Camp, E. (2007): Thinking With Maps

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underline [page 1]: “I investigate the theoretical and practical possibility of non-sentential thought. Ultimately, I am most interested in the contours of distinctively human thought: what forms does human thought take, and how do those different forms interact? How does human thought compare with that of other animals? In this essay, however, I focus on a narrower and more basic theoretical question: could thought occur in maps?”

underline [page 2]: “There are good reasons to believe that much of our own thinking is sentential, but these reasons depend on what we think—on the particular sorts of contents that we represent and reason about—rather than on general features of thought as such.”

underline [page 8]: “The premise that I want to challenge is the one that draws the least explicit attention: Premise 4, the claim that any representational system composed of discrete parts with systematic combinatorial rules is a language.”

underline [page 10]: “In this paper I want to focus more narrowly on another alternative: maps. Cartographic systems range along a continuum from the nearly pictorial, such as Google’s map-satellite hybrids, to the nearly diagrammatic, such as subway maps. In the next section, I show that sentential and cartographic systems do indeed employ different combinatorial principles. Here, I just want to establish that familiar maps, such as Rand-McNally city and road maps, meet the demands that Weak-LOT claims a vehicle of thought must satisfy.”

underline [page 10]: “I see no theoretical reason why one couldn’t define formal updating rules for dynamic reasoning with maps that would mirror semantic changes in the relations among the represented states of affairs, and thus would be reliably and demonstrably truth-preserving. And I believe that such rules could be used in genuine reasoning. Thus, I see no principled reason why maps fail to satisfy the arguments offered above for a compositional system of representational vehicles”

underline [page 11]: “I argue that maps and languages do operate according to importantly different combinatorial principles, and that as a result, thinking in maps is substantively different from thinking in sentences. In principle, we can distinguish two aspects of any representational system. On the one hand, there is the form of its representational vehicles: what the basic representational constituents are and the principles that govern how those constituents are put together. On the other hand, there is their content: what those constituents are about and the principles that determine that they are about this. The overall content of a complete representational vehicle is a function of the content of its basic representational parts and the significance of their mode of combination. In linguistic systems, this distinction is clear, and corresponds to the distinction between syntax and semantics. In other systems, the distinction is less clear, because the two principles interact in interesting ways.”

underline [page 16]: “In §2, I established that both sentential and cartographic systems employ recurrent constituents combined according to systematic rules, but that their compositional principles differ significantly. This demonstrates that maps aren’t just languages written in a funny notation, and hence that they constitute a potential counterexample to Strong-LOT. However, to demonstrate the falsity of Strong-LOT, we also need to show that a non-sentential system could fulfill the basic cognitive functions of representing and reasoning. In this section, I argue that so long as a thinker’s representational needs are sufficiently simple, it could think largely or entirely in maps; indeed, in important respects a cartographic system would be easier for such a thinker to use. However, as the range and complexity of contents a thinker needs to represent and reason about increases, maps become increasingly cumbersome. This gives us good reason to think that much of our own thinking does occur in sentences.”

underline [page 24]: “Cartographic systems are sufficiently systematic to satisfy the basic requirements of representation and reasoning that motivate the arguments for Weak-LOT. And because they employ a different combinatorial principle than sentences, they demonstrate the falsity of Strong-LOT.”

underline [page 29]: “The central point of my discussion of cartographic and pictorial systems has been that they employ a principle of spatial isomorphism between vehicle and content. And this obviously entails that pictures and maps themselves have a spatial structure. We know what this means for a normal physical map—the kind that’s written on paper or built with twigs and twine, and those are the terms in which I’ve been discussing the relative expressive powers and limitations of maps and sentences. But how are we to interpret this claim in the context of thought?”


highlight [page 1]: “even philosophers who take no stand on the relative priority of language and thought still tend to individuate mental states in terms of the sentences we use to ascribe them. Indeed, Dummett (1993) claims that it is constitutive of analytic philosophy that it approaches the mind by way of language.”

highlight [page 1]: “an exclusive focus on thought as it is expressed in language threatens to leave other sorts of thought unexplained, or even to blind us to their possibility. In particular, many cognitive ethologists and psychologists find it useful to talk about humans, chimpanzees, birds, rats, and even bees as employing cognitive maps. We need to make sense of this way of talking about minds as well as more familiar sentential descriptions.”

highlight [page 2]: “The classic reason for thinking that thought must be language-like is that only this assumption can explain or justify the systematicity of thought”

highlight [page 2]: “1. There are systematic relations among the contents that a thinker can represent and reason about. 2. Systematic relations in content must be reflected by correlative structure in a thinker’s representational and reasoning abilities. 3. Structured representational abilities require a system of representational vehicles which are composed of recurring discrete parts combined ac- cording to systematic rules. 4. Any system of representational vehicles composed of recurring discrete parts combined according to systematic rules is a language. Therefore: there must be a language of thought.”

text [page 2]: “The systematicity argument for LOT”

highlight [page 3]: “Premise 1 amounts to the claim that the abilities to think about such states of affairs cluster together: if you can think one thought about John, Harry, the girl, loving, or being happy, you can also think other thoughts about them, such as that Harry loves the girl or that the girl is happy”

highlight [page 3]: “there are also systematic limitations in the contents a thinker can represent: a thinker who can’t entertain the thought that John blighted the girl also can’t think that Harry blighted the girl, that the girl blighted the cow, or anything else about blighting.”

highlight [page 3]: “Tim Crane (1992, 146–7)”

highlight [page 3]: “If we simply wanted to represent facts, then our beliefs would only need to have ‘whole’ contents. All that would matter would be whether a content was true or false. The fact might have constituents (particulars and properties) but they would have no reflection in the content, since (to echo Frege) they would as it were have no role, no ‘meaning of their own’. But once we consider the role our beliefs play in reasoning, then it starts to become clear why their contents need constituents. A thinker who believes that a is F, and that b is F, and that a is not b will be disposed to believe that at least two things are F. Surely the states in this inference cannot just have unstructured contents, or we would not be able to explain its validity. 3”

highlight [page 3]: “Crane, like Evans, talks about “structure” instead of “systematicity,” but the basic point again concerns systematic relations among contents: the reason that the transition from believing that a is F, b is F, and a is not b to believing that at least two things are F is justified is that there are systematic, truth- and justification-preserving relations in the contents of those beliefs.”

highlight [page 4]: “Premise 2 claims that in order to explain this systematicity in contents, we must assume that the thinker’s representational abilities are themselves structured, in the sense that they must be produced by interacting constituent abilities to represent various parts of the world.”

highlight [page 4]: “Fodor and Pylyshyn support this claim by appeal to explanatory parsimony. Unless we posit distinct interacting abilities to represent the objects, properties, and relations that together constitute whole states of affairs, the systematic patterns of abilities and limitations that we observe among the whole contents that a thinker can represent will remain unexplained. More importantly, as the range of contents a thinker can represent increases, it becomes exponentially more efficient to posit distinct, interacting abilities to represent parts of contents rather than distinct, unstructured abilities to represent entire contents.”

highlight [page 4]: “the “Generality Constraint”: If a subject can be credited with the thought that a is F then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has a conception (1982, 104).”

highlight [page 5]: “The third premise in the argument for a Language of Thought claims that structured representational abilities must be underwritten by structured representational vehicles: by mental representations which are composed of recurring, systematically interacting parts.”

highlight [page 5]: “For Fodor and Pylyshyn, the claim that mental representations of related contents “must be made of the same parts” amounts to the claim that at the “cognitive level”—the level of description which specifies how brain states represent information about the world—(a) there must be physical properties which encode each object, property, and relation that enters into those contents; (b) the physical structures among those properties must encode the structural relations among those represented constituents; and (c) these physical structures must cause the overall representational system to behave as it does.”

highlight [page 6]: “each of the thinker’s conceptual abilities must be underwritten by a distinctive physical brain structure.”

note [page 6]: I find this position slightly perplexing, because I would have thought that we would want to explain the fact that we can enjoy mental (brain) states with a particular structure by the fact that we have certain fundamental mental capacities or powers.

highlight [page 6]: “The final premise, which is often conflated with the previous one, is that any system which combines recurrent parts according to systematic rules to generate whole representations is a language.”

highlight [page 6]: “Jos ́e Luis Bermudez (2003, 111) starts with something like Crane’s claim above—that in order to justify inferences between thoughts we must appeal to systematic relations in their contents—and concludes that genuine reasoning requires a linguistic vehicle”

highlight [page 7]: “if we want to explain why, say, a thinker’s inference from John is happy, Harry is happy and John is not Harry to At least two people are happy is an instance of valid reasoning, then it’s not enough to point out that if the first three states of affairs obtain then the last one will also obtain. In addition, this validity must be demonstrable from the thinker’s own perspective, given her way of representing those contents. 6 And this requires that the vehicles by means of which the thinker represents those contents must have a form which makes it possible to justify the transition. 7 But because he assumes that only a linguistic system can have formal rules of valid inference, he concludes that justified inference requires a language of thought.”

highlight [page 7]: “First, one might dispute the claim that thinkers’ representational and reasoning abilities are so systematic”

highlight [page 7]: “Second, one might deny that thought must be structured”

highlight [page 7]: “Third, one might accept that thinkers’ representational and reasoning abilities are structured, but deny that there must be a correlatively structured vehicle of thought.”

highlight [page 8]: “I do not wish to be committed to the idea that having thoughts involves the subject’s using, manipulating, or apprehending symbols—which would be entities with non-semantic as well as semantic properties . . . I should prefer to explain the sense in which thoughts are structured, not in terms of their being composed of several distinct elements, but in terms of their being a complex of the exercise of several distinct conceptual abilities (1982, 100–101).”

highlight [page 8]: “We obviously need some account of the causal underpinnings of mental states, abilities, and processes; but many people believe that structured, stable patterns of representation and reasoning could emerge without precisely correlative underlying physical constituents and mechanisms.”

highlight [page 8]: “one might deny Bermudez’s claim that we must understand inference and reasoning in terms of formal relations among representational vehicles. Perhaps it suffices to appeal to substantive relations among represented contents, where “contents” are understood either as possible worlds, or else as structured Fregean or Russellian propositions”

highlight [page 8]: “It’s also im- portant to see what endorsing a structured vehicle of thought doesn’t entail. First, it doesn’t require that the thinker consciously attends to that vehicle; it is enough for her to represent with the vehicle—for it to play the right functional role in her thinking. 12 Nor does granting that a structured vehicle plays an important causal and explanatory role in thought entail that it does all of that work by itself: the vehicle’s functional role within the overall cognitive system is equally important. As Pylyshyn says, “The appropriate subject of our analysis of representation should be not the representation per se but a representational system consisting of the pair (representation, process)” (cited in Anderson 1978, 250).”

highlight [page 8]: “Weak-LOT: the claim that thought requires a system of representational vehicles with some recurrent constituents that can be recombined according to some set of rules to produce representations of systematically related entire contents.”

note [page 8]: “It seems like Weak-LOT is compatible with the picture principle, as well as the claim that there is no single privileged decomposition. Or does the idea that a vehicle has recurrent constituents entail that there is a privileged decomposition?”

highlight [page 8]: “Strong-LOT: that claim thought requires a specifically sentential structure and semantics.”

text [page 8]: “Evans on abilities trumping LOT symbols "

text [page 8]: “What endorsing a LOT view doesn’t entail”

text [page 8]: “Weak & Strong LOT”

highlight [page 9]: “Devitt (2005, 147) invokes the argument from reasoning in support of a specifically linguistic vehicle: Formal logic gives us a very good idea of how thinking might proceed if thoughts are represented linguistically . . . We still have very little idea how thinking could proceed if thoughts were not language-like but, say, map-like.”

highlight [page 9]: “Dummett (1989, 197) claims that “a fully explicit verbal expression is the only vehicle whose structure must reflect the structure of the thought,” thereby implicitly assuming that thought itself has a language-like structure.”

highlight [page 9]: “The assumption that thought is language-like might not seem so contentious if we’re only considering human thought: after all, normal humans do often express their thoughts verbally, and often experience the phenomenology of thinking in language.”

highlight [page 9]: “Dummett, Crane, and Bermudez are driven by less empirical considerations: they want to identify a condition on genuine thought, or at least on the sort of conceptual thought that’s involved in genuine reasoning. But their identified conditions rely on quite general features of representation and reasoning, and are intended to have commensurately general application.”

note [page 9]: So one way of objecting here is to say that we have tended to mistake conditions for conceptual (or rational thought) for conditions on thought simpliciter.

highlight [page 9]: “Diagrammatic representational systems, such as Venn diagrams, are formed by combining formal elements like circles, dots, and lines according to systematic rules which determine the representational content of the whole. Further, they are governed by formal rules of inference which are sound and complete, up to expressive equivalence with monadic first- order predicate logic (Shin 1994).”

highlight [page 10]: “maps are clearly constructed out of recurrent formal elements that make a common semantic contribution each time they occur: for instance, on many maps any solid line of a certain width signifies a street, any blue line or blob signifies a river or lake, and any cross signifies a church. Further, the representational import of the entire map is a systematic function of the way in which those elements are combined: if two lines intersect, with a blob in one quadrant and a cross in the other (Figure 1a), then this represents two intersecting streets with a church across from a pond. By contrast, if the two lines are drawn in parallel, with the cross above the blob (Figure 1b), then these same elements represent a different but related situation, in which a church is north of a pond and between two parallel roads.”

highlight [page 10]: “Because maps’ constituents are systematically recombinable, in this way, they also satisfy the Generality Constraint: a cartographic system that enables a thinker to represent the locations of City Hall, the Delaware River, Dunkin’ Donuts locations, and bus routes thereby has the representational resources to represent those same features in any spatial configuration”

text [page 10]: “Maps (of a certain kind) satisfy systematicity and the Generality Constraint”

highlight [page 11]: “At the extreme, one might insist that diagrams and maps just are sentences written in a funny notation.”

highlight [page 11]: “Eliot Sober (1976, 141) claims that the fundamental distinction between pictures and sentences is that genuine pictures are analog, in the sense that they represent continuous values (e.g. color) in a continuous way; given this assumption, he then claims that “where [picture-like representational systems] are digital, they simply are linguistic systems of a certain kind.””

highlight [page 12]: “In pictorial systems, both the syntactic, combinatorial principles and the se- mantic, content-determining principles that link vehicle to content rely heavily on direct isomorphism.”

highlight [page 12]: “The syntactic principle generating a realistic picture maps the two-dimensional pattern of retinal excitation onto another two-dimensional medium, and thereby replicates the visual appearance of the three-dimensional scene which would cause that retinal pattern.”

highlight [page 12]: “The semantic principle is also one of replication: each point in the picture replicates the apparent color, or at least luminosity and reflectancy, of the analogous point in the world. (Less realistic pictorial styles, such as impressionism, tweak these isomorphisms.)”

highlight [page 12]: “insofar as we can discern syntactic ‘parts’ to a picture at all, these are either just points in a two-dimensional array, or else regions whose boundaries are given by salient boundaries in the scene being represented; and in either case, the semantic principle simply replicates the visual appearance of that very point or region.”

highlight [page 12]: “Because pictorial systems replicate the visual appearance of a scene by largely replicating that visual appearance itself, pictures can only explicitly represent features that are themselves visually perceptible.”

text [page 12]: “Pictures & isomorphism”

text [page 12]: “Analog status of pictures”

highlight [page 13]: “. The semantic principles mapping the vehicle’s constituents to represented contents are clearly highly arbitrary and conventional: neither the word ‘tree’ in English nor ‘l’arbre’ in French resembles a tree in any salient respect”

highlight [page 13]: “The syntactic principles combining those constituents are less arbitrary, but they too clearly abandon any appeal to physical isomorphism. 19 Instead, some sort of functional relation among syntactic constituents maps onto some sort of logical or metaphysical relation among the semantic values of those constituents”

highlight [page 13]: “Because sentential systems represent by combining discrete, conventional symbols in an abstract structure, they are highly digital: they deliver chunks of information about discrete states of affairs. They also have a very minimal lower bound of informational content: a sentence can represent just that there is a cup, or that something is red, while remaining silent about every other aspect of the world. These features make sentential systems a computationally cheap means for tracking and categorizing information in small bits and at various levels of abstraction.”

highlight [page 14]: “maps abstract away from much of the detail that encumbers pictorial systems. Where pictures are isomorphic to their represented contents along multiple dimensions, maps only exploit an isomor- phism of spatial structure: on most maps, distance in the vehicle corresponds, up to a scaling factor, to distance in the world.”

highlight [page 14]: “Such a configuration is still a map, rather than a sentence, because it deploys the basic combinatorial principle of spatial isomorphism.”

highlight [page 14]: “It is a notable feature of humans’ representational abilities that they are sufficiently flexible to deploy the same expression in such different contexts.”

highlight [page 15]: “the only strong constraint on the icons employed by cartographic systems, and on their potential semantic values, is that the icons’ own physical features can’t conflict with the principle of spatial isomorphism. Thus, one can’t represent a street with a circle, not because it would be too arbitrary, but because this would make it impossible to place the icon in a spatial configuration that reflects the spatial structure of the represented content: for instance, one couldn’t depict two streets as parallel, or as intersecting.”

highlight [page 15]: “The crucial point for our purposes is just that many maps employ discrete, recurring constituents with a highly arbitrary semantics, and combine them according to systematic rules to produce systematically related whole representations. But at the same time, the principle according to which those constituents are combined relies on a spatial rather than purely logical isomorphism between the structure of those constituents and the structure of the corresponding elements in the content. This demonstrates in concrete terms that there is more than one way in which “the syntactic structure of mental states [can] mirror the semantic relations among their intentional objects,” as Fodor et al. take the argument from systematicity to require. As a result, Premise 4 in the Argument for the Language of Thought is simply false: there are non-linguistic combinatorial representational systems.”

highlight [page 16]: “One reason it seems implausible that a thinker could do all or even most of its thinking in pictures, besides heavy computational demand, is that pictures’ high semantic density and syntactic complexity makes it hard to see how one could use them to reason: many of the changes one can make to a picture will destroy its structural coherence”

highlight [page 17]: “An important corollary of this is that maps are holistic representational systems, while sentential systems are atomistic (cf. Braddon-Mitchell and Jackson 1996, 171)”

highlight [page 18]: “A thinker might also operate with multiple maps, though, which won’t automatically accumulate their respective information into an integrated whole. Such a thinker would thus need some way to collate their information. If the maps represent sufficiently continuous regions of space, then conjunction can proceed by concatenation and superimposition, controlling for scale and orientation. However, maps representing spatially discontinuous regions cannot be syntactically conjoined.”

highlight [page 19]: “While normal maps and their cognitive analogues are significantly more efficient than sentences at conjoining information about related spatial locations, such maps lack any means to explicitly represent the other truth-functional relations. This is a significant limitation in expressive power”

highlight [page 19]: “On the familiar maps we ordinarily use to navigate—say, a Rand-McNally map of Philadelphia—the absence of an icon from a point on the map represents the absence of the correlative object/property from the correlative location in the world (cf. Rescorla 2005).”

highlight [page 19]: “A more elegant solution would color icons and background regions to reflect positive and negative information”

highlight [page 19]: “Maps can also be extended, in principle, to deal with disjunction and if-then. Because maps work by placing discrete icons in determinate configurations, standard maps lack any way to represent partial information, such as that either Bob is at the store or he is at the bar; or that if Bob has gone to the store, then he’s walking this way.”

highlight [page 21]: “Maps easily represent some sorts of existential informa- tion, such as that there is a caf ́e here. However, because maps work by placing determinate features at definite locations, they can’t represent information that’s not spatially located, such as that somebody, somewhere is wearing a red shirt and carrying a gun. As we might put it, the bare existential information that something or other, somewhere or other, is F falls below the minimum bound of cartographically representable information.”

highlight [page 22]: “because maps exploit discrete, recurrent syntactic constituents with stable, at least partlyconventionalized semantic properties, one can achieve something close to the effect of sentential structure within a cartographic system by manipulating the basic icons in ways that don’t affect their spatial structure. In effect, we’ve introduced rules for generating syntactically complex icons which represent semantically complex objects and properties: not-Bob, past-Bob, etc.”

highlight [page 22]: “What would fundamentally alter the nature of the representational system would be to assign some other representational significance to the spatial relations among icons—say, so that placing two icons next to each other sometimes meant that the correlative objects were near one another, but other times meant that the leftward one loved the rightward one.”

highlight [page 22]: “one might insist that it would fundamentally alter the representational system if one employed a fully sentential syntax to combine the icons into a complete representational unit in their own right, so that placing the icons for dog, bit, and boy together on the map represented that at that location the boy bit the dog. 31 If we decided to take this limitation seriously, then although one could legitimately introduce the sorts of icons we’ve discussed for higher-order relations like if-then, and although one could introduce icons for properties like food, and icons for types of objects like happy guy, one couldn’t legitimately introduce icons with predicative force, to represent properties like being happy, being bald, or loving.”

highlight [page 23]: “So long as a thinker is merely representing objects’ and properties’ relative spatial locations, maps’ holistic, accumulative quality makes them efficient representational vehicles compared to the cumbersome atomistic representation of sentences. But as we extend them to accommodate the representation of more complex contents, maps become much more unwieldy.”

highlight [page 23]: “No representa- tional system can make its vehicles fully cognitively transparent: even the most ‘obvious’ representational system still requires some background knowledge in order to use its vehicles appropriately.”

highlight [page 23]: “standard maps are comparatively cognitively transparent. They always and only employ icons to represent objects and properties as arranged in a spatial configuration, and they represent this configuration by replicating that very same configuration among the icons themselves.”

highlight [page 23]: “Second, although we haven’t identified any absolute in principle barriers on kinds of information that maps can be extended to represent, there are quite serious limitations on the full generality of their expressive range.”

highlight [page 25]: “To achieve a really robust expressive richness, which is capable of selectively representing and fluidly manipulating the sorts of abstract, hierarchically-structured contents that make human cognition so distinctively powerful, a representational system needs to employ syntactic and semantic principles that are sufficiently abstract that they don’t themselves impose any substantial limitations, either on what semantic values can be assigned to the syntactic constituents or on the complexity with which those constituents can be combined.”

text [page 25]: “Diagrammatic systems”

highlight [page 25]: “Diagrammatic systems come considerably closer to this ideal, because they are free to employ an isomorphism between the vehicle’s physical structure and any sort of structure, including logical and metaphysical structure, in the represented content. This makes them very useful for representing and reasoning about abstract and hierarchically-structured information in a way that is still comparatively intuitive because it still exploits basic geometry.”

highlight [page 25]: “precisely because their syntax still exploits physical properties of the vehicle”

note [page 25]: This is a slightly confusing way to put this, since LOT proponents are going to argue that the syntax of LOT exploits physical properties of the vehicle as well. This is part of the causal realism of the view.

highlight [page 25]: “Sophisticated-LOT: the rep- resentational vehicle which underwrites highly flexible thought about abstract, hierarchically-structured states of affairs is likely to be sentential in form.”

highlight [page 25]: “Because the distinctive power of human cognition seems to depend on our agility at representing and manipulating such contents, this gives us good reason to think that much of our own cognition, in contrast to that of other animals, takes place in language. However, this conclusion depends crucially upon the specific contents that humans think about and what they do with those contents, and not on general features of thought per se.”

highlight [page 26]: “[I]t is not possible for behavioral data to uniquely decide issues of internal representation. . . . One can show that given a set of assumptions about an image representation and a set of processes that operate on it, one can construct an equivalent set of assumptions about a propositional representation and its processes. Or one can be given a propositional theory and construct an equivalent imagery theory. In fact, . . . given any representation-process pair, it is possible to construct other pairs with different representations whose behavior is equivalent to it. These pairs make up for differences in representation by assuming compensating differences in the process.”

highlight [page 26]: “First, it’s obviously true that two systems may be “informationally equiv- alent” in the sense that in principle one can extract the same information from each system, or that they make the same ‘cut’ in the space of possible worlds. However, this notion of “information equivalence” is highly rarified.”

text [page 26]: “Informational equivalence”

highlight [page 27]: “Second, in practice we are also likely to be able to distinguish informationally equivalent vehicle/process pairs behaviorally by observing differences in the two systems’ ‘failure modes’ (cf. Marr 1982). In particular, the fact that maps are holistic forms of representation while sentences are atomistic means that each system is likely to break down in a distinctive way. Thus, to the extent that a thinker fails to exploit the full consequences of information acquired on distinct occasions to achieve her goals—for instance, if a rat undertakes separate trips to get water and food, returning to its nest in between, although it would be shorter to go directly from the water to the food—we have some evidence that it stores information atomistically.”

highlight [page 27]: “Of course, no single piece of behavioral evidence, or even any particular collection of evidence, can be absolutely dispositive here.”

highlight [page 27]: “Still, in a practical context we should expect the different ways that sentential and cartographic representational systems are likely to distribute information between vehicle and process to manifest themselves behaviorally. Thus, the fact that two representational systems are informationally equivalent in principle doesn’t show that there can’t be any significant empirical justification for claiming that a thinker is employing one rather than the other system.”

highlight [page 28]: “A more hard-line version of the objection from informational equivalence insists that the only difference between representational systems that really matters is expressive power. So long as a theorist’s preferred representational format has the power to represent the contents he attributes to a thinker, no behavioral evidence can force him to abandon the hypothesis that the thinker is employing that format.”

highlight [page 28]: “if everything that can be expressed in maps or pictures can also be expressed in sentences, what could ever demonstrate that a thinker is using pictures or maps instead? The objection seems especially forceful given that many philosophers endorse the idea that language is expressively complete (cf. e.g. Searle 1969).”

highlight [page 28]: “sentential systems are highly digital: they combine discrete, arbitrary symbols in an abstract hierarchical structure. But this in turn means that at any given moment, a given sentential system only has the expressive resources to represent countably many contents: those formed by all the combinations of its syntactic constituents. By contrast, because pictures and maps are analog modes of representation, they are potentially continuous; and as such, they can represent continuously many contents. In particular, a cartographic system with the expressive resources to draw continuously differentiated blobs of the sort in Figure 1 already contains within itself the expressive resources to represent ponds of uncountably many shapes, as well as to configure the various types of objects and properties it can represent in uncountably many ways”

highlight [page 29]: “a creature who lives in a messy world with features that differ saliently in a fairly continuous way will need a fairly continuous means to represent those features. Thus, even if a sentential system is capable of encoding the relevant information, it will be much more useful to employ a format, such as a diagram or map, which directly represents fine-grained differences along one dimension while abstracting from detail along other dimensions. Thus, the question of which representational format best reflects a thinker’s representational needs, abilities, and limitations— and with it, the question of which format it is most plausible to assume a thinker is employing—depends largely on what sorts of contents the thinker most often represents, and how she needs to manipulate them.”

note [page 29]: this seems plausible, but there is a worry here about the claim concerning which contents the thinker “most often represents”, since humans seem to be able to represent a lot more than most of them most often do.

highlight [page 29]: “precisely because sentential systems employ such abstract semantic and combinatorial principles, the claim that a thinker employs a language of thought is compatible with an extremely wide range of plausible neurological implementations. Thus, although by itself Weak-LOT leaves open the possibility of thought with a non-sentential form, one might think, only Strong-LOT offers an empirically plausible implementation of Weak-LOT.”

highlight [page 29]: “physically instantated maps are in fact ubiquitous in the brain. Scientists have known since the 1940’s that the mammalian cortex represents many aspects of the world, especially the layout of one’s own body and sensory stimuli, in such a way that the spatial structure of neural firing reflects the physical or psychological structure of the represented”

highlight [page 30]: “Thus, the objection can’t depend on a wholesale rejection of spatial isomorphism in cognitive representations. Rather, the objection must be something more like the worry that it’s implausible that the brain contains enough room for the entire world to be represented cartographically. This objection does have bite against pictures, because they are so computationally expensive. But maps abstract away from much of pictures’ detail, and are free to employ highly abstract icons. Thus, the computational demands imposed by maps are potentially much closer to those for sentential systems than to those for pictures.”

highlight [page 30]: “As Fodor and his co-authors themselves emphasize, the Language of Thought hypothesis is not committed to any particular claim about the particular neural instantiation of cognition; indeed, computationalism is compatible with connectionism at the level of actual neural firing.”

highlight [page 30]: “the Strong Language of Thought hypothesis is the claim that at “the cognitive level of description,” an adequate causal account of a system of mental representations and reasoning must type neural processes in terms of word-like constituents and language-like rules for combining them. But this same interpretation is available to someone who claims that at least some thinkers, such as bees and rats, employ a cartographic system for thought.”

highlight [page 30]: “They do not take LOT to require that the first physical state actually be a part of the second one. Likewise, the cartographic theorist can take claims about cartographic structure quite seriously, if not fully literally, by maintaining that relations like ‘next to’, ‘above’, and ‘intersecting’, which hold between symbols in a map, correspond to some physical relations—not necessarily spatial—among brain states”

highlight [page 31]: “any plausible cognitive system, including especially our own, is likely to be highly multi-modal: storing and manipulating information in the formats of multiple sensory modalities, and centralizing information in cartographic, diagrammatic, and sentential formats. If this is right, of course, then it becomes commensurately more difficult to make principled predictions about what a thinker should or shouldn’t be able to do.”

highlight [page 31]: “Crane’s allusion is to the following passage from Frege (in a letter to Peano): “Where inferences are to be drawn . . . it is essential that the same expression should occur in two propositions and should have exactly the same meaning in both cases. It must therefore have a meaning of its own, independent of the other parts of the proposition.””

highlight [page 33]: “By ‘isomorphism’ I mean a structure-preserving function from elements in one do- main onto elements in another.”

highlight [page 33]: “With respect to pictures in particular, I claim only that they depend heavily on isomorphism in respect of visual appearance, not that isomorphism suffices for depiction.”

highlight [page 33]: “any representational system only fixes content relative to a system of use. At a minimum, some further conditions must be added to explain the fact that depiction, like representation generally, is asymmetrical, while isomorphism is symmetric (cf. Goodman 1968, 1970).”

text [page 33]: “Depiction is not isomorphic b/c it is not symmetrical "

highlight [page 34]: “It’s a matter for substantive linguistic analysis exactly what the combinatorial principle(s) of natural language(s) may be: functional application, predicate modification and abstraction, conjunction, or something else entirely.”

highlight [page 35]: “Kass (1997, 107): “[T]he now widely held opinion is that the topographic features of cortical and subcortical maps are not incidental, but essential to much brain function.” Likewise, Diamond et al (1999, 64) write: “The presence of ‘maps’ in sensory cortex is a hallmark of the mammalian nervous system . . . Topographical cortical representations of sensory events . . . appear to constitute a true structural framework for information processing and plasticity.” Among many other sources, see Hubel and Wiesel 1962, Tootell et al 1988, and Van Essen et al 2001.”


Camp freely discusses iconongraphy in maps but never clearly defines what she thinks an icon is. The main constraint she puts on iconic representation in maps is that icons are constrained by the principle of spatial isomorphism that is necessary for maps to represent at all (158).

Camp also allows for “linguistic icons”, as with a seating map where people’s seats are designated by their names (p 158). But here “icon” is being used in a way that does not obviously satisfy the picture principle, since not every part of the icon represents a part of the represented scene or object.

It seems to me that there cannot be linguistic icons. Either there are linguistic symbols carrying the relevant semantic values, or there are icons. The map Camp describes seems to be a hybrid. The names have their standard semantic function (and also have parts – the individual letters), while the name as a whole has another iconic function (and in this sense lacks parts), where we take the spatial location of the names as relevant to interpreting features of their referents.

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