Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...) mereology (the study of part/whole relations), topology (the study of spatial continuity and compactness), and the theory of spatial location proper. This leads to a unified framework for spatial representation understood quite broadly as a theory of the representation of spatial entities. The framework is then tested against some classical metaphysical questions such as: Are parts essential to their wholes? Is spatial colocation a sufficient criterion of identity? What (if anything) distinguishes material objects from events and other spatial entities? The concluding chapters deal with applications to topics as diverse as the logical analysis of movement and the semantics of maps. (shrink)

Representation is central to contemporary theorizing about the mind/brain. But the nature of representation--both in the mind/brain and more generally--is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received view is that analog representations vary smoothly, while digital representations vary in a step-wise manner. I argue that this characterization is inadequate to account for the ways in which representation is used in cognitive science; in its place, I (...) suggest an alternative taxonomy. I will defend and extend David Lewis's account of analog and digital representation, distinguishing analog from continuous representation, as well as digital from discrete representation. I will argue that the distinctions available in this four-fold account accord with representational features of theoretical interest in cognitive science more usefully than the received analog/digital dichotomy. (shrink)

Most of us create and use a panoply of non-sentential representations throughout our ordinary lives: we regularly use maps to navigate, charts to keep track of complex patterns of data, and diagrams to visualize logical and causal relations among states of affairs. But philosophers typically pay little attention to such representations, focusing almost exclusively on language instead. In particular, when theorizing about the mind, many philosophers assume that there is a very tight mapping between language and thought. Some analyze utterances (...) as the outer vocalizations of inner thoughts (e.g. Grice 1957, Devitt 2005), while others treat thought as a form of inner speech (e.g. Sellars 1956/1997, Carruthers 2002). But 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. In many ways, this linguistic model is salutary. Our thoughts are often intimately intertwined with their linguistic expression, and public language does provide a comparatively tractable proxy for, and a window into, the messier realm of thought. However, 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. In what follows, 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? Many philosophers are convinced that in some important sense, thought per se must be language-like.. (shrink)

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the close (...) connection between measurement and natural law, it makes dimensional analysis intelligible, and explains the concern of scientists and engineers with units in equations. It leaves the philosophical problem of the relation between the structure of magnitudes and the structure of the reals. What explains it? And is it always the same? We will argue that on the whole, construing the values of quantities as magnitudes has some advantages, and that (as Helmholtz seems to suggest in "Numbering and Measuring from an Epistemological Viewpoint") the relation between magnitudes and real numbers can be based on foundational similarities of structure. (shrink)

This book presents an attempt to develop a theory of knowledge and a philosophy of mind using ideas derived from the mathematical theory of communication developed by Claude Shannon. Information is seen as an objective commodity defined by the dependency relations between distinct events. Knowledge is then analyzed as information caused belief. Perception is the delivery of information in analog form for conceptual utilization by cognitive mechanisms. The final chapters attempt to develop a theory of meaning by viewing meaning as (...) a certain kind of information-carrying role. (shrink)

This chapter outlines David Lewis's favored foundational account of linguistic representation, and outlines and briefly evaluates variations and modifications. It gives an opinionated exegesis of Lewis's work on the foundations of reference: his interpretationism. The author looks at the way that the metaphysical distinction between natural and non‐natural properties came to play a central role in his thinking about language. Lewis's own deployment of this notion has implausible commitments. The chapter briefly considers a buck‐passing strategy involving fine‐grained linguistic conventions. Lewis (...) was no fan of primitive intentionality. Much of the Lewisian framework remains attractive. The overall select‐and‐project method, with its promise to deal even‐handedly with all linguistic intentionality, and its epistemic tractability, should be retained. Post‐Lewisian interpretationism results from emphasizing and retaining some of the virtues of Lewis's original proposal promises (e.g. universality and epistemic tractability), while compromising on others (e.g. metaphysical principle). (shrink)

Maps and realist pictures comprise prominent sub-classes of iconic representations. The most basic, most important sub-class is perception. Other types are drawings, photographs, musical notations, diagrams, bar graphs, abacuses, hieroglyphs, and color chits.

We examine the interrelationships between analog computational modelling and analogue (physical) modelling. To this end, we attempt a regimentation of the informal distinction between analog and digital, which turns on the consideration of computing in a broader context. We argue that in doing so one comes to see that (scientific) computation is better conceptualised as an epistemic process relative to agents, wherein representations play a key role. We distinguish between two, conceptually distinct, kinds of representation that, we argue, are both (...) involved in each case of computing. Based on the semantic and syntactic properties of each of these representations, we put forward a new account of the distinction between analog and digital computing. We discuss how the developed account is able to explain various properties of different models of computation, and we finish by conceptually comparing analog computational modelling to analogue (scale) modelling. It is concluded that, contrary to the standard view, the two practices are orthogonal, differing both in their foundations and in the epistemic functions they fulfil. (shrink)

This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...) of the properties of usage associated with signs. In Section 2 we illustrate these ideas with a case study of diagrammatic representation: the evolution from Euler diagrams to Venn diagrams. Section 3 is correspondingly devoted to pictorial representation, illustrated by the comparison between parallel and linear perspective drawing. We conclude with open questions, and then briefly summarize the articles to follow. (shrink)

In the 1980s, a number of philosophers argued that perception is analog. In the ensuing years, these arguments were forcefully criticized, leaving the thesis in doubt. This paper draws on Weber’s Law, a well-entrenched finding from psychophysics, to advance a new argument that perception is analog. This new argument is an adaptation of an argument that cognitive scientists have leveraged in support of the contention that primitive numerical representations are analog. But the argument here is extended to the representation of (...) non-numerical magnitudes, such as luminance and distance, and shown to apply to perception and not just cognition. The relevant sense of ‘analog’ is also clarified, and two powerful objections are addressed. Finally, the question whether perception’s analog vehicles are located in conscious experience is explored and related to a well-known controversy within psychophysics. (shrink)

This essay argues for a model of pictorial representation which aims to explain the relationship between pictorial content and pictorial accuracy. Focusing on cases where pictures are intended to convey accurate information, the model distinguishes between two fundamental representational relations: on one hand, a picture expresses a content; on the other, it aims at a target scene. Such a picture is accurate when the content it expresses fits the target scene it aims at. In addition, the model follows the traditional (...) division of content into two aspects: singular content specifies the particular individuals which a picture is of, and attributive content specifies the properties and relations which the picture ascribes to those individuals. For a picture to be accurate, both aspects must be matched in the target. I call this the Three-Part Model because it distinguishes between the triad of factors, singular content, attributive content, and target, which together determine pictorial accuracy. Though previous work on depiction has not recognized the distinctive role played by target, I will argue that it is essential in order to make sense of accuracy judgements across a range of central cases. (shrink)

Perceptual systems respond to proximal stimuli by forming mental representations of distal stimuli. A central goal for the philosophy of perception is to characterize the representations delivered by perceptual systems. It may be that all perceptual representations are in some way proprietarily perceptual and differ from the representational format of thought (Dretske 1981; Carey 2009; Burge 2010; Block ms.). Or it may instead be that perception and cognition always trade in the same code (Prinz 2002; Pylyshyn 2003). This paper rejects (...) both approaches in favor of perceptual pluralism, the thesis that perception delivers a multiplicity of representational formats, some proprietary and some shared with cognition. The argument for perceptual pluralism marshals a wide array of empirical evidence in favor of iconic (i.e., image-like, analog) representations in perception as well as discursive (i.e., language-like, digital) perceptual object representations. (shrink)

This paper examines the interplay of semantics and pragmatics within the domain of film. Films are made up of individual shots strung together in sequences over time. Though each shot is disconnected from the next, combinations of shots still convey coherent stories that take place in continuous space and time. How is this possible? The semantic view of film holds that film coherence is achieved in part through a kind of film language, a set of conventions which govern the relationships (...) between shots. In this paper, we develop and defend a new version of the semantic view. We articulate it for a pair of conventions that govern spatial relations between viewpoints. One such rule is already well-known; sometimes called the "180° Rule," we term it the X-Constraint; to this we add a previously unrecorded rule, the T-Constraint. As we show, both have the effect, in different ways, of limiting the way that viewpoint can shift through space from shot to shot over the course of a film sequence. Such constraints, we contend, are analogous to relations of discourse coherence that are widely recognized in the linguistic domain. If film is to have a language, it is a language made up of rules like these. (shrink)

According to one important proposal, the difference between perception and cognition consists in the representational formats used in the two systems (Carey, 2009; Burge, 2010; Block, 2014). In particular, it is claimed that perceptual representations are iconic, or image-like, while cognitive representations are discursive, or language-like. Taking object perception as a test case, this paper argues on empirical grounds that it requires discursive label-like representations. These representations segment the perceptual field, continuously pick out objects despite changes in their features, and (...) abstractly represent high-level features, none of which appears possible for purely iconic representations. (shrink)

Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...) philosophical audience by rehearsing empirical evidence for their existence and analysing their format, their content, and the computations they support. 1 Background1.1 Evidence of analogue magnitude representations1.2 Weber’s law1.3 Scepticism about analogue magnitude representations2 Format2.1 Carey’s analogy2.2 Neural realization2.3 Analogue representation2.4 Analogue magnitude representation components3 Content3.1 Do analogue magnitude representations have representational content?3.2 What do analogue magnitude representations represent?3.3 What content types do analogue magnitude representations have?4 Computations4.1 Arithmetic computation4.2 Practical deliberation5 Conclusion. (shrink)

Analog representation is often cast in terms of an engineering distinction between smooth and discrete systems. The engineering notion cuts across interesting representational categories, however, so it is poorly suited to thinking about kinds of representation. This paper suggests that analog representations support a pattern of interaction, specifically open-ended searches for content across levels of abstraction. They support the pattern by sharing a structure with what they represent. Continuous systems that satisfy the engineering notion are exemplars of this kind because (...) they are uninterpretable unless they are structure-preserving. Analog representations, so understood, include pictures, images, diagrams, and most graphs. This conception of analogicity also fits well with a line of thought about what makes perceptual states distinctive: they satisfy a “parts principle”. (shrink)

The ‘received view’ of the analog–digital distinction holds that analog representations are continuous while digital representations are discrete. In this paper I first provide support for the received view by showing how it (1) emerges from the theory of computation, and (2) explains engineering practices. Second, I critically assess several recently offered alternatives, arguing that to the degree they are justified they demonstrate not that the received view is incorrect, but rather that distinct senses of the terms have become entrenched (...) specific fields, perhaps most notably in the cognitive psychology of mental imagery. (shrink)

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by (...) examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

Lewis's notion of a "natural" property has proved divisive: some have taken to the notion with enthusiasm, while others have been sceptical. However, it is far from obvious what the enthusiasts and the sceptics are disagreeing about. This paper attempts to articulate what is at stake in this debate.

This paper outlines Lewis’s favoured foundational account of linguistic representation, and outlines and briefly evaluates variations and modifications. Section 1 gives an opinionated exegesis of Lewis’ work on the foundations of reference—his interpretationism. I look at the way that the metaphysical distinction between natural and non-natural properties came to play a central role in his thinking about language. Lewis’s own deployment of this notion has implausible commitments, so in section 2 I consider variations and alternatives. Section 3 briefly considers a (...) buck-passing strategy involving fine-grained linguistic conventions. (shrink)

What is the relation between the nature of the things you think about, and the ways you think about them? Christopher Peacocke argues that meaning is never prior to metaphysics - to the nature of the world. He shows that this view holds for a wide range of topics, including magnitudes, time, the self, and abstract objects such as numbers.

Summary Analogue models are actual physical setups used to model something else. They are especially useful when what we wish to investigate is difficult to observe or experiment upon due to size or distance in space or time: for example, if the thing we wish to investigate is too large, too far away, takes place on a time scale that is too long, does not yet exist or has ceased to exist. The range and variety of analogue models is too (...) extensive to attempt a survey. In this article, I describe and discuss several different analogue model experiments, the results of those model experiments, and the basis for constructing them and interpreting their results. Examples of analogue models for surface waves in lakes, for earthquakes and volcanoes in geophysics, and for black holes in general relativity, are described, with a focus on examining the bases for claims that these analogues are appropriate analogues of what they are used to investigate. A table showing three different kinds of bases for reasoning using analogue models is provided. Finally, it is shown how the examples in this article counter three common misconceptions about the use of analogue models in physics. (shrink)

An interesting feature of some sets of representations is that their structure mirrors the structure of the items they represent. Founding an account of representational content on isomorphism, homomorphism or structural resemblance has proven elusive, however, largely because these relations are too liberal when the candidate structure over representational vehicles is unconstrained. Furthermore, in many cases where there is a clear isomorphism, it is not relied on in the way the representations are used. That points to a potential resolution: that (...) an isomorphism must be used, hence usable, if it is to be an ingredient in a theory of content. This paper argues that the class of exploitable isomorphisms can indeed play a content-constituting role. (shrink)

The distinction between analog and digital representation is reexamined; it emerges that a more fundamental distinction is that between symbolic and analog simulation. Analog simulation is analyzed in terms of a (near) isomorphism of causal structures between a simulating and a simulated process. It is then argued that a core concept, naturalistic analog simulation, may play a role in a bottom-up theory of adaptive behavior which provides an alternative to representational analyses. The appendix discusses some formal conditions for naturalistic analog (...) simulation. (shrink)

According to a core tenet of contemporary philosophy, aesthetic properties are primarily represented in experiences. Obviously, however, the tenet does not apply in any straightforward manner to many items that nevertheless seem to have aesthetic properties. Examples include literary works, mathematical objects, scientific ideas, and works of conceptual art. Aesthetic properties need not be represented in perceptual experiences, but what is an experience if not a perceptual state? This paper adapts Fred Dretske’s distinction between analogue and digital representation to develop (...) a broad conception of a kind of state that is an experience but need not be perceptual. Aesthetic properties are primarily represented in states so conceived. (shrink)

https://plato.stanford.edu/entries/digital-art/.

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term ‘analog-model’ (...) does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing task.Keywords: Computation; Computational neuroscience; Analog computers; Representation; Simulation. (shrink)