Feng Ye [10]Fengdan Ye [2]
  1. The Applicability of Mathematics as a Scientific and a Logical Problem.Feng Ye - 2010 - Philosophia Mathematica 18 (2):144-165.
    This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce (...)
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  2. What Anti-Realism in Philosophy of Mathematics Must Offer.Feng Ye - 2010 - Synthese 175 (1):13 - 31.
    This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs (...)
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  3. Strict Constructivism and the Philosophy of Mathematics.Feng Ye - 2000 - Dissertation, Princeton University
    The dissertation studies the mathematical strength of strict constructivism, a finitistic fragment of Bishop's constructivism, and explores its implications in the philosophy of mathematics. ;It consists of two chapters and four appendixes. Chapter 1 presents strict constructivism, shows that it is within the spirit of finitism, and explains how to represent sets, functions and elementary calculus in strict constructivism. Appendix A proves that the essentials of Bishop and Bridges' book Constructive Analysis can be developed within strict constructivism. Appendix B further (...)
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  4. Toward a Constructive Theory of Unbounded Linear Operators.Feng Ye - 2000 - Journal of Symbolic Logic 65 (1):357-370.
    We show that the following results in the classical theory of unbounded linear operators on Hilbert spaces can be proved within the framework of Bishop's constructive mathematics: the Kato-Rellich theorem, the spectral theorem, Stone's theorem, and the self-adjointness of the most common quantum mechanical operators, including the Hamiltonians of electro-magnetic fields with some general forms of potentials.
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    Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
    I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...)
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    A Naturalistic Interpretation of the Kripkean Modality.Feng Ye - 2009 - Frontiers of Philosophy in China 4 (3):454-470.
    The Kripkean metaphysical modality (i.e. possibility and necessity) is one of the most important concepts in contemporary analytic philosophy and is the basis of many metaphysical speculations. These metaphysical speculations frequently commit to entities that do not belong to this physical universe, such as merely possible entities, abstract entities, mental entities or qualities not realizable by the physical, which seems to contradict naturalism or physicalism. This paper proposes a naturalistic interpretation of the Kripkean modality, as a naturalist’s response to these (...)
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  7. Naturalized Truth and Plantinga’s Evolutionary Argument Against Naturalism.Feng Ye - 2011 - International Journal for Philosophy of Religion 70 (1):27-46.
    There are three major theses in Plantinga’s latest version of his evolutionary argument against naturalism. (1) Given materialism, the conditional probability of the reliability of human cognitive mechanisms produced by evolution is low; (2) the same conditional probability given reductive or non-reductive materialism is still low; (3) the most popular naturalistic theories of content and truth are not admissible for naturalism. I argue that Plantinga’s argument for (1) presupposes an anti-materialistic conception of content, and it therefore begs the question against (...)
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    Corrigendum: Static and Dynamic Measures of Human Brain Connectivity Predict Complementary Aspects of Human Cognitive Performance.Aurora I. Ramos-Nuñez, Simon Fischer-Baum, Randi C. Martin, Qiuhai Yue, Fengdan Ye & Michael W. Deem - 2018 - Frontiers in Human Neuroscience 12.
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    On Extreme Versus Moderate Methodological Naturalism.Feng Ye - 2017 - Philosophia 45 (1):371-385.
    In a recent debate, Rosenberg claims that only the methods of natural science can deliver genuine knowledge, while Williamson rejects Rosenberg’s extreme methodological naturalism and insists that we have genuine philosophical and humanistic knowledge not achievable by hard-scientific methods alone. This paper responds to the debate. I will argue that physicalism, together with contemporary neurocognitive and evolutionary knowledge, implies that some of our intuitions and mental simulations used in the humanities and philosophy are justified methods for achieving knowledge but are (...)
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    Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Feng Ye - 2007 - Frontiers of Philosophy in China 2 (4):614-628.
    The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical (...)
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    Static and Dynamic Measures of Human Brain Connectivity Predict Complementary Aspects of Human Cognitive Performance.Aurora I. Ramos-Nuñez, Simon Fischer-Baum, Randi C. Martin, Qiuhai Yue, Fengdan Ye & Michael W. Deem - 2017 - Frontiers in Human Neuroscience 11.