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  1. Strict Finitism's Unrequited Love for Computational Complexity.Noel Arteche - manuscript
    As a philosophy of mathematics, strict finitism has been traditionally concerned with the notion of feasibility, defended mostly by appealing to the physicality of mathematical practice. This has led the strict finitists to influence and be influenced by the field of computational complexity theory, under the widely held belief that this branch of mathematics is concerned with the study of what is “feasible in practice”. In this paper, I survey these ideas and contend that, contrary to popular belief, complexity theory (...)
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  2. Computational Complexity in the Philosophy of Mind: Unconventional Methods to Solve the Problem of Logical Omniscience.Safal Aryal - manuscript
    The philosophy of mind is traditionally concerned with the study of mental processes, language, the representation of knowledge and the relation of the mind shares with the body; computational complexity theory is related to the classification of computationally solvable problems (be it via execution time, storage requirements, etc...). While there are well-established links between computer science in general & the philosophy of mind, many possible solutions to traditional problems in the philosophy of mind have not yet been analyzed from the (...)
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  3. 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 this paradox, it (...)
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  4. A Contradiction and P=NP Problem.Farzad Didehvar - manuscript
    Here, by introducing a version of “Unexpected hanging paradox” first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in Theory of Computation about the consistency of this Theory. One of the major claim is:Theory of Computation and Classical Logic leads us to a contradiction.
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  5. By Considering Fuzzy Time, P=BPP (P*=BPP*).Farzad Didehvar - manuscript
    The reason ability of considering time as a fuzzy concept is demonstrated in [7],[8]. One of the major questions which arise here is the new definitions of Complexity Classes. In [1],[2],…,[11] we show why we should consider time a fuzzy concept. It is noticeable to mention that that there were many attempts to consider time as a Fuzzy concept, in Philosophy, Mathematics and later in Physics but mostly based on the personal intuition of the authors or as a style of (...)
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  6. What Have Google’s Random Quantum Circuit Simulation Experiments Demonstrated About Quantum Supremacy?Jack K. Horner & John Symons - forthcoming - In Hamid R. Arabnia, Leonidas Deligiannidis, Fernando G. Tinetti & Quoc-Nam Tran (eds.), Advances in Software Engineering, Education, and e-Learning. Cham, Switzerland: Springer Nature.
    Quantum computing is of high interest because it promises to perform at least some kinds of computations much faster than classical computers. Arute et al. 2019 (informally, “the Google Quantum Team”) report the results of experiments that purport to demonstrate “quantum supremacy” – the claim that the performance of some quantum computers is better than that of classical computers on some problems. Do these results close the debate over quantum supremacy? We argue that they do not. In the following, we (...)
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  7. Towards Tractable Approximations to Many-Valued Logics: The Case of First Degree Entailment.Alejandro Solares-Rojas & Marcello D’Agostino - 2022 - In Igor Sedlár (ed.), The Logica Yearbook, 2021. London, UK: pp. 57-76.
    FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...)
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  8. Sizing Up Free Will: The Scale of Compatibilism.Stuart Doyle - 2021 - Journal of Mind and Behavior 42 (3 & 4):271-289.
    Is human free will compatible with the natural laws of the universe? To “compatibilists” who see free actions as emanating from the wants and reasons of human agents, free will looks perfectly plausible. However, “incompatibilists” claim to see the more ultimate sources of human action. The wants and reasons of agents are said to be caused by physical processes which are themselves mere natural results of the previous state of the world and the natural laws which govern it. This paper (...)
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  9. 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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  10. Two Strategies to Infinity: Completeness and Incompleteness. The Completeness of Quantum Mechanics.Vasil Penchev - 2020 - High Performance Computing eJournal 12 (11):1-8.
    Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...)
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  11. 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 I. (...)
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  12. Representation and Reality by Language: How to Make a Home Quantum Computer?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (34):1-14.
    A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano arithmetics having a remarkable (...)
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  13. Rational Analysis, Intractability, and the Prospects of ‘as If’-Explanations.Iris van Rooij, Cory D. Wright, Johan Kwisthout & Todd Wareham - 2018 - Synthese 195 (2):491-510.
    Despite their success in describing and predicting cognitive behavior, the plausibility of so-called ‘rational explanations’ is often contested on the grounds of computational intractability. Several cognitive scientists have argued that such intractability is an orthogonal pseudoproblem, however, since rational explanations account for the ‘why’ of cognition but are agnostic about the ‘how’. Their central premise is that humans do not actually perform the rational calculations posited by their models, but only act as if they do. Whether or not the problem (...)
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  14. Отвъд машината на Тюринг: квантовият компютър.Vasil Penchev - 2014 - Sofia: BAS: ISSK (IPS).
    Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer might (...)
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  15. Complexity of Judgment Aggregation.Ulle Endriss, Umberto Grandi & Daniele Porello - 2012 - Journal of Artificial Intelligence Research 45:481--514.
    We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the (...)
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  16. Intractability and the Use of Heuristics in Psychological Explanations.Iris Rooij, Cory Wright & Todd Wareham - 2012 - Synthese 187 (2):471-487.
    Many cognitive scientists, having discovered that some computational-level characterization f of a cognitive capacity φ is intractable, invoke heuristics as algorithmic-level explanations of how cognizers compute f. We argue that such explanations are actually dysfunctional, and rebut five possible objections. We then propose computational-level theory revision as a principled and workable alternative.
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  17. Sense and Proof.Carlo Penco & Daniele Porello - 2010 - In M. D'agostino, G. Giorello, F. Laudisa, T. Pievani & C. Sinigaglia (eds.), New Essays in Logic and Philosophy of Science,. College Publicationss.
    In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).
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  18. The Epsilon Calculus and Herbrand Complexity.Georg Moser & Richard Zach - 2006 - Studia Logica 82 (1):133-155.
    Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential (...)
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  19. The Incoherence of Heuristically Explaining Coherence.Iris van Rooij & Cory Wright - 2006 - In Ron Sun (ed.), Proceedings of the 28th Annual Conference of the Cognitive Science Society. Mahwah, NJ 07430, USA: pp. 2622.
    Advancement in cognitive science depends, in part, on doing some occasional ‘theoretical housekeeping’. We highlight some conceptual confusions lurking in an important attempt at explaining the human capacity for rational or coherent thought: Thagard & Verbeurgt’s computational-level model of humans’ capacity for making reasonable and truth-conducive abductive inferences (1998; Thagard, 2000). Thagard & Verbeurgt’s model assumes that humans make such inferences by computing a coherence function (f_coh), which takes as input representation networks and their pair-wise constraints and gives as output (...)
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  20. Epistemic Virtues, Metavirtues, and Computational Complexity.Adam Morton - 2004 - Noûs 38 (3):481–502.
    I argue that considerations about computational complexity show that all finite agents need characteristics like those that have been called epistemic virtues. The necessity of these virtues follows in part from the nonexistence of shortcuts, or efficient ways of finding shortcuts, to cognitively expensive routines. It follows that agents must possess the capacities – metavirtues –of developing in advance the cognitive virtues they will need when time and memory are at a premium.
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  21. The Rapid Recovery of Three-Dimensional Structure From Line Drawings.Ronald A. Rensink - 1992 - Dissertation, University of British Columbia
    A computational theory is developed that explains how line drawings of polyhedral objects can be interpreted rapidly and in parallel at early levels of human vision. The key idea is that a time-limited process can correctly recover much of the three-dimensional structure of these objects when split into concurrent streams, each concerned with a single aspect of scene structure.
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  22. 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 in a more successful and fruitful (...)
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  23. P≠NP, By Considering Time as a Fuzzy Concept.Didehvar Farzad - manuscript
    Here, we try to build the structure of a Theory of computation based on considering time as a fuzzy concept. Actually, there are some reasons to consider time as a fuzzy concept. In this article, we don’t go to this side but we remind that Brower and Husserl ideas about the concept of time were similar [14]. Throughout this article, we present the Theory of Computation with Fuzzy Time. Considering the classical definition of Turing Machine we change and modify the (...)
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  24. (TC* ،زمان فازی ) تاثیر و تاثر منطق و پارادوکسها بر نظریه محاسبات عام. [REVIEW]Didehvar Farzad - manuscript
    در تکوین نظریه محاسبات از اوایل قرن بیستم پارادکسها و خود ارجاعی نقش ویژه ای را بازی کرده اند. هر چند نظریه محاسبات عام بر اساس تعریف ماشین تورینگ، فرض تورینگ_چرچ و کاربردهای آن بنا شده ،اما از همان ابتدا تا به امروز منطق و حوزه های مختلف این علم در ارتباط تنگاتنگ با این تیوری و در ابتدا نظریه محاسبات خاص بوده و این ارتباط روز به روز گسترده و گسترده تر گشته است. از تاثیر پارادوکس دروغگو و پارادکس (...)
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