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  1. A Common Ground and Some Surprising Connections.Edward N. Zalta - 2002 - Southern Journal of Philosophy 40 (S1):1-25.
    This paper serves as a kind of field guide to certain passages in the literature which bear upon the foundational theory of abstract objects. The foundational theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. I explain how my foundational theory of objects serves as a common ground where analytic and phenomenological concerns meet. I try to establish how the theory offers a logic that systematizes a well-known phenomenological kind of entity, and I try to show (...)
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  • Richard Tieszen. After Gödel. Platonism and Rationalism in Mathematics and Logic.Dagfinn Føllesdal - 2016 - Philosophia Mathematica 24 (3):405-421.
  • Is Cantor's Continuum Problem Inherently Vague?Kai Hauser - 2002 - Philosophia Mathematica 10 (3):257-285.
    I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.
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  • Advance in Monte Carlo Simulations and Robustness Study and Their Implications for the Dispute in Philosophy of Mathematics.Chong Ho Yu - 2004 - Minerva - An Internet Journal of Philosophy 8 (1).
    Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversed views. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certain mathematical questions as internal questions appealing to logic and convention. On the contrary, Quine was opposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of this paper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlo simulations, limiting mathematical (...)
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  • Kurt Gödel.Juliette Kennedy - 2008 - Stanford Encyclopedia of Philosophy.
  • Gödel's Path From the Incompleteness Theorems (1931) to Phenomenology (1961).Richard Tieszen - 1998 - Bulletin of Symbolic Logic 4 (2):181-203.
  • Mathematical Realism and Gödel's Incompleteness Theorems.Richard Tieszen - 1994 - Philosophia Mathematica 2 (3):177-201.
    In this paper I argue that it is more difficult to see how Godel's incompleteness theorems and related consistency proofs for formal systems are consistent with the views of formalists, mechanists and traditional intuitionists than it is to see how they are consistent with a particular form of mathematical realism. If the incompleteness theorems and consistency proofs are better explained by this form of realism then we can also see how there is room for skepticism about Church's Thesis and the (...)
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  • Gödel, Kant, and the Path of a Science.Srećko Kovač - 2008 - Inquiry: Journal of Philosophy 51 (2):147-169.
    Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a (...)
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  • 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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  • Intuition and Its Object.Kai Hauser - 2015 - Axiomathes 25 (3):253-281.
    The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal (...)
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