Results for 'Bayes’ theorem'

937 found
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  1. Nature, Science, Bayes 'Theorem, and the Whole of Reality‖.Moorad Alexanian - manuscript
    A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making (...)
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  2. Bayes's theorem[REVIEW]Massimo Pigliucci - 2005 - Quarterly Review of Biology 80 (1):93-95.
    About a British Academy collection of papers on Bayes' famous theorem.
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  3. Modus Tollens probabilized: deductive and Inductive Methods in medical diagnosis.Barbara Osimani - 2009 - MEDIC 17 (1/3):43-59.
    Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on (...)
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  4. Epistemic Probabilities are Degrees of Support, not Degrees of (Rational) Belief.Nevin Climenhaga - 2024 - Philosophy and Phenomenological Research 108 (1):153-176.
    I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had B as (...)
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  5. Logical fallacies as informational shortcuts.Luciano Floridi - 2009 - Synthese 167 (2):317 - 325.
    The paper argues that the two best known formal logical fallacies, namely denying the antecedent (DA) and affirming the consequent (AC) are not just basic and simple errors, which prove human irrationality, but rather informational shortcuts, which may provide a quick and dirty way of extracting useful information from the environment. DA and AC are shown to be degraded versions of Bayes’ theorem, once this is stripped of some of its probabilities. The less the probabilities count, the closer these (...)
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  6. Amending the revisionist model of the Capgras delusion: A further argument for the role of patient experience in delusional belief formation.Garry Young - 2014 - Avant: Trends in Interdisciplinary Studies (3):89-112.
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  7. Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5.Florentin Smarandache - 2023 - Edited by Smarandache Florentin, Dezert Jean & Tchamova Albena.
    This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...)
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  8. Frá skoðunum til trúnaðar og aftur til baka: Yfirlit um bayesíska þekkingarfræði [English title: "From Belief to Credence and Back Again: An Overview of Bayesian Epistemology"].Finnur Dellsén - 2017 - Hugur 28:146-162.
    English abstract: This paper discusses the delicate relationship between traditional epistemology and the increasingly influential probabilistic (or ‘Bayesian’) approach to epistemology. The paper introduces some of the key ideas of probabilistic epistemology, including credences or degrees of belief, Bayes’ theorem, conditionalization, and the Dutch Book argument. The tension between traditional and probabilistic epistemology is brought out by considering the lottery and preface paradoxes as they relate to rational (binary) belief and credence respectively. It is then argued that this tension (...)
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  9. What Confidence Should We Have in Grade?Baigrie Brian & Mercuri Mathew - 2018 - Journal of Evaluation in Clinical Practice 24:1240-1246.
    Rationale, Aims, and Objectives: Confidence (or belief) that a therapy is effective is essential to practicing clinical medicine. GRADE, a popular framework for developing clinical recommendations, provides a means for assigning how much confidence one should have in a therapy's effect estimate. One's level of confidence (or “degree of belief”) can also be modelled using Bayes theorem. In this paper, we look through both a GRADE and Bayesian lens to examine how one determines confidence in the effect estimate. Methods: (...)
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  10. (1 other version)A comprehensive theory of induction and abstraction, part I.Cael L. Hasse -
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  11. Vorlesungsskript: Grundlagen des Entscheidens I.Eckhart Arnold - manuscript
    This is a series of lectures on formal decision theory held at the University of Bayreuth during the summer terms 2008 and 2009. It largely follows the book from Michael D. Resnik: Choices. An Introduction to Decision Theory, 5th ed. Minneapolis London 2000 and covers the topics: -/- Decisions under ignorance and risk Probability calculus (Kolmogoroff Axioms, Bayes' Theorem) Philosophical interpretations of probability (R. v. Mises, Ramsey-De Finetti) Neuman-Morgenstern Utility Theory Introductory Game Theory Social Choice Theory (Sen's Paradox of (...)
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  12. Abductive inference and delusional belief.Max Coltheart, Peter Menzies & John Sutton - 2010 - Cognitive Neuropsychiatry 15 (1):261-287.
    Delusional beliefs have sometimes been considered as rational inferences from abnormal experiences. We explore this idea in more detail, making the following points. Firstly, the abnormalities of cognition which initially prompt the entertaining of a delusional belief are not always conscious and since we prefer to restrict the term “experience” to consciousness we refer to “abnormal data” rather than “abnormal experience”. Secondly, we argue that in relation to many delusions (we consider eight) one can clearly identify what the abnormal cognitive (...)
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  13. If We Can’t Tell What Theism Predicts, We Can’t Tell Whether God Exists: Skeptical Theism and Bayesian Arguments from Evil.Nevin Climenhaga - forthcoming - Oxford Studies in Philosophy of Religion.
    According to a simple Bayesian argument from evil, the evil we observe is less likely given theism than given atheism, and therefore lowers the probability of theism. I consider the most common skeptical theist response to this argument, according to which our cognitive limitations make the probability of evil given theism inscrutable. I argue that if skeptical theists are right about this, then the probability of theism given evil is itself largely inscrutable, and that if this is so, we ought (...)
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  14. A probabilistic analysis of argument cogency.David Godden & Frank Zenker - 2018 - Synthese 195 (4):1715-1740.
    This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...)
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  15. A Note on Johnson’s ‘A Refutation of Skeptical Theism’.Timothy Perrine - 2015 - Sophia 54 (1):35-43.
    In a recent article, David Kyle Johnson has claimed to have provided a ‘refutation’ of skeptical theism. Johnson’s refutation raises several interesting issues. But in this note, I focus on only one—an implicit principle Johnson uses in his refutation to update probabilities after receiving new evidence. I argue that this principle is false. Consequently, Johnson’s refutation, as it currently stands, is undermined.
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  16. Papias's Prologue and the Probability of Parallels.Nevin Climenhaga - 2020 - Journal of Biblical Literature 139 (3):591-596.
    Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order that they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 [2010]: 793–794), Jake H. O’Connell presents a statistical analysis of this argument, according to which the (...)
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  17. Likelihoodism and Guidance for Belief.Tamaz Tokhadze - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):501-517.
    Likelihoodism is the view that the degree of evidential support should be analysed and measured in terms of likelihoods alone. The paper considers and responds to a popular criticism that a likelihoodist framework is too restrictive to guide belief. First, I show that the most detailed and rigorous version of this criticism, as put forward by Gandenberger (2016), is unsuccessful. Second, I provide a positive argument that a broadly likelihoodist framework can accommodate guidance for comparative belief, even when objectively well-grounded (...)
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  18. Evidence, Miracles, and the Existence of Jesus: Comments on Stephen Law.Robert Greg Cavin & Carlos A. Colombetti - 2014 - Faith and Philosophy 31 (2):204-216.
    We use Bayesian tools to assess Law’s skeptical argument against the historicity of Jesus. We clarify and endorse his sub-argument for the conclusion that there is good reason to be skeptical about the miracle claims of the New Testament. However, we dispute Law’s contamination principle that he claims entails that we should be skeptical about the existence of Jesus. There are problems with Law’s defense of his principle, and we show, more importantly, that it is not supported by Bayesian considerations. (...)
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  19. A Little More Logical: Reasoning Well About Science, Ethics, Religion, and the Rest of Life (2nd edition).Brendan Shea - 2024 - Rochester, MN: Thoughtful Noodle Books.
    In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range of topics, (...)
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  20. Maximum Likelihood is Likely Wrong.Paul Mayer - manuscript
    It is argued that Maximum Likelihood Estimation (MLE) is wrong, both conceptually and in terms of results it produces (except in two very special cases, which are discussed). While the use of MLE can still be justified on the basis of its practical performance, we argue there are better estimation methods that overcome MLE's empirical and philosophical shortcomings while retaining all of MLE's benefits.
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  21. A Theory of Bayesian Groups.Franz Dietrich - 2017 - Noûs 53 (3):708-736.
    A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...)
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  22.  12
    The Logic of Counterfactuals and the Epistemology of Causal Inference.Hanti Lin - manuscript
    The 2021 Nobel Prize in Economics recognizes a type of causal model known as the Rubin causal model, or potential outcome framework, which deserves far more attention from philosophers than it currently receives. To spark philosophers' interest, I develop a dialectic connecting the Rubin causal model to the Lewis-Stalnaker debate on a logical principle of counterfactuals: Conditional Excluded Middle (CEM). I begin by playing good cop for CEM, developing a new argument in its favor---a Quine-Putnam-style indispensability argument. This argument is (...)
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  23. Is Racial Profiling a Legitimate Strategy in the Fight against Violent Crime?Neven Sesardić - 2018 - Philosophia 46 (4):981-999.
    Racial profiling has come under intense public scrutiny especially since the rise of the Black Lives Matter movement. This article discusses two questions: whether racial profiling is sometimes rational, and whether it can be morally permissible. It is argued that under certain circumstances the affirmative answer to both questions is justified.
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  24. An Intelligent Tutoring System for Health Problems Related To Addiction of Video Game Playing.Mohran H. Al-Bayed & Samy S. Abu Naser - 2017 - International Journal of Advanced Scientific Research 2 (1):4-10.
    Lately in the past couple of years, there are an increasing in the normal rate of playing computer games or video games compared to the E-learning content that are introduced for the safety of our children, and the impact of the video game addictiveness that ranges from (Musculoskeletal issues, Vision problems and Obesity). Furthermore, this paper introduce an intelligent tutoring system for both parent and their children for enhancement the experience of gaming and tell us about the health problems and (...)
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  25. Intelligent Plagiarism Detection for Electronic Documents.Mohran H. J. Al-Bayed - 2017 - Dissertation, Al-Azhar University, Gaza
    Plagiarism detection is the process of finding similarities on electronic based documents. Recently, this process is highly required because of the large number of available documents on the internet and the ability to copy and paste the text of relevant documents with simply Control+C and Control+V commands. The proposed solution is to investigate and develop an easy, fast, and multi-language support plagiarism detector with the easy of one click to detect the document plagiarism. This process will be done with the (...)
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  26. AI in Leadership: Transforming Decision-Making and Strategic Vision.Mohran H. Al-Bayed, Mohanad Hilles, Ibrahim Haddad, Marah M. Al-Masawabe, Mohammed Ibrahim Alhabbash, Bassem S. Abu-Nasser & Samy S. Abu-Naser - 2024 - International Journal of Academic Pedagogical Research (IJAPR) 8 (9):1-7.
    Abstract: The integration of Artificial Intelligence (AI) into leadership practices is rapidly transforming organizational dynamics and decision-making processes. This paper explores the ways in which AI enhances leadership effectiveness by providing data- driven insights, optimizing decision-making, and automating routine tasks. Additionally, it examines the challenges leaders face when adopting AI, including ethical considerations, potential biases in AI systems, and the need for upskilling. By analyzing current applications of AI in leadership and discussing future trends, this study aims to offer a (...)
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  27. Google and Facebook Vs Rawls and Lao-Tzu: How Silicon Valley’s Utilitarianism and Confucianism Are Bad for Internet Ethics.Morten Bay - 2020 - AoIR 2020: The 21th Annual Conference of the Association of Internet Researchers.
    The proposed paper presents an argument in favor of a Rawlsian approach to ethics for Internet technology companies (den Hoven & Rooksby, 2008; Hoffman, 2017). Ethics statements from such companies are analyzed and shown to be utilitarian and teleological in nature, and therefore in opposition to Rawls’ theories of justice and fairness. The statements are also shown to have traits in common with Confucian virtue ethics (Ames, 2011; Nylan, 2008).
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  28. ITS for health problems related to addiction of video game playing.Mohran Bayed - 2017 - International Journal of Advanced Scientific Research 1 (2):4-10.
    Lately in the past couple of years, there are an increasing in the normal rate of playing computer games or video games compared to the E-learning content that are introduced for the safety of our children, and the impact of the video game addictiveness that ranges from (Musculoskeletal issues, Vision problems and Obesity). Furthermore, this paper introduce an intelligent tutoring system for both parent and their children for enhancement the experience of gaming and tell us about the health problems and (...)
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  29. NGHIÊN CỨU HÀNH VI VÀ MỨC ĐỘ TIẾP CẬN GIÁO DỤC VỀ VẤN ĐỀ RÁC THẢI NHỰA CỦA HỌC SINH TRUNG HỌC PHỔ THÔNG.NGUYỄN THỊ HIỂN & VŨ ĐÌNH BẢY - 2023 - Tạp Chí Khoa Học Quản Lý Giáo Dục 4 (40):48-59.
    Nghiên cứu này được thực hiện nhằm đánh giá thực trạng hành vi và mức độ tiếp cận giáo dục về vấn đề rác thải nhựa của học sinh trung học phổ thông ở khu vực Miền Trung. Kết quả khảo sát trên 2183 học sinh thuộc 10 tỉnh thành ở Miền Trung trong khoảng thời gian từ tháng 9 tới tháng 12 năm 2022 cho thấy: mặc dù, nhận thức của học sinh về vấn đề rác thải nhựa tương (...)
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  30. Detecting Health Problems Related to Addiction of Video Game Playing Using an Expert System.Samy S. Abu Naser & Mohran H. Al-Bayed - 2016 - World Wide Journal of Multidisciplinary Research and Development 2 (9):7-12.
    Today’s everyone normal life can include a normal rate of playing computer games or video games; but what about an excessive or compulsive use of video games that impact on our life? Our kids, who usually spend a lot of time in playing video games will likely have a trouble in paying attention to their school lessons. In this paper, we introduce an expert system to help users in getting the correct diagnosis of the health problem of video game addictions (...)
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  31. (1 other version)Jury Theorems.Franz Dietrich & Kai Spiekermann - 2019 - In Miranda Fricker, Peter Graham, David Henderson & Nikolaj Jang Pedersen (eds.), The Routledge Handbook of Social Epistemology. New York, USA: Routledge.
    We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...)
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  32. Representation theorems and the foundations of decision theory.Christopher Meacham & Jonathan Weisberg - 2011 - Australasian Journal of Philosophy 89 (4):641 - 663.
    Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...)
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  33. Bảy dấu hiệu cảnh báo cần lưu ý để ổn định nền tài chính quốc gia.Phạm Minh Chính & Vương Quân Hoàng - 2008 - Tạp Chí Cộng Sản 2008:1-13.
    Nếu nền kinh tế quốc gia là một cơ thể sống, thì hệ thống tài chính là cơ chế tạo, cung cấp và lưu thông máu tới từng tế bào, bộ phận. Thiếu hay thừa đều phát sinh các vấn đề cần giải quyết. Với quá trình chuyển đổi kinh tế và hội nhập quốc tế mạnh mẽ, liên tục giám sát, kịp thời dự đoán sát thực các dấu hiệu và biến động của thị trường để từ đó xây (...)
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  34. (1 other version)Ứng dụng Bayes trong nghiên cứu KHXH (Buổi 1).Nguyễn Minh Hoàng - 2023 - 2023 Viasm-Hanu Lecture.
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  35. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...)
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  36. Jury Theorems for Peer Review.Marcus Arvan, Liam Kofi Bright & Remco Heesen - forthcoming - British Journal for the Philosophy of Science.
    Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...)
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  37. Ang Ma’i bilang Bay: Isang Muling Pagbasa at Pagtatasa.Jolan Saluria - 2024 - Dalumat: Multikultural at Multidisiplinaryong e-Journal Sa Araling Pilipino 9 (1):126-143.
    Ang papel na ito ay komentaryo sa artikulong—Ma'I in Chinese Records—Mindoro or Bai? An Examination of a Historical Puzzle ni Go Bon Juan. Layunin ng pag-aaral na ito na lumikha ng isang mapanglagom at preliminaryong pagbasa sa Ma’i bilang isang suliraning historiograpikal. Sa muling pagbasang ito ay pagtutuunan ng pansin ang maikling pagbaybay sa historiograpiya nito na susundan naman ng interogasyon at pagbibigay kritik sa kamakailang pag-aaral dito ni Go Bon Juan at mga suliraning kinakaharap ng kaniyang interpretasyon na umiinog (...)
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  38.  87
    Hành vi bầy đàn (herding behavior) trong đầu tư chứng khoán qua góc nhìn xử lý thông tin.Nguyễn Phương Tri & Nguyễn Minh Hoàng - 2024 - Kinh Tế Và Dự Báo.
    Hành vi bầy đàn là hiện tượng khi các cá nhân, trong các quyết định tài chính hoặc đầu tư, hành động theo số đông, bất chấp thông tin cá nhân hoặc phân tích riêng biệt của họ. Lý thuyết mindsponge có thể cung cấp cách tiếp cận hữu ích để khắc phục hiệu ứng bầy đàn trong đầu tư chứng khoán, thông qua việc giúp nhà đầu tư quản lý và xử lý thông tin một cách hiệu quả hơn.
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  39.  78
    Comment on the GHZ variant of Bell's theorem without inequalities.Joy Christian - 2024 - Arxiv.
    I point out a sign mistake in the GHZ variant of Bell's theorem, invalidating the GHZ's claim that the premisses of the EPR argument are inconsistent for systems of more than two particles in entangled quantum states.
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  40. Bayes, predictive processing, and the cognitive architecture of motor control.Daniel C. Burnston - 2021 - Consciousness and Cognition 96 (C):103218.
    Despite their popularity, relatively scant attention has been paid to the upshot of Bayesian and predictive processing models of cognition for views of overall cognitive architecture. Many of these models are hierarchical ; they posit generative models at multiple distinct "levels," whose job is to predict the consequences of sensory input at lower levels. I articulate one possible position that could be implied by these models, namely, that there is a continuous hierarchy of perception, cognition, and action control comprising levels (...)
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  41. A topological completeness theorem for a weak version of Stalnaker's logic of knowledge and belief.Thomas Mormann - manuscript
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  42. A Representation Theorem for Frequently Irrational Agents.Edward Elliott - 2017 - Journal of Philosophical Logic 46 (5):467-506.
    The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise (...)
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  43. The Gödel Incompleteness Theorems (1931) by the Axiom of Choice.Vasil Penchev - 2020 - Econometrics: Mathematical Methods and Programming eJournal (Elsevier: SSRN) 13 (39):1-4.
    Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the relation (...)
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  44. Theorem proving in artificial neural networks: new frontiers in mathematical AI.Markus Pantsar - 2024 - European Journal for Philosophy of Science 14 (1):1-22.
    Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, (...)
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  45. Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
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  46. Theorems and Models in Political Theory: An Application to Pettit on Popular Control.Sean Ingham - 2015 - The Good Society 24 (1):98-117.
    Pettit (2012) presents a model of popular control over government, according to which it consists in the government being subject to those policy-making norms that everyone accepts. In this paper, I provide a formal statement of this interpretation of popular control, which illuminates its relationship to other interpretations of the idea with which it is easily conflated, and which gives rise to a theorem, similar to the famous Gibbard-Satterthwaite theorem. The theorem states that if government policy is (...)
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  47. Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...)
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  48. Theoremizing Yablo's Paradox.Ahmad Karimi & Saeed Salehi - manuscript
    To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these (...)
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  49. Fermat’s Last Theorem Proved by Induction (and Accompanied by a Philosophical Comment).Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (8):1-8.
    A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite (...)
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  50. Bell's Theorem Begs the Question.Joy Christian - manuscript
    I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument (...)
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