Results for 'arithmetic Turing degrees'

949 found
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  1. Upper bounds on locally countable admissible initial segments of a Turing degree hierarchy.Harold T. Hodes - 1981 - Journal of Symbolic Logic 46 (4):753-760.
    Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite (...)
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  2. An Exact Pair for the Arithmetic Degrees Whose Join is Not a Weak Uniform Upper Bound.Harold T. Hodes - 1982 - Recursive Function Theory-Newsletters 28.
    Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.
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  3. Possible m-diagrams of models of arithmetic.Andrew Arana - 2005 - In Stephen Simpson (ed.), Reverse Mathematics 2001. Association for Symbolic Logic.
    In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give (...)
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  4. Jumping through the transfinite: The master code hierarchy of Turing degrees.Harold T. Hodes - 1980 - Journal of Symbolic Logic 45 (2):204-220.
    Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.
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  5. More about uniform upper Bounds on ideals of Turing degrees.Harold T. Hodes - 1983 - Journal of Symbolic Logic 48 (2):441-457.
    Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds (...)
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  6. Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1978 - Journal of Symbolic Logic 43 (3):601-612.
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  7. 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 (...)
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  8. Arithmetic logical Irreversibility and the Halting Problem (Revised and Fixed version).Yair Lapin - manuscript
    The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially, this means that an algorithm can only preserve information about an input, rather than generate new information. This uncertainty arises from characteristics such as arithmetic logical irreversibility, Landauer's principle, and memory erasure, which ultimately lead to a loss of information and an increase in entropy. To measure this (...)
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  9. Gentzen’s “cut rule” and quantum measurement in terms of Hilbert arithmetic. Metaphor and understanding modeled formally.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal 14 (14):1-37.
    Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by (...)
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  10. From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?Antoine Danchin & André A. Fenton - 2022 - Frontiers in Ecology and Evolution 10:796413.
    The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is (...)
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  11. On the Logics with Propositional Quantifiers Extending S5Π.Yifeng Ding - 2018 - In Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe & Thomas Studer (eds.), Advances in Modal Logic 12, proceedings of the 12th conference on "Advances in Modal Logic," held in Bern, Switzerland, August 27-31, 2018. pp. 219-235.
    Scroggs's theorem on the extensions of S5 is an early landmark in the modern mathematical studies of modal logics. From it, we know that the lattice of normal extensions of S5 is isomorphic to the inverse order of the natural numbers with infinity and that all extensions of S5 are in fact normal. In this paper, we consider extending Scroggs's theorem to modal logics with propositional quantifiers governed by the axioms and rules analogous to the usual ones for ordinary quantifiers. (...)
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  12. (1 other version)The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the (...)
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  13. Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  14. Natural Argument by a Quantum Computer.Vasil Penchev - 2020 - Computing Methodology eJournal (Elsevier: SSRN) 3 (30):1-8.
    Natural argument is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary natural arguments in any data. That ability of natural argument is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer (...)
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  15. A Quantum Computer in a 'Chinese Room'.Vasil Penchev - 2020 - Mechanical Engineering eJournal (Elsevier: SSRN) 3 (155):1-8.
    Pattern recognition is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary patterns in any data. That ability of universal pattern recognition is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer (...)
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  16. 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 (...)
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  17. The Boundary between Mind and Machine.Dingzhou Fei - 2018 - Journal of Human Cognition 2 (1):5-15.
    The mind-body problem is one of the important topics in philosophy of mind and cognitive science. Following the analytical tradition of linguistic and logical analysis, we focus on two aspects of the mind- body problem: one is around Gödel's incompleteness theorem, and the other is on cognitive logic, especially on the question of whether Epistemological Arithmetic and machines are private. In the former case, in response to the popular view that the Gödel Incompleteness Theorem supports dualism in the mind-body (...)
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  18. On interpreting Chaitin's incompleteness theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure (...)
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  19. The Kochen - Specker theorem in quantum mechanics: a philosophical comment (part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...)
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  20. Self-referential theories.Samuel A. Alexander - 2020 - Journal of Symbolic Logic 85 (4):1687-1716.
    We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.
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  21. Counterpossibles in Science: The Case of Relative Computability.Matthias Jenny - 2018 - Noûs 52 (3):530-560.
    I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...)
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  22. The Narrative Aesthetics of Protest Images.Hannah Fasnacht - 2021 - Jolma the Journal for the Philosophy of Language, Mind and the Arts 2 (1):212-238.
    In this paper I argue that protest images have a certain aesthetics and a degree of transformative power. Crucial to this aesthetics is the images’ narrative struc- ture, like the representation of goal-directed actions. On this basis, I show that there are more aspects that contribute to the storytelling capacity, like narrative characteristics and an aesthetics of dramatization. Using the example of climate change protests as a case study, I establish that these aspects can contribute to the transformative ability of (...)
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  23. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume I.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali - 2018 - Basel, Switzerland: MDPI. Edited by Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali.
    The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single (...)
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  24. Filozofia praw człowieka. Prawa człowieka w świetle ich międzynarodowej ochrony.Marek Piechowiak - 1999 - Lublin: Towarzystwo Naukowe KUL.
    PHILOSOPHY OF HUMAN RIGHTS: HUMAN RIGHTS IN LIGHT OF THEIR INTERNATIONAL PROTECTION Summary The book consists of two main parts: in the first, on the basis of an analysis of international law, elements of the contemporary conception of human rights and its positive legal protection are identified; in the second - in light of the first part -a philosophical theory of law based on the tradition leading from Plato, Aristotle, and St. Thomas Aquinas is constructed. The conclusion contains an application (...)
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  25. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume II.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali - 2019 - Basel, Switzerland: MDPI.
    The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal neutrosophic (...)
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  26. The Effect of Procedural Justice on the Organizational Loyalty of Faculty Staff in Universities.Al Shobaki Mazen J. - 2018 - International Journal of Academic Management Science Research (IJAMSR) 2 (10):30-44.
    This study aimed to identify the effect of procedural justice on organizational loyalty from the point of view of Faculty Staff at Palestine Technical University- Kadoorei. It also aimed to identify the differences in the views of the study sample on the study variables according to the years of service. In order to achieve this, the researchers used a questionnaire consisting of (22) paragraphs where the first area (10) paragraphs looking at procedural justice while the paragraphs of the second area (...)
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  27. Logical openness in cognitive models.Prof Ignazio Licata - 2008 - Epistemologia:177-192.
    It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions. The Theory of logical openness connects the Physics of system/environment relationships to the system informational structure. In this theory, cognitive models can be ordered according to a hierarchy of complexity depending on their logical openness degree, and their descriptive limits are correlated to Gödel-Turing Theorems on formal systems. The symbolic models with low logical openness describe cognition by (...)
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  28. Efficacy of Colistin Therapy in Patients with Hematological Malignancies: What if There is Colistin Resistance?Zeynep Ture, Gamze Kalın Unüvar, Hüseyin Nadir Kahveci, Muzaffer Keklik & Ayşegül Ulu Kilic - 2023 - European Journal of Therapeutics 29 (1):17-22.
    Objective: The objective of this study was to evaluate the clinical efficacy and appropriateness of colistin therapy in patients with hematological malignancies. -/- Methods: Age, gender, type of hematologic malignancy, and potential carbapenem-resistant microorganism risk factors were all noted in this retrospective study. In empirical and agent-specific treatment groups, differences in demographic features, risk factors, treatment responses, and side effects were compared. -/- Results: Sixty-three patients were included, 54% were male, and the median age was 49. In the last three (...)
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  29. Rethinking Turing’s Test and the Philosophical Implications.Diane Proudfoot - 2020 - Minds and Machines 30 (4):487-512.
    In the 70 years since Alan Turing’s ‘Computing Machinery and Intelligence’ appeared in Mind, there have been two widely-accepted interpretations of the Turing test: the canonical behaviourist interpretation and the rival inductive or epistemic interpretation. These readings are based on Turing’s Mind paper; few seem aware that Turing described two other versions of the imitation game. I have argued that both readings are inconsistent with Turing’s 1948 and 1952 statements about intelligence, and fail to explain (...)
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  30. Turing’s imitation game: still an impossible challenge for all machines and some judges.Luciano Floridi, Mariarosaria Taddeo & Matteo Turilli - 2009 - Minds and Machines 19 (1):145–150.
    An Evaluation of the 2008 Loebner Contest.
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  31. The Turing Machine on the Dissecting Table.Jana Horáková - 2013 - Teorie Vědy / Theory of Science 35 (2):269-288.
    Since the beginning of the twenty-first century there has been an increasing awareness that software rep- resents a blind spot in new media theory. The growing interest in software also influences the argument in this paper, which sets out from the assumption that Alan M. Turing's concept of the universal machine, the first theoretical description of a computer program, is a kind of bachelor machine. Previous writings based on a similar hypothesis have focused either on a comparison of the (...)
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  32. The Turing Guide.Jack Copeland, Jonathan Bowen, Robin Wilson & Mark Sprevak (eds.) - 2017 - Oxford: Oxford University Press.
    This volume celebrates the various facets of Alan Turing (1912–1954), the British mathematician and computing pioneer, widely considered as the father of computer science. It is aimed at the general reader, with additional notes and references for those who wish to explore the life and work of Turing more deeply. -/- The book is divided into eight parts, covering different aspects of Turing’s life and work. -/- Part I presents various biographical aspects of Turing, some from (...)
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  33. Turing and Computationalism.Napoleon M. Mabaquiao - 2014 - Philosophia: International Journal of Philosophy (Philippine e-journal) 15 (1):50-62.
    Due to his significant role in the development of computer technology and the discipline of artificial intelligence, Alan Turing has supposedly subscribed to the theory of mind that has been greatly inspired by the power of the said technology which has eventually become the dominant framework for current researches in artificial intelligence and cognitive science, namely, computationalism or the computational theory of mind. In this essay, I challenge this supposition. In particular, I will try to show that there is (...)
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  34. Turing Test, Chinese Room Argument, Symbol Grounding Problem. Meanings in Artificial Agents (APA 2013).Christophe Menant - 2013 - American Philosophical Association Newsletter on Philosophy and Computers 13 (1):30-34.
    The Turing Test (TT), the Chinese Room Argument (CRA), and the Symbol Grounding Problem (SGP) are about the question “can machines think?” We propose to look at these approaches to Artificial Intelligence (AI) by showing that they all address the possibility for Artificial Agents (AAs) to generate meaningful information (meanings) as we humans do. The initial question about thinking machines is then reformulated into “can AAs generate meanings like humans do?” We correspondingly present the TT, the CRA and the (...)
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  35. Post-Turing Methodology: Breaking the Wall on the Way to Artificial General Intelligence.Albert Efimov - 2020 - Lecture Notes in Computer Science 12177.
    This article offers comprehensive criticism of the Turing test and develops quality criteria for new artificial general intelligence (AGI) assessment tests. It is shown that the prerequisites A. Turing drew upon when reducing personality and human consciousness to “suitable branches of thought” re-flected the engineering level of his time. In fact, the Turing “imitation game” employed only symbolic communication and ignored the physical world. This paper suggests that by restricting thinking ability to symbolic systems alone Turing (...)
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  36. Arithmetic Judgements, First-Person Judgements and Immunity to Error Through Misidentification.Michele Palmira - 2018 - Review of Philosophy and Psychology 10 (1):155-172.
    The paper explores the idea that some singular judgements about the natural numbers are immune to error through misidentification by pursuing a comparison between arithmetic judgements and first-person judgements. By doing so, the first part of the paper offers a conciliatory resolution of the Coliva-Pryor dispute about so-called “de re” and “which-object” misidentification. The second part of the paper draws some lessons about what it takes to explain immunity to error through misidentification. The lessons are: First, the so-called Simple (...)
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  37. Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In (...)
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  38. Turing test: 50 years later.Ayse Pinar Saygin, Ilyas Cicekli & Varol Akman - 2000 - Minds and Machines 10 (4):463-518.
    The Turing Test is one of the most disputed topics in artificial intelligence, philosophy of mind, and cognitive science. This paper is a review of the past 50 years of the Turing Test. Philosophical debates, practical developments and repercussions in related disciplines are all covered. We discuss Turing's ideas in detail and present the important comments that have been made on them. Within this context, behaviorism, consciousness, the 'other minds' problem, and similar topics in philosophy of mind (...)
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  39. Turing’s Three Senses of “Emotional”.Diane Proudfoot - 2014 - International Journal of Synthetic Emotions 5 (2):7-20.
    Turing used the expression “emotional” in three distinct ways: to state his philosophical theory of the concept of intelligence, to classify arguments for and against the possibility of machine intelligence, and to describe the education of a “child machine”. The remarks on emotion include several of the most important philosophical claims. This paper analyses these remarks and their significance for current research in Artificial Intelligence.
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  40. Degrees of Reality.Damian Aleksiev - 2024 - In Yannic Kappes, Asya Passinsky, Julio De Rizzo & Benjamin Schnieder (eds.), Facets of Reality — Contemporary Debates. Contributions of the Austrian Ludwig Wittgenstein Society. Austrian Ludwig Wittgenstein Society. pp. 20-30.
    This essay outlines a hierarchical framework of Reality that allows for degrees of Reality. I use Reality (with a capital “R”) to designate reality in a primitive, metaphysical sense. Reality, grounding, and essence are the key elements of the framework presented here. I assume that Reality must have a fundamental level and all fundamental phenomena must be Real. Moreover, I postulate that everything non-fundamental is ultimately grounded in the fundamental Real. But what about the Reality of the non-fundamental? I (...)
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  41. Gödel Incompleteness and Turing Completeness.Ramón Casares - manuscript
    Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in (...)
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  42. Reducing Arithmetic to Set Theory.A. C. Paseau - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan. pp. 35-55.
    The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not (...)
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  43. Revisiting Turing and His Test: Comprehensiveness, Qualia, and the Real World.Vincent C. Müller & Aladdin Ayesh (eds.) - 2012 - AISB.
    Proceedings of the papers presented at the Symposium on "Revisiting Turing and his Test: Comprehensiveness, Qualia, and the Real World" at the 2012 AISB and IACAP Symposium that was held in the Turing year 2012, 2–6 July at the University of Birmingham, UK. Ten papers. - http://www.pt-ai.org/turing-test --- Daniel Devatman Hromada: From Taxonomy of Turing Test-Consistent Scenarios Towards Attribution of Legal Status to Meta-modular Artificial Autonomous Agents - Michael Zillich: My Robot is Smarter than Your Robot: (...)
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  44. A Turing Machine for Exponential Function.P. M. F. Lemos - manuscript
    This is a Turing Machine which computes the exponential function f(x,y) = xˆy. Instructions format and operation of this machine are intended to best reflect the basic conditions outlined by Alan Turing in his On Computable Numbers, with an Application to the Entscheidungsproblem (1936), using the simplest single-tape and single-symbol version, in essence due to Kleene (1952) and Carnielli & Epstein (2008). This machine is composed by four basic task machines: one which checks if exponent y is zero, (...)
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  45. On Turing Completeness, or Why We Are So Many (7th edition).Ramón Casares - manuscript
    Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing (...)
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  46. Degrees of Consciousness.Andrew Y. Lee - 2023 - Noûs 57 (3):553-575.
    Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is (...)
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  47. Arithmetic is Determinate.Zachary Goodsell - 2021 - Journal of Philosophical Logic 51 (1):127-150.
    Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think (...)
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  48. Exact and Approximate Arithmetic in an Amazonian Indigene Group.Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene - 2004 - Science 306 (5695):499-503.
    Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers (...)
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  49. Turing's three philosophical lessons and the philosophy of information.Luciano Floridi - 2012 - Philosophical Transactions of the Royal Society A 370 (1971):3536-3542.
    In this article, I outline the three main philosophical lessons that we may learn from Turing’s work, and how they lead to a new philosophy of information. After a brief introduction, I discuss his work on the method of levels of abstraction (LoA), and his insistence that questions could be meaningfully asked only by specifying the correct LoA. I then look at his second lesson, about the sort of philosophical questions that seem to be most pressing today. Finally, I (...)
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  50. Arithmetic is Necessary.Zachary Goodsell - 2024 - Journal of Philosophical Logic 53 (4).
    (Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer (...)
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