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Summary Digital computation is computation using digital representations; analog computation is computation using analog representations. While this distinction is largely understood in practice, a precise account of the difference has been of some philosophical interest. Not all differences between the two kinds of representation are essential, and philosophical accounts of which differences are essential comprise most of this literature.
Key works The first serious discussion of analog versus digital representation is found in Goodman 1968. Further discussion is found in Lewis 1971 and Haugeland 1981. Katz 2008 defends Haugeland's view, and a more recent defense and extension of Lewis's ideas is presented in Maley 2011.
Introductions The best introduction to the analog/digital distinction is that presented in Goodman 1968, and Lewis's refutation in Lewis 1971.
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  1. Kazuyuki Aihara & Jun Kyung Ryeu (2001). Chaotic Neurons and Analog Computation. Behavioral and Brain Sciences 24 (5):810-811.
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  2. Kazuyuki Aihara & Jun Kyung Ryeu (2001). Chaotic Neurons and Analog Computation. Behavioral and Brain Sciences 24 (5):810-811.
    Chaotic dynamics can be related to analog computation. A possibility of electronically implementing the chaos -driven contracting system in the target article is explored with an analog electronic circuit with inevitable noise from the viewpoint of analog computation with chaotic neurons.
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  3. Kenneth Aizawa (2010). Computation in Cognitive Science: It is Not All About Turing-Equivalent Computation. Studies in History and Philosophy of Science Part A 41 (3):227-236.
    One account of the history of computation might begin in the 1930's with some of the work of Alonzo Church, Alan Turing, and Emil Post. One might say that this is where something like the core concept of computation was first formally articulated. Here were the first attempts to formalize an informal notion of an algorithm or effective procedure by which a mathematician might decide one or another logico-mathematical question. As each of these formalisms was shown to compute the same (...)
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  4. Eugenio Andrade (2003). The Processing of Information (Analog/Digital) is the Causal Factor of the Emergence of Natural Hierarchies. Ludus Vitalis 11 (20):85-106.
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  5. Francesco Berto & Jacopo Tagliabue (2014). The World is Either Digital or Analogue. Synthese 191 (3):481-497.
    We address an argument by Floridi (Synthese 168(1):151–178, 2009; 2011a), to the effect that digital and analogue are not features of reality, only of modes of presentation of reality. One can therefore have an informational ontology, like Floridi’s Informational Structural Realism, without commitment to a supposedly digital or analogue world. After introducing the topic in Sect. 1, in Sect. 2 we explain what the proposition expressed by the title of our paper means. In Sect. 3, we describe Floridi’s argument. In (...)
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  6. Francesco Berto & Jacopo Tagliabue (2012). Cellular Automata. Stanford Encyclopedia of Philosophy.
    Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following (...)
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  7. James A. Blachowicz (1997). Analog Representation Beyond Mental Imagery. Journal of Philosophy 94 (2):55-84.
  8. Paul Jeremiah Bohan Broderick (2001). The Analog-Digital Distinction and the Flow of Information. Dissertation, Boston University
    The analog vs. digital distinction is frequently used in computer science, computer technology and elsewhere. However, its precise nature is more elusive than might be expected. This dissertation defines a set of problems hidden within the conventions of ordinary and technical language, and suggests solutions to them. ;Chapter 1 examines ordinary language uses of the analog-digital distinction. Chapter 2 considers its use in technical contexts. There are two main ways of making the distinction that appear in both of the opening (...)
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  9. Arthur W. Burks & Alice R. Burks (1988). The History of Early Computer Switching. Grazer Philosophische Studien 32:3-36.
    We distinguish scanning switches, which only enumerate states, from function switches which transform input states into output states. For the latter we introduce a logical network symbolism. Our history of early computer switching begins with the suggestions of Ramon Lull and Gottfried Leibniz, surveys the evolution of mechanical scanning switches and the first mechanical function switches, and then describes the first electromechanical function switches. The main themes of the present paper are that William S. Jevons built the first substantial function (...)
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  10. Paul E. Ceruzzi (2003). A History of Modern Computing. MIT.
    Ceruzzi pens a history of computing from the development of the first electronic digital computer to the Web and dot-com crash.
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  11. David J. Chalmers, Analog Vs. Digital Computation.
    It is fairly well-known that certain hard computational problems (that is, 'difficult' problems for a digital processor to solve) can in fact be solved much more easily with an analog machine. This raises questions about the true nature of the distinction between analog and digital computation (if such a distinction exists). I try to analyze the source of the observed difference in terms of (1) expanding parallelism and (2) more generally, infinite-state Turing machines. The issue of discreteness vs continuity will (...)
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  12. Carol E. Cleland (2002). On Effective Procedures. Minds and Machines 12 (2):159-179.
    Since the mid-twentieth century, the concept of the Turing machine has dominated thought about effective procedures. This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic. I show that Turing machines cannot live up to their billing as paragons of effective procedure; at best, they may be said to provide us with mere procedure schemas. I argue that the concept of an effective procedure crucially depends upon distinguishing procedures as definite courses (...)
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  13. Jack Copeland, Even Turing Machines Can Compute Uncomputable Functions.
    Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability.
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  14. William Demopoulos (1987). On Some Fundamental Distinctions of Computationalism. Synthese 70 (January):79-96.
    The following paper presents a characterization of three distinctions fundamental to computationalism, viz., the distinction between analog and digital machines, representation and nonrepresentation-using systems, and direct and indirect perceptual processes. Each distinction is shown to rest on nothing more than the methodological principles which justify the explanatory framework of the special sciences.
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  15. Gordana Dodig-Crnkovic & Vincent C. Müller (2011). A Dialogue Concerning Two World Systems: Info-Computational Vs. Mechanistic. In Gordana Dodig-Crnkovic & Mark Burgin (eds.), Information and computation: Essays on scientific and philosophical understanding of foundations of information and computation. World Scientific 149-184.
    The dialogue develops arguments for and against a broad new world system - info-computationalist naturalism - that is supposed to overcome the traditional mechanistic view. It would make the older mechanistic view into a special case of the new general info-computationalist framework (rather like Euclidian geometry remains valid inside a broader notion of geometry). We primarily discuss what the info-computational paradigm would mean, especially its pancomputationalist component. This includes the requirements for a the new generalized notion of computing that would (...)
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  16. Chris Eliasmith (2000). Is the Brain Analog or Digital? Cognitive Science Quarterly 1 (2):147-170.
    It will always remain a remarkable phenomenon in the history of philosophy, that there was a time, when even mathematicians, who at the same time were philosophers, began to doubt, not of the accuracy of their geometrical propositions so far as they concerned space, but of their objective validity and the applicability of this concept itself, and of all its corollaries, to nature. They showed much concern whether a line in nature might not consist of physical points, and consequently that (...)
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  17. Nir Fresco (2015). Objective Computation Versus Subjective Computation. Erkenntnis 80 (5):1031-1053.
    The question ‘What is computation?’ might seem a trivial one to many, but this is far from being in consensus in philosophy of mind, cognitive science and even in physics. The lack of consensus leads to some interesting, yet contentious, claims, such as that cognition or even the universe is computational. Some have argued, though, that computation is a subjective phenomenon: whether or not a physical system is computational, and if so, which computation it performs, is entirely a matter of (...)
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  18. Nir Fresco (2013). Information Processing as an Account of Concrete Digital Computation. Philosophy and Technology 26 (1):31-60.
    It is common in cognitive science to equate computation (and in particular digital computation) with information processing. Yet, it is hard to find a comprehensive explicit account of concrete digital computation in information processing terms. An information processing account seems like a natural candidate to explain digital computation. But when ‘information’ comes under scrutiny, this account becomes a less obvious candidate. Four interpretations of information are examined here as the basis for an information processing account of digital computation, namely Shannon (...)
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  19. Nir Fresco & Marty J. Wolf (2014). The Instructional Information Processing Account of Digital Computation. Synthese 191 (7):1469-1492.
    What is nontrivial digital computation? It is the processing of discrete data through discrete state transitions in accordance with finite instructional information. The motivation for our account is that many previous attempts to answer this question are inadequate, and also that this account accords with the common intuition that digital computation is a type of information processing. We use the notion of reachability in a graph to defend this characterization in memory-based systems and underscore the importance of instructional information for (...)
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  20. Nelson Goodman (1968). Languages of Art. Bobbs-Merrill.
    . . . Unlike Dewey, he has provided detailed incisive argumentation, and has shown just where the dogmas and dualisms break down." -- Richard Rorty, The Yale Review.
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  21. D. S. Graca (2004). Some Recent Developments on Shannon's General Purpose Analog Computer. Mathematical Logic Quarterly 50 (4):473.
    This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. Finally, it (...)
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  22. John Haugeland (1981). Analog and Analog. Philosophical Topics 12 (1):213-226.
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  23. Albert S. Jackson (1960). Analog Computation. McGraw-Hill.
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  24. Kenneth J. Janik, Shih-Lien Lu & Ben Lee (1996). An Analog VLSI Chip for Low-Level Computer Vision. Esda 1996: Expert Systems and Ai; Neural Networks 7:211.
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  25. Matthew Katz (2008). Analog and Digital Representation. Minds and Machines 18 (3):403-408.
    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.
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  26. David Lewis (1971). Analog and Digital. Noûs 5 (3):321-327.
  27. Bruce J. MacLennan (1994). Words Lie in Our Way. Minds and Machines 4 (4):421-37.
    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 (...)
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  28. Bruce J. MacLennan (1993). Grounding Analog Computers. Philosophical Explorations 2:8-51.
    In this commentary on Harnad's "Grounding Symbols in the Analog World with Neural Nets: A Hybrid Model," the issues of symbol grounding and analog (continuous) computation are separated, it is argued that symbol graounding is as important an issue for analog cognitive models as for digital (discrete) models. The similarities and differences between continuous and discrete computation are discussed, as well as the grounding of continuous representations. A continuous analog of the Chinese Room is presented.
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  29. Corey J. Maley (2011). Analog and Digital, Continuous and Discrete. Philosophical Studies 155 (1):117-131.
    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 (...)
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  30. Jacques Mallah (forthcoming). Structure and Dynamics in Implementation of Computations. In Yasemin J. Erden (ed.), Proceedings of the 7th AISB Symposium on Computing and Philosophy:. AISB
    Without a proper restriction on mappings, virtually any system could be seen as implementing any computation. That would not allow characterization of systems in terms of implemented computations and is not compatible with a computationalist philosophy of mind. Information-based criteria for independence of substates within structured states are proposed as a solution. Objections to the use of requirements for transitions in counterfactual states are addressed, in part using the partial-brain argument as a general counterargument to neural replacement arguments.
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  31. Drew McDermott (2001). The Digital Computer as Red Herring. Psycoloquy 12 (54).
    Stevan Harnad correctly perceives a deep problem in computationalism, the hypothesis that cognition is computation, namely, that the symbols manipulated by a computational entity do not automatically mean anything. Perhaps, he proposes, transducers and neural nets will not have this problem. His analysis goes wrong from the start, because computationalism is not as rigid a set of theories as he thinks. Transducers and neural nets are just two kinds of computational system, among many, and any solution to the semantic problem (...)
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  32. Torin Monahan (2001). The Analog Divide. Acm Sigcas Computers and Society 31 (3):22-31.
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  33. Vincent C. Müller (2014). Pancomputationalism: Theory or Metaphor? In Ruth Hagengruber & Uwe Riss (eds.), Philosophy, computing and information science. Pickering & Chattoo 213-221.
    The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem it is trying to solve, and how. I propose two interpretations of pancomputationalism as a theory: I) the world is a computer and II) the world can be described as a computer. The first implies a thesis of supervenience of the physical over computation (...)
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  34. Vincent C. Müller (2013). What is a Digital State? In Mark J. Bishop & Yasemin Erden (eds.), The Scandal of Computation - What is Computation? - AISB Convention 2013. AISB 11-16.
    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 (...)
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  35. Vincent C. Müller (2011). On the Possibilities of Hypercomputing Supertasks. Minds and Machines 21 (1):83-96.
    This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such (...)
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  36. Vincent C. Müller (2009). Susan Stuart & Gordana Dodig Crnkovic : 'Computation, Information, Cognition: The Nexus and the Liminal'. [REVIEW] Cybernetics and Human Knowing 16 (3-4):201-203.
    Review of: "Computation, Information, Cognition: The Nexus and the Liminal", Ed. Susan Stuart & Gordana Dodig Crnkovic, Newcastle: Cambridge Scholars Publishing, September 2007, xxiv+340pp, ISBN: 9781847180902, Hardback: £39.99, $79.99 ---- Are you a computer? Is your cat a computer? A single biological cell in your stomach, perhaps? And your desk? You do not think so? Well, the authors of this book suggest that you think again. They propose a computational turn, a turn towards computational explanation and towards the explanation of (...)
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  37. Vincent C. Müller (2008). Representation in Digital Systems. In Adam Briggle, Katinka Waelbers & Brey Philip (eds.), Current issues in computing and philosophy. IOS Press 116-121.
    Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...)
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  38. Gualtiero Piccinini (2008). Computers. Pacific Philosophical Quarterly 89 (1):32–73.
    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 (...)
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  39. Itamar Pitowski (1990). The Physical Church Thesis and Physical Computational Complexity. Iyyun 39:81-99.
  40. Lee A. Rubel (1989). Digital Simulation of Analog Computation and Church's Thesis. Journal of Symbolic Logic 54 (3):1011-1017.
  41. Rahul Sarpeshkar (1998). Analog Versus Digital: Extrapolating From Electronics to Neurobiology. Neural Computation 10 (7):1601--1638.
    We review the pros and cons of analog and digital computation. We propose that computation that is most efficient in its use of resources is neither analog computation nor digital computation but, rather, a mixture of the two forms. For maximum efficiency, the information and information-processing resources of the hybrid form must be distributed over many wires, with an optimal signal-to-noise ratio per wire. Our results suggest that it is likely that the brain computes in a hybrid fashion and that (...)
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  42. Whit Schonbein (2014). Varieties of Analog and Digital Representation. Minds and Machines 24 (4):415-438.
    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 (...)
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  43. Thomas A. Sebeok (1967). The Informational Model of Language: Analog and Digital Coding in Animal and Human Communication (an Excerpt). In Donald C. Hildum (ed.), Language and Thought: An Enduring Problem in Psychology. London,: Van Nostrand, 37--40.
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  44. Hava T. Siegelmann (2003). Neural and Super-Turing Computing. Minds and Machines 13 (1):103-114.
    ``Neural computing'' is a research field based on perceiving the human brain as an information system. This system reads its input continuously via the different senses, encodes data into various biophysical variables such as membrane potentials or neural firing rates, stores information using different kinds of memories (e.g., short-term memory, long-term memory, associative memory), performs some operations called ``computation'', and outputs onto various channels, including motor control commands, decisions, thoughts, and feelings. We show a natural model of neural computing that (...)
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  45. Daniel Silva Graça (2004). Some Recent Developments on Shannon's General Purpose Analog Computer. Mathematical Logic Quarterly 50 (4‐5):473-485.
    This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. Finally, it (...)
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  46. Michael Starks, David Wolpert on Impossibility, Incompleteness, the Liar Paradox, the Limits of Computation, a Non-Quantum Mechanical Uncertainty Principle and the Universe as Computer—the Ultimate Theorem in Turing Machine Theory.
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even (...)
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  47. Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.
    If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They (...)
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  48. Russell Trenholme (1994). Analog Simulation. Philosophy of Science 61 (1):115-131.
    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 (...)
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  49. Jonathan A. Waskan (forthcoming). A Virtual Solution to the Frame Problem. Proceedings of the First IEEE-RAS International Conference on Humanoid Robots.
    We humans often respond effectively when faced with novel circumstances. This is because we are able to predict how particular alterations to the world will play out. Philosophers, psychologists, and computational modelers have long favored an account of this process that takes its inspiration from the truth-preserving powers of formal deduction techniques. There is, however, an alternative hypothesis that is better able to account for the human capacity to predict the consequences worldly alterations. This alternative takes its inspiration from the (...)
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  50. John Zeimbekis (2015). Why Digital Pictures Are Not Notational Representations. Journal of Aesthetics and Art Criticism 73 (4):449-453.