Results for 'incompleteness'

163 found
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  1. Interactivity, Fictionality, and Incompleteness.Nathan Wildman & Richard Woodward - forthcoming - In Grant Tavinor & Jon Robson (eds.), The Aesthetics of Videogames. Routledge.
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  2. 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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  3. Incompleteness and Computability. An Open Introduction to Gödel's Theorems.Richard Zach - 2019
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  4. Gödel's Incompleteness Theorems, Free Will and Mathematical Thought.Solomon Feferman - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. Oup/British Academy.
    The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether the (...)
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  5. On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
    A survey of more philosophical applications of Gödel's incompleteness results.
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  6. Refuting Incompleteness and Undefinability.Pete Olcott - manuscript
    Within the (Haskell Curry) notion of a formal system we complete Tarski's formal correctness: ∀x True(x) ↔ ⊢ x and use this finally formalized notion of Truth to refute his own Undefinability Theorem (based on the Liar Paradox), the Liar Paradox, and the (Panu Raatikainen) essence of the conclusion of the 1931 Incompleteness Theorem.
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  7.  99
    Eliminating Undecidability and Incompleteness in Formal Systems.Pete Olcott - manuscript
    To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.
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  8. Incompleteness of a First-Order Gödel Logic and Some Temporal Logics of Programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Hans Kleine Büning (ed.), Computer Science Logic. CSL 1995. Selected Papers. Berlin: Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...)
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  9. The Incompleteness of Luck Egalitarianism.Ryan Long - 2011 - Social Philosophy Today 27:87-96.
    Luck egalitarianism makes a fundamental distinction between inequalities for which agents are responsible and inequalities stemming from luck. I give several reasons to find luck egalitarianism a compelling view of distributive justice. I then argue that it is an incomplete theory of equality. Luck egalitarianism lacks the normative resources to achieve its ends. It is unable to specify the prior conditions under which persons are situated equivalently such that their choices can bear this tremendous weight. This means that luck egalitarians (...)
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  10.  40
    Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable (...)
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  11. David Wolpert on Impossibility, Incompleteness, the Liar Paradox, the Limits of Computation, a Non-Quantum Mechanical Uncertainty Principle and the Universe as Computer—the Ultimate Theorem in Turing Machine Theory.Michael Starks - manuscript
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and (...)
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  12. Does Gödel's Incompleteness Theorem Prove That Truth Transcends Proof?Joseph Vidal-Rosset - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 51--73.
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  13.  58
    The Gödel Incompleteness Theorems (1931) by the Axiom of Choice.Vasil Penchev - 2020 - Econometrics: Mathematical Methods and Programming eJournal (Elsevier: SSRN) 13 (39):1-4.
    Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the (...)
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  14. Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2004 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. Amsterdam: North-Holland. pp. 917-925.
    This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number (...)
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  15.  76
    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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  16.  41
    沃尔珀特、柴廷和维特根斯坦关于不可能、不完整、说谎的悖论、有论、计算极限、非量子力学不确定性原理和宇宙作为计算机——图灵机器理论的终极定理 (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 T Machine Theory) (修订 2019).Michael Richard Starks - 2020 - In 欢迎来到地球上的地狱: 婴儿,气候变化,比特币,卡特尔,中国,民主,多样性,养成基因,平等,黑客,人权,伊斯兰教,自由主义,繁荣,网络,混乱。饥饿,疾病,暴力,人工智能,战争. Las Vegas, NV USA: Reality Press. pp. 173-177.
    我最近读过许多关于计算极限和宇宙作为计算机的讨论,希望找到一些关于多面体物理学家和决策理论家大卫·沃尔珀特的惊人工作的评论,但没有发现一个引文,所以我提出这个非常简短的总结。Wolpert 证明了一些惊人的不可能或不完整的定理(1992-2008-见arxiv dot org)对推理(计算)的限制,这些极限非常一般,它们独立于执行计算的设备,甚至独立于物理定律,因此,它们适用于计算机、物理和人类行为。他们利用Cantor的对角线、骗子悖论和世界线来提供图灵机器理论的 终极定理,并似乎提供了对不可能、不完整、计算极限和宇宙的见解。计算机,在所有可能的宇宙和所有生物或机制,产生,除其他外,非量子力学不确定性原理和一神论的证明。与柴廷、所罗门诺夫、科莫尔加罗夫和维特根斯 坦的经典作品以及任何程序(因此没有设备)能够生成比它拥有的更大复杂性的序列(或设备)的概念有着明显的联系。有人可能会说,这一工作意味着无政府主义,因为没有比物质宇宙更复杂的实体,从维特根斯坦的观点来看 ,"更复杂的"是毫无意义的(没有满足的条件,即真理制造者或测试)。即使是"上帝"(即具有无限时间/空间和能量的"设备")也无法确定给定的&q uot;数字"是否为"随机",也无法找到某种方式来显示给定的"公式"、"定理"或"句子"或"设备&q uot;(所有这些语言都是复杂的语言)游戏)是特定"系统"的一部分。 那些希望从现代两个系统的观点来看为人类行为建立一个全面的最新框架的人,可以查阅我的书《路德维希的哲学、心理学、Mind 和语言的逻辑结构》维特根斯坦和约翰·西尔的《第二部》(2019年)。那些对我更多的作品感兴趣的人可能会看到《会说话的猴子——一个末日星球上的哲学、心理学、科学、宗教和政治——文章和评论2006-201 9年第二次(2019年)》和《自杀乌托邦幻想》第21篇世纪4日 (2019).
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  17. Remarks on Wittgenstein, Gödel, Chaitin, Incompleteness, Impossiblity and the Psychological Basis of Science and Mathematics.Michael Richard Starks - 2019 - In Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal. Las Vegas, NV USA: Reality Press. pp. 24-38.
    It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than (...)
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  18.  67
    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 (Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 294-299.
    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 dot org) on the limits to inference (computation) that are so general they are independent of the device doing the (...)
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  19.  39
    The Ontic Probability Interpretation of Quantum Theory - Part II: Einstein's Incompleteness/Nonlocality Dilemma.Felix Alba-Juez - manuscript
    After pinpointing a conceptual confusion (TCC), a Reality preconception (TRP1), and a fallacious dichotomy (TFD), the famous EPR/EPRB argument for correlated ‘particles’ is studied in the light of the Ontic Probability Interpretation (TOPI) of Quantum Theory (QT). Another Reality preconception (TRP2) is identified, showing that EPR used and ignored QT predictions in a single paralogism. Employing TFD and TRP2, EPR unveiled a contradiction veiled in its premises. By removing nonlocality from QT’s Ontology by fiat, EPR preordained its incompleteness. The (...)
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  20.  58
    The Ontic Probability Interpretation of Quantum Theory - Part I: The Meaning of Einstein's Incompleteness Claim.Felix Alba-Juez - manuscript
    Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic EPR paper (EPR), the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in (...)
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  21. Von Neumann's Methodology of Science: From Incompleteness Theorems to Later Foundational Reflections.Giambattista Formica - 2010 - Perspectives on Science 18 (4):480-499.
    In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. (...)
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  22. The Semantic Theory of Truth: Field’s Incompleteness Objection.Glen A. Hoffmann - 2007 - Philosophia 35 (2):161-170.
    According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, (...)
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  23.  42
    Predicates of Personal Taste, Semantic Incompleteness, and Necessitarianism.Markus Kneer - forthcoming - Linguistics and Philosophy:1-31.
    According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...)
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  24.  54
    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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  25. 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 computation, and (...)
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  26.  19
    A New Reading and Comparative Interpretation of Gödel’s Completeness (1930) and Incompleteness (1931) Theorems.Vasil Penchev - 2016 - Логико-Философские Штудии 13 (2):187-188.
    Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most (...)
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  27.  18
    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 (...)
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  28. The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics (...)
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  29. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  30. Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p(2013).Michael Starks - 2017 - Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2017 3rd Ed 686p(2017).
    I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky 403(2013) from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how (...)
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  31. “The Animal” After Derrida: Interrogating the Bioethics of Geno-Cide.Norman Swazo - 2013 - Les Ateliers de L'Éthique 8 (1):91-123.
    Bioethics tends to be dominated by discourses concerned with the ethical dimension of medical practice, the organization of medical care, and the integrity of biomedical research involving human subjects and animal testing. Jacques Derrida has explored the fundamental question of the “limit” that identifies and differentiates the human animal from the nonhuman animal. However, to date his work has not received any reception in the field of biomedical ethics. In this paper, I examine what Derrida’s thought about this limit might (...)
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  32.  10
    On Rudimentarity, Primitive Recursivity and Representability.Saeed Salehi - 2020 - Reports on Mathematical Logic 55:73–85.
    It is quite well-known from Kurt G¨odel’s (1931) ground-breaking Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are representable in sufficiently strong arithmetical theories. It is also known, though perhaps not as well-known as the former one, that some primitive recursive relations are not rudimentary. We present a simple and elementary proof of this fact in the first part of the paper. In the second part, we review some (...)
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  33.  27
    Gödelova Věta a Relace Logického Důsledku.Jaroslav Zouhar - 2010 - Teorie Vědy / Theory of Science 32 (1):59-95.
    In his proof of the first incompleteness theorem, Kurt Gödel provided a method of showing the truth of specific arithmetical statements on the condition that all the axioms of a certain formal theory of arithmetic are true. Furthermore, the statement whose truth is shown in this way cannot be proved in the theory in question. Thus it may seem that the relation of logical consequence is wider than the relation of derivability by a pre-defined set of rules. The aim (...)
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  34. What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic, part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  35. Hayek, Gödel, and the Case for Methodological Dualism.Ludwig M. P. van den Hauwe - 2011 - Journal of Economic Methodology 18 (4):387-407.
    On a few occasions F.A. Hayek made reference to the famous Gödel theorems in mathematical logic in the context of expounding his cognitive and social theory. The exact meaning of the supposed relationship between Gödel's theorems and the essential proposition of Hayek's theory of mind remains subject to interpretation, however. The author of this article argues that the relationship between Hayek's thesis that the human brain can never fully explain itself and the essential insight provided by Gödel's theorems in mathematical (...)
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  36. Representation of Strongly Independent Preorders by Sets of Scalar-Valued Functions.David McCarthy, Kalle Mikkola & Teruji Thomas - 2017 - MPRA Paper No. 79284.
    We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.
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  37.  50
    A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
    In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection (...)
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  38.  40
    Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
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  39.  25
    Observations 3 Version 3.Paul Merriam - manuscript
    Observations on qualia, politics, Godel incompleteness, two-dimensional semantics, feminism, Bach, entropy, time, and other things.
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  40.  36
    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 (...)
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  41.  40
    The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This (...)
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  42. Consciousness as Computation: A Defense of Strong AI Based on Quantum-State Functionalism.R. Michael Perry - 2006 - In Charles Tandy (ed.), Death and Anti-Death, Volume 4: Twenty Years After De Beauvoir, Thirty Years After Heidegger. Palo Alto: Ria University Press.
    The viewpoint that consciousness, including feeling, could be fully expressed by a computational device is known as strong artificial intelligence or strong AI. Here I offer a defense of strong AI based on machine-state functionalism at the quantum level, or quantum-state functionalism. I consider arguments against strong AI, then summarize some counterarguments I find compelling, including Torkel Franzén’s work which challenges Roger Penrose’s claim, based on Gödel incompleteness, that mathematicians have nonalgorithmic levels of “certainty.” Some consequences of strong AI (...)
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  43.  68
    Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p (2013) (Review Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 299-316.
    I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how language (...)
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  44.  70
    Wolpert, Chaitin y Wittgenstein sobre la imposibilidad, la incompletitud, la paradoja mentirosa, el teísmo, los límites de la computación, un principio de incertidumbre mecánica no cuántica y el universo como computadora, el teorema definitivo en la teoría de la máquina de Turing (revisado en 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 64-70.
    It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician (...)
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  45.  70
    What Do Paraconsistent, Undecidable, Random, Computable and Incomplete Mean? A Review of Godel's Way: Exploits Into an Undecidable World by Gregory Chaitin, Francisco A Doria, Newton C.A. Da Costa 160p (2012) (Review Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 278-293.
    In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking (...)
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  46.  62
    On the Arithmetical Truth of Self‐Referential Sentences.Kaave Lajevardi & Saeed Salehi - 2019 - Theoria 85 (1):8-17.
    We take an argument of Gödel's from his ground‐breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: "the sentence G says about itself that it is not provable, and G is indeed not provable; therefore, G is true".
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  47. Theories of Properties, Relations, and Propositions.George Bealer - 1979 - Journal of Philosophy 76 (11):634-648.
    This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of (...)
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  48. Algorithmic Information Theory and Undecidability.Panu Raatikainen - 2000 - Synthese 123 (2):217-225.
    Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.
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  49. Unsharpenable Vagueness.John Collins & Achille C. Varzi - 2000 - Philosophical Topics 28 (1):1-10.
    A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are (...)
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  50. Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many (...)
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