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 (...) inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (shrink)

About a British Academy collection of papers on Bayes' famous theorem.

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 (...) a case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

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 (...) their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

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 (...) fallacies become to a reasoning that is not only informationally useful but also logically valid. (shrink)

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 (...) can be alleviated by rejecting the requirement that rational (binary) beliefs must be consistent and closed under logical entailment. Instead, it is suggested that this logical requirement applies to a different type of binary propositional attitude, viz. acceptance. (shrink)

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 (...) Liberalism, Arrow's Theorem) . (shrink)

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 (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

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 (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

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: (...) Philosophical examination. Results: The GRADE framework uses a criteria‐based method to assign a quality of evidence level. The criteria pertain mostly to considerations of methodological rigour, derived from a modified evidence‐based medicine evidence hierarchy. The four levels of quality relate to the level of confidence one should have in the effect estimate. The Bayesian framework is not bound by a predetermined set of criteria. Bayes theorem shows how a rational agent adjusts confidence (ie, degree of belief) in the effect estimate on the basis of the available evidence. Such adjustments relate to the principles of incremental confirmation and evidence proportionism. Use of the Bayesian framework reveals some potential pitfalls in GRADE's criteria‐based thinking on confidence that are out of step with our intuitions on evidence. Conclusions: A rational thinker uses all available evidence to formulate beliefs. The GRADE criteria seem to suggest that we discard some of that information when other, more favoured information (eg, derived from clinical trials) is available. The GRADE framework should strive to ensure that the whole evidence base is considered when determining confidence in the effect estimate. The incremental value of such evidence on determining confidence in the effect estimate should be assigned in a manner that is theoretically or empirically justified, such that confidence is proportional to the evidence, both for and against it. (shrink)

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 (...) data are which prompted the delusion and what the neuropsychological impairment is which is responsible for the occurrence of these data; but one can equally clearly point to cases where this impairments is present but delusion is not. So the impairment is not sufficient for delusion to occur. A second cognitive impairment, one which impairs the ability to evaluate beliefs, must also be present. Thirdly (and this is the main thrust of our chapter) we consider in detail what the nature of the inference is that leads from the abnormal data to the belief. This is not deductive inference and it is not inference by enumerative induction; it is abductive inference. We offer a Bayesian account of abductive inference and apply it to the explanation of delusional belief. (shrink)

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 (...) to be agnostic about whether God exists. (shrink)

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 (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

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.

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.

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 (...) prior probabilities are not available. As I show, the shift from non-relational to comparative probabilities opens up a new space for addressing the belief guidance problem for likelihoodism. (shrink)

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 (...) probability of this correspondence occurring by chance is lower than 1%. O’Connell concludes that it is more than 99% probable that this correspondence is the result of Papias copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence, overstates the correspondence between John and Papias, wrongly assumes that if Papias did not know John he ordered the disciples randomly, and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning. (shrink)

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. (...) Finally, we show that Law’s principle is false in the specific case of Jesus and thereby show, contrary to the main conclusion of Law’s argument, that biblical historians are entitled to remain confident that Jesus existed. (shrink)

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, (...) from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

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 (...) based on the observation that CEM seems to be indispensable to the Rubin causal model, which underpins our best scientific theory of causal inference in health and social sciences---a Nobel Prize-winning theory. Indeed, CEM has long remained a core assumption of the Rubin causal model, despite challenges from within the statistics and economics communities over twenty years ago. I then switch sides to play bad cop for CEM, undermining the indispensability argument by developing a new theory of causal inference that dispenses with CEM while preserving the successes of the original theory (thanks to a new theorem proved here). The key, somewhat surprisingly, is to integrate two approaches to causal modeling: the Rubin causal model, more familiar in health and social sciences, and the causal Bayes net, more familiar in philosophy. The good cop/bad cop dialectic is concluded with a connection to broader philosophical issues, including intertheory relations, the revisability of logic, and the role of background assumptions in justifying scientific inference. (shrink)

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 (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

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.

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 (...) how we can solve them, with an easy user interface that way can our children be happy and excited about the information and their health. (shrink)

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 (...) comprehensive overview of the opportunities AI presents for effective leadership, as well as the strategies required to address its associated challenges. (shrink)

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 (...) support of intelligent system that can learn, change and adapt to the input document and make a cross-fast search for the content on the local repository and the online repository and link the content of the file with the matching content everywhere found. Furthermore, the supported document type that we will use is word, text and in some cases, the pdf files –where is the text can be extracting from them- and this made possible by using the DLL file from Word application that Microsoft provided on OS. The using of DLL will let us to not constrain on how to get the text from files; and will help us to apply the file on our Delphi project and walk throw our methodology and read the file word by word to grantee the best working scenarios for the calculation. In the result, this process will help in the uprising the documents quality and enhance the writer experience related to his work and will save the copyrights for the official writer of the documents by providing a new alternative tool for plagiarism detection problem for easy and fast use to the concerned Institutions for free. (shrink)

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).

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 (...) how we can solve them, with an easy user interface that way can our children be happy and excited about the information and their health. (shrink)

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 (...) đối cao song kiến thức và hành vi đối với vấn đề rác thải nhựa vẫn còn nhiều hạn chế; công tác giáo dục về rác thải nhựa hiện nay trong các trường học chủ yếu ở mức thỉnh thoảng thực hiện và hiệu quả chưa thật sự cao như kì vọng; hành vi đối với vấn đề rác thải nhựa của học sinh có sự khác biệt liên quan tới giới tính; khối lớp và giữa các địa bàn nghiên cứu. Kết quả nghiên cứu là cơ sở để đề xuất các biện pháp giáo dục phù hợp cho học sinh trung học phổ thông tại các tỉnh Miền Trung. [This study evaluates the current status of behavior and level of access to education on the issue of plastic waste among high school students in Central Vietnam. Survey results on 2,183 students from 10 provinces and cities in the Central region from September to December 2022 show that although students' awareness of the plastic waste issue is relatively high, but their knowledge and behavior towards plastic waste still has many limitations; current education about plastic waste in schools is mainly done occasionally, and the effectiveness is lower than expected; students' behavior towards plastic waste has gender-related differences; grade levels and between research areas. The research results are the basis for proposing appropriate educational measures for high school students in Central Vietnam.]. (shrink)

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 (...) that range from (Musculoskeletal issues, Vision problems and Obesity). Moreover, this expert system provides information about the problem and tell us how we can solve it. SL5 Object expert system language was used to design and implement the expert system. (shrink)

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 (...) sa pagpapalagay nito na ang Ma’i ay natagpuan ng mga banyagang mangangalakal sa kasalukuyang rehiyon ng lawa ng Laguna. Mangyari pa, hindi lamang nakatali sa nakasanayan at makitid na pagtitiyak ng pook ang tutok ng pag-aaral. Pagtatangka rin ito na bigyang diin ang “saysay” nito sa pamamagitan ng pagpopook sa Ma’i sa malawak na kontekstong pangkasaysayan na kinasasangkutan nito. Una, bilang isang mahalagang yugto ng napakahabang kasaysayan ng rehiyon ng lawa ng Laguna, at; pangalawa, bilang mikrokosmong bahagi ng naging historikal na pagsulong ng buong Dunia Melayu. Sa huli, sa pamamagitan ng kritikal na panunuri sa mga pundamental na proposisyon ni Go Bon Juan ay ang pag-uwi ng pag-aaral sa konklusyong bagaman kasalukuyang maipapalagay na ang Ma’i ay ang Bay nga ng Laguna, mapaninindiganang hindi talaga sa kasalukuyang kinalalagyan nito sa Laguna nadatnan ng mga mangangalakal ang Ma’I, kung hindi sa kasalukuyang erya ng Verde Island Passage na kinabibilangan ng kasalukuyang Batangas-Mindoro axis kung saan nakaugnay ang Puliran o Lawa ng Laguna. (shrink)

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.

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 $ (...) - and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

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; (...) (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

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 (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

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 (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

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, (...) machine learning results in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

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 (...) of generative models. I argue that this view is not entailed by a general Bayesian/predictive processing outlook. Bayesian approaches are compatible with distinct formats of mental representation. Focusing on Bayesian approaches to motor control, I argue that the junctures between different types of mental representation are places where the transitivity of hierarchical prediction may be broken, and I consider the upshot of this conclusion for broader discussions of cognitive architecture. (shrink)

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby (...) establishing an even more general impossibility theorem. (shrink)

This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's (...) class='Hi'>theorem in RCA0, and thus in PRA, since Arrow's theorem can be formalised as a Π01 sentence. Finally we show that Fishburn's possibility theorem for countable societies is equivalent to ACA0 over RCA0. (shrink)

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 (...) degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

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 (...) impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

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 (...) dựng chính sách điều tiết thị trường tài chính và toàn bộ nền kinh tế một cách hợp lý là việc làm cần thiết bảo đảm tăng trưởng kinh tế bền vững, đúng định hướng. Đối với nền tài chính của Việt Nam, hiện đang tồn tại bảy dấu hiệu cảnh báo cần được các nhà nghiên cứu và hoạch định chính sách quan tâm. (shrink)

This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...) this paper, I will argue that Lewis' conclusion is correct: choices radically underdetermine beliefs and desires, and representation theorems provide us with no good reasons to think otherwise. Any tension with those theorems is merely apparent, and relates ultimately to the difference between how 'choices' are understood within Lewis' theory and the problematic way that they're represented in the context of the representation theorems. For the purposes of radical interpretation, representation theorems like Ramsey's and Savage's just aren't very relevant after all. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

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 (...) subject to popular control, as Pettit interprets it, and policy responds positively to changes in citizens' normative attitudes, then there is a single individual whose normative attitudes unilaterally determine policy. I use the model and theorem as an illustrative example to discuss the role of mathematics in normative political theory. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we (...) thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

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 (...) descent. The infinite descent is linked to induction starting from n = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n = 4, one can suggest that the proof for n ≥ 4 was accessible to him. An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995). (shrink)

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...) truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory. (shrink)