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Reflections on Kurt Gödel

Bradford (1990)

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  1. Um filósofo da evidência.M. S. Lourenço - 2009 - Disputatio 3 (27):1-13.
    Embora algumas posições filosóficas de Gödel sejam bem conhecidas, como o platonismo, a sua teoria do conhecimento é, em comparação, menos divulgada. A partir do «Problema da Evidência» de Hilbert-Bernays, I, pg. 20 seq., apresento a seguir os traços essenciais da posição de Gödel sobre a caracterização epistemológica da evidência finitista, com especial relevo para a história dos conceitos utilizados.
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  • Sets, Logic, Computation. An Open Introduction to Metalogic.Richard Zach - 2017
    An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.
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  • 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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  • Gödel's Cantorianism.Claudio Ternullo - 2015 - In Eva-Maria Engelen & Gabriella Crocco (eds.), 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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  • Godel's Unpublished Papers on Foundations of Mathematics.W. W. Tatt - 2001 - Philosophia Mathematica 9 (1):87-126.
  • Gödel and Philosophical Idealism.Charles Parsons - 2010 - Philosophia Mathematica 18 (2):166-192.
    Kurt Gödel made many affirmations of robust realism but also showed serious engagement with the idealist tradition, especially with Leibniz, Kant, and Husserl. The root of this apparently paradoxical attitude is his conviction of the power of reason. The paper explores the question of how Gödel read Kant. His argument that relativity theory supports the idea of the ideality of time is discussed critically, in particular attempting to explain the assertion that science can go beyond the appearances and ‘approach the (...)
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  • The Objectivity of Mathematics.Stewart Shapiro - 2007 - Synthese 156 (2):337-381.
    The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.
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  • On Logic in the Law: "Something, but Not All".Susan Haack - 2007 - Ratio Juris 20 (1):1-31.
    In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...)
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  • Gödel's Incompleteness Theorems.Panu Raatikainen - 2013 - The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (Ed.).
    Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot (...)
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  • 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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  • Reasoning, Logic and Computation.Stewart Shapiro - 1995 - Philosophia Mathematica 3 (1):31-51.
    The idea that logic and reasoning are somehow related goes back to antiquity. It clearly underlies much of the work in logic, as witnessed by the development of computability, and formal and mechanical deductive systems, for example. On the other hand, a platitude is that logic is the study of correct reasoning; and reasoning is cognitive if anything Is. Thus, the relationship between logic, computation, and correct reasoning makes an interesting and historically central case study for mechanism. The purpose of (...)
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  • Editorial.[author unknown] - forthcoming - Editorial 3 (27).
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  • On the Mathematical Nature of Logic, Featuring P. Bernays and K. Gödel.Oran Magal - unknown
    The paper examines the interrelationship between mathematics and logic, arguing that a central characteristic of each has an essential role within the other. The first part is a reconstruction of and elaboration on Paul Bernays’ argument, that mathematics and logic are based on different directions of abstraction from content, and that mathematics, at its core it is a study of formal structures. The notion of a study of structure is clarified by the examples of Hilbert’s work on the axiomatization of (...)
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  • Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable†.Timm Lampert - 2018 - Philosophia Mathematica 26 (3):324-345.
    According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...)
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  • ‘Orientation’ and Religious Discourse.Leslie Armour - 2013 - International Journal of Philosophy and Theology 74 (5):391-409.
    Religious discourse is in some way about the world, but its relation to other kinds of discourse – scientific historical, and moral – is a matter of dispute. Suggestions to avoid conflict with other kinds of discourse – the suggestion that religion invokes a distinct ‘language game’ and the suggestion that it should be taken as ‘basic’ for instance – have not, I argue, been successful. Essentially religion is involved in orienting us to the world and our goals, and orientation (...)
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  • Gödel’s Philosophical Program and Husserl’s Phenomenology.Xiaoli Liu - 2010 - Synthese 175 (1):33 - 45.
    Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much (...)
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  • Gödel’s Philosophical Program and Husserl’s Phenomenology.Xiaoli Liu - 2010 - Synthese 175 (1):33-45.
    Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much (...)
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  • The Comprehensibility Theorem and the Foundations of Artificial Intelligence.Arthur Charlesworth - 2014 - Minds and Machines 24 (4):439-476.
    Problem-solving software that is not-necessarily infallible is central to AI. Such software whose correctness and incorrectness properties are deducible by agents is an issue at the foundations of AI. The Comprehensibility Theorem, which appeared in a journal for specialists in formal mathematical logic, might provide a limitation concerning this issue and might be applicable to any agents, regardless of whether the agents are artificial or natural. The present article, aimed at researchers interested in the foundations of AI, addresses many questions (...)
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  • The Logic of Instance Ontology.D. W. Mertz - 1999 - Journal of Philosophical Logic 28 (1):81-111.
    An ontology's theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions $R_{i}$ . The power of PPL is illustrated (...)
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  • Time in Philosophy and in Physics: From Kant and Einstein to Gödel.Hao Wang - 1995 - Synthese 102 (2):215 - 234.
    The essay centers on Gödel's views on the place of our intuitive concept of time in philosophy and in physics. It presents my interpretation of his work on the theory of relativity, his observations on the relationship between Einstein's theory and Kantian philosophy, as well as some of the scattered remarks in his conversations with me in the seventies — namely, those on the philosophies of Leibniz, Hegel and Husserl — as a successor of Kant — in relation to their (...)
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  • On the Failure of Mathematics' Philosophy: Review of P. Maddy, Realism in Mathematics; and C. Chihara, Constructibility and Mathematical Existence.David Charles McCarty - 1993 - Synthese 96 (2):255-291.
  • To and From Philosophy — Discussions with Gödel and Wittgenstein.Hao Wang - 1991 - Synthese 88 (2):229 - 277.
    I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (...)
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  • Reflections on Kurt Gödel. [REVIEW]James Franklin - 1991 - History of European Ideas 13 (5):637-638.
    A review of Hao Wang's Reflections on Kurt Goedel, emphasising Goedel's reaction against his Vienna Circle background.
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  • Gödel’s ‘Disproof’ of the Syntactical Viewpoint.Victor Rodych - 2001 - Southern Journal of Philosophy 39 (4):527-555.
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  • Set Theory and Physics.K. Svozil - 1995 - Foundations of Physics 25 (11):1541-1560.
    Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible “solution of supertasks,” and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for physical applications are discussed: (...)
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  • Disturbing, but Not Surprising: Did Gödel Surprise Einstein with a Rotating Universe and Time Travel? [REVIEW]Giora Hon - 1996 - Foundations of Physics 26 (4):501-521.
    The question is raised as to the kind of methodology required to deal with foundational issues. A comparative study of the methodologies of Gödel and Einstein reveals some similar traits which reflect a concern with foundational problems. It is claimed that the interest in foundational problems stipulates a certain methodology, namely, the methodology of limiting cases.
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  • Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery.Vladimir Drekalović - 2015 - Axiomathes 25 (3):313-333.
    The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...)
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  • Gödel's Functional Interpretation and its Use in Current Mathematics.Ulrich Kohlenbach - 2008 - Dialectica 62 (2):223–267.