Results for 'Godel metric'

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  1. THE PHILOSOPHY OF KURT GODEL - ALEXIS KARPOUZOS.Alexis Karpouzos - 2024 - The Harvard Review of Philosophy 8 (14):12.
    Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the finite (...)
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  2. Four Possible Ways to Model Rotating Universe.Victor Christianto & Florentin Smarandache - manuscript
    It is known that most existing cosmology models do not include rotation, with few exceptions such as rotating Bianchi and rotating Godel metrics. Therefore in this paper we aim to discuss four possible ways to model rotating universe, including Nurgaliev’s Ermakov-type equation. It is our hope that the new proposed method can be verified with observations, in order to open new possibilities of more realistic nonlinear cosmology models.
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  3. A Comparative Analysis of David Lewis' Modal Realism and Everett's Many Worlds on Closed Time-like Curves and Time Travel.Fabian Kerj - 2023 - Dissertation, King's College London
    This paper explores the physical and metaphysical implications of time travel, focusing on the possibility of changing the past, through a comparative analysis of David Lewis' modal realism and Everett's many-worlds interpretation of quantum mechanics. The existence of closed timelike curves (CTCs) in certain solutions to Einstein's field equations provides a theoretical basis for the possibility of backwards time travel, but this leads to a range of paradoxes, most notably the grandfather paradox. David Lewis argues that time travel must maintain (...)
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  4. Vor dem Starten ankommen. Über Zeitreisen und Warp-Antriebe.Kay Herrmann - 2016 - Universitätsverlag Chemnitz.
    The question of time travel stimulates the imagination and provides material for whimsical stories. A work on the topic of "time travel" forces us to deal with the concept of "time". The complexity and the antinomic character of this concept make it difficult to grasp "time" more precisely. We encounter time as a form of perception in its deeply subjective aspect, as a biological rhythm, as a social phenomenon in the sense of a collective determination of time, but also as (...)
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  5. 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 our finitary (...)
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  6. 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 match (...)
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  7. (1 other version)Gödel’s Cantorianism.Claudio Ternullo - 2015 - In E.-M. Engelen (ed.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence. pp. 417-446.
    Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.
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  8. Что означают парапоследовательные, неопределимые, случайные, вычислительные и неполные? Обзор: “Путь Годеля - Приключения в неопределенном мире” (Godel's Way: Exploits into an undecidable world) by Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012) (обзор пересмотрен 2019).Michael Richard Starks - 2020 - In ДОБРО ПОЖАЛОВАТЬ В АД НА НАШЕМ МИРЕ. Las Vegas, NV USA: Reality Press. pp. 171-186.
    В «Godel's Way» три видных ученых обсуждают такие вопросы, как неплатежеспособность, неполнота, случайность, вычислительность и последовательность. Я подхожу к этим вопросам с точки зрения Витгенштейна, что есть две основные проблемы, которые имеют совершенно разные решения. Есть научные или эмпирические вопросы, которые являются факты о мире, которые должны быть исследованы наблюдений и философские вопросы о том, как язык может быть использован внятно (которые включают в себя определенные вопросы в математике и логике), которые должны быть решены, глядят, как мы на самом (...)
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  9. Kurt Gödel, paper on the incompleteness theorems (1931).Richard Zach - 2004 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. 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 theory that are (...)
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  10. Kurt Gödel and Computability Theory.Richard Zach - 2006 - In Beckmann Arnold, Berger Ulrich, Löwe Benedikt & Tucker John V. (eds.), Logical Approaches to Computational Barriers. Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. Springer. pp. 575--583.
    Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...)
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  11. Compact propositional Gödel logics.Matthias Baaz & Richard Zach - 1998 - In Baaz Matthias (ed.), 28th IEEE International Symposium on Multiple-Valued Logic, 1998. Proceedings. IEEE Press. pp. 108-113.
    Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.
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  12. Godel, Escherian Staircase and Possibility of Quantum Wormhole With Liquid Crystalline Phase of Iced-Water - Part II: Experiment Description.Victor Christianto, T. Daniel Chandra & Florentin Smarandache - 2023 - Bulletin of Pure and Applied Sciences 42 (2):85-100.
    The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and (...)
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  13. Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9):1-56.
    The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...)
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  14. Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930).Vasil Penchev - 2023 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 15 (1):1-61.
    The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...)
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  15. Gödel's "slingshot" argument and his onto-theological system.Srećko Kovač & Kordula Świętorzecka - 2015 - In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper. pp. 123-162.
    The paper shows that it is possible to obtain a "slingshot" result in Gödel's theory of positiveness in the presence of the theorem of the necessary existence of God. In the context of the reconstruction of Gödel's original "slingshot" argument on the suppositions of non-Fregean logic, this is a natural result. The "slingshot" result occurs in sufficiently strong non-Fregean theories accepting the necessary existence of some entities. However, this feature of a Gödelian theory may be considered not as a trivialisation, (...)
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  16. Metrics in research impact assessment and grant funding: Insights from researchers in the “Reviewer 2 Must Be Stopped!” Facebook group.Valentine Joseph Owan, Victor Ubugha Agama, John O. Odey & Delight Omoji Idika - 2024 - Journal of Applied Learning and Teaching 7 (1):1-12.
    Research assessment and grant funding are vital to higher education. However, the reliance on quantitative metrics in these processes has raised concerns about their validity and potential negative consequences. This study aims to investigate the game of numbers in research assessment and grant funding, focusing on the perspectives of experienced researchers from around the globe. Accidental sampling elicited responses from more than 15 experienced researchers across different academic disciplines, institutions, and countries. The data were collected from the popular “Reviewer 2 (...)
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  17. Questioning Gödel's Ontological Proof: Is Truth Positive?Gregor Damschen - 2011 - European Journal for Philosophy of Religion 3 (1):161-169.
    In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given (...)
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  18. Godel, Escherian Staircase and Possibility of Quantum Wormhole With Liquid Crystalline Phase of Iced-Water - Part I: Theoretical Underpinning.Victor Christianto, T. Daniel Chandra & Florentin Smarandache - 2023 - Bulletin of Pure and Applied Sciences 42 (2):70-75.
    As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s (...)
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  19. Gödel's incompleteness theorems, free will and mathematical thought.Solomon Feferman - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. New York: 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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  20. 불일치, 결정 불가능, 임의, 계산 가능 및 불완전한 의미는 무엇입니까? '고델의 길 : 결정 불가능한 세상으로의 착취'에 대한 검토 (Godel's Way: Exploits into an undecidable world) by Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012).Michael Richard Starks - 2020 - In 지구상의 지옥에 오신 것을 환영합니다 : 아기, 기후 변화, 비트 코인, 카르텔, 중국, 민주주의, 다양성, 역학, 평등, 해커, 인권, 이슬람, 자유주의, 번영, 웹, 혼돈, 기아, 질병, 폭력, 인공 지능, 전쟁. Las Vegas, NV USA: Reality Press. pp. 187-203.
    'Godel's Way'에서 세 명의 저명한 과학자들은 부정성, 불완전성, 임의성, 계산성 및 파라불일치와 같은 문제에 대해 논의합니다. 나는 완전히 다른 해결책을 가지고 두 가지 기본 문제가 있다는 비트 겐슈타인의 관점에서 이러한 문제에 접근. 과학적 또는 경험적 문제가 있다, 관찰 하 고 철학적 문제 언어를 어떻게 이해할 수 있는 (수학 및 논리에 특정 질문을 포함) 에 대 한 조사 해야 하는 세계에 대 한 사실,우리가 실제로 특정 컨텍스트에서 단어를 사용 하는 방법을 보고 하 여 결정 될 필요가. 우리가 어떤 언어 게임을 (...)
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  21. Multiplicative Metric Fairness Under Composition.Milan Mossé - 2023 - Symposium on Foundations of Responsible Computing 4.
    Dwork, Hardt, Pitassi, Reingold, & Zemel [6] introduced two notions of fairness, each of which is meant to formalize the notion of similar treatment for similarly qualified individuals. The first of these notions, which we call additive metric fairness, has received much attention in subsequent work studying the fairness of a system composed of classifiers which are fair when considered in isolation [3, 4, 7, 8, 12] and in work studying the relationship between fair treatment of individuals and fair (...)
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  22. Gödel's Incomplete Theorem: a sequel to Logic and Analytic Philosophy.Yusuke Kaneko - 2021 - The Basis : The Annual Bulletin of Research Center for Liberal Education 11:81-107.
    Although written in Japanese, this article handles historical and technical survey of Gödel's incompleteness theorem thoroughly.
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  23. Causal interpretation of Gödel's ontological proof.Srećko Kovač - 2015 - In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper. pp. 163.201.
    Gödel's ontological argument is related to Gödel's view that causality is the fundamental concept in philosophy. This explicit philosophical intention is developed in the form of an onto-theological Gödelian system based on justification logic. An essentially richer language, so extended, offers the possibility to express new philosophical content. In particular, theorems on the existence of a universal cause on a causal "slingshot" are formulated.
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  24. The Philosophical Insignificance of Gödel's Slingshot.G. Oppy - 1997 - Mind 106 (421):121-142.
    This paper is a critical examination of Stephen Neale's *The Philosophical Significance of Godel's slingshot*. I am sceptical of the philosophical significance of Godel’s Slingshot (and of Slingshot arguments in general). In particular, I do not believe that Godel’s Slingshot has any interesting and important philosophical consequences for theories of facts or for referential treatments of definite descriptions. More generally, I do not believe that any Slingshot arguments have interesting and important philosophical consequences for theories of facts (...)
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  25. 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 nor disprovable (...)
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  26. Compound Metric Assisted Trust Aware Routing for Internet of Things through Firefly Algorithm.Mohammad Osman, Kaleem Fatima & P. Naveen Kumar - 2023 - International Journal of Intelligent Engineering and Systems 16 (3):280-291.
    Security and privacy are the major concerns in the internet of things (IoT) which are uncertain and unpredictable. Trust aware routing is one of the recent and effective strategies which ensure better resilience for IoT nodes from different security threats. Towards such concern, this paper proposes a new strategy called independent onlooker withstanding trust aware routing (IOWTAR) for IoT. IOWTAR introduced a new compound trust metric by combining three individual metrics namely independent trust, onlooker trust, and withstanding trust (a (...)
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  27. Godel Meets Carnap: A Prototypical Discourse on Science and Religion.Alfred Gierer - 1997 - Zygon 32 (2):207-217.
    Modern science, based on the laws of physics, claims validity for all events in space and time. However, it also reveals its own limitations, such as the indeterminacy of quantum physics, the limits of decidability, and, presumably, limits of decodability of the mind-brain relationship. At the philosophical level, these intrinsic limitations allow for different interpretations of the relation between human cognition and the natural order. In particular, modern science may be logically consistent with religious as well as agnostic views of (...)
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  28. Kant, Gödel and Relativity.Mauro Dorato - 2002 - In Gardenfors, Wolenski & Katarzina Kijania-Placek (eds.), In the Scope of Logic, Methodology and Philosophy of Science, Proceedings of the Invited Lectures for the 11th International Congress of Logic Methodology and Philosophy of Science. Dordrecht: Kluwer. pp. 331-348..
    Since the onset of logical positivism, the general wisdom of the philosophy of science has it that the kantian philosophy of (space and) time has been superseded by the theory of relativity, in the same sense in which the latter has replaced Newton’s theory of absolute space and time. On the wake of Cassirer and Gödel, in this paper I raise doubts on this commonplace by suggesting some conditions that are necessary to defend the ideality of time in the sense (...)
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  29. Beyond Gödel’s Time.Peter J. Riggs - 2018 - Inference: International Review of Science 4 (1).
    Letter to the Editors in response to Alasdair Richmond's 'Time Travelers'.
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  30. Modal collapse in Gödel's ontological proof.Srećko Kovač - 2012 - In Miroslaw Szatkowski (ed.), Ontological Proofs Today. Ontos Verlag. pp. 50--323.
    After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...)
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  31. Axiomatic Foundations for Metrics of Distributive Justice Shown by the Example of Needs-Based Justice.Alexander Max Bauer - 2017 - Forsch! 3 (1):43-60.
    Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that (...)
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  32. Hilbert Mathematics versus Gödel Mathematics. III. Hilbert Mathematics by Itself, and Gödel Mathematics versus the Physical World within It: both as Its Particular Cases.Vasil Penchev - 2023 - Philosophy of Science eJournal (Elsevier: SSRN) 16 (47):1-46.
    The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...)
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  33. Kurt Gödels mathematische Anschauung und John P. Burgess’ mathematische Intuition.Eva-Maria Engelen - 2014 - XXIII Deutscher Kongress Für Philosophie Münster 2014, Konferenzveröffentlichung.
    John P. Burgess kritisiert Kurt Gödels Begriff der mathematischen oder rationalen Anschauung und erläutert, warum heuristische Intuition dasselbe leistet wie rationale Anschauung, aber ganz ohne ontologisch überflüssige Vorannahmen auskommt. Laut Burgess müsste Gödel einen Unterschied zwischen rationaler Anschauung und so etwas wie mathematischer Ahnung, aufzeigen können, die auf unbewusster Induktion oder Analogie beruht und eine heuristische Funktion bei der Rechtfertigung mathematischer Aussagen einnimmt. Nur, wozu benötigen wir eine solche Annahme? Reicht es nicht, wenn die mathematische Intuition als Heuristik funktioniert? Für (...)
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  34. パラコンシステント、決定不能、ランダム、計算可能、不完全とはどういう意味 ですか? 「ゴーデルの方法:決定不可能な世界への冒険:」のレビュー(Godel's Way: exploits into an Undecidable World) byA. da Costa 160p (2012) (2019年のレビュー改訂).Michael Richard Starks - 2020 - In 地獄へようこそ : 赤ちゃん、気候変動、ビットコイン、カルテル、中国、民主主義、多様性、ディスジェニックス、平等、ハッカー、人権、イスラム教、自由主義、繁栄、ウェブ、カオス、飢餓、病気、暴力、人工知能、戦争. Las Vegas, NV USA: Reality Press. pp. 158-171.
    「ゴーデルの道」では、3人の著名な科学者が、デシッド不能、不完全性、ランダム性、計算可能性、パラコンシステンションなどの問題について議論しています。私は、ウィトゲンシュタイニアンの視点から、全く異なる 解決策を持つ2つの基本的な問題があることをこれらの問題に取り組んでいます。科学的または経験的な問題は、言語がどのように理解的に使用できるか(数学と論理に特定の質問を含む)、特定の文脈で実際にどのように 単語を使用するかを調べて決定する必要がある、観察的および哲学的な問題を調査する必要がある世界に関する事実です。私たちがプレイしている言語ゲームについて明確になると、これらのトピックは他の人と同じように 普通の科学的、数学的な質問であると見なされます。ウィトゲンシュタインの洞察はめったに等しくなく、決して上回ることはなく、彼がブルーブックスとブラウンブックスを口述した80年前と同じくらい適切です。失敗 にもかかわらず、本当に完成した本ではなく一連のノートは、半世紀以上にわたって物理学、数学、哲学の出血エッジで働いてきたこれらの3人の有名な学者の作品のユニークな源です。ダ・コスタとドリアは、普遍的な計 算に書いて以来、ウォルパート(以下または私の記事を参照)によって引用されています(ウォルパートとヤナフスキーの「理由の外側の限界」の私のレビューを参照)、,そして彼の多くの成果の中で、ダ・コスタはパラ コンシタンションのパイオニアです。 現代の2つのシス・エムスの見解から人間の行動のための包括的な最新の枠組みを望む人は、私の著書「ルートヴィヒ・ヴィトゲンシュタインとジョン・サールの第2回(2019)における哲学、心理学、ミンと言語の論 理的構造」を参照することができます。私の著作の多くにご興味がある人は、運命の惑星における「話す猿--哲学、心理学、科学、宗教、政治―記事とレビュー2006-2019 第3回(2019)」と21世紀4日(2019年)の自殺ユートピア妄想st Century 4th ed (2019)などを見ることができます。 .
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  35. Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Voronkov Andrei & Parigot Michel (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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  36. Hilbert Mathematics Versus Gödel Mathematics. IV. The New Approach of Hilbert Mathematics Easily Resolving the Most Difficult Problems of Gödel Mathematics.Vasil Penchev - 2023 - Philosophy of Science eJournal (Elsevier: SSRN) 16 (75):1-52.
    The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...)
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  37. Diagonalization & Forcing FLEX: From Cantor to Cohen and Beyond. Learning from Leibniz, Cantor, Turing, Gödel, and Cohen; crawling towards AGI.Elan Moritz - manuscript
    The paper continues my earlier Chat with OpenAI’s ChatGPT with a Focused LLM Experiment (FLEX). The idea is to conduct Large Language Model (LLM) based explorations of certain areas or concepts. The approach is based on crafting initial guiding prompts and then follow up with user prompts based on the LLMs’ responses. The goals include improving understanding of LLM capabilities and their limitations culminating in optimized prompts. The specific subjects explored as research subject matter include a) diagonalization techniques as practiced (...)
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  38. Developing a Metric of Usable Space for Zoo Exhibits.Heather Browning & Terry L. Maple - 2019 - Frontiers in Psychology 10:791.
    The size of animal exhibits has important effects on their lives and welfare. However, most references to exhibit size only consider floor space and height dimensions, without considering the space afforded by usable features within the exhibit. In this paper, we develop two possible methods for measuring the usable space of zoo exhibits and apply these to a sample exhibit. Having a metric for usable space in place will provide a better reflection of the quality of different exhibits, and (...)
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  39. Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge. [REVIEW]Panu Raatikainen - 2018 - History and Philosophy of Logic 39 (4):401-403.
    Austrian-born Kurt Gödel is widely considered the greatest logician of modern times. It is above all his celebrated incompleteness theorems—rigorous mathematical results about the necessary limits...
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  40. Depictive and Metric Body Size Estimation in Anorexia Nervosa and Bulimia Nervosa: A Systematic Review and Meta-Analysis.Simone Claire Mölbert, Lukas Klein, Anne Thaler, Betty J. Mohler, Chiara Brozzo, Peter Martus, Hans-Otto Karnath, Stefan Zipfel & Katrin Elisabeth Giel - 2017 - Clinical Psychology Review 57:21-31.
    A distorted representation of one's own body is a diagnostic criterion and core psychopathology of both anorexia nervosa (AN) and bulimia nervosa (BN). Despite recent technical advances in research, it is still unknown whether this body image disturbance is characterized by body dissatisfaction and a low ideal weight and/or includes a distorted perception or processing of body size. In this article, we provide an update and meta-analysis of 42 articles summarizing measures and results for body size estimation (BSE) from 926 (...)
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  41. Mathematical instrumentalism, Gödel’s theorem, and inductive evidence.Alexander Paseau - 2011 - Studies in History and Philosophy of Science Part A 42 (1):140-149.
    Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism (...)
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  42. Wittgenstein x Gödel: reflexões sobre o Teorema da Incompletude.Rafael Ongaratto - 2024 - Dissertation, Unicamp
    In the Appendix I of his "Remarks on the Foundations of Mathematics", Wittgenstein elaborates a different interpretation of Gödel’s First Incompleteness Theorem, which we have come to refer to as "Gödel’s Theorem" or "Incompleteness Theorem". This nomenclature arises from the recognition that the so-called "Second Incompleteness Theorem" is essentially a corollary of the primary theorem. Wittgenstein aims to reassess Gödel’s conclusion that there exist true formulas not demonstrable within formal systems capable of representing a sufficient amount of arithmetic theory. Gödel’s (...)
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  43. Meaning, Presuppositions, Truth-relevance, Gödel's Sentence and the Liar Paradox.X. Y. Newberry - manuscript
    Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...)
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  44. Spinoza and Gödel: Causa Sui and Undecidable Truth.Martin Zwick - 2007 - North American Spinoza Society Monograph 13:46-52.
    Spinoza distinguishes between causation that is external, as in A causing B where A is external to B, and causation that is internal, where C causes itself (causa sui), without any involvement of anything external to C. External causation is easy to understand, but self causation is not. This note explores an approach to self-causation based upon Gödelian undecidability and draws upon ideas from an earlier study of Gödel’s proof and the quantum measurement problem (Zwick, 1978).
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  45. 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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  46. 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: Assessing Philosophy of Logic and Mathematics Today. Dordrecht, Netherland: Springer. pp. 51--73.
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  47. Gödel's slingshot revisited: does russell's theory of descriptions really evade the slingshot.João Daniel Dantas - 2016 - Dissertation, Ufrn
    “Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that there (...)
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  48. Metrics of Patient, Public, Consumer, and Community Engagement in Healthcare Systems: How Should We Define Engagement, What Are We Measuring, and Does It Matter for Patient Care? Comment on "Metrics and Evaluation Tools for Patient Engagement in Healthcare Organization- and System-Level Decision-Making: A Systematic Review". [REVIEW]Zackary Berger - 2018 - International Journal of Health Policy and Management 8:49-50.
    In a rigorous systematic review, Dukhanin and colleagues categorize metrics and evaluative tools of the engagement of patient, public, consumer, and community in decision-making in healthcare institutions and systems. The review itself is ably done and the categorizations lead to a useful understanding of the necessary elements of engagement, and a suite of measures relevant to implementing engagement in systems. Nevertheless, the question remains whether the engagement of patient representatives in institutional or systemic deliberations will lead to improved clinical outcomes (...)
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  49. Executing Gödel's Programme in Set Theory.Neil Barton - 2017 - Dissertation, Birkbeck, University of London
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  50. A Metasemantic Analysis of Gödel's Slingshot Argument.Hans-Peter Leeb - manuscript
    Gödel’s slingshot-argument proceeds from a referential theory of definite descriptions and from the principle of compositionality for reference. It outlines a metasemantic proof of Frege’s thesis that all true sentences refer to the same object—as well as all false ones. Whereas Frege drew from this the conclusion that sentences refer to truth-values, Gödel rejected a referential theory of definite descriptions. By formalising Gödel’s argument, it is possible to reconstruct all premises that are needed for the derivation of Frege’s thesis. For (...)
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