to meet my argument would be to offer  a convincing existence proof to the contrary.  Are there convincing and unproblematic examples of deep unconscious computational rule following?

     I have argued elsewhere that a specific aspectual shape requires accessibility to consciousness at least in principle. In  many cases, blind sight for example,   the content is not accessible to consciousness, in fact, but we understand such cases precisely as pathological, as due to  deficits, repression, etc.  I wont repeat that argument here but will try to ask a different question, are there any unproblematic examples of deep unconscious rule following?

      If we had some convincing examples, then we would have fewer doubts about the overall principle.   If we could agree that there are cases of rule following in this technical sense which departed from our ordinary common sense notion of rule following, and could agree further that these explanations had genuine explanatory power, then we would at least have a good beginning for a justification of a general cognitive science strategy postulating such deep unconscious rule explanations.  The two examples that have been presented to me are the operation of Modus Ponens and other logical rules, and secondly, the operation of the vestibular ocular reflex.  (There is a certain irony about the VOR because I have earlier presented it as what I thought was a clear example of a case that looked as if it satisfied the causal reality constraint, but where it was obvious that it didn't.)

     I will consider each of these in turn. People have a capacity for making logical inferences.  They do this, so the account goes, by following rules that they are totally unaware of and that they could not even formulate without  professional assistance.  So, for example, people are able to make modus ponens inferences, and thus follow the rule of modus ponens, even though most of them could not formulate the rule of modus ponens, and indeed, do not have the concept of modus ponens.

       Well, let's try this out and see how it works.  Here is a typical inference using modus ponens.  Before the 1996 election I believed that if Clinton could carry the state of California, he would win the election.  Having looked over the poll results in California, I come to the conclusion that Clinton would carry California, so I inferred that he would win the election.  Now, how did I make that inference?

     Well, the cognitive science explanation would go:  When you made the inference you were in fact following an unconscious rule.  This is the rule of modus ponens,  the rule that says if you have premises of the form p, and if p then q, then you can validly infer q.  It seems to me, however, that in cases like this, the rule plays no explanatory role whatsoever.  If I believe that Clinton will carry California, and believe that if he carries California he will win the election, that is already enough to enable me to infer that he will win the election.  The rule adds nothing to the explanation of my inference.  The explanation of the inference is that I can see that the conclusion follows from the premises. But doesn't the conclusion only follow from the premises because it instantiates the rule of modus ponens---doesn't it derive its validity of modus ponens?  The answer to these question is clearly, No.  Modus ponens construed as syntactical computational rule, is simply a pattern that we use for describing inferences that are  independently   valid.  We don't follow the rule of modus ponens in order to make the inference.  Rather, we make the valid inference, and the logician can formulate the so-called rule of modus ponens to describe an infinite number of such valid inferences.  But the inferences do not derive their validity from modus ponens.  Rather, modus ponens derives its validity from the independent validity of the inferences. To think otherwise leads to the Lewis Carroll paradox.[1]. So, it seems to me modus ponens plays no explanatory role whatever in an inference of the sort I just described.

     But what about purely formal proof theoretic inferences?  Suppose I just have a bunch of symbols and I infer from p and p arrow q to q?  Now, it seems to me, that once we have subtracted the semantic content from the propositions, there actually is a role for the rule of modus ponens.  But then precisely because there is such a rule, we are no longer talking about valid inferences as part of human cognitive processes. We are talking about a formal analogue to these valid inferences in some formal proof theoretic system.  That is, if you are given a rule that says whenever you have symbols of the form:  "squiggle blotch sguaggle", followed by "sguiggle", you can write down "squaggle", that is a genuine rule.  It tells you what you can do in certain circumstances and it has all of those features that I described as typical of rule governed behavior, or rule explanations---every single one.  But that is precisely not the operation of the rule of modus ponens in ordinary reasoning.  To put this point precisely, if we think of modus ponens as an actual description of the operation of mental contents, then modus ponens plays no explanatory role in valid inferences. If we think of it as a proof theoretical rule describing operations on meaningless symbols, then it does indeed plays a role, but its role is not that of explaining how we actually make inferences in ordinary cognitive processes, but how we can represent the formal or syntactical structure of those inferences in artificially created systems.     

      I now turn to the vestibular ocular reflex. It  looks as if we are unconsciously following the rule:  ``Move the eyeball equal and opposite to the movement of the head,'' when in fact we are not following any such rule.  There is a complex reflex mechanism in the brain that produces this  behavior.  I thought the point was obvious, but not so. Recently, some of my critics have said that there are  even subdoxastic computational states intrinsic to the system that are at a more fine grained level than the rule I just stated.  Martin Davies says,

     "Another way to describe the VOR is as a system in which

      certain information processing takes place, not just from

      head movements of certain velocities to eye movements of

      certain velocities, but from representations of head

      movement velocities to  representations of eye movement

      velocities..... It is only against the background of this

      second kind of description that there is any question of

      crediting the  system with tacit knowledge of the rules

      relating head velocity to eye velocity."[1] p.386

      This assumption of "semantic content" in the input and output states is a necessary but not a sufficient condition of tacit knowledge  of rules. The sufficient condition requires that "the various input-output transitions that are in conformity with the rule should have the same causal explanation" p. 386

      The VOR easily satisfies that conditions so it turns out that  the VOR is a case of unconscious tacit knowledge of rules and  is a case of rule governed behavior.  To support this Davies gives various statements of computational descriptions of the VOR from David Robinson,  Patricia Churchland, and Terry Sejnowski. He thinks mistakenly  that I am arguing that the computational ascriptions are trivial. But  that is not my point. My point is about the  psychological reality   of the computational ascriptions.  I see no reason to treat the computation description of the VOR any differently than the computation description of the stomach or other organs.  My question is, is there a causal level distinct from the  level of the neurophysiology at which the agent is actually  unconsciously carrying out certain computational, information  processing task in order to move his eyeball? I see nothing in Davies's account to suppose that the postulation  of such a level meets the causal reality constraint. What fact  about the vestibular nuclei makes it the case that they are  carrying out specifically mental operations at the level of  intrinsic intentionality? I do not see an answer to that question. It is not an objection to the usefulness of the computational  models of the VOR  to point out that they are models of neurophysiology not examples of actual psychological processes,  they are at the level of observer relative neuronal information, processing not intrinsic intentionality. It is one thing to have a computational description of a process, quite another to actually carry out a mental process of computing.

                IX. Conclusion

     On the account I am proposing computational descriptions play exactly the same role in cognitive science that they play in any other branch of  biology or other natural sciences. Except for cases where an agent is actually intentionally carrying out a computation,  the computational description does not identify a separate causal level distinct from the level of the physical structure of  the organism.   When you give a causal explanation,. always ask yourself what causal fact corresponds to the claim you are  making. In the case of computational descriptions of deep unconscious brain processes, the processes are rule described and not rule governed.

      And what goes for computation goes a fortiori for "information processing".  You can give an information processing description of the brain as you can of the stomach or an internal combustion engine. But if this is to be psychologically real it must identify a form of information that is intrinsically intentionalistic, and cognitive science explanations using the deep unconscious typically fail to do that. 

     I would like to conclude this discussion with a diagnosis of what I think is the mistake. It is very difficult for human beings to accept non-animistic, non-intentionalistic forms of  explanation.  In our culture we only fully came to accept such explanations in  the seventeenth century. Our paradigmatic forms of explanation  are intentionalistic: I am eating this food because I am hungry, I am drinking this water because I am thirsty, I am driving on the  left because that is the rule of the road.  The idea that there are mechanical explanations that cite no intentionality is a very hard idea to grasp. A form of animism still survives in cognitive science. Marr's intermediate level of rule following at the subdoxastic level in the brain is a form of animism. Now, since these postulated processes are not conscious, are not even accessible to consciousness in principle, we postulate deep unconscious rules following  behavior.  This is the mistake of primitive animism.  Now, this is aided by a  second mistake:  We are misled by the apparent intentionality of computers, thermostats, carburetors and other functional systems that we have designed.  It seems obvious to us that these systems have an intentionalistic level of description.  Indeed, standard textbooks of  cognitive science give Marr's intermediate level description of the thermostat, as if the algorithmic level explanation obviously satisfied the causal reality constraint.  But I think it is clear that it does not. The intentional, rule-following computation of the thermostat is entirely observer relative.  It is only because we have designed and used these systems that we can make  intentionalistic explanations at all.  Now, what goes for the thermostat goes for other functional systems, such as clocks, carburators, and above all, computers.  So, we are making two mistakes.  The first is a mistake of preferring  animistic over naturalistic explanations, and the second is the failure to make the distinction between observer-relativity and observer-independence. In particular, we fail to distinguish the cases where we have genuine intrinsic  intentionality from the cases of observer-relative intentionality. The intentionality in thermostats, clocks and computers is entirely observer relative.

      Now, the hard thing to see is that many  of the intentionalistic descriptions of brain processes are also observer relative, and consequently, they do not give us a causal explanation.  What then is the correct model for cognitive science explanation?  And, indeed, how do we account for much of the apparent rationality of cognition if we do not postulate rule-governed behavior at Marr's intermediate level?  To answer this, it seems to me we have to remind ourselves of how Darwin solved a similar problem by showing that the apparent goal directedness in the structure of species could be explained without postulating any intentionality.  Darwin substituted two explanatory levels for one.  Instead of saying ``the fish has the shape it has in order to survive in water,'' we say 1)  The fish has the shape it has because of its genetic structure, and 2) fish that have that shape are going to survive better than fish that don't.  Notice that survival stills functions in the explanation but it is no longer a goal.  It is just something that  happens.  Now, analogously, we should not say ``The eyeball moves because it is falling a rule of the vestibular ocular reflex."  We should say that the eyeball moves because of the structure of the visual system---it is just a mechanical process.  There is no rule  following   at all. The rule, however, does  describe   the behavior of the eyeball and the eyeball satisfies that description for basically Darwinian reasons.  Eyeballs that behave that way are going to produce a more stable retinal image, and organisms that have a stable retinal image are more likely to survive than organisms that don't. Analogously, Ludwig does not follow the parabolic trajectory rule, rather he tries figure where the ball is going to be and jump  to put his mouth at that point. He has paw - eye coordination skills which can be described by the parabolic trajectory rule, but he is not following that rule. Dogs that can develop such skills are more likely to survive than dogs that don't -- or at least they are more likely to catch tennis balls.


.sp     \fBAppendix      

      The heart of the argument is this:  The computational attribution to the human brain is either intrinsic or observer relative.  That is, either we are to think of the brain as performing computations intrinsically or we are to think of it as relative to an outside agent.  Well, if it is observer relative, then it doesn't satisfy the causal realty constraint, because we are not talking about something computational that is going on intrinsically, we are just talking about some outside interpreter interpreting it that way.  But if it is intrinsic, then we have another problem and that is we have committed the homunculus fallacy.  Here is why.

 The whole doctrine of recursive decomposition requires that there be a homunculus inside who is thinking in terms of zeroes and ones.  That is, it is not enough to suppose that it is like the guy following the rule, ``drive on the lefthand side of the road,'' because the whole doctrine of computationalism is that the guy has to have  set of symbols that he is intentionally manipulating.  That is how we satisfy the causal reality constraint.  But that means that the content is not stated in terms of commonsense notions like, "Drive on the lefthand side", it is stated all in terms of zeroes and ones, and that is going to require a homunculus. So, we have a homunculus fallacy.  The real work is done by the homunculus, not by the symbols themselves.

 We will understand this point better if we go into the history of the subject.  The initial idea of computation is that psychological process of  computing  is performed by conscious human beings.  So you add ``3 + 5'' and get ``8'' for example.   This was Hobbes' idea, when he said ``All reasoning is but reckoning.'' He meant "reckoning" in the commonsense meaning of the term, in which for example  you add and subtract.  Now, what we have discovered is that you can do these things with machines.  But in what sense do you  do these things  ?  That is, what is the same and what is different in the machine?  Well, the machine is not supposed to be conscious, indeed it not supposed to have mental states at all.  The machine just goes through certain formal analogues of reasoning, and we discovered because of Church's Thesis, and the invention of a Turing machine, that you can "do these things" with binary symbols.  Now, those are very important discoveries, but then something paradoxical happened.  We tried to read back the machine process into the brain.  But of course, the brain is quite different.  When we are reckoning in Hobbes's sense,  we are consciously going through certain mathematical processes.  But the reckoning done by the machine is now entirely observer relative.  It requires an outside  interpreter to interpret these symbol manipulations as "reckoning" at all. 

 \fB Basic cognition  

 I need to introduce a new notion, the notion of basic cognition. Many years ago, Arthur Danto introduced the notion of a basic action.  And I am not sure exactly what Danto meant, but the way I have always used this notion and the way that I found it useful is this:  There are a lot of things that we do intentionally without intending to do anything else by  way of which or by means of which we do these things.  So, if you ask me, how do you get to San Jose, I will describe a series of steps by means of which I get to San Jose.  I you ask me, how do I raise my arm, the answer is, I just do it.  I don't do it by means of doing anything else.  A basic action, then, on my definition is an action that you can do intentionally without intending to do anything by means of which you do that thing.   It is obvious from the definition that what is basic for one agent may not be basic for another.

 Now, I want to suggest that the notion of a  basic action so-defined, is just an instance of a much more general notion, the notion of a basic cognition.   A basic cognition is any cognition that I can have without having some other cognitive state or process by way of which or by means of which I have the cognition in question.  Thus, if you ask me, how do I find my cognitive science directory on my computer, I can tell you a series of steps that I go through.  But, if you ask me how do I see the computer, there isn't any cognitive answer to that---I just do it.  There is a brain process answer explaining  how it works in the brain,  but that answer is nonintentionalistic.

 So, we might say that just as every complex action must presuppose the notion of a basic action, so every complex cognitive state or process presupposes basic cognition. The reason for this is that the answer to the question, ``how do you do it?'' cannot go on for ever.  Eventually it must bottom out.  There is an answer to the question, ``how do you start your car?'' but if I say, ``I start my car by turning the key in the ignition,'' there isn't any answer to the question, ``And how do you turn the  key in the ignition?'' because I just do it.  But if there were an answer---say, I turn the key in the ignition by grasping the key between thumb and forefinger of my right hand and rotating my wrist to the right, eventually I would have to reach a point where the answer is ``I just do it.'' There are further neurobiological explanations of how it is possible that I perform the basic actions. These are explanations in terms of calcium ions, neurotransmitters, etc. 

 The recognition of a state of basic cognitive processes then forces us to the following conclusion:  All explanations of cognition are either intentionalistic until they reach the basic form of intentionality, or they are neurobiological.  To see this point, let's go back to Ludwig.  The explanation of his behavior is that he is trying to catch the tennis ball and he is able to jump in such a way that he catches the ball in his mouth and the means by which he does this is to jump to the point where he thinks ball and mouth will meet simultaneously.  Now, there will, in addition, be a rather elaborate neurobiological explanation about muscle contractions and visual experiences and the coordination that the brain has between those two, but there will be no intentionalistic component of those phenomena.  

 We might summarize the distinction between the view that I am beginning to put forward and the cognitivist view by saying that on the view that I am putting forward, the intentionalistic explanations bottom out in common-sense forms of intentionality and that further explanations are neurobiological.  The rival view says that the neurobiology is only the implementation of a much more fundamental form of intentionality which is unconscious and much of it is sub-personal, below the level of personal awareness.

[1] John  R. Searle,  The Rediscovery of the Mind, MIT Press, Cambridge, 1992

[1] David  Marr, Vision, Freeman and Co. San Francisco, 1972

[1] Marr, op. Cit. P..

[1] Palmer, S and Kimchi ..

[1] Quine, W.V.O..1972

[1] Dodgson, C.. What Achilles Said to the Tortoise, Mind  , 190x

[1] Martin Davies in Marshall and Marshall eds. p. 386