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Reflections on Kurt Gödel

Bradford (1990)

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  1. 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 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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  • 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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  • 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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  • 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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  • 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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  • ‘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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  • On the Failure of Mathematics' Philosophy: Review of P. Maddy, Realism in Mathematics; and C. Chihara, Constructibility and Mathematical Existence. [REVIEW]David Charles McCarty - 1993 - Synthese 96 (2):255-291.
  • 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 'Disproof' of the Syntactical Viewpoint.Victor Rodych - 2001 - Southern Journal of Philosophy 39 (4):527-555.
  • Gödel’s Philosophical Program and Husserl’s Phenomenology.Xiaoli Liu - 2010 - Synthese 175 (1):33-45.
  • Gödel's Functional Interpretation and its Use in Current Mathematics.Ulrich Kohlenbach - 2008 - Dialectica 62 (2):223–267.
  • The Idea of Phenomenology: Reading Husserliana as Reductions.Juha Himanka - 2010 - Dialogue 49 (4):617-640.
    Edmund Husserl strongly emphasized the importance of reduction to his phenomenology. For his followers, however, it has proved a formidable task to specify exactly how this intricate accomplishment that opens up the possibility for phenomenological research is to be performed. In this article, we study different approaches to gaining access to reduction and conclude by suggesting that we should read Husserliana itself as a set of accomplished reductions. In other words, our task is to pinpoint chapters where the movement of (...)
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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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