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)

In this paper, I argue for three claims. The first is that the difference between analog and digital representation lies in the format and not the medium of representation. The second is that whether a given system is analog or digital will sometimes depend on facts about the user of that system. The third is that the first two claims are implicit in Haugeland's (1998) account of the distinction.

What counts as a computation and how it relates to cognitive function are important questions for scientists interested in understanding how the mind thinks. This paper argues that pragmatic aspects of explanation ultimately determine how we answer those questions by examining what is needed to make rigorous the notion of computation used in the (cognitive) sciences. It (1) outlines the connection between the Church-Turing Thesis and computational theories of physical systems, (2) differentiates merely satisfying a computational function from true computation, (...) and finally (3) relates how we determine a true computation to the functional methodology in cognitive science. All of the discussion will be directed toward showing that the only way to connect formal notions of computation to empirical theory will be in virtue of the pragmatic aspects of explanation. (shrink)

After briefly discussing the relevance of the notions computation and implementation for cognitive science, I summarize some of the problems that have been found in their most common interpretations. In particular, I argue that standard notions of computation together with a state-to-state correspondence view of implementation cannot overcome difficulties posed by Putnam's Realization Theorem and that, therefore, a different approach to implementation is required. The notion realization of a function, developed out of physical theories, is then introduced as a replacement (...) for the notional pair computation-implementation. After gradual refinement, taking practical constraints into account, this notion gives rise to the notion digital system which singles out physical systems that could be actually used, and possibly even built. (shrink)

Fodor and Pylyshyn's critique of connectionism has posed a challenge to connectionists: Adequately explain such nomological regularities as systematicity and productivity without postulating a "language of thought" (LOT). Some connectionists like Smolensky took the challenge very seriously, and attempted to meet it by developing models that were supposed to be non-classical. At the core of these attempts lies the claim that connectionist models can provide a representational system with a combinatorial syntax and processes sensitive to syntactic structure. They are not (...) implementation models because, it is claimed, the way they obtain syntax and structure sensitivity is not "concatenative," hence "radically different" from the way classicists handle them. In this paper, I offer an analysis of what it is to physically satisfy/realize a formal system. In this context, I examine the minimal truth-conditions of LOT Hypothesis. From my analysis it will follow that concatenative realization of formal systems is irrelevant to LOTH since the very notion of LOT is indifferent to such an implementation level issue as concatenation. I will conclude that to the extent to which they can explain the law-like cognitive regularities, a certain class of connectionist models proposed as radical alternatives to the classical LOT paradigm will in fact turn out to be LOT models, even though new and potentially very exciting ones. (shrink)

The notion of a "mental representation" is, arguably, in the first instance a theoretical construct of cognitive science. As such, it is a basic concept of the Computational Theory of Mind, according to which cognitive states and processes are constituted by the occurrence, transformation and storage (in the mind/brain) of information-bearing structures (representations) of one kind or another.

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

It is commonly assumed that images, whether in the world or in the head, do not have a privileged analysis into constituent parts. They are thought to lack the sort of syntactic structure necessary for representing complex contents and entering into sophisticated patterns of inference. I reject this assumption. “Image grammars” are models in computer vision that articulate systematic principles governing the form and content of images. These models are empirically credible and can be construed as literal grammars for images. (...) Images can have rich syntactic structure, though of a markedly different form than sentences in language. (shrink)

I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

Building on Christopher Peacocke’s account of analog perceptual contentand my own account of analog perceptual vehicles, I defend three claims: that theperception of magnitudes often has analog contents; that the perception of magni-tudes often has analog vehicles; and that the first claim is true in virtue of the second—that is, the analog vehicles help to ground the analog contents.

The aim of this paper is to argue that there is no unproblematic way of delineating perceptual beliefs from non-perceptual beliefs. The concept of perceptual belief is one of the central concepts not only of philosophy of perception but also of epistemology in a broad foundationalist tradition. Philosophers of perception talk about perceptual belief as the interface between perception and cognition and foundationalist epistemologists understand perceptual justification as a relation between perceptual states and perceptual beliefs. We consider three ways of (...) cashing out the difference between perceptual and non-perceptual beliefs (semantic, justificatory, and etiological) and argue that none of them works. Finally, we explore the possibility of understanding perceptual justification without relying on the concept of perceptual beliefs. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

Relative to digital computation, analogue computation has been neglected in the philosophical literature. To the extent that attention has been paid to analogue computation, it has been misunderstood. The received view—that analogue computation has to do essentially with continuity—is simply wrong, as shown by careful attention to historical examples of discontinuous, discrete analogue computers. Instead of the received view, I develop an account of analogue computation in terms of a particular type of analogue representation that allows for discontinuity. This account (...) thus characterizes all types of analogue computation, whether continuous or discrete. Furthermore, the structure of this account can be generalized to other types of computation: analogue computation essentially involves analogue representation, whereas digital computation essentially involves digital representation. Besides being a necessary component of a complete philosophical understanding of computation in general, understanding analogue computation is important for computational explanation in contemporary neuroscience and cognitive science. (shrink)

There is tension between commonly held views concerning phenomenal imagery on the one hand and our first-person epistemic access to it on the other. This tension is evident in many individual issues and experiments in philosophy and psychology (e.g. inattentional and change blindness, the speckled hen, dream coloration, visual periphery). To dissolve it, we can give up either (i) that we lack full introspective access to the phenomenal properties of our imagistic experiences, or (ii) that phenomenal imagery is fully determined, (...) or (iii) that phenomenal imagery does not exist. Which option is preferable? I explore the feasibility of option (ii) in more details by distinguishing between di erent kinds of indeterminacy. One of the most often proclaimed versions of indeterminacy is tied to Representationalism. However, I argue that in this context, Representationalism appears to be the least satisfying option, for which I give ten reasons. By abduction, we should reject Representationalism in favour of (i) or (iii)—the most parsimonious option being eliminativism, and the most conservative being the rejection of privileged access. The decision between these two, however, should be made on a case-by-case basis, depending on which is most adequate given the data. I illustrate this with the comparison between visual agnosia and Charles-Bonnet-Syndrome. (shrink)

This paper argues that many so-called digital technologies can be construed as notational technologies, explored through the example of Monegraph, an art and digital asset management platform built on top of the blockchain system originally developed for the cryptocurrency bitcoin. As the paper characterizes it, a notational technology is the performance of syntactic notation within a field of reference, a technologized version of what Nelson Goodman called a “notational system.” Notational technologies produce abstracted entities through positive and reliable, or constitutive, (...) tests of socially acceptable meaning. Accordingly, this account deviates from typical narratives of blockchains, instead demonstrating that blockchain technologies are effective at managing digital assets because they produce abstracted identities through the performance of notation. Since notational technologies rely on configurations of socially acceptable meaning, this paper also provides a philosophical account of how blockchain technologies are socially embedded. (shrink)

Recent philosophical and empirical contributions strongly suggest that perception attributes determinable properties to its objects. But a characterisation of determinability via attributed properties is restricted to the level of content and does not capture the difference between perceptual belief and perception on this score. In this paper, I propose a formal way of cashing out the difference between determinable belief and perception. On the view presented here, determinability in perception distinctively involves homogeneous representation or representation that exhibits special sorts of (...) formal type variability. This formal characterisation, I suggest, goes beyond traditional approaches to analog representation and parallels a baseline notion of analog computation. (shrink)

The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis.

There is much discussion about whether the human mind is a computer, whether the human brain could be emulated on a computer, and whether at all physical entities are computers (pancomputationalism). These discussions, and others, require criteria for what is digital. I propose that a state is digital if and only if it is a token of a type that serves a particular function - typically a representational function for the system. This proposal is made on a syntactic level, assuming (...) three levels of description (physical, syntactic, semantic). It suggests that being digital is a matter of discovery or rather a matter of how we wish to describe the world, if a functional description can be assumed. Given the criterion provided and the necessary empirical research, we should be in a position to decide on a given system (e.g. the human brain) whether it is a digital system and can thus be reproduced in a different digital system (since digital systems allow multiple realization). (shrink)

Characterizing different kinds of representation is of fundamental importance to cognitive science, and one traditional way of doing so is in terms of the analog–digital distinction. Indeed the distinction is often appealed to in ways both narrow and broad. In this paper I argue that the analog–digital distinction does not apply to representational schemes but only to representational systems, where a representational system is constituted by a representational scheme and its user, and that whether a representational system is analog or (...) non-analog depends on facts about that user. This aspect of the distinction has gone unnoticed, and I argue that the failure to notice it can be an impediment to scientific progress. (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)

Maps, notes, descriptions, diagrams, flowcharts, photographs, paintings, and prints, all, in one way or another, manage to be about things or stand for them. This article looks at three ways in which philosophers have explained the way that pictures represent the world. It starts by describing some leading perceptual accounts and then surveys contemporary content and structural alternatives.

One central debate in cognitive science is over imagery. Do images constitute, or constitute evidence for, a distinctive, depictive form of mental representation? The most sophisticated advocacy of this view has been developed by Kosslyn and his coworkers. This paper focuses on his position and argues (i) that though Kosslyn has not developed a satisfactory account of depiction, there is nothing in principle unintelligible about the idea of depictive neural representation, but (ii) Kosslyn's model of imagery rescues the intelligibility of (...) pictorialism at the cost of its explanatory power. (shrink)

Nelson Goodman’s theory of symbol systems expounded in his Languages of Art has been frequently criticized on many counts (cf. list of secondary literature in the entry “Goodman’s Aesthetics” of Stanford Encyclopedia of Philosophy and Sect. 3 below). Yet it exerts a strong influence and is treated as one of the major twentieth-century theories on the subject. While many of Goodman’s controversial theses are criticized, the technical notions he used to formulate them seem to have been treated as neutral tools. (...) One such technical notion is that of the density of symbol systems. This serves to distinguish linguistic symbols from pictorial representations (after Goodman entirely rejected resemblance in that role) and is a crucial part of Goodman’s explanation of what constitutes aesthetic experience (and so indirectly what is art). Thus its significance for Goodman’s theory is fundamental. The aim of this paper is a detailed, logical analysis of this notion. It turns out that Goodman’s definition is highly problematic and cannot be applied to symbol systems in the way Goodman envisaged. To conclude, Goodman’s theory is problematic not just because of its controversial theses but also because of logical problems with the technical notions used at its very core. Hence the controversial claims are not simply contestable, but inaccurately expressed. (shrink)

I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic (...) properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. (shrink)

In contrast to China’s efforts to upgrade its system of governance around a stupefying amount of data collection and electronic scoring, countries committed to democracy and human rights did not upgrade their systems. Instead, those countries ended up with surveillance capitalism. It is vital for the survival of those ideas about governance to perform such an upgrade. This paper aims to contribute to that goal. I propose a framework of epistemic actorhood in terms of four roles and characterize digital lifeworlds (...) and what matters about them both in terms of how they fit in with Max Tegmark’s distinctions among stages of life and in terms of how they generate their own episteme, the data episteme, with its immense possibilities of infopower. Epistemic rights that strengthen existing human rights – as part of a fourth generation of rights – are needed to protect epistemic actorhood in those roles. In the long run, we might well need a new kind of right, the right to the exercise of genuinely human intelligence. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...) computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

This paper challenges two orthodox theses: (a) that computational processes must be algorithmic; and (b) that all computed functions must be Turing-computable. Section 2 advances the claim that the works in computability theory, including Turing's analysis of the effective computable functions, do not substantiate the two theses. It is then shown (Section 3) that we can describe a system that computes a number-theoretic function which is not Turing-computable. The argument against the first thesis proceeds in two stages. It is first (...) shown (Section 4) that whether a process is algorithmic depends on the way we describe the process. It is then argued (Section 5) that systems compute even if their processes are not described as algorithmic. The paper concludes with a suggestion for a semantic approach to computation. (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 central claim of computationalism is generally taken to be that the brain is a computer, and that any computer implementing the appropriate program would ipso facto have a mind. In this paper I argue for the following propositions: (1) The central claim of computationalism is not about computers, a concept too imprecise for a scientific claim of this sort, but is about physical calculi (instantiated discrete formal systems). (2) In matters of formality, interpretability, and so forth, analog computation and (...) digital computation are not essentially different, and so arguments such as Searle''s hold or not as well for one as for the other. (3) Whether or not a biological system (such as the brain) is computational is a scientific matter of fact. (4) A substantive scientific question for cognitive science is whether cognition is better modeled by discrete representations or by continuous representations. (5) Cognitive science and AI need a theoretical construct that is the continuous analog of a calculus. The discussion of these propositions will illuminate several terminology traps, in which it''s all too easy to become ensnared. (shrink)

Ground Representationism is the position that for each phenomenal feature there is a representational feature that accounts for it. Against this thesis, Ned Block (The Puzzle of Phenomenal Precision, 2015) has provided an intricate argument that rests on the notion of “phenomenal precision”: the phenomenal precision of a percept may change at a different rate from its representational counterpart. If so, there is then no representational feature that accounts for a specific change of this phenomenal feature. Therefore, Ground Representationism cannot (...) be generally true. -/- Although the notion of phenomenal precision is intuitive, it is admittedly in need of clarification. Here I reconstruct Block’s argument by suggesting a way of estimating phenomenal precision that is based on the assumption that parts of perceptual wholes can share phenomenal features independently of their place in the whole. Understood like this, the overall argument shows what it is supposed to show. -/- A more thorough look at the notion of phenomenal precision suggests tension with Block’s other work: in order to be non-trivial, we have to accept that some of our phenomenality is not concrete, but only generic. Such “solely generic phenomenology”, however, is a position mainly held by opponents to Block’s Access- vs. Phenomenal Consciousness-distinction. Interpreting phenomenal imprecision as constituted by introspective imprecision does not suffice as a way out. It seems that phenomenal precision is either trivial, self-contradictory, or incompatible with Block’s position elsewhere. So some additional elucidation on this crucial notion is needed. (shrink)

Tenenbaum and Griffiths (Behavioral and Brain Sciences 24(4):629–640, 2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (Science 237(4820): 1317–1323, 1987) and Tversky’s (Psychological Review 84(4): 327–352, 1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that (...) generalisation as a Bayesian inference should be seen as a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

RÉSUMÉCet article est une défense de la position exposée par Nelson Goodman dans Langages de l'art. Goodman affirme que les images fonctionnent dans des systèmes symboliques denses. La différence entre texte et image ne se situe pas là où nous l'aurions spontanément cherchée : dans l'expérience perceptuelle que nous avons des images. Une telle théorie de la dépiction peut sembler iconoclaste, voire complètement fausse, et ce, parce que nous y voyons à tort une explication de la représentation picturale. Elle offre (...) cependant, rapportée à d'autres intuitions philosophiques qui essaiment ailleurs dans l’œuvre de Goodman, une meilleure compréhension du fonctionnement des images.ABSTRACTIn this paper, I draw unexpected conclusions from Nelson Goodman's views on depiction. Faithful to the symbolic turn of aesthetics in the twentieth century, Goodman argues that pictures are as conventional and natural as scripts. Unlike scripts, however, pictures work in dense symbolic systems. The difference between image and script cannot be found where we would have spontaneously looked: in our perceptual experience of pictures. Obviously, the structural approach which is at stake in Languages of Art is iconoclast; we often consider it surprising, or even absolutely misleading, perhaps because we do not connect the analyses Goodman conducts in his essay with the experience we ordinarily have of pictures. I argue that Goodman's position becomes clearer when it is reduced to a much more modest philosophical purpose: to offer a criterion for discrimination between scripts and pictures. Pictures, unlike scripts, are dense. Of course, that does not explain depiction. However, my account of Goodman's view, when connected to intuitions about cognitive processes that have spread elsewhere in his work, sheds light on the way pictures are connected with the objects they depict. (shrink)