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  1.  93
    A Logical Journey: From Gödel to Philosophy.Hao Wang - 1996 - Bradford.
    Hao Wang was one of the few confidants of the great mathematician and logician Kurt Gödel. _A Logical Journey_ is a continuation of Wang's _Reflections on Gödel_ and also elaborates on discussions contained in _From Mathematics to Philosophy_. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem (...)
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  2. From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: Routledge.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method (...)
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  3. Reflections on Kurt Gödel.Hao Wang - 1990 - Bradford.
    In this first extended treatment of his life and work, Hao Wang, who was in close contact with Godel in his last years, brings out the full subtlety of Godel's ideas and their connection with grand themes in the history of mathematics and ...
  4. AI through the looking glass: an empirical study of structural social and ethical challenges in AI.Mark Ryan, Nina De Roo, Hao Wang, Vincent Blok & Can Atik - 2024 - AI and Society 1 (1):1-17.
    This paper examines how professionals (N = 32) working on artificial intelligence (AI) view structural AI ethics challenges like injustices and inequalities beyond individual agents' direct intention and control. This paper answers the research question: What are professionals’ perceptions of the structural challenges of AI (in the agri-food sector)? This empirical paper shows that it is essential to broaden the scope of ethics of AI beyond micro- and meso-levels. While ethics guidelines and AI ethics often focus on the responsibility of (...)
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  5. From Mathematics to Philosophy.Hao Wang - 1975 - British Journal for the Philosophy of Science 26 (2):170-174.
     
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  6. A Logical Journey. From Gödel to Philosophy.Hao Wang - 1998 - Philosophy 73 (285):495-504.
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  7.  65
    Transparency as Manipulation? Uncovering the Disciplinary Power of Algorithmic Transparency.Hao Wang - 2022 - Philosophy and Technology 35 (3):1-25.
    Automated algorithms are silently making crucial decisions about our lives, but most of the time we have little understanding of how they work. To counter this hidden influence, there have been increasing calls for algorithmic transparency. Much ink has been spilled over the informational account of algorithmic transparency—about how much information should be revealed about the inner workings of an algorithm. But few studies question the power structure beneath the informational disclosure of the algorithm. As a result, the information disclosure (...)
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  8. Reflections on Kurt Gödel.Hao Wang - 1988 - Mind 97 (388):634-638.
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  9. Algorithmic Colonization of Love.Hao Wang - 2023 - Techné Research in Philosophy and Technology 27 (2):260-280.
    Love is often seen as the most intimate aspect of our lives, but it is increasingly engineered by a few programmers with Artificial Intelligence (AI). Nowadays, numerous dating platforms are deploying so-called smart algorithms to identify a greater number of potential matches for a user. These AI-enabled matchmaking systems, driven by a rich trove of data, can not only predict what a user might prefer but also deeply shape how people choose their partners. This paper draws on Jürgen Habermas’s “colonization (...)
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  10.  12
    A Survey of Mathematical Logic.Hao Wang - 1962 - Amsterdam: North-Holland Publishing Company.
  11.  38
    Why Should We Care About the Manipulative Power of Algorithmic Transparency?Hao Wang - 2023 - Philosophy and Technology 36 (1):1-6.
    Franke Philosophy & Technology, 35(4), 1-7, (2022) offers an interesting claim that algorithmic transparency as manipulation does not necessarily follow that it is good or bad. Different people can have good reasons to adopt different evaluative attitudes towards this manipulation. Despite agreeing with some of his observations, this short reply will examine three crucial misconceptions in his arguments. In doing so, it defends why we are morally obliged to care about the manipulative potential of algorithmic transparency. It suggests that we (...)
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  12. Beyond Analytic Philosophy: Doing Justice to What We Know.Hao Wang - 1988 - Bradford.
    This cogent and knowledgeable critique of the tradition of modern analytic philosophy focuses on the work of its central figures -- Russell, Carnap, and Quine -- and finds it wanting. In its place, Hao Wang unfolds his own original view of what philosophy could and should be. The base of any serious philosophy, he contends, should take as its point of departure the actual state of human knowledge. He explains the relation of this new tradition to mathematical logic and reveals (...)
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  13. The axiomatization of arithmetic.Hao Wang - 1957 - Journal of Symbolic Logic 22 (2):145-158.
  14. Ethical Research on Artificial Perception Technologies.Hao Wang - 2024 - Journal of Human Cognition 8 (2):29-38.
    The development of artificial perception technologies has surpassed the limitations of human natural senses, expanding humanity's perspectives on the world and self-awareness. However, it has simultaneously introduced new ethical challenges. These emerging challenges necessitate a philosophical reexamination of concepts such as 'nature,' 'artificial,' and ' invasiveness ' to better address associated issues. The advancement of artificial perception technologies not only involves scientific and practical applications but also profoundly influences human values, social ethics, and the future trajectory of human civilization. Amidst (...)
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  15. Logic of many-sorted theories.Hao Wang - 1952 - Journal of Symbolic Logic 17 (2):105-116.
  16.  19
    (1 other version)Number theoretic concepts and recursive well-orderings.G. Kreisel, J. Shoenfield & Hao Wang - 1960 - Archive for Mathematical Logic 5 (1-2):42-64.
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  17. Some facts about Kurt gödel.Hao Wang - 1981 - Journal of Symbolic Logic 46 (3):653-659.
  18.  57
    Review Essay: Reflections on Kurt GodelReflections on Kurt Godel.Palle Yourgrau & Hao Wang - 1989 - Philosophy and Phenomenological Research 50 (2):391.
  19.  40
    (1 other version)Eighty years of foundational studies.Hao Wang - 1958 - Dialectica 12 (3‐4):466-497.
    A survey is made of work since 1879 on foundational problems viewed as an analysis, by reduction and formalization, of the concepts proof, feasible, number, set, and constructivity. It is suggested that there are five domains of concepts and methods, viz., anthropologism, finitism, intuitionism, predicativism, and platonism. It is also suggested that the central problem is to characterize these domains by formalization and to determine their interrelations by different forms of reduction. Finally, the range of logic in the narrower sense (...)
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  20.  27
    Truth Definitions and Consistency Proofs.Hao Wang - 1957 - Journal of Symbolic Logic 22 (4):365-367.
  21. Popular lectures on mathematical logic.Hao Wang - 1981 - New York: Dover Publications.
    Noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. After historical survey, lucid treatment of set theory, model theory, recursion theory and constructivism and proof theory. Place of problems in development of theories of logic, logic’s relationship to computer science, more. Suitable for readers at many levels of mathematical sophistication. 3 appendixes. Bibliography. 1981 edition.
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  22. (1 other version)The formalization of mathematics.Hao Wang - 1954 - Journal of Symbolic Logic 19 (4):241-266.
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  23.  92
    (1 other version)Non-standard models for formal logics.J. Barkley Rosser & Hao Wang - 1950 - Journal of Symbolic Logic 15 (2):113-129.
    In his doctor's thesis [1], Henkin has shown that if a formal logic is consistent, and sufficiently complex, then it must admit a non-standard model. In particular, he showed that there must be a model in which that portion of the model which is supposed to represent the positive integers of the formal logic is not in fact isomorphic to the positive integers; indeed it is not even well ordered by what is supposed to be the relation of ≦.For the (...)
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  24.  35
    Why putting artificial intelligence ethics into practice is not enough: Towards a multi-level framework.Hao Wang & Vincent Blok - 2025 - Big Data and Society 1 (1):1.
    Artificial intelligence (AI) ethics is undergoing a practical shift towards putting principles into design practices in developing responsible AI. While this practical turn is essential, this paper highlights its potential risk of overly focusing on addressing issues at the level of individual artifacts, which can neglect more profound structural challenges and the need for significant systemic change. Such oversight makes AI ethics lose its strength in addressing some hidden, long-term harms within broader contexts. In this paper, we propose that the (...)
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  25.  16
    Mathematical interpretation of formal systems.Thoralf Skolem, G. Hasenjaeger, G. Kreisel, A. Robinson, Hao Wang, L. Henkin & J. Łoś (eds.) - 1971 - Amsterdam: North-Holland Pub. Co..
  26.  14
    Logic, computers, and sets.Hao Wang - 1962 - New York,: Chelsea Pub. Co..
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  27. 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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  28. 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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  29.  83
    Inquisitive logic as an epistemic logic of knowing how.Haoyu Wang, Yanjing Wang & Yunsong Wang - 2022 - Annals of Pure and Applied Logic 173 (10):103145.
  30.  74
    Negative types.Hao Wang - 1952 - Mind 61 (243):366-368.
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  31. (1 other version)On formalization.Hao Wang - 1955 - Mind 64 (254):226-238.
  32.  65
    Note on Rules of Inference.Hao Wang - 1965 - Mathematical Logic Quarterly 11 (3):193-196.
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  33.  82
    The Calculus of Partial Predicates and Its Extension to Set Theory I.Hao Wang - 1961 - Mathematical Logic Quarterly 7 (17-18):283-288.
  34.  87
    Undecidable sentences generated by semantic paradoxes.Hao Wang - 1955 - Journal of Symbolic Logic 20 (1):31-43.
  35. On physicalism and algorithmism: Can machines think?Hao Wang - 1993 - Philosophia Mathematica 1 (2):97-138.
    This essay discusses a number of questions which arise from attempts to reduce the mental to the physical or the mental and the physical to the computational. It makes, in an organized way, several basic distinctions between different kinds of accounts of the mind. It reconstructs and elaborates many discussions between Gödel and the author on the nature of the human mind, with special emphasis on its mathematical capabilities.
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  36.  24
    Possibilities and challenges in the moral growth of large language models: a philosophical perspective.Guoyu Wang, Wei Wang, Yiqin Cao, Yan Teng, Qianyu Guo, Haofen Wang, Junyu Lin, Jiajie Ma, Jin Liu & Yingchun Wang - 2025 - Ethics and Information Technology 27 (1):1-11.
    With the rapid expansion of parameters in large language models (LLMs) and the application of Reinforcement Learning with Human Feedback (RLHF), there has been a noticeable growth in the moral competence of LLMs. However, several questions warrant further exploration: Is it really possible for LLMs to fully align with human values through RLHF? How can the current moral growth be philosophically contextualized? We identify similarities between LLMs’ moral growth and Deweyan ethics in terms of the discourse of human moral development. (...)
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  37.  40
    Towards feasible solutions of the tautology problem.Bradford Dunham & Hao Wang - 1976 - Annals of Mathematical Logic 10 (2):117-154.
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  38.  25
    Arithmetic Models for Formal Systems.Hao Wang - 1955 - Journal of Symbolic Logic 20 (1):76-77.
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  39.  15
    On Denumerable Bases of Formal Systems.Hao Wang - 1957 - Journal of Symbolic Logic 22 (3):292-293.
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  40.  38
    Beyond Analytic Philosophy: Doing Justice to What we Know.Barbara Humphries & Hao Wang - 1988 - Philosophical Review 97 (2):270.
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  41.  22
    Impaired Activation of Visual Attention Network for Motion Salience Is Accompanied by Reduced Functional Connectivity between Frontal Eye Fields and Visual Cortex in Strabismic Amblyopia.Hao Wang, Sheila G. Crewther, Minglong Liang, Robin Laycock, Tao Yu, Bonnie Alexander, David P. Crewther, Jian Wang & Zhengqin Yin - 2017 - Frontiers in Human Neuroscience 11.
  42. Reflections on Gôdel.Hao Wang - 1987 - MIT Press.
  43.  26
    Some Applications of Formalized Consistency Proofs.G. Kreisel & Hao Wang - 1956 - Journal of Symbolic Logic 21 (4):404-405.
  44.  84
    (1 other version)A formal system of logic.Hao Wang - 1950 - Journal of Symbolic Logic 15 (1):25-32.
    The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the discovery (...)
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  45.  11
    Process and Existence in Mathematics.Hao Wang - 1965 - Journal of Symbolic Logic 30 (2):244-244.
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  46. What is Logic?Hao Wang - 1994 - The Monist 77 (3):261-277.
    Logic as an activity deals with the interplay or the dialectic, as one thinks, between the known and the unknown, form and content, or the formal and the intuitive. For this purpose it is useful to select from what is taken to be known a universal part which remains fixed throughout all particular instances of the interplay. The propositions in such a universal part make up the logical truths. There are alternative answers to the question: What is to be required (...)
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  47. Wittgenstein’s and Other Mathematical Philosophies.Hao Wang - 1984 - The Monist 67 (1):18-28.
    I construe mathematical philosophy not in the narrow sense of philosophy of mathematics but in a broad indefinite sense of different manners of giving mathematics a privileged place in the study of philosophy. For example, in one way or another, mathematics plays an important part in the philosophy of Plato, Descartes, Spinoza, Leibniz, and Kant. In contrast, history plays a central role in the philosophy of Vico, Hegel, and Marx. In more recent times, Frege, Husserl, Russell, Ramsey, and Gödel all (...)
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  48.  60
    Beyond Analytic Philosophy. Doing Justice to What we Know.Michael D. Resnik & Hao Wang - 1988 - Journal of Symbolic Logic 54 (4):1484.
  49.  91
    Ordinal Numbers and Predicative Set Theory.Hao Wang - 1959 - Mathematical Logic Quarterly 5 (14-24):216-239.
  50.  25
    Entscheidungsproblem Reduced to the ∀∃∀ Case.A. S. Kahr, Edward F. Moore & Hao Wang - 1962 - Journal of Symbolic Logic 27 (2):225-225.
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