Cognitive Maps and the Language of Thought Michael Rescorla Forthcoming in The British Journal for the Philosophy of Science Abstract: Fodor advocates a view of cognitive processes as computations defined over the language of thought (or Mentalese). Even among those who endorse Mentalese, considerable controversy surrounds its representational format. What semantically relevant structure should scientific psychology attribute to Mentalese symbols? Researchers commonly emphasize logical structure, akin to that displayed by predicate calculus sentences. To counteract this tendency, I discuss computational models of navigation drawn from probabilistic robotics. These models involve computations defined over cognitive maps, which have geometric rather than logical structure. They thereby demonstrate the possibility of rational cognitive processes in an exclusively non-logical representational medium. Furthermore, they offer much promise for the empirical study of animal navigation. 1 Mental representations 2 Mental imagery, perception, and cognitive maps 3 Cognitive maps in psychology 4 Cognitive maps in robotics 5 Cognitive maps in the strict sense? 6 Logically structured representations? 7 Systematicity and productivity 8 Consequences for philosophy and psychology 9 Appendix: cartographic semantics2 1 Mental representations Fodor ([1975], [1987]) and Pylyshyn ([1984, [2003]) espouse a theory of cognition based on two doctrines: (1) Certain core mental processes studied by scientific psychology are mechanical, rule-governed operations upon symbols. In that sense, the processes are computational. (2) The symbols that figure in computational mental activity have syntactic structure and a compositional semantics. Both doctrines are popular albeit controversial within philosophy and psychology. Following Fodor, philosophers typically refer to the representational system posited by (2) as the language of thought, or Mentalese. Even among those who endorse Mentalese, considerable controversy surrounds its representational format. What semantically relevant structure should scientific psychology attribute to Mentalese symbols? How closely do such symbols resemble familiar concrete representations like sentences, pictures, diagrams, or maps? An extreme view, tracing back at least to William of Ockham, holds that all mental representations operate analogously to sentences. Modern exponents often emphasize the sentential structures studied by formal logic. Many AI researchers, including Genesereth and Nilsson ([1987]) and McCarthy and Hayes ([1969]), pursue a “logicist” agenda that treats the predicate calculus, or a suitably supplemented variant of it, as the primary, paradigmatic, or even exclusive medium of thought. At the opposite extreme, some commentators hold that all mental representation operates pictorially, diagrammatically, or cartographically. This “pictorialist” view, popular among medieval philosophers and the British empiricists, finds such recent advocates as Armstrong ([1973]), Barsalou ([1998]), Braddon-Mitchell and Jackson ([2007]), and Cummins ([1996]). Between the extremes of logicism and pictorialism lies a pluralistic3 position that embraces both logical and non-logical mental representations, assigning neither explanatory primacy over the other. Johnson-Laird ([2004], p. 187), McDermott ([2001], p. 69), Pinker ([2005], p. 7), Sloman ([1978], pp. 144-76), and many others advocate this pluralistic position. Although Fodor’s emphasis upon the “languagelike” character of Mentalese might seem to suggest logicism, he inclines more towards pluralism ([2007], pp. 105-16). My goal is to clarify the pluralistic viewpoint through detailed philosophical analysis of a particularly instructive case study. Two principal challenges face the pluralistic conception: to provide compelling examples of non-logical mental representation, and to explain how such representations differ in a principled way from those patterned after formal logic. To meet these challenges, I will discuss some models of navigation drawn from psychology and robotics. The models posit representations, cognitive maps, whose structure is geometric rather than logical. As I will argue, cognitive maps offer key advantages over the putative examples of non-logical representation more commonly studied by philosophers, such as perception and mental imagery.1 The computational models I discuss in §4 are thoroughly “cognitivist,” without any hint of behaviorism, associationism, Gibsonianism, or connectionism. Specifically, the models embody a commitment to (1)-(2). Thus, they enshrine the “classical” conception of cognition as rule-governed symbol manipulation. From a connectionist or dynamical systems perspective, the contrast between logicist, pictorialist, and pluralistic theories may seem trifling. From within the classical conception, however, the contrast matters a great deal. Logicism would have us ignore an important class of promising computational models. Even from a connectionist or dynamical systems perspective, we require a suitably general understanding of the classical conception so as to assess its strengths and weaknesses.4 2 Mental imagery, perception, and cognitive maps Recent discussion of mental imagery focuses on a series of experimental results due to Shepard and Kosslyn, along with various collaborators. Shepard and Chipman ([1970]) and Kosslyn ([1980]) argue that we can best explain these results by positing an imagistic medium of mental representation. Dennett ([1981]) and Pylyshyn ([1984], [2003]) disagree. For analysis of the debate, see (Block, [1983]; Grush [2004], pp. 393-84; Thomas [2007]; Tye [1991]). Even overlooking that the imagery debate seems no closer to resolution than it was two decades ago, there are several reasons why studying cognitive maps rather than mental images may yield philosophical dividends. First, evidence for mental imagery depends largely (though not entirely) upon linguistic interactions through which experimenters instruct subjects to perform certain cognitive tasks. This evidence does not readily generalize to non-linguistic creatures. In contrast, overwhelming evidence indicates that even insects perform sophisticated navigational feats. Thus, navigational models enjoy wider applicability than models of mental imagery. Second, navigation is more psychologically fundamental than mental imagery. It is vital for