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)

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)

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)

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)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ claims that cognition is and can be (...) understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

This article argues that if panpsychism is true, then there are grounds for thinking that digitally-based artificial intelligence may be incapable of having coherent macrophenomenal conscious experiences. Section 1 briefly surveys research indicating that neural function and phenomenal consciousness may be both analog in nature. We show that physical and phenomenal magnitudes—such as rates of neural firing and the phenomenally experienced loudness of sounds—appear to covary monotonically with the physical stimuli they represent, forming the basis for an analog relationship between (...) the three. Section 2 then argues that if this is true and micropsychism—the panpsychist view that phenomenal consciousness or its precursors exist at a microphysical level of reality—is also true, then human brains must somehow manipulate fundamental microphysical-phenomenal magnitudes in an analog manner that renders them phenomenally coherent at a macro level. However, Sect. 3 argues that because digital computation abstracts away from microphysical-phenomenal magnitudes—representing cognitive functions non-monotonically in terms of digits—digital computation may be inherently incapable of realizing coherent macroconscious experience. Thus, if panpsychism is true, digital AI may be incapable of achieving phenomenal coherence. Finally, Sect. 4 briefly examines our argument’s implications for Tononi’s Integrated Information Theory theory of consciousness, which we contend may need to be supplanted by a theory of macroconsciousness as analog microphysical-phenomenal information integration. (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 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)