
460What antirealism in philosophy of mathematics must offerSynthese 175 (1). 2010.This article attempts to motivate a new approach to antirealism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to antirealism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current antirealistic 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 ap…Read more

287Toward a constructive theory of unbounded linear operatorsJournal of Symbolic Logic 65 (1): 357370. 2000.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 KatoRellich theorem, the spectral theorem, Stone's theorem, and the selfadjointness of the most common quantum mechanical operators, including the Hamiltonians of electromagnetic fields with some general forms of potentials

202Naturalized truth and Plantinga’s evolutionary argument against naturalismInternational Journal for Philosophy of Religion 70 (1): 2746. 2011.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 nonreductive 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 antimater…Read more

180The applicability of mathematics as a scientific and a logical problemPhilosophia Mathematica 18 (2): 144165. 2010.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…Read more

131Indispensability argument and antirealism in philosophy of mathematicsFrontiers of Philosophy in China 2 (4): 614628. 2007.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 antirealistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, …Read more

111Naturalism and Abstract EntitiesInternational Studies in the Philosophy of Science 24 (2): 129146. 2010.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 s…Read more

92A naturalistic interpretation of the Kripkean modalityFrontiers of Philosophy in China 4 (3): 454470. 2009.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 naturalis…Read more

74Studies in NoSelf PhysicalismSpringer Nature Singapore. 2023.This book demonstrates how a radical version of physicalism (‘NoSelf Physicalism’) can offer an internally coherent and comprehensive philosophical worldview. It first argues that a coherent physicalist should explicitly treat a cognitive subject merely as a physical thing and should not vaguely assume an amorphous or even soullike subject or self. This approach forces the physicalist to reexamine traditional core philosophical notions such as truth, analyticity, modality, apriority because o…Read more

62On Extreme versus Moderate Methodological NaturalismPhilosophia 45 (1): 371385. 2017.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 hardscientific 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…Read more

23Strict Finitism and the Logic of Mathematical ApplicationsSpringer. 2011.This book intends to show that radical naturalism, nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semiRiemann geometry. The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also …Read more

1Strict Constructivism and the Philosophy of MathematicsDissertation, Princeton University. 2000.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 Constru…Read more

This book intends to show that, in philosophy of mathematics, radical naturalism (or physicalism), nominalism and strict finitism (which does not assume the reality of infinity in any format, not even potential infinity) can account for the applications of classical mathematics in current scientific theories about the finite physical world above the Planck scale. For that purpose, the book develops some significant applied mathematics in strict finitism, which is essentially quantifierfree elem…Read more
Feng Ye
Capital Normal University, Beijing, China

Capital Normal University, Beijing, ChinaProfessor
Areas of Specialization
Philosophy of Mind 
Philosophy of Mathematics 
Areas of Interest
Philosophy of Mind 
Philosophy of Mathematics 