Results for 'Mathematical Theory of Computation'

997 found
Order:
  1. The Mathematical Theory of Categories in Biology and the Concept of Natural Equivalence in Robert Rosen.Franck Varenne - 2013 - Revue d'Histoire des Sciences 66 (1):167-197.
    The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  2. Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  33
    Towards a Theory of Computation Similar to Some Other Scientific Theories.Antonino Drago - manuscript
    At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it (...)
    Download  
     
    Export citation  
     
    Bookmark  
  4. A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory.Vasil Penchev - 2020 - Information Theory and Research eJournal 1 (15):1-13.
    A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section (...)
    Download  
     
    Export citation  
     
    Bookmark  
  5.  52
    Observability of Turing Machines: A Refinement of the Theory of Computation.Yaroslav Sergeyev & Alfredo Garro - 2010 - Informatica 21 (3):425–454.
    The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   3 citations  
  6.  86
    The Changing Practices of Proof in Mathematics: Gilles Dowek: Computation, Proof, Machine. Cambridge: Cambridge University Press, 2015. Translation of Les Métamorphoses du Calcul, Paris: Le Pommier, 2007. Translation From the French by Pierre Guillot and Marion Roman, $124.00HB, $40.99PB.Andrew Arana - 2017 - Metascience 26 (1):131-135.
    Review of Dowek, Gilles, Computation, Proof, Machine, Cambridge University Press, Cambridge, 2015. Translation of Les Métamorphoses du calcul, Le Pommier, Paris, 2007. Translation from the French by Pierre Guillot and Marion Roman.
    Download  
     
    Export citation  
     
    Bookmark  
  7. Two Concepts of "Form" and the so-Called Computational Theory of Mind.John-Michael Kuczynski - 2006 - Philosophical Psychology 19 (6):795-821.
    According to the computational theory of mind , to think is to compute. But what is meant by the word 'compute'? The generally given answer is this: Every case of computing is a case of manipulating symbols, but not vice versa - a manipulation of symbols must be driven exclusively by the formal properties of those symbols if it is qualify as a computation. In this paper, I will present the following argument. Words like 'form' and 'formal' are (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  8.  92
    Review of Denis R. Hirschfeldt, Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles. [REVIEW]Benedict Eastaugh - 2017 - Studia Logica 105 (4):873-879.
    The present volume is an introduction to the use of tools from computability theory and reverse mathematics to study combinatorial principles, in particular Ramsey's theorem and special cases such as Ramsey's theorem for pairs. It would serve as an excellent textbook for graduate students who have completed a course on computability theory.
    Download  
     
    Export citation  
     
    Bookmark  
  9. Toward a General Theory of Knowledge.Luis M. Augusto - 2020 - Journal of Knowledge Structures and Systems 1 (1):63-97.
    For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the so-called knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science of knowledge (SoK) and additionally (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  10. Mathematical Models of Abstract Systems: Knowing Abstract Geometric Forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely (...)
    Download  
     
    Export citation  
     
    Bookmark  
  11. Discovering Empirical Theories of Modular Software Systems. An Algebraic Approach.Nicola Angius & Petros Stefaneas - 2016 - In Vincent Müller (ed.), Computing and Philosophy: Selected Papers from IACAP 2014 (Synthese Library). Springer. pp. 99-115.
    This paper is concerned with the construction of theories of software systems yielding adequate predictions of their target systems’ computations. It is first argued that mathematical theories of programs are not able to provide predictions that are consistent with observed executions. Empirical theories of software systems are here introduced semantically, in terms of a hierarchy of computational models that are supplied by formal methods and testing techniques in computer science. Both deductive top-down and inductive bottom-up approaches in the discovery (...)
    Download  
     
    Export citation  
     
    Bookmark  
  12. Artificial Evil and the Foundation of Computer Ethics.Luciano Floridi & J. W. Sanders - 2001 - Springer Netherlands.
    Moral reasoning traditionally distinguishes two types of evil:moral (ME) and natural (NE). The standard view is that ME is the product of human agency and so includes phenomena such as war,torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...)
    Download  
     
    Export citation  
     
    Bookmark   28 citations  
  13.  49
    Artificial Evil and the Foundation of Computer Ethics.L. Floridi & J. Sanders - 2000 - Etica E Politica 2 (2).
    Moral reasoning traditionally distinguishes two types of evil: moral and natural. The standard view is that ME is the product of human agency and so includes phenomena such as war, torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...)
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  14. Cognitive Computation Sans Representation.Paul Schweizer - 2017 - In Thomas Powers (ed.), Philosophy and Computing: Essays in epistemology, philosophy of mind, logic, and ethics,. Cham, Switzerland: Springer. pp. 65-84.
    The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  15.  91
    Mathematical Nature of Gravity, Which General Relativity Says is Space-Time : Topology Unites With the Matrix, E=Mc2, Advanced Waves, Wick Rotation, Dark Matter & Higher Dimensions.Rodney Bartlett - manuscript
    General Relativity says gravity is a push caused by space-time's curvature. Combining General Relativity with E=mc2 results in distances being totally deleted from space-time/gravity by future technology, and in expansion or contraction of the universe as a whole being eliminated. The road to these conclusions has branches shining light on supersymmetry and superconductivity. This push of gravitational waves may be directed from intergalactic space towards galaxy centres, helping to hold galaxies together and also creating supermassive black holes. Together with the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  16.  33
    असंभव, अपूर्णता, अपूर्णता, झूठा विरोधाभास, सिद्धांतवाद, गणना की सीमा, एक गैर-क्वांटम यांत्रिक अनिश्चितता सिद्धांत और कंप्यूटर के रूप में ब्रह्मांड पर Wolpert, Chaitin और Wittgenstein ट्यूरिंग मशीन थ्योरी में अंतिम प्रमेय --Wolpert, Chaitin and Wittgenstein on impossibility, incompleteness, the liar paradox, theism, the limits of computation, a non-quantum mechanical uncertainty principle and the universe as computer—the ultimate theorem in Turing Machine Theory (संशोधित 2019).Michael Richard Starks - 2020 - In पृथ्वी पर नर्क में आपका स्वागत है: शिशुओं, जलवायु परिवर्तन, बिटकॉइन, कार्टेल, चीन, लोकतंत्र, विविधता, समानता, हैकर्स, मानव अधिकार, इस्लाम, उदारवाद, समृद्धि, वेब, अराजकता, भुखमरी, बीमारी, हिंसा, कृत्रिम बुद्धिमत्ता, युद्ध. Las Vegas, NV, USA: Reality Press. pp. 215-220.
    मैं कंप्यूटर के रूप में गणना और ब्रह्मांड की सीमा के कई हाल ही में चर्चा पढ़ लिया है, polymath भौतिक विज्ञानी और निर्णय सिद्धांतकार डेविड Wolpert के अद्भुत काम पर कुछ टिप्पणी खोजने की उम्मीद है, लेकिन एक भी प्रशस्ति पत्र नहीं मिला है और इसलिए मैं यह बहुत संक्षिप्त मौजूद सारांश. Wolpert कुछ आश्चर्यजनक असंभव या अधूरापन प्रमेयों साबित कर दिया (1992 से 2008-देखें arxiv dot org) अनुमान के लिए सीमा पर (कम्प्यूटेशन) कि इतने सामान्य वे गणना कर (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  17.  50
    Computability, Notation, and de Re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7).
    Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  18. Computational Reverse Mathematics and Foundational Analysis.Benedict Eastaugh - manuscript
    Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  19. A Review Of:“Information Theory, Evolution and the Origin of Life as a Digital Message How Life Resembles a Computer” Second Edition. Hubert P. Yockey, 2005, Cambridge University Press, Cambridge: 400 Pages, Index; Hardcover, US $60.00; ISBN: 0-521-80293-8. [REVIEW]Attila Grandpierre - 2006 - World Futures 62 (5):401-403.
    Information Theory, Evolution and The Origin ofLife: The Origin and Evolution of Life as a Digital Message: How Life Resembles a Computer, Second Edition. Hu- bert P. Yockey, 2005, Cambridge University Press, Cambridge: 400 pages, index; hardcover, US $60.00; ISBN: 0-521-80293-8. The reason that there are principles of biology that cannot be derived from the laws of physics and chemistry lies simply in the fact that the genetic information content of the genome for constructing even the simplest organisms is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  20. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  21. Virtue Theory of Mathematical Practices: An Introduction.Andrew Aberdein, Colin Jakob Rittberg & Fenner Stanley Tanswell - 2021 - Synthese 199 (3-4):10167-10180.
    Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  22. Wolpert, Chaitin and Wittgenstein on Impossibility, Incompleteness, the Limits of Computation, Theism and the Universe as Computer-the Ultimate Turing Theorem.Michael Starks - 2017 - Philosophy, Human Nature and the Collapse of Civilization Michael Starks 3rd Ed. (2017).
    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 (...), and even independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility, incompleteness, the limits of computation,and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things,a non- quantum mechanical uncertainty principle and a proof of monotheism. There are obvious connections to the classic work of Chaitin, Solomonoff, Komolgarov and Wittgenstein and to the notion that no program (and thus no device) can generate a sequence (or device) with greater complexity than it possesses. One might say this body of work implies atheism since there cannot be any entity more complex than the physical universe and from the Wittgensteinian viewpoint, ‘more complex’ is meaningless (has no conditions of satisfaction, i.e., truth-maker or test). Even a ‘God’ (i.e., a ‘device’ with limitless time/space and energy) cannot determine whether a given ‘number’ is ‘random’ nor can find a certain way to show that a given ‘formula’, ‘theorem’ or ‘sentence’ or ‘device’ (all these being complex language games) is part of a particular ‘system’. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my article The Logical Structure of Philosophy, Psychology, Mind and Language as Revealed in Wittgenstein and Searle 59p(2016). For all my articles on Wittgenstein and Searle see my e-book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Wittgenstein and Searle 367p (2016). Those interested in all my writings in their most recent versions may consult my e-book Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2016’ 662p (2016). -/- All of my papers and books have now been published in revised versions both in ebooks and in printed books. -/- Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B071HVC7YP. -/- The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) https://www.amazon.com/dp/B071P1RP1B. -/- Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B0711R5LGX . (shrink)
    Download  
     
    Export citation  
     
    Bookmark  
  23. The Theory of Computability Developed in Terms of Satisfaction.James Cain - 1999 - Notre Dame Journal of Formal Logic 40 (4):515-532.
    The notion of computability is developed through the study of the behavior of a set of languages interpreted over the natural numbers which contain their own fully defined satisfaction predicate and whose only other vocabulary is limited to "0", individual variables, the successor function, the identity relation and operators for disjunction, conjunction, and existential quantification.
    Download  
     
    Export citation  
     
    Bookmark  
  24. Aristotle and Modern Mathematical Theories of the Continuum.Anne Newstead - 2001 - In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
    This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed intervals (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   5 citations  
  25. The Physics of God and the Quantum Gravity Theory of Everything.James Redford -
    Analysis is given of the Omega Point cosmology, an extensively peer-reviewed proof (i.e., mathematical theorem) published in leading physics journals by professor of physics and mathematics Frank J. Tipler, which demonstrates that in order for the known laws of physics to be mutually consistent, the universe must diverge to infinite computational power as it collapses into a final cosmological singularity, termed the Omega Point. The theorem is an intrinsic component of the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (...)
    Download  
     
    Export citation  
     
    Bookmark  
  26. What Mathematical Theories of Truth Should Be Like (and Can Be).Seppo Heikkilä - manuscript
    Hannes Leitgeb formulated eight norms for theories of truth in his paper [5]: `What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  27. A Mathematical Theory of Truth and an Application to the Regress Problem.S. Heikkilä - forthcoming - Nonlinear Studies 22 (2).
    In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  28. Computation in Physical Systems: A Normative Mapping Account.Paul Schweizer - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer Verlag. pp. 27-47.
    The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  29. Can Mathematics Explain the Evolution of Human Language?Guenther Witzany - 2011 - Communicative and Integrative Biology 4 (5):516-520.
    Investigation into the sequence structure of the genetic code by means of an informatic approach is a real success story. The features of human language are also the object of investigation within the realm of formal language theories. They focus on the common rules of a universal grammar that lies behind all languages and determine generation of syntactic structures. This universal grammar is a depiction of material reality, i.e., the hidden logical order of things and its relations determined by natural (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  30.  84
    Computing, Modelling, and Scientific Practice: Foundational Analyses and Limitations.Philippos Papayannopoulos - 2018 - Dissertation,
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  31. Computational Theories of Conscious Experience: Between a Rock and a Hard Place.Gary Bartlett - 2012 - Erkenntnis 76 (2):195-209.
    Very plausibly, nothing can be a genuine computing system unless it meets an input-sensitivity requirement. Otherwise all sorts of objects, such as rocks or pails of water, can count as performing computations, even such as might suffice for mentality—thus threatening computationalism about the mind with panpsychism. Maudlin in J Philos 86:407–432, ( 1989 ) and Bishop ( 2002a , b ) have argued, however, that such a requirement creates difficulties for computationalism about conscious experience, putting it in conflict with the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  32.  53
    Thought, Sign and Machine - the Idea of the Computer Reconsidered.Niels Ole Finnemann (ed.) - 1999 - Copenhagen: Danish Original: Akademisk Forlag 1994. Tanke, Sprog og Maskine..
    Throughout what is now the more than 50-year history of the computer many theories have been advanced regarding the contribution this machine would make to changes both in the structure of society and in ways of thinking. Like other theories regarding the future, these should also be taken with a pinch of salt. The history of the development of computer technology contains many predictions which have failed to come true and many applications that have not been foreseen. While we must (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. Mathematics and Argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.
    Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  34. Tractability and the Computational Mind.Rineke Verbrugge & Jakub Szymanik - 2018 - In Mark Sprevak & Matteo Colombo (eds.), The Routledge Handbook of the Computational Mind. Oxford, UK: pp. 339-353.
    We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effective algorithms is hardly possible. Some problems need too much computational resource, e.g., (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  35. Tools or Toys? On Specific Challenges for Modeling and the Epistemology of Models and Computer Simulations in the Social Sciences.Eckhart Arnold - manuscript
    Mathematical models are a well established tool in most natural sciences. Although models have been neglected by the philosophy of science for a long time, their epistemological status as a link between theory and reality is now fairly well understood. However, regarding the epistemological status of mathematical models in the social sciences, there still exists a considerable unclarity. In my paper I argue that this results from specific challenges that mathematical models and especially computer simulations face (...)
    Download  
     
    Export citation  
     
    Bookmark  
  36. Consciousness and the Collapse of the Wave Function.David J. Chalmers & Kelvin J. McQueen - forthcoming - In Shan Gao (ed.), Consciousness and Quantum Mechanics. Oxford University Press.
    Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  37. Computability in Quantum Mechanics.Wayne C. Myrvold - 1995 - In Werner De Pauli-Schimanovich, Eckehart Köhler & Friedrich Stadler (eds.), Vienna Circle Institute Yearbook. Kluwer Academic Publishers. pp. 33-46.
    In this paper, the issues of computability and constructivity in the mathematics of physics are discussed. The sorts of questions to be addressed are those which might be expressed, roughly, as: Are the mathematical foundations of our current theories unavoidably non-constructive: or, Are the laws of physics computable?
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  38. A Theory of Implicit Commitment for Mathematical Theories.Mateusz Łełyk & Carlo Nicolai - manuscript
    The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains so far an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection (...)
    Download  
     
    Export citation  
     
    Bookmark  
  39. Mathematics and the Theory of Multiplicities: Badiou and Deleuze Revisited.Daniel W. Smith - 2003 - Southern Journal of Philosophy 41 (3):411-449.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  40. Computation and Functionalism: Syntactic Theory of Mind Revisited.Murat Aydede - 2005 - In Gurol Irzik & Guven Guzeldere (eds.), Boston Studies in the History and Philosophy of Science. Springer.
    I argue that Stich's Syntactic Theory of Mind (STM) and a naturalistic narrow content functionalism run on a Language of Though story have the same exact structure. I elaborate on the argument that narrow content functionalism is either irremediably holistic in a rather destructive sense, or else doesn't have the resources for individuating contents interpersonally. So I show that, contrary to his own advertisement, Stich's STM has exactly the same problems (like holism, vagueness, observer-relativity, etc.) that he claims plague (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  41. Interpretation of Percolation in Terms of Infinity Computations.Yaroslav Sergeyev, Dmitri Iudin & Masaschi Hayakawa - 2012 - Applied Mathematics and Computation 218 (16):8099-8111.
    In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach does (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   3 citations  
  42.  47
    P≠NP, By Accepting to Make a Shift in the Theory (Time as a Fuzzy Concept) The Structure of a Theory (TC*, Theory of Computation Based on Fuzzy Time).Farzad Didehvar - manuscript
    In a series of articles we try to show the need of a novel Theory for Theory of Computation based on considering time as a Fuzzy concept. Time is a central concept In Physics. First we were forced to consider some changes and modifications in the Theories of Physics. In the second step and throughout this article we show the positive Impact of this modification on Theory of Computation and Complexity Theory to rebuild it (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  43.  87
    Syntactic Characterizations of First-Order Structures in Mathematical Fuzzy Logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
    Download  
     
    Export citation  
     
    Bookmark  
  44. Toward a Theoretical Account of Strategy Use and Sense-Making in Mathematics Problem Solving.H. J. M. Tabachneck, K. R. Koedinger & M. J. Nathan - 1994 - In Ashwin Ram & Kurt Eiselt (eds.), Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Erlbaum.
    Much problem solving and learning research in math and science has focused on formal representations. Recently researchers have documented the use of unschooled strategies for solving daily problems -- informal strategies which can be as effective, and sometimes as sophisticated, as school-taught formalisms. Our research focuses on how formal and informal strategies interact in the process of doing and learning mathematics. We found that combining informal and formal strategies is more effective than single strategies. We provide a theoretical account of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  45.  13
    Mathematical and Non-Causal Explanations: An Introduction.Daniel Kostić - 2019 - Perspectives on Science 1 (27):1-6.
    In the last couple of years, a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e., explanations that don’t cite causes in the explanans) sometimes take a form of the question of what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  46. Computability and Human Symbolic Output.Jason Megill & Tim Melvin - 2014 - Logic and Logical Philosophy 23 (4):391-401.
    This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  47.  41
    Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
    A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The approach developed has a pronounced applied character and is based on the principle “The part is less than the whole” introduced by the ancient Greeks. This principle is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The point of view on infinities and infinitesimals (and in general, on Mathematics) presented in this paper (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  48. Validation of Computer Simulations From a Kuhnian Perspective.Eckhart Arnold - 2019 - In Claus Beisbart & Nicole J. Saam (eds.), Computer Simulation Validation - Fundamental Concepts, Methodological Frameworks, and Philosophical Perspectives. Heidelberg, Deutschland: Springer. pp. 203-224.
    While Thomas Kuhn's theory of scientific revolutions does not specifically deal with validation, the validation of simulations can be related in various ways to Kuhn's theory: 1) Computer simulations are sometimes depicted as located between experiments and theoretical reasoning, thus potentially blurring the line between theory and empirical research. Does this require a new kind of research logic that is different from the classical paradigm which clearly distinguishes between theory and empirical observation? I argue that this (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  49. Manufacturing Morality A General Theory of Moral Agency Grounding Computational Implementations: The ACTWith Model.Jeffrey White - 2013 - In Floares (ed.), Computational Intelligence. Nova Publications. pp. 1-65.
    The ultimate goal of research into computational intelligence is the construction of a fully embodied and fully autonomous artificial agent. This ultimate artificial agent must not only be able to act, but it must be able to act morally. In order to realize this goal, a number of challenges must be met, and a number of questions must be answered, the upshot being that, in doing so, the form of agency to which we must aim in developing artificial agents comes (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  50. A Computational Theory of Perspective and Reference in Narrative.Janyce M. Wiebe & William J. Rapaport - 1988 - In Proceedings of the 26th Annual Meeting of the Association for Computational Linguistics. Association for Computational Linguistics. pp. 131-138.
    Narrative passages told from a character's perspective convey the character's thoughts and perceptions. We present a discourse process that recognizes characters'.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
1 — 50 / 997