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Kurt Gödel: Collected Works Vol. Ii

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Oxford University Press (1990)

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  1. Monads and Mathematics: Gödel and Husserl.Richard Tieszen - 2012 - Axiomathes 22 (1):31-52.
    In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of (...)
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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.
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  • What is the Nature of Mathematical–Logical Objects?Stathis Livadas - 2017 - Axiomathes 27 (1):79-112.
    This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...)
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  • The Subjective Roots of Forcing Theory and Their Influence in Independence Results.Stathis Livadas - 2015 - Axiomathes 25 (4):433-455.
    This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their deeper subjectively founded content (...)
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  • Extending the Non-extendible: Shades of Infinity in Large Cardinals and Forcing Theories.Stathis Livadas - 2018 - Axiomathes 28 (5):565-586.
    This is an article whose intended scope is to deal with the question of infinity in formal mathematics, mainly in the context of the theory of large cardinals as it has developed over time since Cantor’s introduction of the theory of transfinite numbers in the late nineteenth century. A special focus has been given to this theory’s interrelation with the forcing theory, introduced by P. Cohen in his lectures of 1963 and further extended and deepened since then, which leads to (...)
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  • On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79.
    This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.
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