INFERENTIAL-ROLE SEMANTICS: A THEORY OF CONCEPTS FOR PHILOSOPHY AND PSYCHOLOGY

Transcription

1 INFERENTIAL-ROLE SEMANTICS: A THEORY OF CONCEPTS FOR PHILOSOPHY AND PSYCHOLOGY by Joshua D. Cowley A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHILOSOPHY In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA

2 UMI Number: INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml

3 2 The University of Arizona Graduate College As members of the Final Examination Committee, we certify that we have read the dissertation prepared by Joshua D. Cowley entitled INFERENTIAL-ROLE SEMANTICS: A THEORY OF CONCEPTS FOR PHILOSOPHY AND PSYCHOLOGY and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy date date foseph~thomas Tolliver ' dkte Massimo Platte --f 1 1 Terence E. Horg Palmarinl date S/i"// date V Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be aqcc^d as fulfilling the dissertation requirement. Di^rt^onDirector; John L. Pollock %]3±L JL date

4 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SiGNE

5 4 ACKNOWLEDGEMENTS A number of people have helped me in the course of writing this dissertation. I would like to thank Merrill Garrett, Terry Horgan, Massimo Piattelli-Palmarini, and Joseph Tolliver for their advice as my committee members. David Chalmers made valuable comments on early drafts of the dissertation. I am particularly grateful to Ashley McDowell for countless hours spent in countless coffee shops. Finally, I would like to thank my director, John Pollock, for both his philosophical guidance and his friendship.

6 5 DEDICATION For my parents, David and Maria.

7 6 TABLE OF CONTENTS LIST OF FIGURES 7 ABSTRACT 8 CHAPTER 1. CONCEPTS The Target of a Theory of Concepts Two Models of Concepts Inferential-Role Semantics Challenges for Inferential-Role Semantics 26 CHAPTER 2. IN DEFENSE OF THE INFERENTIAL MODEL The Classical Theory of Concepts Prototype Theory The Exemplar Theory Dual Theories of Concepts Conclusion 57 CHAPTER 3. INFERENTIAL-ROLE SEMANTICS Inferential-Role Semantics: The Simple Version The Problem of Plenitude Restricting Contentful Role Prototype Theory and Inferential-Role Semantics 74 CHAPTER 4. HOLISM AND CONCEPT SHARING Does Inferential-Role Semantics Imply Holism? Holism with Concept Sharing Local Inferential Role Conclusion 106 CHAPTER 5. COMPOSITIONALITY Arguments for the Compositionality of Concepts Fodor and the Composition of Inferential Roles Ill 5.3. Composition through Wide Content Composition through Reasoning Concepts of Compositional Functions Conclusion 124 REFERENCES 127

8 7 LIST OF FIGURES FIGURE 3.1. Graph of inferential role 64 FIGURE 3.2. Inferential role for one concept 65 FIGURE FIGURE 3.4. Inferential role of realistic concept 67 FIGURE 4.1. Inferential connections for Lilly before change 85 FIGURE 4.2. Inferential connections for Lilly after change 85 FIGURE 4.3. Concepts for Mary (left) and Jane (right) 92 FIGURE 4.4. Conceptual Role for Jack and Bill 101 FIGURE 4.5. Local Conceptual Role for Jack and Bill 102 FIGURE

9 8 ABSTRACT Concepts are not sets of necessary and sufficient conditions. This fact has caused trouble for both psychologists and philosophers. The resultant psychological theories of concepts, which are primarily aimed at the functional role of concepts, are very specific but this specificity is at the expense of excluding some types of concepts. The resultant philosophical theories of concepts, which are primarily aimed at the content of concepts, are general but this generality is at the expense of understanding the role concepts play in the mind. My dissertation proposes a bridge between psychological and philosophical theories of concepts. This bridge has two parts: The first part is a general model of the functional role of concepts which is philosophically rigorous but can house existing psychological theories of concepts. The second part is a theory of the (narrow) content of concepts, which is informed by the mass of psychological evidence, but is general enough to encompass all concepts. The key in both parts is the role that concepts play in inference. I argue for the inferential model of concepts, which claims that the functional role of a concept is its inferential role. I also argue for inferential-role semantics which claims that the (narrow) content of a concept is determined by its inferential role. The overlooked advantage of this inferentialist position is the ability to draw on an account of reasoning to solve problems in developing a theory of concepts. My dissertation can then be seen as unifying philosophical and psychological work on concepts with philosophical and psychological work on reasoning. This is most obviously seen in the final chapter which offers an account of compositionality for inferential-role semantics.

10 9 Chapter 1 CONCEPTS It is often claimed that concepts are the building blocks of thoughts. If this claim is true, as I think it is, any adequate theory of cognition will require a theory of concepts. Both philosophers and psychologists have attempted to give such a theory, however, as with most of nature's building blocks, developing a theory of concepts has not been an easy task. I want to argue that the difficulty is due, in part, to a fundamental error in how one ought to approach a theory of concepts. Most theories of concepts seek to explain the internal structure or the proper parts of concepts. For example, the classical theory of concepts claims that a concept is a set of necessary and sufficient conditions. On the classical theory, each of these conditions is a part of the concept. As another example, the prototype theory claims a concept is a collection of typical features. Again, each feature is a part of the concept. Borrowing a term from Laurence and Margolis (1999) I will say that a theory which emphasizes the internal structure of concepts fits the containment model of concepts. I think that better theories of concepts can be constructed by placing an emphasis on how concepts relate to one another. In particular one should emphasize the inferential relationships between concepts. Borrowing another term for Laurence and Margolis, I will say that a theory which emphasizes the inferential relationships between concepts fits the inferential model of concepts. That a concept's role in inference should be important part of a theory of concepts is not a novel proposal (e.g.. Field, 1977; Block, 1986; Harman, 1987; Pollock, 1989; Brandom, 2000). However, the proposal has largely been treated as a theory of concepts. My suggestion is that the proposal is not a theory of concepts at all. Rather it is a model in which specific theories of concepts can be constructed. I want

11 10 to argue that theories constructed under the inferential model are better than theories constructed under the containment model because the inferential model provides tools for constructing a theory of concepts which are not available when constructing theories under the containment model. How a theory makes use of those tools, though, is dependent upon the particular theory of concepts. As a result, my argument will have two parts. The first part of the argument will discuss the relationship between various theories of concepts and the inferential model. The second part of the argument will defend the inferential model from three important criticisms of the inferential model: the problem of plentitude, the problem of holism, and the problem of compositionality. 1,1 The Target of a Theory of Concepts In this section I will lay some of the ground work for the remainder of the thesis. There is a large literature on concepts including several prominent defenses of inferentialrole semantics. It would be foolish to ignore these and start from scratch. Defending a theory of concepts requires making a number of choices. Several of these are made easier by reference to arguments made by others. In other cases I am breaking away from traditional views or theories of inferential-role semantics. The one thing that is obvious from this literature is that people don't always mean the same thing by "concept." This section should help clarify what I mean by the term as well as setting out the very general view of inferential-role semantics I am defending. It will be useful to start with some notation. It will often be necessary to distinguish between a concept and the English word which represents that concept. I will use SMALL CAPS whenever I mean to refer to a concept. I will often need to make reference to a particular inference or inference schema. I will use quasi quotes ^ to indicate something as an inference or as the premise or conclusion of an inference. There are a number of terms used in the philosophical and psychological literature

12 11 that clear up the discussion of concepts. First, it is important to distinguish between the application of a concept and an instance of a concept. The application of a concept is a kind of mental event in which an agent judges that something falls under the concept. An instance of a concept is something to which a correct application of the concept could be made. For example, I may apply the concept HORSE to a donkey. The judgment that the donkey is a horse is a case of applying HORSE, but the donkey is not an instance HORSE. There are a number of things to which a concept could be applied. I might apply HORSE to an actual horse, a donkey, the donkey's tail, a pine tree, or the year I will use the term "object" to mean anything to which a concept might be applied. Sometimes an agent has a concept in mind and is looking for an object to which the concept can be applied. However, it is just as common that an agent has an object in mind and is looking for the correct concept to apply to the object. In the psychological literature on categorization this is called a "target." A target is a particular object which an agent is attempting to classify under some concept. So we might say that the agent wants to determine if the target is a horse or a donkey. Finally, the instances of a concept can come in two varieties. First, are the particular instances of the concept. The particular bird chirping outside my window is an instance of the concept BIRD. Second, are subclasses of instances of a concept. When we say that bluejays are birds we are saying that BLUE JAY is a sub-concept of BIRD. Unless stated otherwise I will reserve the term "instance" for particular instances of a concept and use "sub-concepts" to refer to subtypes within a concept. It is popular to give a set of desiderata that a theory of concepts should meet. Block (1986) gives a Hst of 8 desiderata, Fodor (1998) has five non-negotiable desiderata, and Prinz (2002) has seven. Rather than give my own list I will simply operate on two basic principles: 1. A theory of concepts which explains more is better than a theory which explains less. 2. A theory of concepts should be both philosophically rigid and psychologically plausible. As it turns out most, if not quite

13 12 all, of the desiderata listed by Block, Fodor, and Prinz are handled by inferential-role semantics. However, I do not take the satisfaction of these particular desiderata to be necessarily more important that the satisfaction of others. Abstracta verses mental representations Traditionally there are two questions which lead one to develop a theory of concepts - How do things come to have semantic value? and How does the mind work? These two traditional questions lead to two traditional approaches to the nature of concepts. According to the first tradition concepts are independent of any specific minds. Put another way, concepts do not affect minds. According to the second tradition concepts are a kind of mental entity which play a direct role in mental processes. I do not claim this is an exhaustive list of ways to look at concepts nor that all theories of concepts fall neatly into one tradition or the other. However, the tradition one follows tends to influence the resulting theory. On the extreme end of this tradition we might find Plato's theory of forms. For a Platonist, forms exist whether or not there are any minds at all. Those that think of concepts as abstract objects also follow this tradition. A recent proponent of this view is Peacocke (1992). In a chapter on the metaphysics of concepts Peacocke begins, "Concepts are abstract objects" (p. 99). On Peacocke's view a what individuates one concept from another is the set of possession conditions which a thinker would have to meet to grasp the concept. However, it is not clear that one has to believe in forms or abstract objects to believe that concepts are independent of specific minds. For example, those who hold that concepts are fundamentally linguistic or social constructs (e.g. Brandom, 2000) would say that concepts are independent of the specific minds that have thern. However, this isn't obviously a commitment to abstract objects. Furthermore, they are not committed to saying that there could be concepts if there were not minds at

14 13 all. Social constructs may very well require groups of minds. The second tradition stems from an interest in how the mind works. Concepts, in this tradition, are a kind of mental entity. I suspect that psychologists always follow this second tradition and many philosophers do as well. The most common proponents of this view are those that think that concepts are mental representations (e.g. Block, 1986; Harman, 1987; Fodor, 1998; Prinz, 2002). I am primarily interested in looking at concepts as the constituents from which an individual's thoughts are constructed. Thus it will be concepts as understood by the second tradition that will be the topic of this dissertation. To be specific, I will be developing a theory on the presupposition that concepts are mental representations whose tokens combine in various ways to form thoughts. One of the reasons for taking this stance is that I want concepts to play a direct role in psychological explanation and psychological theories. For example, theories of categorization, reasoning, and language learning typically make use of concepts. I take it to be an important benchmark for a theory of concepts that it is compatible with at least most psychological theories which make use of them. Following the first tradition makes it considerably more difficult, if not impossible, for concepts to play a role in psychological explanation. This is because concepts do not directly affect individual minds. However, there may be some relationship between concepts and psychology while following the first tradition. Peacocke (1992), for instance, defends what he calls the Simple Account: "When a thinker possesses a particular concept, an adequate psychology should explain why the thinker meets the concept's possession condition" (p. 177). Notice that such a view simply creates a new goal for psychological theories rather than helping to clarify existing theories. The term "mental representation" often comes loaded with a number of background assumptions. In so far as I am presupposing that concepts are a kind of mental representation, I am using the term in a very general sense. I am not presupposing any particular theory of mental representation such as, "mental representations are

15 14 atomic elements in a language of thought," or "mental representations are distributed structures in a connectionist network." All I mean by "mental representation" is a mental object that has content. Saying that concepts are mental representations also should not be confused with saying that all mental representations are concepts. Presumably, most mental representations are not concepts. For example, it seems clear that mental representations are formed in early visual processing, but to call these concepts would be a stretch. Content verses psychological structure Given that concepts are some kind of mental entity, there are two distinct ways one might go about pinpointing them. The first is to look for entities with a particular kind of content. The second is to look for entities with a particular kind of psychological structure. In the psychological literature these are often muddled together. To ask for a concept's content is, roughly, to ask what it means. To ask how a concept is structured is, roughly, to ask for its functional role. The latter case necessarily involves understanding how concepts are related, via psychological processes, to each other and to other psychological entities. If concepts have proper parts, then it is also necessary to know how those parts are related to other psychological entities. However, how one determines a concept's functional role may have nothing to do with how that concept comes to have the content it does. An analogy might help to clarify this. Automobiles are a kind of transportation. There are at least two ways one might go about picking out the automobiles among all the transportation devices and processes. One method would be to describe traffic laws and roads; automobiles are the things which travel on roads and obey traffic laws. A second method would be to describe internal combustion engines, transmissions, steering wheels, etc.; automobiles are the things that are constructed like that. In the 1950s these two methods would have picked out pretty much the same things. With

16 15 the advent of the electric car, the two methods pick out somewhat different things. Both methods are useful in certain contexts and for the most part they carve the world up the same way. However, each method is independent of the other. Using one method doesn't necessitate knowledge of the other. Likewise, picking concepts out by their content or their psychological structure can be useful in different contexts and for the most part each method carves the world up the same way. Some theories, such as inferential-role semantics, claim that conceptual content is determined by psychological structure. But even here, it isn't necessarily the case that conceptual content is identical to conceptual structure. Psychology may well choose to individuate concepts via some aspects of their overall structure while a theory of content chooses other aspects of that structure. Ideally each of these methods would pick out the same things in the end. But this needn't be the case for both descriptions to be useful. What I will be arguing in this dissertation is that a concept can be picked out by the role it plays in inference. But really I'm arguing for two different points. The first is an argument for what I will call the inferential model of conceptual structure. The inferential model claims that a concept's structure or functional role is a set of inferential relationships between the concept and other representations. The second argument is for a version inferential-role semantics as a theory of conceptual content. Inferential-role semantics claims that a concept's content is determined by the role it plays in reasoning.^ It may appear that these two claims amount to saying that the content of a concept is the concept's functional role. However, the inferences that make up a concept's structure or functional role may not be the same as the inferences which determine its content. ^Strictly speaking the version inferential-role semantics I am defending claims that a concept's narrow content is the role it plays in inference. This is covered in more detail below.

17 Two Models of Concepts The impetuous for Chapter 2 comes from two paragraphs from Laurence and Margohs (1999) where they point out that there are two general models one might adopt toward conceptual organization. They call these the containment model and the inferential model. The containment model places emphasis on the internal structure of a concept, such as lists of common features or a collection of necessary and sufficient conditions. For theories that fit the containment model, any time a concept is accessed, all of its internal structure is accessed as well. For example, tokening BACHELOR in the thought This room is full of bachelors, necessarily includes tokening a more basic psychological structure representing male. The inferential model deemphasizes the internal structure of concepts. Instead, it places the emphasis on how a concept is connected to other concepts. Let's say that whenever two concepts, Ci and C2, could be tokened in an inference, there is an inferential connection between Ci and C2. A more precise definition will be given in the next section but this captures the basic idea. What theories cast under the inferential model claim is that a concept, Cs, functional role consists of a privileged subset of C"s inferential connections to other concepts. Exactly which inferential connections compose C"s functional role depends upon the particular theory of concepts. Because concepts do not have proper parts on the inferential model, tokening a concept like BACHELOR does not necessitate tokening MALE as well. However, tokening BACHELOR may generate a disposition to draw an inference that tokens MALE. Fodor (1998) has gone to great lengths to argue that any "inferentialist" view of concepts is untenable(see also Fodor, 2004). For the most part I will not be addressing the problems Fodor raises until Chapter 4 and Chapter 5. This is because, from Fodor's standpoint, the debate between the containment and inferential models is internal to inferentialist views in general. For Fodor, any view which treats concepts as involving relations between any mental representations is an inferentialist view.

18 17 Both the containment and inferential model meet this criterion. I take Fodor's characterization of all these views as inferentialist to be a implicit recognition that these theories can be reworked to fit either the containment or inferential model. The goal of Chapter 2 will be to elucidate how theories falling in the containment model can be made to be theories under the inferential model. Where the containment and inferential models pull apart is in (1) the nature of the representations that concepts are related to and (2) the nature of the relation between the concepts and the representations. The containment model takes concepts to be related to representations which are not themselves concepts (e.g. features or conditions) and it states that tokening a concept requires tokening these other representations. The inferential model takes concepts to be related to other concepts and it states that tokening a concept only creates a disposition to token other concepts. 1.3 Inferential-Role Semantics Versions of inferential-role semantics have been in the literature for some time. The basic idea appears to have a number of advantages. The most obvious is the possibility that inferential-role semantics can deal with the problem of intensionality. This is the problem of explaining how two concepts can have the same instances while, nevertheless, being different concepts. For example, one might have a concept WATER and a concept H2O. All instances of WATER happen to be instances of H2O as well. Yet, despite this, WATER and H2O are different concepts. This causes difficulties for any theory of concepts which only distinguishes concepts by their instances. According to inferential-role semantics, however, the explanation for this is that one reasons with the two concepts in different ways. From is water^ one might infer is drinkable^. While from is H20^ one might infer contains hydrogen^. inferential-role semantics says that this different role in reasoning just is the difference in content between WATER and H2O.

19 18 A related problem that inferential-role semantics shows promise in solving is how two people can have the same concept despite that concept's referring to different things. For example, my concept HERE is, in a very important sense, the same as your concept HERE despite the fact that each concept refers to two different places. Again, inferential-role semantics explains this by pointing to the fact that HERE plays the same inferential role in my mind as it does in yours. Inferential-role semantics also looks like it has the potential to naturalize conceptual content. Pollock (1989) for instance has argued that the inferential role of a concept is identical to its functional role. At the very least it seems plausible that inferential role could be reduced to or supervene on the causal role of a concept. Fodor makes a similar remark about the possible benefits of inferential-role semantics when he says, "given two networks - the causal and the inferential - we can establish partial isomorphisms between them. Under such an isomorphism, the causal role of a propositional attitude mirrors the semantic role of the proposition that is its object" (author's emphasis, Fodor, 1985, p. 19). These advantages have been enough to convince a number of people that some version of inferential-role semantics is the best bet for a theory of conceptual content (e.g., Field, 1977; Block, 1986; Harman, 1987; Pollock, 1989; Brandom, 1994, 2000). However, agreement on a general strategy still leaves room for plenty of disagreement. For the remainder of this section I will look at some important differences in inferential-role theories and defend my position on these differences. Propositional or sub-propositional The first divergence between inferential-role theorists centers on the whether inferential roles are to be attributed to something propositional (e.g. beliefs or sentences) or something sub-propositional (e.g. concepts or words). Brandom (1994, 2000) is the most ardent propositionalist, though Field (1977) and Block (1986) also take this

20 19 line. In the sub-propositionalist camp are Harman (1987); Rey (1997) and myself. In general propositionalists claim that concepts (or words) get their content from the role they play in the propositions (or beliefs, sentences etc) in which they appear. But concepts do not play an inferential role within a proposition. Rather, it is the proposition which has an inferential role. As an example. Field (1977) contends that beliefs get their content from the role they play in a Bayesian probability network. That is, a belief's content is determined by how changes in the subjective probability of that belief can affect the subjective probabilities of other beliefs and vice versa. Since subjective probabilities don't attach to concepts in and of themselves, the important inferential relations have to between the beliefs, which are propositional. Similarly, Block states, "A crucial component of a sentence's conceptual role is a matter of how it participates in inductive and deductive inferences. A word's conceptual role is a matter of its contribution to the role of sentences" (Block, 1986, p. 93). Unlike Field, there is virtually nothing in Block's defense of inferential-role semantics which demands that he be a propositionalist. Brandom, on the other hand, explicitly argues for the propositionalist line on inferential-role semantics. He states, According to an inferentialist line of thought, the fundamental form of the conceptual is the propositional, and the core of concept use is applying concepts in propositionally contentful assertions, beliefs, and thoughts... [This] entails treating the sort of conceptual content that is expressed by whole declarative sentences as prior in the order of explanation to the sort of content that is expressed by sub-sentential expressions such as singular terms and predicates (Brandom, 2000, p. 12). At first glance inferentialism seems to suggest propositionalism. After all it is propositions, not concepts, which can be the premises and conclusions of inferences. For example, one does not infer the concept MALE from the concept BACHELOR, but one could infer "Chris is a male" from "Chris is a bachelor". However, Brandom's claim that inferentialism entails explaining propositional content before conceptual content is too strong. To see why inferentialism does not entail propositionalism, we

21 20 need to make sense of the idea that one concept can be inferentially related to another without making explicit use of propositional content. In Section 1.2 I gave a rough characterization of the notion of an inferential connection between two concepts. It is now time to make that rough characterization more explicit. To begin, we need a brief characterization of inference. This account is based largely on Pollock (1990). First, there are two kinds of inference: forwards and backwards. In forwards inference an agent moves from a belief in F to a belief in Q. This is the sort of inference that everyone is familiar with but it is just as common to engage in backwards inference. In backwards inference an agent begins with an interest in beheving Q. She then develops an interest in believing P for the purpose of concluding Q. Of course, this is a little simplistic. An agent may conclude Q from more than just P and she may develop an interest in more than just P from an interest in Q. Let A and B be concepts and Ao B symbolize that A is inferentially connected to B. ^'s inferential connections to B will come in two forms. In the first case an agent can make an inference from the application of A to the application of 5. In the second case an agent can make an inference from the application of B to the application of A. The former I will call a forward connection and symbolize as A'oB. The later I will call a backward connection and symbolize as A o B. We can then define Ao B as follows: Inferential Connection: A concept A is inferentially connected to a concept B, A ob, for an agent s if either of the following conditions hold. 1. If s applies A to x, then s is disposed believe Bx on the basis of Ax (A^B) OR 2. If s has an interest in applying A to x, then s will adopt an interest in applying B to x for the purpose of believing Ax on the basis of Bx (A'^B).

22 21 This notation may seem overly complex since as it is defined, Ao B, then A o B. So we should simply be able to represent forwards and backwards inferential connections by the order of the A and B. In later chapters, however, it will be useful to distinguish A's forwards inferential connection to B from S's backwards inferential connection to A. Inferential connections play an important role in this thesis and the idea will be developed further as we progress. For the moment, however, notice that inferential connections are defined without making explicit use of prepositional content. Instead they are defined by concept application and by what we might call an inference schema(pollock, 1995). Ax and Bx are not propositions since x is a variable and there are no quantifiers ranging over x. What connects A and B is an inference schema in which many different propositions can be inserted, rather than the propositions themselves. Having defined inferential connections without mentioning prepositional content, we can now see how the inferential role of a concept can be determined without reference to prepositional content. Inferential Role: The inferential role of a concept, A, is the set of A's inferential connections. So far, all I have done is to show that inferentialism does not entail that we explain prepositional content before we define conceptual content. We still need to establish that we ought to explain conceptual content before we explain prepositional content. I think there are two significant costs to explaining prepositional centcnt before conceptual content. The first issue concerns compositienality. For reasons briefly discussed below and covered in depth in Chapter 5 it is clear that (at least most) prepositions are compositional. That is, the meaning of a preposition is a function of the meaning of its constituents and syntax. There are two obvious responses to this. The propositienalist response would claim that there are atomic

23 22 propositions from which more complex propositions are built. The propositionalist could say that the content of atomic propositions is determined by their inferential role, the content of more complex propositions is determined their constituent atomic propositions and syntax, and the content of concepts is determined by the role they play in propositions. The sub-propositionalist response would claim that the content of concepts is determined by their inferential role and the content of all propositions, simple or complex, is determined by the constituent concepts and syntax. There are two problems with the propositionalist response. First, it is difficult to see how we can define atomic propositions. One proposal is that atomic propositions are propositions with only one concept. However, concepts themselves can be quite complex (e.g. NORTH-AMERICAN-HOOFED-ANIMAL). Second, no matter how atomic sentences are characterized, there will be an outrageously large number of them. For example, suppose that "Jill is tall" is an atomic proposition. Then "Frank is tall," "Jane is tall," "Henry is tall", etc. will all be atomic propositions as well. A simpler approach would simply define the content of TALL and let the content of the propositions be derived from this. A second problem with propositionalism is that it is in tension with characterizing content in psychologically plausible or naturalistic ways. This is closely related to the problem propositionalism has dealing with compositionality. Presumably people do not store all the possible propositions they are capable of understanding. Consider for example, the proposition "Horses live only on land." From this one could conclude "Horses do not live underwater." However, there are a lot of propositions of this form such as, "monkeys live only on land," "cows live only on land," or "cats live only on land." For each of these animals one could conclude that the animal does not live underwater. It would be unreasonable to think that each of these propositions is stored in any very explicit sense within a person. If propositionalism were true, then the content of a proposition is determined by its inferential relationships with other propositions, most of which are not explicitly stored in actual people. A reahstic

24 23 theory of psychology would then have very little to say about content. Compare this with a sub-propositional account of inferential-role semantics. In a sub-propositional account content is determined by concepts and their inferential connections. A complete theory of psychology will have to account for concepts. It also will need to explain how a person moves from the application of some concepts to the application of others. One factor or two A second divergence between inferential-role theorists centers on whether inferentialrole semantics is taken to be a complete theory of content. Block (1986) is among those that thinks inferential-role is important but not enough. Like myself, Block is interested in a theory of content which is useful for psychology. Block does little to develop a positive account of inferential-role semantics instead he focusing on what a theory of content needs to be useful to psychology. He then argues that some version inferential-role semantics is most likely to do the job. One of Block's most important desiderata is his last: "Explain why different aspects of meaning are relevant in different ways to the determination of reference and to psychological explanation" (Block, 1986, p.84). He argues that this desideratum leads to distinguishing between narrow and wide content. The narrow content of a concept consists of those characteristics of content which are internal to the mind in which the concept is employed. Narrow content is contrasted with wide content which consists of those characteristics of content which are external to the mind in which the content is employed. Block gives two reasons for drawing this distinction: "One is that how you represent something that you refer to can affect your psychological states and behavior... [Two] is that there is more to semantics than what is 'in the head'"(block, 1986, p. 88). Block concludes that this will lead to two theories of content. Inferential-role semantics, he takes it, is a theory of narrow content. He is

25 24 not specific about which theory he regards as best for wide content, but he suggests that some version of a causal or informational theory is likely to work. A similar idea also goes under the rubric 2-dimensional semantics (see Chalmers, 1996; Jackson, 1998). Harman (1987), holds that conceptual content can be completely accounted for by what he calls "conceptual role" and that there is no narrow/wide content distinction. According to Harman a concept is a computational symbol whose content is determined by the functional role of the symbol. However, his notion of functional role is broader than others. "Of primary importance are functional relations to the external world in connection with perception, on the one hand, and action, on the other," he says (Harman, 1987, p. 218). This is essentially an extension of Harman's notion of long-armed functionalism to mental content. According to Harman some concepts, such as logical concepts, get their content only from the way the are related to other computational symbols. However, general concepts, such as CAT, and what he calls individual concepts, such as THAT-GUY-OVER-THERE, get content in part from how they are related to the world. Harman's reason for extending the functional role of a symbol outside the head is an interesting one that needs to be accounted for by anyone that thinks that narrow content can be accounted for by functional role. On a naturalistic account of inferential-role semantics, the inferential role of a concept is a special case of its functional role. Block argues for a similar reading saying "[Inferential] role is total causal role, abstractly described... [It] abstracts away from all causal relations except the ones that mediate inferences, inductive or deductive, descision making, and the like" (Block, 1986, p. 94). What Haxman argues is that when specifying functional role, there is no non-arbitrary way to say where the mind ends and the outside world begins. Hearing is a good case for demonstrating the problem. On a typical view of functionalism, part of the functional role of the perceptual state of hearing a bell is that it tends to be caused by the presence of ringing bells. The actual ringing

26 25 of bells is clearly outside the mind and so would not be useful for defining narrow content. A step in the right direction would be to say that the perceptual state tends to be caused by a certain kind of stimulation of cilia in the ear. This would be in the head, but it still doesn't seem to be in the mind. For instance, if someone had their auditory nerves stimulated by microphones rather than cilia, it seems they would still have the same narrow content. By the same line of reasoning, the nerves themselves could be replaced with wires that run directly to the brain. The brain is perhaps the most plausible place to draw the line, but even this seems arbitrary. The following actual case makes this clear. In recent years a new device has been developed for patients that have lost hearing as a result of nerve damage close to the ear. The device, called an auditory brainstem implant, is inserted directly into the auditory center. The microchip has a small radio receiver which picks up signals from a microphone taped to the head. These microchips have probes which send electrical stimuli to the surrounding neurons. Over time the neurons begin to interpret these electrical stimuli just as they did the original nerve impulses from the ear. The patient eventually re-acquires the ability to hear (Toh &; Luxford, 2002). We can imagine a twin-earth scenario in which one twin acquired the implants at birth and the other did not. I am inclined to say that these twins would still have the same narrow content in this case. However, the nature of the input to the brain is clearly quite different. So drawing the line at the brain also seems wrong. It is interesting to note that Harman's criticisms do not apply generally to the idea of wide and narrow content. The specific criticisms he gives only say that conceptual role cannot be strictly internal because conceptual role is a kind of functional role. Thus, the conclusion of Harman's arguments would is: if conceptual-role semantics is the correct theory of content, then there is no narrow content. Since this could mean that there is no narrow content or it could mean that conceptual-role semantics is wrong.

27 26 I think these are interesting points, but they don't make the case that conceptual role must extend outside the mind. The reason is that as Harman uses the term, "conceptual role" is really "inferential role." Harman and Block both agree that that a symbol's role in inference is a large part or perhaps all of its conceptual role. However the inferential role of a symbol is strictly an internal thing. The inferential role of a symbol consists of a set of functional relationships between one symbol and other symbols. It does not consist of the relationship between the symbols and in the world. Block offers another argument against Harman. The idea of a two-factor theory of content is that there are two distinct theories of content. One is a theory of narrow content and the other is a theory of wide content. Harman is suggesting that there is only one theory of content. What Block argues is that there really is not much difference between Harman's long-armed conceptual role and a two-factor theory of content where one factor is narrow and the other wide. This doesn't seem right though. Harman's view is that there is no principled distinction between the internal and external when you are defining conceptual role. For a two factor theory to be meaningful it must say there is some distinction between the internal and external. 1.4 Challenges for Inferential-Role Semantics Some problems remain common to all defenders of inferential-role semantics. Three problems stand out as particularly troublesome; the problem of plentitude, the problem of holism and the problem of compositionality. I will briefly describe each of these but a more thorough examination of them will occur in later chapters. The problem of plentitude The largest problem with inferential-role semantics as stated is that the theory is incomplete. Any given concept is likely to play a role in an extremely large set of possible inferences. Most proponents of inferential-role semantics agree that not all

28 27 of these inferences are relevant in determining the content of a concept (Block, 1986; Field, 1977; Pollock, 1986, 1989). Consider the concept COFFEE. COFFEE is tokened in the inference from ^ x is coffee^ to is coffee or a; is a flounder^. But it seems doubtful that this inference has anything to do with the content of COFFEE. Despite a general recognition of this problem, very few have actually given proposals about which inferences do matter. Block (1986) says that this is the largest problem facing inferential-role semantics at this time. Holism If the content of a concept is determined by inferential role then different inferential roles should indicate different concepts. Suppose Lilly has a concept, C, whose content, according to inferential-role semantics, includes an inferential connection to another concept D. D has its own conceptual role part of which is a connection to E. Now suppose Lilly acquires some new information leading her to remove the connection between D and E. Now the concept formerly know as D has a different conceptual role. In D^s place there is now a new concept, D*, with a content similar, though not identical, to that of D. But this implies the concept formerly know as C is now connected to D* not D. In other words, Cs conceptual role has changed such that C really is now C*; a concept with a conceptual role similar to the role of C. It is easy to see that the changes won't stop with C*. If C is now C* then any concept whose conceptual role included a link to C now has a link to C*. If a set of concepts is highly connected, as our concepts presumably are, a change to the conceptual role of one concept could ripple throughout all of an agent's concepts. The result is that an agent cannot have any of the same concepts if she changes one of them. The problem of holism applies across agents as well. My concept ELECTRON can not be the same as yours unless virtually all of our concepts are the same. Compositionality One of the most interesting things about thoughts is that we can have a lot of them. Off hand there seems to be no boundary on the number of different kinds of

29 28 thoughts that one might have. In much the same way it seems there are an unlimited number of different kinds of concepts one might have. It is unreasonable to say that we come prepackaged with all of these concepts. What is more reasonable is that new concepts are constructed out of old concepts. The problem for inferential-role semantics is explaining how two or more concepts, with different inferential roles, can combine to make a new concept with its own inferential role. What is particularly difficult is that many seemingly compositional concepts do not have an inferential role that looks much like the inferential role of either of the concepts from which it was composed. The issue here is not so much that that there are not relevant inferences in the compositional concept. Rather it is coming up with a principled way to decide which inferences are going to be used from the composing concepts and how they will be combined. A look ahead This dissertation can be seen as defending two basic claims. 1. Psychological theories of conceptual structure are better theories when cast under the inferential model than when cast under the containment model. 2. Inferential-role semantics is one component of a complete theory of conceptual content. Chapter 2 is dedicated to defending the first claim. I will consider several theories of conceptual structure originally designed under the containment model. With some minimal tweaking these theories can be augmented to fit the inferential model. Doing this not only makes the motivations for the theories stronger, but it can also alleviate problems which arise for the theories in their original formulations. Chapter 3 begins the defense of the second claim. In this chapter I show that using insights from a variety of other theories to constrain the definition of conceptual role solves the problem of plentitude.

30 29 Chapter 4 continues the defense of the second claim, by defending inferential-role semantics from the problem of holism. In this chapter I argue that although concepts are fundamentally holistic, it nevertheless possible for individuals to share concepts. Chapter 5 finishes the defense of the second claim, by showing how concepts compose to make new concepts. In this chapter I argue that an adequate theory of reasoning makes it clear how the inferential role of one concept will compose with the inferential role of a second concept.

31 30 Chapter 2 IN DEFENSE OF THE INFERENTIAL MODEL In the previous chapter I introduced the inferential model of concepts and contrasted it with the containment model. In this chapter I will defend the claim that, for the purposes of psychology theories cast under the inferential model are better than theories cast under the containment model. The The idea is not to defend a particular theory of concepts, but rather to show that theories constructed under the inferential model fair better than similar theories constructed under the containment model. To make this argument I will consider several prominent theories of concepts. For each theory I will first lay out what it looks like in its original, containment model, description. I will then show how to modify the theory to fit the inferential model. Finally, I will demonstrate the advantages of the modified theory. This chapter is comprised of four sections. Section 2.1 discusses the classical theory of concepts. First, I give a detailed account of the classical theory as constructed under the containment model. I then show how to modify the classical theory to fit the inferential model. I conclude the section by discussing the advantages of the modified theory. Sections 2.2, 2.3, and 2.4 consider the prototype, exemplar, and dual theories of concepts respectively. The structure of these sections is otherwise identical to that of Section 2.1. Finally, Section 2.5 demonstrates some of the general advantages of the inferential model. 2.1 The Classical Theory of Concepts Most philosophers are familiar with the classical theory of concepts. In its most typical formulation the classical theory says that a concept is composed of the set of necessary and sufficient conditions required for application of the concept. For example, the

32 31 concept BACHELOR might be composed of three conditions; adult, unmarried, and male. Other formulations of the theory state that a concept is a mental representation that encodes a definition or that a concept is a list of essential characteristics. In each formulation, conditions, definitions, or characteristics are treated as proper parts of a concept. Thus, it is reasonable to say that these formulations of the classical theory assume the containment model. In the first part of this section I will lay out the classical theory as it is formulated under the containment model and list some of its advantages. In the second part I will show how the classical theory can be modified to fit the inferential model and discuss the advantages of this modification. The classical theory under the containment model The classical theory has been the dominant theory, in one guise or another, through much of the history of philosophy. The view still lies hidden in the background of a good deal of contemporary philosophy. For instance, much of the work done on the Gettier problem in epistemology is an attempt to find the fourth condition to add to justified true belief as an analysis of knowledge. In general, any philosopher doing classical conceptual analysis is at least implicitly adopting the classical theory for some concepts. The large role that the classical theory has played in philosophy is enough of a reason to explore the theory. However, my reasons for looking at the classical theory here are 1. it is simple, 2. it is well known, and 3. it is clear that the classical theory is cast under the containment model.^ What I will now do is go through some of the advantages of the classical theory to point out both why it was such an appealing theory and what more recent theories have to accomplish to compete with the classical do not mean to imply that everyone that has given a theory similar to the classical theory has done so under the containment model. I only mean that the common formulation of the classical theory - concepts are sets of necessary and sufficient conditions - is a theory which falls under the containment model. For instance, one could read Peacocke (1992) as developing the classical theory under the inferential model.

33 32 theory. I will then turn to showing how the arguments supporting the classical theory are made better when the theory is modified to fit the inferential model. The basic intuition behind the classical view is easy to see. There is something it is for an object to satisfy the concept TRIANGLE.^ If an object is a closed figure with three sides, then it is a triangle. On the other hand, if an object is an open figure or has 4 sides then it is not a triangle. Satisfying the concept TRIANGLE just is to satisfy the necessary and sufficient conditions of triangle. The classical theory fits nicely with the means by which we typically communicate concepts to one another. When asked to describe a concept one typically lists some conditions which need to be satisfied for its application. For example, one might describe an airplane as a vehicle with fixed wings and a propulsion system that allows it to move through the air. This looks roughly like the set of necessary and sufiicient conditions for the application of AIRPLANE. Possibly the most appealing feature of the classical theory is its simplicity. The entire theory can be stated in the single sentence, A concept is composed of the set of necessary and sufficient conditions required for application of the concept. Philosophers have a good grip on what necessary and sufficient conditions are, even if we cannot always find them for the concepts in which we are most interested. Likewise, psychologists have little trouble understanding how a concept could be represented as a definition or list of necessary and sufficient conditions. The classical theory also has a good deal of explanatory power. Philosophers are concerned with issues regarding the reference of concepts and epistemological questions concerning when an agent is justified in applying a concept to an object. According to the classical theory, a concept refers to all the things which satisfy the necessary and sufficient conditions of the concept. An adequate theory of reference will still need to explain what it means for a condition to be satisfied, but this is plausibly an easier problem to solve. By adopting the classical theory we also get a ^Recall that the term object refers to anything too which concepts might apply.

34 33 fairly simple analysis of when an agent is justified in her application of a concept. For the classical theory, an agent is justified in believing that C applies to an object o if she is justified in believing that each of the necessary and sufficient conditions which compose C are met by o. Concepts play a role in a number of psychological theories, and a theory of concepts which fits easily into these other psychological theories is exceptionally useful. For instance, one psychological issue intimately tied to concepts is categorization. Categorization is the psychological term used for a person's ability to group objects together. More precisely, it is the psychological process by which an agent applies a concept to an object. According to the classical theory this is accomplished quite easily. To apply a particular concept to an object an agent only needs to judge that each of the concept's necessary and sufficient conditions holds of the object. The classical theory does such a nice job of explaining categorization that it may not look like anything needed explaining in the first place. Another challenge for psychologists is determining the process of concept acquisition. Once again, the classical theory has an easy explanation. A person learns a new concept by having a mental representation which groups together a set of necessary and sufficient conditions. For example, to acquire BACHELOR an agent need only generate a mental representation composed of the conditions is an adult male and is unmarried. Having shown some of the advantages of the classical theory, I now want to turn to modifying it to fit the inferential model. What I will show is that the modified theory either retains or improves upon the advantages of the classical theory. The classic-inferential theory Although the classical theory has traditionally been cast under the containment model, it does not have to be. I now want to turn to the classic-inferential the

35 34 ory, a modification of the classical theory designed to fit the inferential model. Recall that the inferential model states that the functional role of a concept, C, consists of a privileged set of inferential connections between C and other concepts. I now want to suggest that the classical theory is best seen as an attempt to determine which inferential connections are privileged. Under the containment model the classical theory states that a concept is composed of the set of necessary and sufficient conditions that must be satisfied to apply the concept. If the satisfaction of a condition is necessary for the application of a concept, then the application of the concept entails the satisfaction of the condition. Along the same lines, if the satisfaction of a set of conditions is sufficient for the application of a concept, then satisfaction of the set of conditions entails that the concept is applicable. These entailment relations are the key to the classic-inferential theory. The classic-inferential theory proposes that the inferential connections that make up the inferential role of C are entailment relations between C and other concepts. Each condition which composes the necessary and sufficient conditions for C will correspond to some other concept, D, and there will be entailment relations between C and D. For example, is a bachelor ^ entails x is unmarried^ and it entails ^ x is male. ^ Likewise, ^x is unmarried and male^ entails is a bachelor. ^ Thus, there are entailment relations from BACHE LOR to MALE, from BACHELOR to UNMARRIED, and from the conjunction (MALE and UNMARRIED) to BACHELOR. Each of these is an inferential connection or, in other words, a disposition to make the following inferences: 1. From is a bachelor^ infer ^x is unmarried^. 2. From is a bachelor^ infer ^x is male^. 3. From ^x is male and x is unmarried^ infer Tx is a bachelor^. We can now see the major difference between the classical theory as characterized under the containment model and the classic-inferential theory. In the classical theory

36 35 as characterized under the containment model, a concept literally contains a list of conditions which are mutually necessary and jointly sufficient for the concept's application. The classic-inferential theory does away with conditions completely and simply links concepts via entailment relations. Having laid out how one would modify the classical theory to fit the inferential model, I now want turn to the some of the advantages of this modification. The classic-inferential theory has all the advantages of the classical theory as well as a few of its own. Like the classical theory, the classic-inferential theory is very simple and both philosophers and psychologists have an even better grip on entailment than they do on necessary and sufficient conditions. Recall that categorization is the psychologists term for concept application. For the classic-inferential theory, categorization is just an inference. Suppose C is a concept, Di... Dn are concepts representing the necessary and sufficient conditions of C, and o is an object. Since Di... Dn are the necessary and sufficient conditions of C, ^D-ixA...ADnX^ entails ^Cx}. Therefore, if an agent beheves DioA... AD O, then she can infer Co. It is precisely these kinds of inferences that account for categorization. Furthermore, since any complete theory of psychology has to account for inference anyway, the classic-inferential theory actually offers a more parsimonious explanation of categorization than is offered by the classical theory alone. Concept acquisition is also easily explained by classic-inferential theory. To acquire a new concept, C, an agent forms connections between a new mental symbol, V?, and other preexisting mental symbols, pi... p, where pi... pn correspond to the concepts 1) whose application is entailed by the application of C and 2) which jointly entail Cs application. The second clause is important for distinguishing a concept from its subcategories. For example, it is a necessary condition of something's being a square that it have four sides and that it have four right angles. However, these conditions are both necessary and sufficient for a rectangle. So if C plays a role in an inference from ^x has four sides and four right angles^ to ^Cx'^, then the concept is

37 36 of a rectangle not a square. The problem of reference for classic-inferential theory is handled essentially as it is for standard classical theory. If ^Dix A... A entails Cx, then C refers to any X for which a belief in ^Dix A... A Dn^ would be true. Likewise, an agent is justified in believing Cx just in case she is justified in believing ^DiX f\... f\. The classicinferential theory's approach to justification is, in fact, more elegant than the classical theories. Epistemology is typically concerned with the justification of beliefs, not the justification of concept application. Under the classic-inferential theory the structure of a concept just is a set of reason schemas for moving from one belief to another. No additional structure is needed to understand how a belief in the application of a concept is justified. The classical theory is a well known and relatively simple theory of concepts. These qualities make it a useful theory to demonstrate how we might modify a theory to fit the inferential model. However, because the classical theory is simple the advantages of the classic-inferential theory over the classical theory are not very dramatic. In the next section I will consider a more complicated theory of concepts, prototype theory. Modifying prototype theory to fit the inferential model is much more difficult than modifying the classical theory, but the payoffs are higher. 2.2 Prototype Theory During the 1970's an alternative view of concepts came on the scene. Hilary Putnam suggested that concepts are structured statistically rather than definitionally. On Putnam's view a concept is roughly the set of characteristics commonly (but not always) associated with the concept. Consider, for example, the concept LEMON: "To say that something is a lemon... is to say that it belongs to a natural kind whose normal members have certain properties; but not to say that it necessarily has those properties itself" (Putnam, 1970, p. 189).

38 37 Around the same time psychologists took note of a growing body of evidence pointing towards a statistical structure to concepts. This body of evidence, called typicality effects, is focused on the finding that subjects will regard some features or instances of a concept as more typical than others (Rosch, 1973b; Rosch & Mervis, 1975; Mervis, Catlin, & Rosch, 1976). A number of effects, such as the speed and accuracy of categorization, vary with how typical a subject views a feature or instance of a concept (Smith, Shoben, Sz Rips, 1974). Rosch (1973a) and later Rosch and Mervis (1975) were the first to develop a Putnamesque theory as an explanation for typicality effects. Rosch's work led to two theories of concepts called prototype theory and exemplar theory. According to prototype theory, a concept is a list of typical features; while according to exemplar theory a concept is composed of representations of its most typical instances (Medin Sz Schaffer, 1978; Nosofsky, 1986). In this section, I will discuss prototype theory and how to augment it to fit inferential model. Prototype theory under the containment model As the name suggests, prototype theory claims that a concept is a prototype. Exactly what constitutes a prototype depends upon the particular theory, but in its weakest form, a prototype is simply a collection of features (or properties) that are typical of instances of the concept. Thus, the prototype for BIRD might include: {feathers, wings, beak, sings}. In some ways, this is similar to the classical theory. In both theories, a concept is a list of features/conditions to be satisfied by instances of the concept. The difference is in how these features are selected. According to prototype theory, an agent will categorize an object under BIRD precisely to the degree that the object is similar to (has the same features as) the prototype. An object that has feathers, wings, a beak, and sings is almost certainly a bird, while an object that only has wings and sings is only probably a bird. In other words, none of the features that compose the prototype are necessary to apply the concept. Most versions of prototype

39 38 theory also include some kind of weight that is associated with each feature (Smith, Osherson, Rips, &: Keane, 1988; Hampton, 1995). These weights are intended to reflect exactly how typical a feature is of a given concept. BIRD, for instance, may have a greater weight associated with feathered than with sings. The primary motivation for prototype theory has been its ability to explain typicality effects. To find typicality effects, subjects are first asked to rank how typical a feature or instance is of a given concept. For instance, a subject may be asked to rank, on a 1 to 10 scale, how typical the feature green is of the concept APPLE. Presumably, green will be ranked above yellow but below red. Once the rankings have been made, a separate task is used to look for an effect which corresponds to the rankings. Typicality ratings are quite similar across subjects (though see Barsalou (1987), for some evidence to the contrary) and can be demonstrated even for concepts for which the necessary and sufficient conditions can be made explicit. As an illustration, a whole number not divisible by 2 constitutes the necessary and sufficient conditions for ODD NUMBER. Despite there being no ambiguity in whether something fits these conditions, subjects happily rate 7 as a better example of an odd number than 91 (Armstrong, Gleitman, & Gleitman, 1983). One might be tempted to think that a subject's ability to rank instances of a concept as more or less typical might have little to do with the actual structure of a concept. But the influence of typicality can be seen in more than just a subject's ratings. If a subject is asked to judge whether a concept, C, applies to some object o, both the response time and the chance of error are correlated with how typical the subject would rate o as an instance of C (Rosch, 1973b; Smith et al., 1974). That is to say, a subject is likely to judge o as C both faster and with a reduced chance of error the more typical a is of C. Typicality ratings can also be correlated with biases in probabilistic reasoning (Sloman, 1993). Our use of natural language can also be influenced by typicality. If one is willing to say "o is mostly C" then the typicality rating of o as a C is lower than something

40 39 for which the subject would not use mostly. Rosch gives the example, "It is correct to say that a penguin is technically a bird but not that a robin is technically a bird, because a robin is more than just technically a bird; it is a real bird, a bird par excellence" (Rosch, 1978, p. 39). In order to reconstruct prototype theory under the inferential model, it will be worthwhile to consider a specific example of prototype theory. Smith et al. (1988) present one of the most complete versions of the theory. They say, "In our view, a prototype is a prestored representation of the usual [features] associated with the concept's instances" (Smith et al., 1988, p. 487). On this view, a feature has four parts: an attribute, a value, and two numbers. An attribute names the class to which the feature belongs. Examples of attributes might be color, shape, and taste. Paired with each attribute is a value. A value is a specific instance of a given attribute. Red, round, and sweet would be possible values corresponding to the attributes color, shape, and taste. A feature then is an ordered pair consisting of an attribute and a value. An example may help to clarify the view. A prototype for the concept APPLE would be a list of (attribute, value) pairs such as: (color, red) (color, green) (shape, round) (taste, sweet) For each attribute and value, there is also a number that roughly represents how important the attribute or value is to the concept. For attributes, this number represents the diagnosticity of the attribute. Diagnosticity reflects how useful the attribute is in judging whether the concept applies to an object. For the concept APPLE, taste and shape might have high diagnosticity, while smell might not. A value, on the other hand, has a degree of salience. Smith et al. do not explicitly state what they

41 40 take the sahence of a value to be. As examples, they suggest that the red in APPLE is more salient than the round in APPLE and it is also more salient than the red in BRICK. My interpretation of salience is that it represents how typical a feature is of the objects that satisfy the concept. This interpretation makes it clear why salience is different from diagnosticity. Knowing that an object is red is not very helpful in determining that the object is an apple. However, knowing that an object is an apple strongly suggests that the object is red. It is clear from their description that Smith et al. are committed to the containment model. For them, a concept is a complex structure consisting of a number of proper parts, features, which are, themselves, composed of more proper parts, attributes and values. This places a heavy emphasis on the structure of concepts as opposed to the functional role of concepts. Furthermore, there is no mention of how concepts are related to one another. Having laid out the prototype theory, I now want to show how it can be modified to fit the inferential model. Among other things, it will turn out that the modified theory is significantly simpler than the theory proposed by Smith ct al. Prototype-inferential theory As a first approximation, we can augment prototype theory to fit the inferential model simply by changing each feature to a concept. Let's call the resulting theory the prototype-inferential theory. According to the prototype-inferential theory a concept, C, has inferential connections to the concepts representing C's typical features. This would suggest the following definition of the structure of a concept: Definition 2.1. The conceptual structure of a concept, C, with typical features,... F, is the set of inferential connections that link C and one or more Fj.

42 41 The problem with Definition 2.1 is that there are an infinite number of inferences which will token C and one or more of Cs typical features. Let o be an object and suppose an agent forms the belief on grounds that are independent from Fi... Fn- For each Fi, she can infer any of the following ^FiO^, ^FiO V Fi+io\ or ^Fioy Gx\ The first two inferences seem fine. The third, however, has a free variable that could be substituted with anything. Although it is an inference which tokens both C and some of Cs typical features, it is not an inference prototype theory would want to include in the inferential role of C. The obvious solution to this problem is to limit the inferences in the inferential role to those that token only C and one or more of the F^. Modifying Definition 2.1 to reflect this suggestion results in the follow improved definition: Definition 2.2. The conceptual structure of a concept, C, with typical features Fi... Fn, is the set of inferential connections that link C and only one or more Fj. One striking difference between modifying prototype theory to fit the inferential model and doing the same for the classical theory is that Co^ does not necessarily provide a conclusive reason for any Because features are merely typical of a concept, it is possible to defeat an inference from an instance of the concept to an instance of its features. The second and more difficult step in changing prototype theory to the inferential model is dealing with the weights that are associated with the features. It seems clear that one of the weights associated with Fj in prototype theory ought to be related to the strength of Cx as a reason for FiX in the prototype-inferential theory. What is less clear is how to move from a belief in FiX to Cx. To determine this we need to look more closely at how weights are meant to be used in prototype theory. Smith et al. provide two numbers here which we might want to associate with reason strength. Recall that diagnosticity reflects how useful an attribute is in judging

43 42 whether a concept applies to an object, while salience represents how typical a feature is of the objects that satisfy the concept. Of these two numbers, the diagnosticity seems to more closely capture the strength of a reason from FiX to Cx. If an attribute has a high diagnosticity then, presumably, the presence of that attribute in o would give an agent a better reason for believing Co than the presence of an attribute with a low diagnosticity. The strength of the reason from F^x to Cx, cannot be related only to diagnosticity. Consider the concept APPLE again. Color may have a high diagnosticity for APPLE. However, believing ^o is red^ (along with some other beliefs) gives one a stronger reason for thinking is an apple^ than believing ^o is green^. If is red^ and ^o is green^ give reasons of different strength for ^o is an apple^ then the salience must also be related to the reason strength from FiX to Cx. At this point it might be useful to consider why Smith et al. give properties both an attribute and a value. Their explanation is that the attribute is needed for an agent to know how to compare two values. For example, an agent needs a way of knowing that GREEN means NOT BLUE. Each attribute can only be filled by one value at a time. Therefore, if (color, green) is a feature of an object, then the agent knows that (color, red) is not. All of this seems overly complicated. More importantly, though, it is inaccurate. Consider the color of an apple. That an object is red, round, and smooth is a reason to think that it is an apple. That an object is green, round, and smooth, is a weaker reason for thinking that it is an apple because most apples are red and because lots of other fruits are green. For the concept APPLE, color has a lower diagnosticity when the color is green and a higher diagnosticity when the color is red. It seems then, that diagnosticity is not really a function of the attribute, but a function of the value. The "attributes" in Smith et al.'s theory are playing two roles. The first is to keep track of how useful the property is in determining whether the concept can be applied to an object, (i.e., the feature's diagnosticity). The second role is to classify two features (e.g., red and green) as mutually incompatible. We have seen

44 43 that diagnosticity is really a function of values, not attributes. Now let's tackle the second role an attribute is to play. Suppose an agent knows that o is smooth, round and purple. Being smooth and round is a reason for thinking that o is an apple. However, being purple should be a reason for thinking that o is not an apple. However, to get to this conclusion an agent needs a way of moving from o's being purple to its not being red. Smith et al. handle this by having the feature contain the information that red is a color. Since, purple is a different color and different values of the same attribute are always mutually incompatible, o cannot be red if it is purple. On the inferential model, this is completely unnecessary. An obvious aspect of the concept RED is that it is a color. And an obvious aspect of the concept COLOR is that if something is one color, then it is not another color. All that is really needed is an inferential connection from APPLE to RED. The inferential connections between PURPLE, RED and COLOR already build in that if something is purple, it is not red. By modifying prototype theory to the prototype-inferential theory we see that attributes are not needed to play either of the roles for which Smith et al. proposed them. Furthermore, features no longer have internal structure as they did in prototype theory. This lack of internal structure makes it more obvious that the features of one concept are just other concepts. Smith et al. do have one important insight. There does seem to be a difference between the diagnosticity of a feature and its salience. There are cases where a feature can be very salient for a concept, while not necessarily being particularly useful in applying the concept to an object. For example, one of the salient properties of maple leaves is that they are green. However, most leaves and plants are green, so green may have very little diagnostic value. Smith et al. say the following about salience; When asked to verify that a property is true of a particular concept, people respond faster to properties that have previously been rated as more related or associated to the concept than to those rated less related (e.g.. Glass & Holyoak, 1975). Thus, people are faster at deciding that apples are red than that apples are round, suggesting that red is more

45 44 salient than round in the prototype for apple. (Smith et al., 1988, p. 487) In this passage they are suggesting that two things determine the salience of a feature: the subjective frequency with which the value occurs in instances of the concept and the perceptibility of the value. If there is a difference between salience and diagnosticity, then how would that be represented under the inferential model? In prototype theory, diagnosticity determines how one moves from features to application of the concept. In the prototypeinferential theory this will be reflected in the reason strengths for inferences from (sets of) features to concepts. But one can also make inferences from a concept to a feature, and this is where salience enters the picture. Salient features are just those which can be inferred easily from the application of the concept. In many cases features which have a high salience also have a high diagnosticity. But in some cases, (e.g., the greenness of maple leaves) the diagnosticity is much lower than the salience. To say that the salience and diagnosticity of prototype theory are related to reason strength in the prototype-inferential theory is a little unclear. I do not mean to suggest that there is a function which will convert salience and diagnosticity into an appropriate representation of reason strengths. Smith et al. have psychological evidence for two values. However, when designing their experiments they had prototype theory in mind, not the prototype-inferential theory. The values they get for salience and diagnosticity are influenced by the reason strengths, but they may not be the only things influencing those values. I now want to consider the advantages of the prototype-inferential theory. As with the classical theory, prototype theory's advantages come in two forms: psychological advantages and philosophical advantages. The first thing to recall is that prototype theory was intended as a response to classical theory. Classical theory got into trouble because there just do not seem to be necessary and sufficient conditions for most concepts. Prototype theory does not require necessary and sufficient conditions for a

46 45 concept, and neither does the prototype-inferential theory. The prototype-inferential theory says that the functional role of a concept is the set of inferential connections which satisfy Definition 2.2. Neither individual features nor sets of them need to be necessary and/or sufficient to satisfy this constraint. By building concepts out of inferential connections, the prototype-inferential theory also has an easy time explaining much of the psychological evidence that motivated prototype theory in the first place. First of all, prototype theory has to posit some kind of psychological process whereby a concept's features can be extracted and manipulated from the concept. In the prototype-inferential theory this is already handled by adopting a theory of reasoning. A theory of reasoning provides some very powerful explanatory tools for dealing with typicality effects. For example, the reason a subject is more likely to guess that an apple is red than to guess that it is green is that l^x is an apple^ is a stronger reason for '^x is red ^ than it is for is green^. Each of these inferences counts as a defeater for the other, but since the first inference is stronger, it ultimately defeats the second. The prototype-inferential theory is also simpler than prototype theory. According to prototype theory, a concept is a list of typical features. Each feature is an (attribute, value) pair and associated with each member of the pair is a diagnosticity or salience. According to the prototype-inferential theory, however, there are concepts, inferential connections between the concepts, and reason strengths. These three items not only capture all of the important elements of prototype theory, they also capture facts about concepts that are not handled by prototype theory. For example, the concept RED presumably bears some relationship to the concept APPLE. Prototype theory, however, only discusses a relationship between the feature red and the concept APPLE. Exactly how features are connected to their corresponding concepts is still in need of explaining. Although Smith et al. present one of the most complete versions of prototype theory, it is not the only version on the market. I think it is clear that their version

47 46 benefits greatly when reconstructed under the inferential model. The basic techniques I have used to modify Smith et al.'s version of prototype theory to the inferential model could be applied to other versions as well and doing so would produce theories that have many of the same advantages. 2.3 The Exemplar Theory Exemplar theory is a close cousin of prototype theory. Like prototype theory, exemplar theory suggests that concepts are structured around typicality. Unlike prototype theory, however, exemplar theory does not suggest concepts are structured as sets of features. Instead, exemplar theory claims that a concept is composed of its most typical instances. More precisely, exemplar theory states that a concept is a collection of one or several mental representations of specific examples, or exemplars, of the concept. These exemplars are meant to be representative of the whole group. For example, a concept like BIRD might contain mental representations of a sparrow, a dove, and a hawk. To determine if a target is an instance of BIRD one compares the mental representation of the target to each of BIRD'S exemplars. If the target is sufficiently similar to the sparrow, dove or hawk representations, then the target is classified as a bird. The example above shows how exemplar theory can explain categorization and this has been the primary motivation for suggesting exemplar theory. Rarely do proponents of exemplar theory go beyond categorization, preferring to either remain silent or to suggest a dual theory of concepts. Because dual theories of concepts are discussed in the next section, I will take exemplar theory to be a stand alone theory here. The first question to be settled in exemplar theory is how abstract an exemplar representation can be. Nosofsky and Zaki (2000), for example, suggest "People represent categories by storing individual members or exemplars of a category as separate

48 47 traces..."(nosofsky & Zaki, 2000, p. 924). "Individual members" suggests a representation of a specific token. Smith and Medin (1981), on the other hand, offer a different account of exemplars - "The representation of a concept consists of separate descriptions of some of its exemplars (either instances or subsets)" (p. 208). A subset is more abstract than a representation of a specific token, but it is still, properly speaking, an instance. For example, dog is a subset of ANIMAL while Rex is a token of ANIMAL, but both are instances of ANIMAL. We can think of exemplars as being defined recursively in Smith and Medin's view. A subset can be defined recursively as a mental representation which is itself composed of mental representations of tokens or other subsets. The base cases in this recursive definition are the representations of specific tokens (henceforth, I will call these token-representations). Exemplar theory is importantly different from prototype theory, where the focus is on the most common features. For example, fur is a common feature of ANIMAL. In prototype theory this feature would appear under the prototype for ANIMAL along with some weighting to indicate how typical it is. In exemplar theory fur would never appear directly in ANIMAL. In order to get FUR from ANIMAL an agent would have to recognize that most of ANIMAL'S exemplars have fur. Suppose dogs, cats, birds, and rabbits were the subsets which composed ANIMAL. Each of these subsets might be composed of token-representations (e.g. the family dog). Since 3 of the 4 subsets have token-representations which have fur, fur would be recognized as a common feature of animals. But this requires descending a potentially long series of subsets to get to the token-representations.^ There are several versions of the exemplar theory, but they are largely derived from Medin and Schaffer's (1978) Context Model. I will be looking at adaptations of the context model from Smith and Medin (1981); Nosofsky (1986); Nosofsky and ^This points to one processing difference between the prototype theory and the exemplar theory. It should take longer to determine if a particular feature is common in a high level concept than a low level concept for exemplar theory. But in prototype theory the time should be the same.

49 48 Zaki (2000). The basic idea in in Smith & Medin is that an agent will apply a concept to a target if the target is similar to several of the concept's exemplars. They offer two specific processing rules for the this theory: Exemplar Rule 1 An entity x is categorized as an instance or subset of a concept Y if and only if x retrieves a critical number of F's exemplars before retrieving a critical number of exemplars from any contrasting concept. Exemplar Rule 2 The probability that entity x retrieves any specific exemplar is a direct function of the similarity of x and that exemplar (Smith & Medin, 1981). To see how these rules work, suppose an agent attempts to classify a target which is, in fact, a black chihuahua. The representation of the chihuahua causes exemplars to be retrieved based on the similarity of the chihuahua representation to the agent's stored exemplars. Suppose that the most similar exemplar is a representation of a dachshund, the second is a black rat, the third is a black terrier, and the fourth is a grey rat. Finally, suppose that the critical number of exemplars needed for all animal concepts is two. In this case the agent is more likely to apply DOG to the target than RAT because the dachshund and terrier exemplars are likely to be be retrieved first. But there is a chance that the agent will apply RAT. That the dachshund exemplar is more similar to the target than the black rat exemplar only makes it more likely that the dachshund exemplar will be retrieved first - it does not guarantee it. The critical number of exemplars mentioned in Exemplar Rule 1 can vary from one concept to another. At the minimum the critical number is just one, in which case the target is most likely to be classified by the exemplar it is most similar to. It is worth noting that several concepts may apply to a given target. For example, a particular shade of red may count as an exemplar for both RED and COLORED. On

50 49 the one hand, this is exactly what one would like from a theory of concepts. After all most targets do satisfy several concepts. On the other hand, exemplar theory owes an explanation of how we select among the multitude of available concepts. For instance, many things are physical objects, but it seems unlikely that the PHYSICAL- OBJECT concept is explicitly applied each time an agent attempts to categorize a physical object. Exemplar theory has many of the same advantages and disadvantages as prototype theory. Like prototype theory it can deal easily with most typicality effects. This is because exemplars are thought to be the most common or "prototypical" instance of the concept. Exemplar theory is particularly good at explaining why more typical targets of a concept are easier to categorize than those that are less typical. This is simply because more typical targets are more similar to the stored exemplars. Exemplar theory also explains why typical instances are generally listed as members of a category before less typical instances. The actual exemplars will be listed first followed by instances that are decreasing in similarity to the exemplars. Like prototype theory, exemplar theory was partially a reaction to the inadequacies of the classical theory. It is ironic then that one of exemplar theory's failings is an inability to specify necessary conditions. A target can be very similar to an exemplar, without satisfying any necessary conditions of the exemplar's parent concept. For example, a target which is a young male living alone in a messy apartment and dating several women might be very similar to an exemplar for BACHELOR. Nevertheless, such a person might still be married. It is quite possible that all of an agent's bachelor exemplars are more similar to the target than to any exemplar of a married man. Exemplar Rules 1 and 2 do not suggest any solution to this problem. A more serious problem for exemplar theory is that it requires a general theory for calculating the similarity between a target and an exemplar. Similarity is a notoriously difficult notion to make precise. As Goodman (1972) put it, "Similarity, ever ready to solve philosophical problems and overcome obstacles, is a pretender.

51 50 an imposter, a quack. It has, indeed, its place and its uses, but is more often found where it does not belong, professing powers it does not possess" (p. 437). However, exemplar theorists have offered some accounts for computing similarity between a target and an exemplar. Taking their guide from Rosch, Smith and Medin (1981) suggest "the similarity between a test instance [target] and an exemplar is a direct measure of shared features" (p. 212). Nosofsky (1986); Nosofsky and Zaki (2000) offer a somewhat more sophisticated account of similarity. On this account similarity is a function of the distance between the target and the exemplar in a multi-dimensional space. Each dimension in the space essentially represents a feature which may take on different values. Distance between a target and an exemplar is calculated using a city block metric. This means that the distance between the target and exemplar along one dimension is added to the distance along other dimensions. If t and e are the target and exemplar, then the distance between them, dte, is M dte ^ ^ m=l ^em where M is the number of dimensions, Xtm and Xem is the value of the target or exemplar in dimension m, and Wm is an attention weight associated with that dimension. The attention weight is intended to capture the fact that an agent may view some dimensions as more important than others at a particular time. For example, when determining the similarity of the observed chihuahua to the exemplar of a black rat, certain dimensions may not be attended to at all because they cannot be determined visually (e.g. whether the animal obeys verbal commands). The actual similarity of a target to an exemplar is a function of this distance. In particular, Nosofsky says that the similarity, Ste is captured by where c determines the rate at which similarity declines with distance.

52 51 In the case where features only take binary values (i.e. an exemplar has the feature or it doesn't), Nosofsky's and Smith and Medin's models are quite similar. However, Nosofsky ultimately allows more flexibility by allowing a target and an exemplar to differ in the degree to which they share a feature. In either case, similarity is ultimately judged by comparing featural representations. Since prototype theory also uses featural representations it is worth stressing exactly how exemplar theory differs from prototype theory. According to prototype theory a concept is a list or set of typical features along with some weightings which indicate how likely an instance of the concept is to have the feature or how likely a target having the feature is to be an instance of the concept. The featural representation then is a list of typical features of all instances. Although exemplar theory uses featural representations they are very different kinds of featural representations. According to exemplar theory a concept is a list or set of exemplars. Setting aside the case of subsets, each exemplar is a featural representation. But each exemplar is not a list o typical features, but rather it is a list of actual features of a typical instance. This results in at least 3 differences in the featural representation. First, exemplars will often have more features than prototypes. This is because all the features of the instance will be represented even if some of those features are not "typical". An instance of a table might be typical because of its size and shape even though the large scratch on it is atypical of tables in general. Second, there will be no weights associated with how typical a feature is. A feature is simply a part of the representation of an instance. Finally, the features in an exemplar representation are automatically consistent. For example, red and green might both be features listed in the prototype for APPLE, but a given exemplar will only have red or it will have green.

53 52 Exemplcir-inferential theory Recasting exemplar theory in the inferential model is not as straight forward as it is for the classical or prototype theories. According to the classical and prototype theories a concept is constructed from "conditions" or "features." It is fairly easy to see how these things relate to other concepts. For each condition or feature there is a corresponding concept. All that is then needed it to explain the inferential connections to those concepts. Unfortunately it doesn't seem plausible that there is a concept for every exemplar. Exemplars are representations of specific instances and it is not obvious that a specific instance is always related to a concept. However, it is still advantageous to view exemplar theory inferentially. According to exemplar theory a concept consists of a set of exemplars and an exemplar can either be a mental representation of a specific instance or of a subset. I'll deal with subsets first. Subsets, recall are abstractions. Some subsets of DOG might be GERMAN-SHEPHERD and LABRADOR. But each of these is its own abstract mental entity. Smith and Medin (1981) say, "If the exemplar is a subset, its representation can consist either of other exemplars, or of a description of the relevant properties... "(page 208). In either case a subset is effectively a concept. This is obvious if the subset consists of other exemplars since that is how exemplar theory defines concepts. If, on the other hand, the subset is a description of the relevant properties, then we have a concept similar to those in the classical or prototype theories. The nature of the inferences connecting an exemplar to its parent concept will depend on whether the exemplar is a subset, a property description or a tokenrepresentation. Suppose C is a concept, E is an exemplar of C, and t is a target. If E is a. subset, then by exemplar theory's own definition it is a concept. Furthermore it is the kind of concept such that if E is applied to t, then C can also be applied to t.

54 53 In the case where an exemplar theorist would say is a property description, we treat the application of E to t in precisely the same way as we would treat it in the inferential version of the classical or prototype theories. Whether the exemplar is a subset or a property description the believing of Et is a conclusive reason for Ct since Et is an example of C. So in the inferential model, the link between C and E when E is subset or property description is: is a conclusive reason to believe ^ Ct^. The strength of the belief in Ct is the same as the strength of the belief in Et. The tricky case is when the exemplar is a token-representation. The problem is that there are no obvious concepts that we can identify with token-representations. As a result we cannot apply a token-representation to a target. This means that we cannot make the same move for token-representations as we did for subsets and property descriptions. Exemplar theory relies on similarity to match a token-representation and a target. There are several avenues here for exemplar-inferential theory. First, we could cash out token-representations as highly specific prototypes. Then each tokenrepresentation would be a list of guaranteed features rather than typical features. We can then apply the work from the previous section on prototype theory to explain how to deal with token-representations inferentially. Unfortunately, there is a problem with this idea. Since E's features are guaranteed to be a part of anything to which we can apply E, Ex would be a conclusive reason for concluding x has those features. Should the target, t, be lacking one of those features, then there will be a conclusive reason for concluding -i Et^. In other words, if the target differs at all from the exemplar then an agent would have to infer that the exemplar does not apply. The only way to maintain the major insight of exemplar theory - that targets are compared to instances when applying concepts - is to treat judgments of similarity

55 54 as derived from a primitive inference rule: t is similar to E'^ is a defeasible reason to believe Ct^ with the strength of the reason dependent upon the degree of similarity. In general the degree of similarity between the target and the exemplar would be determined using something similar to Nosofsky's rule. However, shifting exemplar theory to the inferential model we find that an agent does not need to do a brute calculation of similarity. An agent may come to believe that t is similar to E for other reasons. For example, having never seen nor heard of chihuahuas, one might be told, "A chihuahua looks like a rat with big ears." Although no calculation of similarity was done, the agent still ends up with a belief that the target is similar to an exemplar. From here she might conclude that a chihuahua is a kind of rodent. 2.4 Dual Theories of Concepts Dual theories of concepts claim that concepts have two parts which are structured in different ways.^ There isn't one particular dual theory of concepts in psychology. Typically dual theories combine a stereotype theory with a classical theory or neoclassical theory. The attraction of combining theories is that the strengths of one theory can overcome the weaknesses of the other. For example, classical theory has a difficult time explaining why people categorize typical instances faster than less typical instances. Prototype theory, on the other hand, explains this quite easily. But prototype theory has difficulty explaining people's essentialist beliefs. For example, subjects will judge that something with bird DNA is a bird even if it has all the other features of a skunk. This is something that the classical theory has no trouble with. By combining the two theories both typicality effects and essentialism can be handled. ''Dual theories of concepts in psychology should not be confused with two factor theories proposed in the philosophical literature. A two factor theory of concepts claims that there is an internal and external component to the content of a concept. Dual theories are strictly internal.

56 55 It is rare in the literature for both halves of a dual theory to be laid out in full. In general, one half of the dual theory is defended in detail and the other theory is only hinted at. Given this, I won't cover any particular dual theory as I did with the prototype and exemplar theories. Rather I will make some general comments regarding how one might combine theories under the inferential model. Under the containment model there are two major drawbacks to any dual theory. The first is an appearance of being ad hoc. The structures and processing rules proposed by these theories are quite different. This problem is only exaggerated when so few proponents of dual theories offer more than hand waving towards one the two theories. The result of this is a half finished theory with several problems and the promise that the second half will fix problems without upsetting the positive work the first half has done. This points to the second difficulty in dual theories. Most dual theories do not explain how the two theories will interact. Consider, for example, a dual theory combining prototype theory with classical theory. In such a theory categorization is primarily handled by comparing the target to a prototype. In unusual cases or when there is time for more consideration, the agent consults the necessary and sufficient conditions. But this requires new processing rules governing the interplay between the prototype and the necessary and sufficient conditions. For example, when is a situation sufficiently unusual to require the agent to consult the necessary and sufficient conditions and how will conflicts be dealt with? Determining these rules isn't easy when the two theories involved have radically different structures and processing rules. These two difficulties are inherent in the attempt to combine two very different kinds of theories of conceptual structure. But viewing the theories under the inferential model provides tools for solving these problems more naturally. Before we can see how the problems can be solved, we must look at what dual theory would look like under inferential model. The first step is to reformulate each theory on its own, as we did for the classical and prototype theories. Once each theory has been

57 56 reformulated it is much easier to combine them. In reformulating any theory into the inferential model the general idea is to treat the processing rules of the original theory as determining which inferences get to factor into the conceptual role of a concept. Reformulating a dual theory can be viewed as simply extending the inferences which comprise the inferential role by allowing those inferences which would have been included under each theory individually. The first major advantage of a dual theory under the inferential model is that it provides a vehicle for explaining how the two theories will interact. Since the theories are being characterized inferentially, one's general theory of reasoning can be used to account for most of the interactions between the theories. For example, it was mentioned that a dual theory combing prototype theory and classical theory would be left needing to explain how categorization occurred when there was a conflict between how a target was categorized according to the prototype theory and how it was categorized according to the necessary and sufficient conditions. A dual theory under the inferential model can handle this situation just as it would for any other conflicting inferences. A target's having some of the prototypical features of the concept A, would provide a defeasible reason for concluding that the target is an A. Similarly, a target's satisfying the necessary and sufficient conditions of a concept, B, would provide conclusive (i.e. non-defeasible) reason for categorizing the target as a B. All else being equal, if an agent has a defeasible reason to classify a target under a concept A and a conclusive reason to classify the target under a conflicting concept, B, the agent will classify the target as a. B. Sometimes all things are not equal though. Suppose an agent draws a defeasible conclusion that a target is a robin based on the targets appearance. However, there is independent evidence that the target has pigeon DNA. We can imagine that having pigeon DNA counts as a conclusive reason to believe that something is not a robin. But suppose the evidence that the target has pigeon DNA is itself very weak. If the appearance of the target provides a stronger

58 57 reason for believing that the target is a robin than the independent evidence does that the target has pigeon DNA, then the target should be classified as a robin rather than a pigeon. And this result is exactly what we get in the inferential model. A conclusive argument is only as strong as the premises on which it is based. By converting the theories to the inferential model, this sort of case is handled automatically by the rules of inference already in play. But under the containment model it would be necessary to formulate special rules to deal with cases like this. Merely saying that the conceptual core (i.e. the necessary and sufficient conditions) always wins will not do, as this example shows. The preceding sections have focused on how specific theories of concepts can be made better by being modified to fit the inferential model. However, these advantages are specific to modifying the theories discussed. The same benefits may not be available after reconstructing other theories under the inferential model. In the next section I will consider some of the general advantages of the inferential model. 2.5 Conclusion The classical, prototype, and exemplar theories are representative examples of theories of concepts cast under the containment model. I have argued that these theories can be modified to fit the inferential model and that doing so makes them better theories. However, there are many other theories of concepts, and I have not given a general argument that all of them would benefit from the same modification. The inferential model does not solve many problems that are common to all theories of concepts. Rather, it provides tools for solving the specific problems confronting a given theory. In particular, the inferential model enables us to utilize our general theory of reasoning in developing a theory of concepts. In converting prototype theory to prototypeinferential theory, for instance, we saw that a theory of reasoning can be used to explain why a subject is more likely to guess that an apple is red than to guess it is

59 58 green. However, this specific problem does not come up for the classical theory so it cannot be considered a general advantage of the inferential model. For the most part, how a theory of reasoning will be useful depends on the theory of concepts being developed. However, this is not always the case and I will conclude this chapter by considering several general advantages of adopting the inferential model. The first advantage concerns the application of concepts to targets while the second concerns issues of parsimony in a general theory of mind. A common explanatory problem for theories of concept application is dealing with cases in which an agent has two concepts which seem to apply to a target, but those concepts are inconsistent with one another. For instance, seen from a distance a horse standing on a hill at night may look as much like a cow as a horse. However, an agent in this situation, can't apply both HORSE and COW to the object. On the inferential model, this situation results when an agent has reasons for believing Ho and reasons for believing Co. Since HORSE and COW are incompatible, Ho is a reason for ^Co and Co is a reason for ^Ho. These are cases of rebutting defeaters. Any theory of reasoning will have a solution for this kind of situation. According to Pollock (1995) if the agent has a stronger reason for believing Ho than for believing Co, then Ho defeats Co. If, on the other hand, the reason strengths for Ho and Co are of equal strength, then Ho and Co suffer from collective defeat and neither should be believed. I don't mean to profess that most theories of concepts can't deal with the application of conflicting concepts. It is such a basic issue that any reasonable theory of concepts will have a solution. However, any theory cast under the inferential model gets the solution for free. I take this to be an advantage of constructing theories of concepts under the inferential model. Another issue, frequently overlooked in developing a theory of concepts, is retracting the application of a concept. We are often in the position of having applied a concept to an object and then after further reasoning or acquiring new information, we find that we must unapply the concept. This situation can crop up for several

60 59 reasons. Suppose an agent applies C to o. One reason to unapply C is if, at a later time, the agent applies a new concept, H, to o and H is incompatible with C. Notice though, that applying H to o isn't enough to retract the application of C to o. The agent must also recognize that H is incompatible with C and go back to unapply C to o. Another case where an agent may need to unapply a concept is when she has retracted something that led her to apply the concept in the first place. To illustrate, suppose that an agent applies APPLE to o partially on the basis of o's being red. If she later learns that o was illuminated by red light, she no longer has a reason to think that o is red. If she does not have reason to believe that o is red, then she should also unapply APPLE. This example, is importantly different from the previous. In the previous case that o is i/ is a reason to think that o is not C. In the latter case, there is no reason to think that o is not an apple. Rather, the reason for thinking it is an apple has been removed. In other words, she ought to withhold judgment on the issue. Unapplying concepts is not often dealt with in theories of concepts. However, it is clear that it ought to be a fundamental part of any complete theory of concepts. One advantage of the inferential model is that the process by which a concept is unapplied comes free with a theory of defeasible reasoning. Any adequate theory of defeasible reasoning will include methods for retracting beliefs either because of stronger arguments for the negation of the belief or because the original argument for the belief has been undercut. On the inferential model, the application of C to o just is the formation of an argument for believing Co. Likewise, unapplying C to o just is defeating the argument for Co. This ability to utilize a general theory of reasoning to solve specific problems for one's theory of concepts also creates a more parsimonious theory of the mind as a whole. A complete theory of the mind requires both a theory of concepts and a general theory of reasoning. If one of these theories can be used to explain all or part of the other, then the overall theory of mind will be simpler. The inferential

61 60 model accomplishes this by enabling a theory of reasoning to be used in constructing a theory of concepts. As I mentioned before, the benefits of constructing a theory of concepts under the inferential model are largely specific to the theory. In this section, I have shown two of the general advantages of constructing a theory under the inferential model. Primarily, these advantages are created by the ability to use one's theory of reasoning while building the theory of concepts. The classical, prototype, and exemplar theories, discussed in the previous sections, are examples of how a theory can be improved when modified to fit the inferential model. I take these to be a good reason to think that the correct theory of concepts will fit the inferential model as well.

62 61 Chapter 3 INFERENTIAL-ROLE SEMANTICS The last chapter dealt primarily with the psychological structure of concepts. In particular I demonstrated how the inferential model can be used to strengthen theories of concepts originally formulated under the containment model. In this chapter I turn away from the psychological structure of concepts to look at a concept's content. I will be defending a version of inferential-role semantics. In the Section 3.1 I will lay out the simple version of inferential-role semantics. Not surprisingly, the simplest version of inferential-role semantics is not an adequate theory of conceptual content. This is primarily because it has the consequence that the content of any given concept is composed of an exceptionally large number of things. I call this the problem of plenitude and it is the topic of Section 3.. Section 3.3 considers several promising ways of handling this problem and shows how they fall short. Section 3.4 presents a new solution to the problem of plenitude. This solution is related to the prototypeinferential theory discussed in Chapter Inferential-Role Semantics: The Simple Version In its simplest form inferential-role semantics claims that the content of a concept is constituted by the role the concept plays in the mind. If we interpret "role" as entire causal role then this amounts to functionalism about content. Few, however, have been willing to say that a concept's entire causal role in the mind gets to count as part of its content. Consider, for example, a claustrophobic for whom merely reflecting on her concept CLOSET causes a great deal of anxiety. This is part of the causal role of CLOSET, but it would be odd to say that her anxiety is part of the content of CLOSET. Examples like this have persuaded most proponents of inferential-role semantics to

63 62 restrict conceptual content to the role a concept plays in reasoning. On a naturalistic account, the role that a concept plays in reasoning is just a subset of the concept's functional role. Limiting content to just inferential-role is a way of trimming out the seemingly irrelevant elements of a concept's total functional role. Though the simple version of inferential-role semantics says that a concept's content is its role in reasoning, in fact, most proponents of inferential-role semantics have taken it as a theory of the narrow content of a concept.^ The narrow content of a concept are those characteristics of content which are completely internal to the mind in which the concept is employed. Narrow content is contrasted with wide content which are those characteristics of content which are external to the mind in which the concept is employed. Putnam's famous Twin-earth examples can make this notion clearer. Imagine a planet which is molecule for molecule identical to this world, though in a different spatio-temporal location in the universe. The only difference between Earth and Twin-Earth is that on Twin-Earth what they call water is not H2O, but a slightly different molecule XYZ. Now consider Twin-Josh. Like me, Twin-Josh believes there is a lukewarm cup of coffee before him. In a very important way, Twin-Josh and I believe the same thing. There is a psychological similarity between us and that similarity is easily characterized by pointing to the psychological similarity of our concepts of coffee. The sense in which Twin-Josh and I have the same concept is the narrow content of my concept COFFEE. However, there is also an important way in which Twin-Josh and I believe something different. For me COF FEE is often tokened by the presence of H2O which has been passed through coffee grounds. For Twin-Josh COFFEE is often tokened by the presence of XYZ which has been passed through coffee grounds. Essentially my COFFEE concept refers to something different for me than it does for Twin-Josh. The sense in which Twin-Josh and I have a different concept of coffee is the wide content of the concept. Some reasons for thinking that inferential-role semantics is a theory of narrow ^See Harman (1987) an exception.

64 63 content were given in Chapter 1.3. To briefly summarize, inferential-role semantics is interested in inferential relationships that concepts have with other concepts. But these relationships are determined entirely by what is in the mind. It is, after all, minds which engage in inference and reasoning. So if we grant that there is narrow and wide content, it is reasonable to say that inferential-role semantics is an attempt to capture the narrow content. It is important to recognize that inferential-role semantics is not identical to the inferential model discussed in Chapter 2. The inferential model is a generalized model for the psychological structure of a concept. Inferential-role semantics is a theory of a concept's narrow content and how it comes to have that content. One can think of the inferential model as a theory of how concepts work while inferential-role semantics is a theory of semantics for concepts. Although the inferential model and inferential-role semantics fit very nicely together, they are not same nor does one entail the other. As a theory of psychological structure, the inferential model is intended to explain how the mind organizes and manipulates a particular class of representations. The adoption of the inferential model places constraints on how a mind can be built. It places constraints on what kinds of mental processes there can be and how those processes might be ordered. For example, it states that concepts have no internal structure - their role in computation is determined entirely by how they are connected to other concepts. Moving to specific theories which fall under the inferential model, we find even narrower constraints such as the relative speed of one process in comparison with another or why one kind of target would be easier to identify than another. Although narrow content is about something internal to the mind, that does not mean that it says anything about the structure of the mind. Consider, for example, a theory which said that the narrow content of a concept is determined by how the concept is causally connected to perceptual states (where perceptual states are strictly internal). This is completely compatible with a view which says that concepts are

65 64 computationally structured as prototypes in the inferential model. It is natural to think that the narrow content and the psychological structure of a concept will be related, but this is merely suggestive. 3,2 The Problem of Plenitude < A X < B ' > \ X /' / ^ > ' \[ / \ E, > V FIGURE 3.1. Graph of inferential role The simple version of inferential-role semantics claims that the content of a concept is determined by its entire inferential role. The first problem with the simple version is that the entire inferential role of a concept is tremendously large. To see this it will be useful to represent the inferential role of a concept graphically. In Figure 3.1, each concept is represented by a node in the graph. A concept's inferential role is represented by the lines connecting the concept to other concepts. These are the concept's inferential connections. Recall, that inferential connections were defined in Chapter 1.3 as follows: Inferential Connection: A concept A is inferentially connected to a concept 5, ^ o JB, for an agent s if either of the following conditions hold. 1. If s applies ^ to x, then s is disposed believe Bx on the basis of Ax (call these forwards inferential connections, Ao B) OR

66 65 \ B I FIGURE 3.2. Inferential role for one concept 2. If s has an interest in applying A to x, then s will adopt an interest in applying B to x for the purpose of believing Ax on the basis of Bx (call these backwards inferential connections, A*^B). In Figure 3.1, the concept C has four inferential connections {C o A,C o B,C o D,C o E} and D has three inferential connections {D o A, D o C, D o F}. Obviously, in a realistic agent there would be far more concepts than occur in this graph. Notice that in this graph it makes no sense to label the inferential connections because how we label them depends on the concepts in which we are interested. We can refine the graph to focus on just one concept as in Figure 3.2. With a focused graph we can label the inferential connections. Graphically, everything in Figure 3.2 goes in to determining the content of C. This would be fine if a graph like Figure 3.2 represented the inferential role of a realistic concept. Unfortunately, it does not. The inferential role of most concepts will be much much larger because a concept can play a role in an exceptionally large number of inferences. This can be easily seen by considering chains of reasoning. For example, I^BACHELORxl implies I^MALEA:,^ and I^MALEXL implies I^HAS-Y-CHROMOSOMEA;,^ so (^BACHELORA;! implies THAS-Y-CHROMOSOMEa;. ^ This means one of BACHELOR'S inferential connections is, (BACHELOR O HAS-Y-CHROMOSOME). In general, if Cx is a reason for Dx, Dx is a reason for Ex, and Ex is a reason for

67 66 FIGURE 3.3. Fx, then each of these yields an inferential connection between the concepts involved, {C o D, D o E, E o F}. However, given the definition of inferential connection, there will be more than just these three. Applying C to x disposes the agent to conclude Dx on the basis of Cx, and Dx disposes the agent to conclude Ex on the basis of Dx. But this means that applying Cx disposes the agent to conclude Ex on the basis of Cx. So we must include the inferential connection C o E. For similar reasons we must include C o F. Figure 3.3 shows the result with the bold hnes indicating C's inferential connections. This is one straightforward way of seeing that there will be many inferential connections for C. A variety of similar "tricks" make it clear that a concept could have as many inferential connections as the agent has other concepts.^ Tricks of reasoning are not the only way that a concept can have inferential connections that seem irrelevant to its narrow content. Consider the concept BACHELOR. Clearly, the inferential connections (BACHELOR O MALE) and (BACHELOR o UNMAR RIED) should be factored into a BACHELOR'S content. But consider (BACHELOR O MESSY). Knowing that someone is a bachelor is certainly a reason for thinking he is messy. However, it is a defeasible reason and not necessarily a very strong defeasible reason. The question is whether this kind of inferential connection should count as part of the content of BACHELOR. More is at stake in this decision than just our intuitions about what it means to be a bachelor. Defeasible inferences are more likely ^Compositional concepts make this problem even more significant. A concept may have an inferential connection to every concept of which it is a component. Compositionahty is the topic of Chapter 5 so I will set this aside here.

68 67 FIGURE 3.4. Inferential role of realistic concept to vary between one agent and another. If such inferences count toward the narrow content of a concept, then it will be less likely that people share concept's with the same narrow content. A theory with this implication is violating the publicity constraint. The publicity constraint is dealt with more fully in the next chapter but it is worth keeping in mind here. I call this the problem of plenitude. Figure 3.4 depicts only a small number of the inferential connections for a realistic concept. There are simply too many inferential connections in a concept's entire inferential role. If each of these connections factored into the concept's narrow content, then narrow content would cease to be a useful notion. What is needed is a way to trim the inferences which count towards the narrow content of a concept to something like those inside the bold line in Figure 3.4. Let's call the contentful role of a concept that portion of its inferential role which factors in determining the content of the concept. The simple version of inferential-role semantics simply equates contentful role with inferential role. The

69 68 problem of plenitude is the first serious hurdle to developing this theory. I say it is the first hurdle because, as we shall see in Chapters 4 and 5, the problem of plenitude must be solved before we can deal with holism and compositionality. 3.3 Restricting Contentful Role It is clear that a concept's contentful role cannot consist of its entire inferential role. What is needed is a way of limiting the set of inferential connections that are included in a concept's contentful role. This section will consider three possible solutions to the problem of plenitude. First, I consider restricting contentful role to only analytic inferential connections. Second, I consider restricting contentful role to unmediated inferential connections. Finally, I look at restricting contentful role to either forwards or backwards inferential connections. Each of suggestions ultimately falls short of solving the problem. In the next section I will present an alternative suggestion taking a guide from the prototype theory. Analytic inferential connections The the most obvious constraint, and the one which has been most often proposed in the literature, is that contentful role should be limited to analytic inferences. Traditionally a belief or statement is considered analytic if it is true in virtue of its meaning. Following a similar line we can say that an inference is analytic if the conclusion follows from the premises solely on the basis of the content of the premises and conclusion. Unfortunately, the preceding definition isn't helpful in the present situation. Our objective is to understand narrow content via analytic inferences but this is circular if we define an analytic inference in terms of content. What is needed is an analysis of analytic inference which does not, itself, make reference to content or meaning.

70 69 Traditionally, philosophers have been interested in the analytic because it was seen as a path to the a priori. Analytic statements were seen to be statements which were knowable independent of experience. One possibility would be to flip this around and cash out the analytic as what is knowable a priori. There is a large body of literature on the relationship between the analytic and the a priori, starting with Kant and moving through Quine's (1953,1960) objections to the analytic/synthetic distinction. However, there is a straight forward objection to defining the analytic as the a priori if we then want to define the contentful role of a concept in terms of its analytic inferences. There are two important observations here. First, we are interested in analytic inferences and not analytic statements. If the analytic is defined as the a priori then we need to determine which inferences are a priori. More precisely, we need a definition of a priori inferential connections. Inferential connections are more like schema for individual inferences than inferences themselves. Second, since the goal is to explain the narrow content of a concept, a priori inferential connections cannot themselves be cashed out in terms of content. The difficulty here is that it isn't clear what it could mean for an inference or inferential connection to be a priori. An a priori belief is one that is knowable independent of experience. An inference, on the other hand, is not something that is known, but something that is done. Similarly, inferential connections are roughly dispositions to draw inferences and this also isn't the kind of thing that is known. We might say that an a priori inference is one whose conclusion can be known independent of experience. However, this permits inferences which clearly are not what we would intuitively regard as analytic and restricts inferences which intuitively are analytic. As an example of the first case, from "George says that all bachelors are male," an agent can justifiably conclude that "all bachelors are male." This conclusion is knowable a priori, but the inference itself has nothing to do with the a prioricity of the conclusion. As an example of the second case, from '^BACHELORX^ an agent can conclude I^MALEX.^ But the conclusion, is not knowable a priori. It is

71 70 only a priori given that I^BACHELORX^ is already established. Even assuming the definition of an analytic inference could be worked out in a non-circular way, analyticity poses other problems when used to define contentful role. Here I use "analytic" in its intuitive philosophical sense. Even those who don't believe in an analytic/synthetic distinction can classify some inferences as "the kind that would count as analytic if there were such a thing" and "the kind that would count as synthetic if there were such a thing." For example, the inference from I^BACHELORa:^ to I^MALEa;,^ is the kind of inference which would be analytic if there were analytic inferences. If a theory of analyticity denied this, we could justifiably ask whether it was really a theory of analytic inference or if it was merely borrowing the term for some other purpose. Put another way, ANALYTIC is at least a fuzzy concept in so far as we can categorize many inferences or beliefs using it. Most of the debate over the analytic is whether that fuzzy concept can be made precise enough to do any interesting philosophical work. For our purposes, we only need to look at the fuzzy concept to see that it won't be useful. Restricting contentful role to only analytic inferences is both too restrictive and to permissive. That is, it rules out inferential connections which seem relevant to the content of a concept and allows inferential connections which ought not be relevant. For example, under any definition of analyticity it is not analytic that a bird has feathers. But the inference from I^BlRDx^ to I^FEATHEREDa;^ seems very relevant to the narrow content of BIRD. Feathers are one of the first attributes ascribed to an object once it is categorized as a bird. Having feathers is also a very strong indication that something is a bird. If someone thought "birds do not have feathers" it would be a strong indication that she does not attach the word "bird" to my concept BIRD. None of this means that having feathers is necessary for something to be a bird, but it seems relevant to the narrow content of BIRD. Restricting contentful role to only analytic inferences is also too permissive. There are a number of inferences which would traditionally be called analytic, but which

72 71 intuitively have nothing to do with the content of the concept. Consider an inference from I^BACHELORA;^ to '^BACHELOR-OR-PUMPKLNXJ This is an analytic inference which tokens BACHELOR but it doesn't seem to have any bearing on the content of BACHELOR. In fact, this is one of the kinds of inference which generates the problem of plenitude in the first place. Unmediated inferential connections Another plausible solution is to restrict contentful role to only the simple or what I will call the unmediated inferential connections. By "unmediated inferential connections" whose corresponding inferences would not require multiple steps. For example, there are no intermediate steps in inferring I^MALEX^ from I^BACHELORX. ^ An immediate advantage of this proposal is that it would eliminate inferential connections that were the result of chains of reasoning. In an example above we found that there was an inferential connection between BACHELOR and HAS-Y-CHROMOSOME. However, the inference from BACHELOR to I^HAS-Y-CHROMOSOMEXT requires an intermediate inference to I^MALEx.^ If only unmediated inferential connections were permitted (BACHELOR o MALE) would be part of the contentful role of BACHELOR but (BACHELOR O HAS-Y-CHROMOSOME) would not. The first problem with using unmediated inferential connections is that different agents may have different unmediated inferential connections while appearing to have the same narrow content. For one agent the inferential connection (BACHELOR O MALE) might be unmediated. For a different agent (BACHELOR o NOT-MALE) might be unmediated rather than (BACHELOR O MALE). Agents with different primitive inference rules might also have different unmediated inferential connections. For an agent lacking modus ponens it would take several steps to infer I^MALEX^ from

73 72 ^ BACHELORS J Below are the steps using modus ponens and using modus tollens. So agents constructed in different ways could have different unmediated inferences. Therefore, different inferential connections would count in the contentful role of their respective concepts. Another possible cause of differences in unmediated inferential connections is learning. It seems plausible that mediated inferential connections can become unmediated.for example it would be efficient for an agent that made the same multistep inference repeatedly to learn to skip the intermediate steps. Introspectively, this seems to be the case in ourselves. These examples are problematic because it seems implausible that agents with these differences would have different narrow content. (BACHELOR o MALE) is part of the contentful role of BACHELOR whether or not an agent can use modus ponens or modus tollens. As with trying to restrict contentful role to analytic inferential connections, restricting to unmediated inferential connections also leaves some inferential connections which seem irrelevant to the narrow content of a concept, (BACHELOR O BACHELOR-OR-PUMPKIN) is presumably an unmediated inferential connections. But, as noted above, this is the very sort of inferential connection which creates the problem of plenitude. Using modus ponens Using modus tollens BACHELORX MALES BACHELORX ^ MALEX BACHELORS MALEX BACHELOR^ -IMALEX => -IBACHELORX -I-IBACHELORX -I-IMALEX MALEX A final problem for unmediated inferential connections is that it is difficult to tell either via psychology or introspection whether an inference is actually unmediated. Many intermediate steps in our reasoning may be unconscious. Although it introspectively seems that I move directly from I^BACHELORX^ to I^MALEX^, it is en

74 73 tirely possible that there is an intermediate step through NOT-FEMALE that happens quickly and unconsciously. Forward and backwcird inferential connections Another thing that might be done to solve the problem of plenitude would be to limit contentful role to only forwards or only backwards inferential connections. This kind of idea is similar to those that say that a concept's content consists of its application conditions(peacocke, 1992). The application conditions of a concept are, roughly, its backwards inferential connections. The idea would be that what is important to the narrow content of a concept is how an agent determines that something is an instance of the concept. Similarly, limiting content to forward inferential connections, would be to say that what is important to the narrow content of a concept is what is implied by knowing that something is an instance of the concept. There are reasons for thinking that either of these strategies could be right. One reason for looking at forward connections is that concepts are largely useless without them. As Hume argued, the point of concepts is to generalize about the things to which they apply. Likewise, application conditions have also been seen as very important to the content of a concept. Clearly, a part of what makes it the case that we share concepts, is that we apply them to the same things. Radically different application conditions would mean radically different things that the concept would be applied to. I'm inclined to think that both forward and backward inferential connections are important to the narrow content of a concept. Consider an agent that had all the same backwards inferential connections to BACHELOR, but none of the same forward inferential connections. She would claim that an unmarried male is a BACHELOR but would not conclude that a bachelor is unmarried or a male. Reversing the example would give us an agent that agreed that bachelors were unmarried and male, but would not conclude that an unmarried male person was a bachelor. In both of these

75 74 examples, I am disinclined to say that the agent has the same concept I do. Even if we do limit contentful role to only forward or backward connections, we accomplish very little towards solving the problem of plenitude. The examples that established the problem in the first place were all cases of forwards inferential connections. Clearly, restricting contentful role to only the forward inferential connections does little good. But parallel cases can easily be created for backwards inferential connections. In order to solve the problem of plenitude we need a principle that picks out only a small number of inferential connections. Primarily this means finding a principle which is not susceptible to the kinds of tricks mentioned in Section 3.2. In the next section I will suggest that research in psychology may provide such a principle. 3.4 Prototype Theory and Inferential-Role Semantics In order to solve the problem of plenitude we need a principled way of narrowing a concept's inferential role to its contentful role. What I now want to argue is that a theory, not originally intended as a theory of inferential-role semantics, may offer the narrowing constraint we are looking for. This is the prototype theory discussed in Chapter 2. However, we will now be viewing it as a theory of conceptual content as opposed to a theory of conceptual structure. Philosophers have largely treated prototype theory as an alternative to inferentialrole semantics.^ I suspect this is because prototype theory was initially proposed under the containment model of conceptual structure. In Chapter 2 we saw that a better theory, the prototype-inferential theory, can be made by modifying prototype theory to fit the inferential model. Doing so makes it clear how the insights in prototype theory might be used to get the contentful role of a concept out of its ^Rey (1997) briefly considers using stereotype inferences as the important aspects of inferential role. He rejects the idea though. Fodor and Lepore (1992) in arguing against inferential-role semantics suggest that people are waiting for something like prototype theory to restrict the inferences.

76 75 inferential role. The moves necessary to change prototype theory into a narrowing constraint for inferential-role semantics are similar to the moves made in modifying prototype theory to fit the inferential model. There are, however, some important differences between prototype theory under the inferential model and using prototype theory to define conceptual role. The core thesis of prototype theory is that a concept is a representation of the typical features of the concept's instances (Rosch, 1978; Smith et al., 1988). Under the inferential model prototype-inferential theory amounts to the claim that the psychological structure of a concept consists of inferential connections to concepts representing its most typical features. But in using prototype theory to define contentful role, no claims are made about which inferential connections make up the psychological structure of a concept.^ In fact, it isn't even necessary that the correct account of psychological structure be a theory which fits the inferential model. For instance, one could consistently be a pure exemplar theorist (under the containment model) about psychological structure and still inferential-role semantics, restricted by prototype theory, best explains conceptual content. There is another important difference between prototype-inferential theory and using prototype theory in conjunction with inferential-role semantics. A theory of conceptual structure needs to be able to explain all of the psychologically interesting aspects of concepts. For example, the theory needs to be able to explain concept acquisition, how concepts change over time (if they change), categorization, etc.^ However, a theory of narrow content does not need to do any of these things in order to be a complete theory. All that is strictly needed is to explain the semantics a;spects of concepts which are strictly internal to the mind in which the concepts are ^See Chapter 1.1 for a discussion of the difference between psychological structure and content. ^Although concept acquisition is not discussed in this dissertation, the stage for it is set in Chapter 5 on compositionality. The ability to compose concepts is one, and likely the most important, method of acquiring new concepts. However, compositionahty is not all that is needed to explain concept acquisition. For instance, compositionality does not explain how we acquired our first concepts or why we form some concepts rather than others.