About this topic
Summary The theory of computation is a mathematical theory about the properties of abstract computational objects, such as algorithms and Turing machines. They are abstract in the sense that they ignore or leave out considerations about by features of physical implementations, such as finite memory.  In contrast, computations are done by physical systems: concrete machines made of silicon and metal, or brains made of biological materials, can run algorithms or implement Turing machines. This area is concerned with questions about how the abstract objects that are in the purview of the theory of computation relate to physical systems.
Key works The relationship between abstract computation and physical systems such as brains is a central issue in philosophy of mind, particularly given the rise of computational functionalism as a foundation for the study of the mind.  Here the work of Chalmers 1996 provides a good starting point for bridging the theory of computation with theories of physical systems by means of an implementation relation. 
Introductions A good introduction is Piccinini 2010
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  1. Khai thác và tối ưu hóa trí tuệ nhân tạo cho chuyển đổi xã hội–sinh thái công bằng và hài hòa.Thi-Huong Pham, Nguyen Hong-Kong T. & Manh-Tung Ho - manuscript
    Các trào lưu như hiện tượng “túi mù”, hầu hết các xu hướng tiêu dùng dựa trên nền tảng và được điều khiển bởi thuật toán, dù thúc đẩy tăng trưởng kinh tế và tạo việc làm, hoàn toàn thiếu tính bền vững—chúng góp phần làm gia tăng đa khủng hoảng hơn là mang lại lợi ích. Những vấn đề này bao gồm: (i) khủng hoảng giá trị; (ii) khủng hoảng sức khỏe tinh thần; (iii) khủng hoảng hệ sinh thái. (...)
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  2. PHÂN TÍCH VÔ THỨC THUẬT TOÁN QUA TÂM LÝ HỌC PHÂN TÍCH CỦA CARL JUNG: TỪ LÝ THUYẾT CỔ MẪU ĐẾN HIỆN TƯỢNG PHÓNG CHIẾU TRONG MỐI QUAN HỆ GIỮA AI VÀ CON NGƯỜI.Nguyen Duc-Hung, Pham Thi-Quynh & Manh-Tung Ho - manuscript
    Trong kỷ nguyên bùng nổ của trí tuệ nhân tạo (AI), việc hiểu biết đúng và kịp thời về bản chất của AI trở thành yêu cầu cấp thiết đối với cả cá nhân lẫn quốc gia nhằm tận dụng hiệu quả các cơ hội và giải quyết được các thách thức cũng như yêu cầu của thời đại. Trên cơ sở đó, bài viết nghiên cứu khái niệm “vô thức thuật toán” (algorithmic unconscious) như một khái niệm chứa đựng (...)
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  3. CODES_ Structured Resonance as a Deterministic Alternative to Stochastic Emergence.Devin Bostick - manuscript
    Note: this and "Constants as Phase Conditions_ Reframing ε₀, α, and the Mass Defect via Structured Resonance" are part of a twin series to make CODES easier to understand. -/- Abstract Modern scientific and computational systems rely on probabilistic modeling as a default approach to emergence, intelligence, and complexity. Yet, these stochastic paradigms remain epistemologically incomplete and structurally fragile. In this paper, I introduce CODES (Chirality of Dynamic Emergent Systems) as a new coherence-first framework that replaces randomness with deterministic phase (...)
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  4. Decentralized Key Protocol (DKP): A Hybrid Framework for Privacy-Preserving File Storage and Sharing in Social Networking.Temesgen Degu - manuscript
    The Decentralized Key Protocol (DKP) is a hybrid framework designed to enhance privacy, security, and user control in social networking applications transitioning from centralized to decentralized architectures. DKP combines centralized storage for scalability with blockchain-based access control and integrity verification. Files are stored on centralized servers with random tags, anonymizing user data, while key-tag-hash tuples on the blockchain ensure secure access and file integrity. A permission request smart contract enables secure file sharing, where followers must request access for each file (...)
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  5. From Spiral to Structure_ How Prime Harmonic Resonance Resolves Nature’s Irrational Forms and Kelvin’s Conjecture.Devin Bostick - manuscript
    Abstract This paper reinterprets classical biological and geometric phenomena—phyllotaxis and Kelvin’s truncated octahedral tiling—through the CODES framework (Chirality of Dynamic Emergent Systems). We show that irrational constants, Fibonacci series, and space-filling polyhedra are not mathematical accidents, but deterministic outcomes of prime-driven structured resonance. While calculus and probability provided useful approximations during the era of uncertainty, they now give way to coherence-first models. These new models describe reality not through limit-based derivation or stochastic estimation, but through direct alignment between phase-locked systems. (...)
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  6. A Statistical Time Machine: How Phylogenetic Methods Illuminate Life’s Evolutionary Story.Bói Cá Nhỏ - 2025 - Xomchim.Com.
    Phylogenetic comparative methods (PCMs) are transforming how scientists study the evolution of traits by integrating statistical tools with evolutionary theory.
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  7. Stock Market Prediction using Artificial Neural Network & Text Mining.Sahoo Amiya Kumar - 2020 - International Journal of Recent Technology and Engineering (IJRTE) 8 (5):4040 - 4043.
    The art of prediction of stock market volatility has always been a most challenged interdisciplinary research problem among scientist due to its highly non- linear nature of market flow. This paper tries to analysis the historical data of BSE Sensex using extreme volatilities estimators, GARCH, ANN and new proposed Text Mining approach for stock market predictions. Finally experimental results illustrates that the new proposed Text model can able to predict the volatilities of the stock price better than other models.
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  8. Frames of Discovery and the Formats of Cognitive Representation.Alfredo Vernazzani & Dimitri Coelho Mollo - forthcoming - In Gualtiero Piccinini, Neurocognitive Foundations of Mind. Routledge.
    Abstract: Research on the nature and varieties of the format of cognitive representations in philosophy and cognitive science have been partly shaped by analogies to external, public representations. In this paper, we argue that relying on such analogies contributes to framing the question of cognitive formats in problematic, potentially counterproductive ways. We show that cognitive and public representations differ in many of their central features, making analogies to public representations ill-suited to improving our understanding of cognitive formats. We illustrate these (...)
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  9. Consciousness without biology: An argument from anticipating scientific progress.Leonard Dung - manuscript
    I develop the anticipatory argument for the view that it is nomologically possible that some non-biological creatures are phenomenally conscious, including conventional, silicon-based AI systems. This argument rests on the general idea that we should make our beliefs conform to the outcomes of an ideal scientific process and that such an ideal scientific process would attribute consciousness to some possible AI systems. This kind of ideal scientific process is an ideal application of the iterative natural kind (INK) strategy, according to (...)
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  10. Two senses of medium independence.Danielle J. Williams - forthcoming - Mind and Language.
    The term “medium independence” has different meanings. One sense maps onto “abstract-as-abstracta” descriptions while the other maps onto “abstract-as-omission” descriptions. Both senses have been deployed when it comes to understanding the nature of physical computation. However, because medium independence is a polysemic term, the sense being used should be clearly stated. If the sense is not clearly stated, then those who wish to engage in debates regarding medium independence and physical computation run the risk of conflating different but related issues (...)
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  11. It takes two to make a view go right. [REVIEW]Danielle J. Williams - 2024 - The Brains Blog.
    The Physical Signature of Computation is the most “robust” mapping view that’s ever hit the market. It is impressive in its detail and the careful attention paid to its characterization of both the physical system and the formal computational description—a true service to the philosophical literature. The book promises a “unified account of artifact and biological computation,” but here’s where things take a turn: after handling artifacts, the Robust Mapping Account fades from view and the Mechanistic Account of Physical Computation (...)
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  12. The Self-Evidencing Agent.Jakob Hohwy - forthcoming - Cambridge, Mass.: MIT Press.
    The Self-Evidencing Agent offers a unique method for addressing difficult philosophical questions. Self-evidencing occurs when an agent uses their model of the world and of themselves to explain what they observe in the world and in themselves, such that those observations become evidence for their model – the more agents explain, the more they self-evidence. This book argues that there is good reason to cast an agent’s existence itself in terms of self-evidencing, and that if we begin from this as (...)
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  13. Ethical Concerns in Computational Linguistic Field National Defense: A Philosophical Investigation of Language and Security.Mhd Halkis Malkis4 - 2024 - Linguistic and Philosophical Investigations 23 (1):386–396.
    This research examines ethical issues in computational linguistics that can be applied to national defense by analyzing philosophical and security language. The increasing use of language contexts, such as intelligence and communication data analysis, raises ethical and philosophical challenges related to privacy, control, and accuracy. This research aims to identify and analyze ethical issues, especially in the use of computational linguistics in defense applications, as well as their implications for the protection of individual rights and privacy. This method involves reviewing (...)
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  14. Ingenious Genes: How Gene Regulation Networks Evolve to Control Development.Roger Sansom - 2011 - MIT Press.
    A proposal for a new model of the evolution of gene regulation networks and development that draws on work from artificial intelligence and philosophy of mind. Each of us is a collection of more than ten trillion cells, busy performing tasks crucial to our continued existence. Gene regulation networks, consisting of a subset of genes called transcription factors, control cellular activity, producing the right gene activities for the many situations that the multiplicity of cells in our bodies face. Genes working (...)
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  15. Wide computationalism revisited: distributed mechanisms, parismony and testability.Luke Kersten - 2024 - Philosophical Explorations 27 (2):1-18.
    Recent years have seen a surge of interest in applying mechanistic thinking to computational accounts of implementation and individuation. One recent extension of this work involves so-called ‘wide’ approaches to computation, the view that computational processes spread out beyond the boundaries of the individual. These ‘mechanistic accounts of wide computation’ maintain that computational processes are wide in virtue of being part of mechanisms that extend beyond the boundary of the individual. This paper aims to further develop the mechanistic account of (...)
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  16. Serendipity and inherent non-linear thinking can help address the climate and environmental conundrums.Quan-Hoang Vuong, Viet-Phuong La & Minh-Hoang Nguyen - 2025 - Sustainability: Science, Practice and Policy 21 (1):2480428.
    Humankind is currently confronted with a critical challenge that determines its very existence, not only on an individual, racial, or national level but as a whole species: the fight against climate change and environmental degradation. To win this battle, humanity needs innovations and non-linear thinking. Nature has long been a substantial information source for unthinkable discoveries that save human lives. This Commentary suggests that by understanding the nature, emergence, and mechanism of serendipity, the survival skill of humans, humanity can capitalize (...)
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  17. 对数字全球化时代未来智慧城市的思考 [Reflections on the Future of Smart Cities in the Era of Digital Globalization] (2nd edition).David Bartosch - 2022 - Xinhua Wenzhai (Ban Yue Kan) 新华文摘 (半月刊) 738:138-140. Translated by Peng Bei 彭蓓.
  18. 对数字全球化时代未来智慧城市的思考 [Reflections on the Future of Smart Cities in the Era of Digital Globalization].David Bartosch - 2021 - Guowai Shehui Kexue 国外社会科学 Social Sciences Abroad 347 (5):74-79. Translated by Peng Bei 彭蓓.
  19. Electrical analysis of logical complexity: Brain Informatics Open Access an exploratory eeg study of logically valid/ invalid deducive inference.Salto Francisco, Requena Carmen, Rodríguez Víctor, Poza Jesús & Hornero Roberto - 2023 - Brain Informatics 10 (13):1-15.
    Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid (...)
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  20. Electrophysiological connectivity of logical deduction: Early cortical MEG study.Anton Toro Luis F., Salto Francisco, Requena Carmen & Maestu Fernando - 2023 - Cortex 166:365-376.
    Complex human reasoning involves minimal abilities to extract conclusions implied in the available information. These abilities are considered “deductive” because they exemplify certain abstract relations among propositions or probabilities called deductive arguments. However, the electrophysiological dynamics which supports such complex cognitive pro- cesses has not been addressed yet. In this work we consider typically deductive logico- probabilistically valid inferences and aim to verify or refute their electrophysiological functional connectivity differences from invalid inferences with the same content (same relational variables, same (...)
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  21. Implementing a Computing System: A Pluralistic Approach.Syed AbuMusab - 2023 - Global Philosophy 33 (1):1-19.
    In chapter eleven of "On The Foundation of Computing," Primiero takes on the implementation debate in computer science. He contrasts his theory with two other views—the Semantic and the specification—artifact. In this paper, I argue that there is a way to fine-tune the implementation concept further. Firstly, contrary to Primiero, I claim it is problematic to separate the implementation relationship from the conditions which make it correct. Secondly, by taking a pluralistic approach to implementation, I claim it is a mistake (...)
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  22. TC*.Didehvar Farzad - manuscript
    One of the possible hypotheses about time is to consider any instant of time as fuzzy number, so that two instants of time could be overlapped. Historically, some Mathematicians and Philosophers have had similar ideas like Brouwer and Husserl [5]. Throughout this article, the impact of this change on Theory of Computation and Complexity Theory are studied. In order to rebuild Theory of Computation in a more successful and productive approach to solve some major problems in Complexity Theory, the present (...)
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  23. Bruce D'Ambrosio, Qualitative Process Theory Using Linguistic Variables[REVIEW]Varol Akman - 1991 - ACM SIGART Bulletin 2 (2):25-27.
    Ken Forbus's Qualitative Process Theory (QPT) is a popular theory for reasoning about the physical aspects of the daily world. Qualitative Process Theory Using Linguistic Variables by Bruce D'Ambrosio (Springer-Verlag, New York, 1989) is an attempt to fill some gaps in QPT.
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  24. Strengthening Weak Emergence.Nora Berenstain - 2020 - Erkenntnis 87 (5):2457-2474.
    Bedau's influential (1997) account analyzes weak emergence in terms of the non-derivability of a system’s macrostates from its microstates except by simulation. I offer an improved version of Bedau’s account of weak emergence in light of insights from information theory. Non-derivability alone does not guarantee that a system’s macrostates are weakly emergent. Rather, it is non-derivability plus the algorithmic compressibility of the system’s macrostates that makes them weakly emergent. I argue that the resulting information-theoretic picture provides a metaphysical account of (...)
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  25. A Dilemma for Solomonoff Prediction.Sven Neth - 2023 - Philosophy of Science 90 (2):288-306.
    The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...)
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  26. Originemology: Science behind the Beginning of Everything.Joey Lawsin - 2022 - Morrisville, NC, USA: Lulu Press Inc.
    How did information emerge into the early minds of our very first humans? Who supplied our primitive ancestors with information? Where did it originate? Where did it come from? Was the source of information a who or a what? Was it god, space aliens, or something else? How was information stored and retrieved by an aneural organism? -/- These basic questions were the keys that opened the conceptualization of a new school of thought known as Originemology, a pioneering discipline that (...)
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  27. Why Simpler Computer Simulation Models Can Be Epistemically Better for Informing Decisions.Casey Helgeson, Vivek Srikrishnan, Klaus Keller & Nancy Tuana - 2021 - Philosophy of Science 88 (2):213-233.
    For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many times over, and because computing resources are finite, uncertainty assessment is more feasible using models that demand less computer processor time. Such models are generally simpler in the sense of being more idealized, or less realistic. So modelers face a trade-off between realism and uncertainty quantification. Seeing this trade-off for the important epistemic issue (...)
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  28. How to be concrete: mechanistic computation and the abstraction problem.Luke Kersten - 2020 - Philosophical Explorations 23 (3):251-266.
    This paper takes up a recent challenge to mechanistic approaches to computational implementation, the view that computational implementation is best explicated within a mechanistic framework. The challenge, what has been labelled “the abstraction problem”, claims that one of MAC’s central pillars – medium independence – is deeply confused when applied to the question of computational implementation. The concern is that while it makes sense to say that computational processes are abstract (i.e. medium-independent), it makes considerably less sense to say that (...)
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  29. Complying with norms. a neurocomputational exploration.Matteo Colombo - 2012 - Dissertation, University of Edinburgh
    The subject matter of this thesis can be summarized by a triplet of questions and answers. Showing what these questions and answers mean is, in essence, the goal of my project. The triplet goes like this: Q: How can we make progress in our understanding of social norms and norm compliance? A: Adopting a neurocomputational framework is one effective way to make progress in our understanding of social norms and norm compliance. Q: What could the neurocomputational mechanism of social norm (...)
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  30. Integrating computation into the mechanistic hierarchy in the cognitive and neural sciences.Lotem Elber-Dorozko & Oron Shagrir - 2019 - Synthese 199 (Suppl 1):43-66.
    It is generally accepted that, in the cognitive and neural sciences, there are both computational and mechanistic explanations. We ask how computational explanations can integrate into the mechanistic hierarchy. The problem stems from the fact that implementation and mechanistic relations have different forms. The implementation relation, from the states of an abstract computational system to the physical, implementing states is a homomorphism mapping relation. The mechanistic relation, however, is that of part/whole; the explaining features in a mechanistic explanation are the (...)
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  31. Punched Card Methods in Scientific Computation. Wallace J. EckertCalculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics and Calculating Instruments and Machines. Douglas R. Hartree. [REVIEW]Paul Ceruzzi - 1986 - Isis 77 (1):154-156.
  32. Qu’est-ce que l’informatique.Franck Varenne - 2009 - Paris: Librairie Philosophique Vrin.
    Que peut bien etre l'informatique pour nous envahir a ce point? Se fondant sur des travaux recents de philosophie de l'informatique, ce livre revient sur la notion de Machine de Turing et sur la These de Church: l'ordinateur peut-il tout simuler? (le vivant, l'esprit). Eclairant les notions de computation et d'abstraction a la lumiere de celles de simulation et d'ontologie, il montre en quoi l'informatique n'est ni simplement une branche des mathematiques, ni une technologie de l'information, mais une technologie des (...)
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  33. Extruding Intentionality from the Metaphysical Flux.Josefa Toribio - 1999 - Journal of Experimental and Theoretical Ai 11:501-518.
    On the Origin of Objects is, at heart, an extended search for a non-circular and nonreductive characterization of two key notions: intentionality and computation. Only a non-circular and non-reductive account of these key notions can, Smith believes, provide a secure platform for a proper understanding of the mind. The project has both a negative and a positive aspect. Negatively, Smith rejects views that attempt to identify the key notions with lower-level physical properties, arguing instead for a more abstract and systemic (...)
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  34. Social learning by observation is analogue, instruction is digital.Marion Blute - 2001 - Behavioral and Brain Sciences 24 (2):327-327.
    Social learning in the strict sense is learning by observation or instruction. Learning by observation appears to be an analogue process while learning by instruction is digital. In evolutionary biology this distinction is currently thought to have implications for the extent to which mechanisms can function successfully as an inheritance system in an evolutionary process.
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  35. Turing-, human- and physical computability: An unasked question. [REVIEW]Eli Dresner - 2008 - Minds and Machines 18 (3):349-355.
    In recent years it has been convincingly argued that the Church-Turing thesis concerns the bounds of human computability: The thesis was presented and justified as formally delineating the class of functions that can be computed by a human carrying out an algorithm. Thus the Thesis needs to be distinguished from the so-called Physical Church-Turing thesis, according to which all physically computable functions are Turing computable. The latter is often claimed to be false, or, if true, contingently so. On all accounts, (...)
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  36. (1 other version)Representation of sequential circuits in combinatory logic.Frederic B. Fitch - 1958 - Philosophy of Science 25 (4):263-279.
    We will be dealing with “sequential circuits” in the sense of E. F. Moore and G. H. Mealy. Each such circuit is assumed to have a finite number of input wires and a finite number of output wires. Each element of such a circuit will be assumed to be an and-circuit, an or-circuit, a not-circuit, or a delay circuit, for some specified temporal delay. Each element has one output wire which, however, may branch in order to serve several purposes simultaneously. (...)
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  37. The interactive nature of computing: Refuting the strong church–turing thesis. [REVIEW]Dina Goldin & Peter Wegner - 2008 - Minds and Machines 18 (1):17-38.
    The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new (...)
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  38. (2 other versions)Infinite time Turing machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  39. Computational empiricism.Paul Humphreys - 1995 - Foundations of Science 1 (1):119-130.
    I argue here for a number of ways that modern computational science requires a change in the way we represent the relationship between theory and applications. It requires a switch away from logical reconstruction of theories in order to take surface mathematical syntax seriously. In addition, syntactically different versions of the same theory have important differences for applications, and this shows that the semantic account of theories is inappropriate for some purposes. I also argue against formalist approaches in the philosophy (...)
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  40. Synchronic and diachronic emergence.Paul Humphreys - 2008 - Minds and Machines 18 (4):431-442.
    I discuss here a number of different kinds of diachronic emergence, noting that they differ in important ways from synchronic conceptions. I argue that Bedau’s weak emergence has an essentially historical aspect, in that there can be two indistinguishable states, one of which is weakly emergent, the other of which is not. As a consequence, weak emergence is about tokens, not types, of states. I conclude by examining the question of whether the concept of weak emergence is too weak and (...)
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  41. Reflections on gödel's and Gandy's reflections on Turing's thesis.David Israel - 2002 - Minds and Machines 12 (2):181-201.
    We sketch the historical and conceptual context of Turing's analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland's views.
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  42. The elementary units of meaning.Paul J. M. Jorion - 2000 - Behavioral and Brain Sciences 23 (4):483-484.
    Examining the implications of a localist model for linguistic performance, I show the strengths of the P-graph, a network of elementary units of meaning where utterance results from relaxation through the operation of a dynamics of affect values. A unit of meaning is stored in a synaptic connection that brings together two words. Such a model, consistent with the anatomy and physiology of the neural tissue, eschews a number of traditional pitfalls of “semantic networks”: (1) ambiguity ceases to be an (...)
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  43. Programs, grammars and arguments: A personal view of some connections between computation, language and logic.J. Lambek - 1997 - Bulletin of Symbolic Logic 3 (3):312-328.
    As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...)
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  44. Theories of structure versus theories of change.Melanie Mitchell - 1998 - Behavioral and Brain Sciences 21 (5):645-646.
    The dynamics/computation debate recalls a similar debate in the evolutionary biology community concerning the relative primacy of theories of structure versus theories of change. A full account of cognition will require a rapprochement between such theories and will include both computational and dynamical notions. The key to making computation relevant to cognition is not making it analog, but rather understanding how functional information-processing structures can emerge in complex dynamical systems.
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  45. The problem of the many minds.Bradley Monton & Sanford Goldberg - 2006 - Minds and Machines 16 (4):463-470.
    It is argued that, given certain reasonable premises, an infinite number of qualitatively identical but numerically distinct minds exist per functioning brain. The three main premises are (1) mental properties supervene on brain properties; (2) the universe is composed of particles with nonzero extension; and (3) each particle is composed of continuum-many point-sized bits of particle-stuff, and these points of particle-stuff persist through time.
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  46. Comments on `two undecidable problems of analysis'.Bruno Scarpellini - 2003 - Minds and Machines 13 (1):79-85.
    We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is (...)
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  47. Physical hypercomputation and the church–turing thesis.Oron Shagrir & Itamar Pitowsky - 2003 - Minds and Machines 13 (1):87-101.
    We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.
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  48. Logically possible machines.Eric Steinhart - 2002 - Minds and Machines 12 (2):259-280.
    I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...)
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  49. On physicalism and algorithmism: Can machines think?Hao Wang - 1993 - Philosophia Mathematica 1 (2):97-138.
    This essay discusses a number of questions which arise from attempts to reduce the mental to the physical or the mental and the physical to the computational. It makes, in an organized way, several basic distinctions between different kinds of accounts of the mind. It reconstructs and elaborates many discussions between Gödel and the author on the nature of the human mind, with special emphasis on its mathematical capabilities.
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  50. Is there a nonrecursive decidable equational theory?Benjamin Wells - 2002 - Minds and Machines 12 (2):301-324.
    The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, (...)
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