Results for 'METAMATHEMATICS'

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  1.  27
    Efficient Metamathematics. Rineke - 1993 - Dissertation, Universiteit van Amsterdam
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  2. What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  3. Minimal Sartre: Diagonalization and Pure Reflection.John Bova - 2018 - Open Philosophy 1:360-379.
    These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Godel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through (...)
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  4. Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08.John Corcoran - 1972 - Philosophy of Science 39 (1):106-108.
    Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. -/- Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD and, in recognition of (...)
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  5. Meanings of Word: Type-Occurrence-Token.John Corcoran - 2005 - Bulletin of Symbolic Logic 11 (1):117.
    Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: (...)
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  6. REVIEW OF Alfred Tarski, Collected Papers, Vols. 1-4 (1986) Edited by Steven Givant and Ralph McKenzie. [REVIEW]John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...)
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  7. CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI's COLLECTED PAPERS.John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (I):110-114.
    CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most (...)
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  8.  86
    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 as (...)
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  9.  59
    Kolmogorov Randomness, Complexity and the Laws of Nature.Giovanni Sommazzi - 2016 - Dissertation,
    A formal introduction to Kolmogorov complexity is given, along with its fundamental theorems. Most importantly the theorem of undecidability of a random string and the information-theoretic reformulation of Gödel’s first theorem of incompleteness, stated by Chaitin. Then, the discussion moves on to inquire about some philosophical implications the concept randomness has in the fields of physics and mathematics. Starting from the notion of “understanding as compression” of information, as it is illuminated by algorithmic information theory, it is investigated (1) what (...)
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  10. Замечания о невозможности, неполноте Paraconsistency, Нерешающость, Случайность вычислительности, парадокс, и неопределенность в Чайтин, Витгенштейн, Хофштадтер Вольперт, Дориа, да Коста, Годель, Сирл, Родыч Берто, Флойд, Мойал-Шаррок и Янофски.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    Принято считать, что невозможность, неполнота, Парапоследовательность, Несоответствие, Случайность, вычислительность, парадокс, неопределенность и пределы разума являются разрозненными научными физическими или математическими вопросами, имеющими мало или ничего общего. Я полагаю, что они в значительной степени стандартные философские проблемы (т.е. языковые игры), которые были в основном решены Витгенштейном более 80 лет назад. -/- Я предоставляю краткое резюме некоторых из основных выводов двух из самых выдающихся студентов поведения о Fсовременности, Людвиг Витгенштейн и Джон Сирл, на логическую структуру преднамеренности (ум, язык, поведение), принимая в качестве (...)
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  11.  62
    关于在柴廷、维特根斯坦、霍夫施塔特、沃尔珀特、多里亚、达科斯塔、戈德尔、西尔、罗迪赫、贝托、弗洛伊德、贝托、弗洛伊德、莫亚尔-沙罗克和亚诺夫斯基.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    人们普遍认为,不可能性、不完整性、不一致性、不可度、随机性、可预见性、悖论、不确定性和理性极限是完全不同的科学物理或数学问题,在常见。我认为,它们主要是标准的哲学问题(即语言游戏),这些问题大多在80 多年前由维特根斯坦解决。 -/- "在这种情况下,我们'想说'当然不是哲学,而是它的原材料。因此,例如,数学家倾向于对数学事实的客观性和现实性说的,不是数学哲学,而是哲学处理的东西。维特根斯坦 PI 234 -/- "哲学家们经常看到科学的方法,他们不可抗拒地试图以科学的方式提问和回答问题。这种倾向是形而上学的真正源泉,将哲学家带入完全的黑暗之中。 维特根斯坦 -/- 我简要地总结了现代两位最杰出的学生路德维希·维特根斯坦和约翰·西尔关于故意的逻辑结构(思想、语言、行为)的一些主要发现,作为我的起点Wittgenstein 的基本发现——所有真正的"哲学"问题都是相同的——关于在特定上下文中如何使用语言的困惑,因此所有解决方案都是一样的——研究如何在相关上下文中使用语言,使其真实性条件(满意度或 COS 条件)是明确的。基本问题是,人们可以说什么,但一个人不能意味着(状态明确COS)任何任意的话语和意义只有在非常具体的上下文中才可能。 -/- 在两种思想体系的现代视角(被推广为"思维快,思维慢")的框架内,我从维特根斯坦人的角度剖析了一些主要评论员关于这些问题的一些著作,并采用了一个新的表意向性和新的双系统命名法。 我表明,这是一个强大的启发式描述这些假定的科学,物理或数学问题的真实性质,这是真正最好的处理作为标准哲学问题,如何使用语言(语言游戏在维特根斯坦的术语)。 -/- 我的论点是,这里突出特征的意向表(理性、思想、思想、语言、个性等)或多或少地准确地描述了,或者至少作为启发式,我们思考和行为的方式,所以它包含不只是哲学和心理学,但其他一切(历史,文学,数学,政治等) 。特别要注意,我(以及西尔、维特根斯坦和其他人)认为,故意和理性包括有意识的审议语言系统2和无意识的自动预语言系统1行为或反射。 .
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  12.  73
    اظهارات در مورد عدم امکان ، بی کامل بودن ، پاراستشتها، Undecidability ، اتفاقی ، Computability ، پارادوکس ، و عدم قطعیت در Chaitin ، ویتگنشتاین ، Hofstadter ، Wolpert ، doria ، دا کوستا ، گودل ، سرل ، رودیچ ، برتو ، فلوید ، مویال-شرراک و یانفسکی.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    معمولا تصور می شود که عدم امکان ، بی کامل بودن ، پارامونشتها ، Undecidability ، اتفاقی ، قابلیت های مختلف ، پارادوکس ، عدم قطعیت و محدودیت های دلیل ، مسائل فیزیکی و ریاضی علمی و یا با داشتن کمی یا هیچ چیز در مشترک. من پیشنهاد می کنم که آنها تا حد زیادی مشکلات فلسفی استاندارد (به عنوان مثال ، بازی های زبان) که عمدتا توسط ویتگنشتاین بیش از 80 سال پیش حل و فصل شد. -/- "آنچه ما (...)
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  13.  79
    असंभव, अपूर्णता, अनिर्णय, अनिर्णय, यादृच्छिकता, गणना, विरोधाभास, और चैटिन, विटगेनस्टीन, Hofstadter, Wolpert, डोरिया, दा कोस्टा, गोडेल, सीरले, Rodych, Berto, Floyd में अनिश्चितता पर टिप्पणी मोयाल-शररॉक और यानोफ्स्की.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    यह आमतौर पर सोचा जाता है कि असंभवता, अपूर्णता, Paraconsistency, अनिर्णितता, Randomness, Computability, विरोधाभास, अनिश्चितता और कारण की सीमा अलग वैज्ञानिक शारीरिक या गणितीय मुद्दों में कम या कुछ भी नहीं कर रहे हैं आम. मेरा सुझाव है कि वे काफी हद तक मानक दार्शनिक समस्याओं (यानी, भाषा का खेल) जो ज्यादातर 80years पहले Wittgenstein द्वारा हल किए गए थे. -/- "क्या हम 'इस तरह के एक मामले में कहने के लिए' कर रहे हैं, ज़ाहिर है, दर्शन नहीं है, लेकिन (...)
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  14.  56
    ملاحظات على استحالة, عدم اكتمال, بارااتساق,عدم تحديد, عشوائية, الحوسبة, مفارقة, وعدم اليقين في Chaitin, Wittgenstein, Hofstadter, Wolpert, دوريا, دا كوستا, جوديل, سيرل, روديش, بيرتو, فلويد, مويال شاروك ويانوفسكي.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    ويعتقد عادة أن الاستحالة، وعدم اكتمال، وParaconsistency، وعدم تحديد، العشوائية، والحوسبة، والمفارقة، وعدم اليقين وحدود العقل هي قضايا علمية مادية أو رياضية متباينة وجود القليل أو لا شيء في المشتركه. أقترح أنها مشاكل فلسفية قياسية إلى حد كبير (أي ألعاب اللغة) التي تم حلها في الغالب من قبل فيتغنشتاين أكثر من 80years منذ. -/- "إن ما نميل إلى قوله في مثل هذه الحالة هو، بطبيعة الحال، ليس فلسفة، ولكنه مادة خام. وهكذا، على سبيل المثال، ما يميل عالم الرياضيات إلى قوله (...)
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  15. Pernyataan tentang kemustahilan, ketidaklengkapan, Paraconsistency,Undecidability, Randomness, Komputabilitas, paradoks, dan ketidakpastian dalam Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal-Sharrock dan Yanofsky.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    Hal ini sering berpikir bahwa kemustahilan, ketidaklengkapan, Paraconsistency, Undecidability, Randomness, komputasi, Paradox, ketidakpastian dan batas alasan yang berbeda ilmiah fisik atau matematika masalah memiliki sedikit atau tidak ada dalam Umum. Saya menyarankan bahwa mereka sebagian besar masalah filosofis standar (yaitu, Permainan bahasa) yang sebagian besar diselesaikan oleh Wittgenstein lebih dari 80years yang lalu. -/- "Apa yang kita ' tergoda untuk mengatakan ' dalam kasus seperti ini, tentu saja, bukan filsafat, tetapi bahan baku. Jadi, misalnya, apa yang seorang matematikawan cenderung mengatakan (...)
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  16.  46
    Remarques sur l'impossibilité l'incomplétude, la paracohérence l'indécision, le hasard, la calculabilité, le paradoxe et l'incertitude - dans Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria da Costa, Godel, Searle, Rodych, Berto Floyd, Moyal-Sharrock et Yanofsky.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    On pense généralement que l'impossibilité, l'incomplétdulité, la paracohérence, l'indécidabilité, le hasard, la calcul, le paradoxe, l'incertitude et les limites de la raison sont des questions scientifiques physiques ou mathématiques disparates ayant peu ou rien dans terrain d'entente. Je suggère qu'ils sont en grande partie des problèmes philosophiques standard (c.-à-d., jeux de langue) qui ont été la plupart du temps résolus par Wittgenstein plus de 80 ans. Je fournis un bref résumé de quelques-unes des principales conclusions de deux des plus éminents (...)
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  17. The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  18. Jakob Friedrich Fries (1773-1843): Eine Philosophie der Exakten Wissenschaften.Kay Herrmann - 1994 - Tabula Rasa. Jenenser Zeitschrift Für Kritisches Denken (6).
    Jakob Friedrich Fries (1773-1843): A Philosophy of the Exact Sciences -/- Shortened version of the article of the same name in: Tabula Rasa. Jenenser magazine for critical thinking. 6th of November 1994 edition -/- 1. Biography -/- Jakob Friedrich Fries was born on the 23rd of August, 1773 in Barby on the Elbe. Because Fries' father had little time, on account of his journeying, he gave up both his sons, of whom Jakob Friedrich was the elder, to the Herrnhut Teaching (...)
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  19. Lies, Half-Truths, and Falsehoods About Tarski’s 1933 “Liar” Antinomies.John Corcoran & Joaquin Miller - 2012 - Bulletin of Symbolic Logic 18 (1):140-141.
    We discuss misinformation about “the liar antinomy” with special reference to Tarski’s 1933 truth-definition paper [1]. Lies are speech-acts, not merely sentences or propositions. Roughly, lies are statements of propositions not believed by their speakers. Speakers who state their false beliefs are often not lying. And speakers who state true propositions that they don’t believe are often lying—regardless of whether the non-belief is disbelief. Persons who state propositions on which they have no opinion are lying as much as those who (...)
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  20.  71
    Robot Consciousness: Physics and Metaphysics Here and Abroad.Stephen Ripley - manuscript
    Interest has been renewed in the study of consciousness, both theoretical and applied, following developments in 20th and early 21st-century logic, metamathematics, computer science, and the brain sciences. In this evolving narrative, I explore several theoretical questions about the types of artificial intelligence and offer several conjectures about how they affect possible future developments in this exceptionally transformative field of research. I also address the practical significance of the advances in artificial intelligence in view of the cautions issued by (...)
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  21.  40
    Review of Wittgenstein's Metaphilosophy by Paul Horwich 248p (2013) (Review Revised 2019).Michael Starks - 2019 - In The Logical Structure of Human Behavior. Las Vegas, NV USA: Reality Press. pp. 142-165.
    Horwich gives a fine analysis of Wittgenstein (W) and is a leading W scholar, but in my view, they all fall short of a full appreciation, as I explain at length in this review and many others. If one does not understand W (and preferably Searle also) then I don't see how one could have more than a superficial understanding of philosophy and of higher order thought and thus of all complex behavior (psychology, sociology, anthropology, history, literature, society). In a (...)
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  22.  85
    Review of Wittgensteins Metaphilosophy by Paul Horwich (2013).Michael Starks - 2017 - Philosophy, Human Nature and the Collapse of Civilization Michael Starks 3rd Ed. (2017).
    Horwich gives a fine analysis of Wittgenstein (W) and is a leading W scholar, but in my view they all fall short of a full appreciation, as I explain at length in this review and many others. If one does not understand W (and preferably Searle also) then I don't see how one could have more than a superficial understanding of philosophy and of higher order thought and thus of all complex behavior(psychology, sociology, anthropology, history, literature, society). In a nutshell, (...)
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