Probabilistic Reasoning

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity. There is always a halo of indeterminism, since in the end it is chance itself—the random variations of what we call reality, although we do not quite know what it is—that becomes the cause of causes. From (...) an interpretation not devoid of a certain nihilism. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity. There is always a halo of indeterminism, since in the end it is chance itself—the random variations of what we call reality, although we do not quite know what it is—that becomes the cause of causes. From (...) an interpretation not devoid of a certain nihilism. (shrink)

Understanding the original meaning of the Global Artificial Intelligence. Its origins can be traced back to my writings in 2002 on Astro-ecology, the science that understands the cosmos as a single environment that must be studied from a unified, single science. In essence, this is what the Global Artificial Intelligence seeks to achieve. At the same time, in 2002 I developed the formulations of Impossible Probability, beginning in the early hours of September 11, 2001 with the Impact of the Defect, (...) which was later expanded into the Second Method on October 16, 2002. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Receivers in standard signaling game models struggle with learning compositional information. Even when the signalers send compositional messages, the receivers do not interpret them compositionally. When information from one message component is lost or forgotten, the information from other components is also erased. In this paper I construct signaling game models in which genuine compositional understanding evolves. I present two new models: a minimalist receiver who only learns from the atomic messages of a signal, and a generalist receiver who learns (...) from all of the available information. These models are in many ways simpler than previous alternatives, and allow the receivers to learn from the atomic components of messages. (shrink)

We prove that the P vs NP problem is formally unprovable within classical computational complexity theory by demonstrating that it exhibits the same self-referential structure as the Halting Problem and logical paradoxes. The core issue is that P vs NP began as a philosophical question about the nature of mathematical insight, hypothetical verification, and the discovery of solving algorithms but was inappropriately formalized within computational complexity theory. It was done so in such away that it secretly became analogous to asking (...) a supercomputer the “ultimate question of life, the universe, and everything.” Through rigorous multidisciplinary analysis, we show that verification presupposes contextual information that the formal NP definition explicitly removes, creating a semantic loop that makes the question undecidable by construction. We establish this through: (1) formal proof of the verification-solving circularity via the Certificate Construction Paradox, (2) demonstration of structural equivalence to the Liar Paradox, and (3) rigorous analysis showing that context-stripping creates category errors. Our result explains why P vs NP has resisted proof for over fifty years and provides foundations for context-aware computational frameworks that treat ambiguity as a core feature of mathematical reality rather than a limitation to overcome. (shrink)

Probabilidad Imposible Vol 1 reúne los fundamentos de una investigación desarrollada entre 2001 y 2018, cuyo propósito es replantear las bases del conocimiento racional y su relación con la probabilidad empírica y teórica. La obra introduce conceptos como el Impacto del Defecto y el Segundo Método, proponiendo un marco alternativo frente a la epistemología de Karl Popper y orientado hacia la búsqueda del conocimiento puro. Este proyecto, originado en el cruce entre matemáticas, inteligencia artificial y psicología, constituye una semilla teórica (...) para el desarrollo de la Inteligencia Artificial Global y para la construcción de una sociedad tecnológica basada en un nuevo paradigma del saber. (shrink)

Particular Application System is a groundbreaking exploration into one of the most critical operational layers of the Global Artificial Intelligence framework. This book unveils, in precise and accessible detail, how instructions—born from complex decision-making processes—are matched, classified, and executed with flawless precision by robotic systems.

Imprecise Bayesianism, as opposed to orthodox Bayesianism, aims to model agents who do not have enough information to form precise credences. Under this account, an agents' doxastic state is allowed to be made up of not one but many different credence functions, to model imprecision in the assignment of credences to propositions. Fragmentation, on the other hand, aims to represent agents with fragmented doxastic states, where fragments are individuated via differences in the agent's epistemic and non-epistemic circumstances, such as differences (...) in accessible information, or different practical goals and decisions. The formal model underlying this account is identical to imprecise Bayesianism: the agent's doxastic state is represented via not one but many different credence functions. -/- The literature on fragmentation and imprecision do not comment on the striking similarity between these two different accounts. This paper is devoted to presenting and comparing their similarities and differences. The upshot will be that the main difference lies in, first, the interpretation of the formalisms, as well as how these two accounts deal with questions of practical rationality. (shrink)

Es wurde lange diskutiert, ob zwischen NP-Problemen und P-Problemen eine Unterscheidung besteht. Das lässt sich mithilfe der Strengen Logik beweisen. Es ergibt sich, dass NP-Probleme in der Reinen Logik eine Entsprechung der Angewandten Logik haben.

The consensus is that a normal person, regarding a normal fair lottery, under ordinary, realistic conditions, can’t know ahead of time that a given ticket is a loser. I disagree, sort of. Suppose you learn that a lottery involves extreme probabilities. You also hear, perhaps via the lottery’s website, that someone who bought just one ticket got the winning number. In response to the acquisition of those two pieces of knowledge, you come to think that either the announcement is false (...) (no one who bought a single ticket won), or it's true but either something superhuman was going on or the lottery was fixed. I say: if your belief is true, then it amounts to knowledge. That is, you can know that the lottery’s outcome won’t be an ordinary case of someone with one ticket winning a fair lottery, with no superhuman assistance. -/- . (shrink)

This book motivates and systematically develops the view that knowledge should be at the centre of our theory of practical rationality. Only act on what you know -- the book offers the first comprehensive defence of this slogan in the form of a knowledge-based decision theory. The proposed view is shown to be the most straightforward explanation of emerging bodies of evidence for a link between knowledge and rational action. The book provides novel solutions to well-known challenges that invoke high-stakes (...) scenarios, seemingly rational actions based on reasonable but false beliefs, and decision-making under risk and uncertainty. The emerging view brings together traditional and formal approaches to epistemology and the study of practical rationality. The resulting knowledge-based decision theory is embedded in a rich normative landscape, encompassing innovative accounts of excuses, rational acceptance, and the simplification of reasoning. Knowledge and Rational Action will be of great interest to researchers and graduate students interested in epistemology, practical rationality, and decision theory. (shrink)

Presentation of the contribution paper to the K-CLUB World Conference, Korea University, on July 3-5, 2025. -/- (*Paper: “Peer-mentoring mechanism: A proof of concept”) -/- Updated map: Outreach network of bayesvl BMF analytics users as of Jun-2025. Total downloads of the package bayesvl: 25,215 (25/6/2025).

Chúng tôi mong muốn thông qua một cuốn sách nhỏ này ghi chép lại một hành trình từ ý tưởng đơn sơ ban đầu đi tới một sản phẩm công nghệ, phục vụ công việc khoa học, trước tiên và trên hết cho chính mình. Nhưng ngay tiếp theo đó, sản phẩm được sử dụng ngày một rộng rãi hơn, cho nhiều người (phần lớn là các nhà nghiên cứu trẻ) ở nhiều trường đại học, tại nhiều quốc gia khác (...) nhau. Hôm nay, khi sản phẩm đó đã hỗ trợ hơn một trăm người hoàn thành rất nhiều công việc, thì chúng tôi chợt nhận ra, sản phẩm ấy cũng đã có mặt trên Trái Đất này năm thứ 7. (shrink)

The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that (...) if evidence can be unspecific, then an alleged counterexample to causal decision theory fails. This implies that what theory of decision we think is true may depend on our opinions regarding the nature of evidence. Even when we are theorizing about subjective theories of rationality, we cannot set aside questions about the objective nature of evidence. (shrink)

Và cũng tới tận khi những con số này đã tích lũy qua thời gian, bayesvl mới trút bỏ chiếc áo beta cũ, tức version 0.8.5, để nâng cấp thành phiên bản package bayesvl version 1.0.0. Đúng vào ngày 18/5/2025, ngày Khoa học & Công nghệ Việt Nam.

Package ‘bayesvl’ version 1.0.0 provides users with its associated functions for pedagogical purposes in visually learning Bayesian networks and Markov chain Monte Carlo (MCMC) computations. It enables users to: a) Create and examine the (starting) graphical structure of Bayesian networks; b) Create random Bayesian networks using a dataset with customized constraints; c) Generate Stan code for structures of Bayesian networks for sampling the data and learning parameters; d) Plot the network graphs; e) Perform Markov chain Monte Carlo computations and produce (...) graphs for posteriors checks. The package refers to one reference item, which describes the methods and algorithms: Vuong, Quan-Hoang and La, Viet-Phuong (2019) The 'bayesvl' R package. Its previous CRAN version is bayesvl v0.8.5. -/- Authors: Professor Vuong Quan Hoang, Engineer La Viet Phuong. (shrink)

The question “Why is there something rather than nothing?” has long puzzled philosophers, theologians, and physicists alike. In this paper, I propose a novel probabilistic argument against absolute nothingness. By treating the totality of possible states of being as a formal probability space, I argue that the configuration corresponding to “nothingness” is a singular point with measure zero. Assuming a uniform or unbiased probability distribution across the configuration space, the likelihood of nothingness being actualized is exactly zero, whereas the probability (...) of something existing is one. Hence, existence is not merely a philosophical mystery, but a mathematical inevitability. This approach reframes a metaphysical puzzle as a question of formal modeling and probabilistic reasoning, providing a fresh perspective grounded in established mathematical frameworks. (shrink)

How do psychiatrists arrive at their diagnostic conclusions? Though several philosophers of psychiatry have proposed how to understand psychiatric diagnostic reasoning over the last decade, this essential question of the epistemology of psychiatric practice has received little attention. This article introduces the reader to this topic, its importance, and the major theoretical positions presented in the debate, while also pointing to future relevant research in this area of philosophy of psychiatry.

Kì í ṣe nipa ronu la fi ń ṣẹda àwọn ayé; ṣùgbọ́n nípa agbọye ayé wa la fi ń kọ ẹ̀kọ bí a ṣe lè ronu. Cosmovision jẹ ọrọ kan ti o yẹ ki o tumọ si ipilẹ awọn ipilẹ lati eyiti o ṣe afihan oye eto ti Agbaye, awọn paati rẹ bi igbesi aye, agbaye ti a ngbe, iseda, iṣẹlẹ eniyan, ati awọn ibatan wọn. Nítorí náà, ó jẹ́ pápá ìmọ̀ ọgbọ́n orí ìtúpalẹ̀ tí àwọn sáyẹ́ǹsì ń jẹ, ẹni (...) tí ète rẹ̀ jẹ́ àkópọ̀ àti ìmọ̀ alágbero nípa ohun gbogbo tí a jẹ́ tí ó sì ní nínú, tí ó yí wa ká, tí ó sì ní í ṣe pẹ̀lú wa lọ́nàkọnà. O jẹ nkan ti o ti dagba bi ero eniyan, ati, ni afikun si lilo awọn eroja ti imọ-jinlẹ imọ-jinlẹ, o yika ohun gbogbo ni imọ-jinlẹ ati imọ-jinlẹ ti o tọka si agbaye ati igbesi aye. Cosmovision kii ṣe akojọpọ awọn imọran, awọn idawọle, ati awọn arosinu ṣugbọn eto ti o da lori akiyesi, itupalẹ, ẹri, ati ifihan. Ko si cosmovision ti o pinnu lati ṣalaye, fi idi mulẹ, tabi daba ṣugbọn loye nikan, ṣe itupalẹ, ati itumọ. Olukuluku wa kọ ati gbe oju-aye rẹ jakejado igbesi aye, laisi iṣeto awọn fọọmu, bi ipilẹṣẹ fun ironu ati ihuwasi wa. (shrink)

In recent years, several prominent authors have criticized fine-tuning arguments for failing to show that the universe’s purported fine-tuning for intelligent life calls for explanation. In this paper, I provide a systematic categorization and a detailed evaluation of the proffered critiques. I argue that these critiques cast doubt on various instances of fine-tuning reasoning, but fail to undermine fine-tuning arguments’ conclusion that the universe’s purported fine-tuning for intelligent life can be justifiably taken to call for explanation. I then explicate the (...) implications of this result for the ongoing philosophical debate concerning the merits of fine-tuning arguments and the conditions under which specific events or states of affairs are justifiably taken to call for explanation. (shrink)

It is argued that that the desire attributed to an agent, X, in sentences of the form ‘X wants to know whether P’, is not X’s overall desire for ‘X knows that P or X knows that “not P”’, but rather X’s expected conditional desire for knowing the truth about P, given the truth. An implication of this account for distributive justice is discussed.

The principle of total evidence says that all relevant information should be considered when making an inference about a hypothesis. In this article, we argue that the criminalist’s paradox from the literature on the methodology of forensic science constitutes a counterexample against the principle of total evidence. The paradox arises, for example, when a forensic scientist uses the results from other forensic procedures to inform their own analysis. In such cases, their results can become more reliable, but at the same (...) time also dependent on those other forensic results and therefore less useful for decisions in court cases. Consequently, such influences are generally avoided in forensic science. We argue that structurally similar problems plague also other scientific disciplines, anticipate an objection to the counterexample, and propose two new versions of the principle of total evidence that do not fall prey to the criminalist’s paradox. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. The unity of our universe originates from its creation from the same nothingness under the zero energy universe theory. However, (...) nothingness cannot actually cause a universe to exist on its own under superdeterminism due to the absence of cause and effect in physics. Moreover, nothingness is the absence of anything real and cannot logically be the reality underlying our universe. Consequently, our universe must exist from the reality of the logic or Logos underlying our physical reality resulting from the origination of our universe from the same nothingness or common creation. Because logic allows for a definer of logical states to the exclusion of other logical states, such as “if A, then not B,” then a supremely intelligent definer of those logical states must have the ability to define logical states to the exclusion of other logical states resulting in the creation of physical reality. (shrink)

Many biologists, especially in ecology and evolution, analyze their data by estimating fits to a set of candidate models and selecting the best model according to the Akaike Information Criterion (AIC) or the Bayesian Information Criteria (BIC). When the candidate models represent alternative hypotheses, biologists may want to limit the chance of a false positive to a specified level. Existing model selection methodology, however, allows for only indirect control over error rates by setting a threshold for the difference in AIC (...) scores. We present a novel theoretical framework for parametric Neyman-Pearson (NP) model selection using information criteria that does not require a pre-data null and applies to three or more non-nested models simultaneously. We apply the theoretical framework to the Error Control for Information Criteria (ECIC) procedure introduced by Cullan et al. (J Appl Stat 47: 2565–2581, 2019), and we show it shares many of the desirable properties of AIC-type methods, including false positive and negative rates that converge to zero asymptotically. We discuss implications for the compatibility of evidentialist and severity-based approach to evidence in philosophy of science. (shrink)

Hybrid belief aggregation addresses aggregation of individual probabilistic beliefs into collective binary beliefs. In line with the development of judgment aggregation theory, our research delves into the identification of precise agenda conditions associated with some key impossibility theorems in the context of hybrid belief aggregation. We determine the necessary and sufficient level of logical interconnection between the propositions in an agenda for some key impossibilities to arise. Specifically, we prove three characterization theorems about hybrid belief aggregation: (i) Precisely the path-connected (...) and pair-negatable agendas lead to the ‘oligarchy result’—only oligarchic rules satisfy universal domain, proposition-wise independence, respect for unanimity, and deductive closure of collective beliefs. (ii) Precisely the negation-connected agendas lead to the ‘triviality result’—only unanimity rules satisfy those conditions as well as anonymity. (iii) Precisely the blocked agendas lead to the ‘non-existence result’—no rules satisfy those conditions as well as completeness and consistency of collective beliefs. Furthermore, we compare these novel findings with existing agenda-theoretic characterization theorems in the domains of judgment aggregation and belief binarization. (shrink)

हम सोच कर दुनिया नहीं बनाते। दुनिया को समझ कर हम सोचना सीखते हैं। कॉस्मोविज़न एक ऐसा शब्द है जिसका मतलब नींव का एक समूह होना चाहिए जिससे ब्रह्मांड, जीवन के रूप में इसके घटकों, जिस दुनिया में हम रहते हैं, प्रकृति, मानवीय घटनाओं और उनके संबंधों की एक व्यवस्थित समझ उभरती है। इसलिए, यह विज्ञान द्वारा पोषित विश्लेषणात्मक दर्शन का एक क्षेत्र है, जिसका उद्देश्य हम जो हैं और जो हमारे चारों ओर है, और जो किसी भी तरह से (...) हमसे संबंधित है, उसके बारे में यह एकत्रित और ज्ञानमीमांसीय रूप से स्थायी ज्ञान है। यह मानव विचार जितना ही पुराना है, और वैज्ञानिक ब्रह्मांड विज्ञान के तत्वों का उपयोग करने के अलावा, यह दर्शन और विज्ञान में ब्रह्मांड और जीवन को संदर्भित करने वाली हर चीज को शामिल करता है। एक कॉस्मोविज़न विचारों, परिकल्पनाओं और मान्यताओं का एक समूह नहीं है, बल्कि अवलोकन, विश्लेषण, साक्ष्य और प्रदर्शन पर आधारित एक प्रणाली है। कोई भी कॉस्मोविज़न परिभाषित करने, स्थापित करने या प्रस्तावित करने का इरादा नहीं रखता है, बल्कि केवल समझने, विश्लेषण करने और व्याख्या करने का इरादा रखता है। हममें से प्रत्येक व्यक्ति अपने सोच और व्यवहार के लिए पृष्ठभूमि के रूप में, रूपों को स्थापित किए बिना, जीवन भर अपने कॉस्मोविज़न का निर्माण और परिवहन करता है। भाषाई रूप से, "कॉस्मोविज़न" शब्द जर्मन से लिया गया है, जो कई दार्शनिकों द्वारा इस्तेमाल किए गए "वेल्टनशाउंग" की अवधारणा के बराबर है। हालाँकि, यह भाषाई संबंध लागू नहीं होता है क्योंकि यह हमारे द्वारा प्रस्तावित ब्रह्मांड-दृष्टि के विपरीत है। यह जर्मन शब्द वास्तविकता के एक पूर्व-तार्किक या प्रोटो-प्रयोगात्मक दृष्टिकोण को संदर्भित करता है, जिसमें एक सहज संदर्भ होता है और आलोचनात्मक ज्ञान से बहुत दूर होता है जो इसके निर्माण के समय भी अस्तित्व में नहीं था। निस्संदेह, ब्रह्मांड-दृष्टि, जिस अर्थ में हम उन्हें समझते हैं, इन प्रोटो-प्रयोगात्मक या पूर्व-तार्किक तत्वों को समाहित करता है और उनका उपयोग करता है जिसमें इतिहास, सामूहिक अचेतन और हमारे द्वारा धारण किए जाने वाले सभी मूलरूप शामिल हैं। हालाँकि, जिस अवधारणा को हम यहाँ लागू करते हैं, उसमें ब्रह्मांड-दृष्टि इस सामग्री से बहुत आगे निकल जाती है, सबसे पहले इसे लगातार वर्तमान आलोचनात्मक सोच के अधीन करके, और अंत में विश्लेषणात्मक अनुभव (और न कि विचार या अंतर्ज्ञान) को अपना वास्तविक ब्रह्मांड बनाकर। एंटोनियो लोपेस इस विषय-वस्तु की व्यापकता को उजागर करते हैं: "ब्रह्मांडीय दर्शन विचार की उपज नहीं हैं। वे जानने की सरल इच्छा से उत्पन्न नहीं होते हैं। वास्तविकता की समझ इसकी संरचना में एक महत्वपूर्ण क्षण है, लेकिन फिर भी, यह केवल एक है। यह जीवन के मूल्यांकन के अनुभव से, और हमारी मानसिक समग्रता की संरचना से, जीवन को वास्तविकता के ज्ञान में, मूल्यांकन में, और इच्छाधारी वास्तविकता में चेतना तक ऊपर उठाना वह धीमा और कठिन कार्य है जो मानवता ने जीवन की अवधारणाओं के विकास में किया है।" -/- . (shrink)

Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, problems arise for using safety as a condition on knowledge: safety is not necessary for knowledge and cannot always explain the Gettier cases and cases of statistical evidence it is meant to address. In this paper, I argue for a new modal condition designed to capture the non-accidental relationship between facts and evidence required for knowledge: (...) causal safety. I argue that possible errors in belief can be captured by accounting for deviations in causal relationships and that there is a natural way to characterize which causal errors are relevant in an epistemic situation. Using this, I develop a causal analogue to safety, where one’s belief in _p_ is causally safe if it is true in all causally relevant worlds where one believes _p_. Causal safety, I argue, can better explain the cases safety is meant to address and can avoid the arguments raised against the necessity of safety. (shrink)

It is argued that suitably trained neural language models exhibit key properties of epistemic agency: they hold probabilistically coherent and logically consistent degrees of belief, which they can rationally revise in the face of novel evidence. To this purpose, we conduct computational experiments with rankers: T5 models [Raffel et al. 2020] that are pretrained on carefully designed synthetic corpora. Moreover, we introduce a procedure for eliciting a model’s degrees of belief, and define numerical metrics that measure the extent to which (...) given degrees of belief violate (probabilistic, logical, and Bayesian) rationality constraints. While pretrained rankers are found to suffer from global inconsistency (in agreement with, e.g., [Jang et al. 2021]), we observe that subsequent self-training on auto-generated texts allows rankers to gradually obtain a probabilistically coherent belief system that is aligned with logical constraints. In addition, such self-training is found to have a pivotal role in rational evidential learning, too, for it seems to enable rankers to propagate a novel evidence item through their belief systems, successively re-adjusting individual degrees of belief. All this, we conclude, confirms the Rationality Hypothesis, i.e., the claim that suitable trained NLMs may exhibit advanced rational skills. We suggest that this hypothesis has empirical, yet also normative and conceptual ramifications far beyond the practical linguistic problems NLMs have originally been designed to solve. (shrink)

This dialogue builds on a previous critique that highlights a methodological paradox in the empirical application of probability theory. In the earlier work, it was suggested that while probability is mathematically sound, conceptual challenges arise when it is used to model real-world uncertainty. In this dialogue, Laplace, a proponent of classical probability, and Incredulus, a philosophical skeptic, engage in a thoughtful examination of these issues. Their inquiry explores the interplay between logic, probability, and empirical observation, raising questions about how past (...) experiences shape our understanding of possible outcomes and the limits this may impose on probabilistic reasoning. (shrink)

This article synthesizes some classic methodological keys about sample decisions in social research and attempts to highlight some dimensions that are not always problematized. First, we define the concepts of sample and universe, and ask general questions about what sampling decisions involve. Then, it is proposed to think the variety of sampling procedures by organizing them in two large families: case selection guided by experimental logic and case selection based on random sampling. Although the types of samples are not reduced (...) to these two, nor are they exclusive, they allow us to understand the rationales underlying different kinds of research. (shrink)

Ibeling et al. (2023) axiomatize increasingly expressive languages of causation and probability, and Mossé et al. (2024) show that reasoning (specifically the satisfiability problem) in each causal language is as difficult, from a computational complexity perspective, as reasoning in its merely probabilistic or “correlational” counterpart. Introducing a summation operator to capture common devices that appear in applications—such as the do-calculus of Pearl (2009) for causal inference, which makes ample use of marginalization—van der Zander et al. (2023) partially extend these earlier (...) complexity results to causal and probabilistic languages with marginalization. We complete this extension, fully characterizing the complexity of probabilistic and causal reasoning with summation, demonstrating that these again remain equally difficult. Surprisingly, allowing free variables for random variable values results in a system that is undecidable, so long as the ranges of these random variables are unrestricted. We finally axiomatize these languages featuring marginalization (or more generally summation), resolving open questions posed by Ibeling et al. (2023). (shrink)

Background: Microbiome biomarker discovery for patient diagnosis, prognosis, and risk evaluation is attracting broad interest. Selected groups of microbial features provide signatures that characterize host disease states such as cancer or cardio-metabolic diseases. Yet, the current predictive models stemming from machine learning still behave as black boxes and seldom generalize well. Their interpretation is challenging for physicians and biologists, which makes them difficult to trust and use routinely in the physician-patient decision-making process. Novel methods that provide interpretability and biological insight (...) are needed. Here, we introduce "predomics", an original machine learning approach inspired by microbial ecosystem interactions that is tailored for metagenomics data. It discovers accurate predictive signatures and provides unprecedented interpretability. The decision provided by the predictive model is based on a simple, yet powerful score computed by adding, subtracting, or dividing cumulative abundance of microbiome measurements. -/- Results: Tested on >100 datasets, we demonstrate that predomics models are simple and highly interpretable. Even with such simplicity, they are at least as accurate as state-of-the-art methods. The family of best models, discovered during the learning process, offers the ability to distil biological information and to decipher the predictability signatures of the studied condition. In a proof-of-concept experiment, we successfully predicted body corpulence and metabolic improvement after bariatric surgery using pre-surgery microbiome data. -/- Conclusions: Predomics is a new algorithm that helps in providing reliable and trustworthy diagnostic decisions in the microbiome field. Predomics is in accord with societal and legal requirements that plead for an explainable artificial intelligence approach in the medical field. (shrink)

This manuscript is about how to start from relying on science to be more certain about Christianity. This is because science is so pervasive in our everyday life that we expect that it works almost every time. However, when it comes to Christianity, we need to have faith because most of the time God does not appear to respond to us. Therefore, we feel uncertain about beliefs in Christianity. Instead of being uncertain, this manuscript tries to find a way so (...) that we are more certain about our beliefs in Christianity. We borrow our method to be certain from science. Science faces a similar situation as in believing in Christianity because its knowledge is fallible. Scientists themselves cannot be certain that the scientific knowledge is true all the time. So, they rely on a method called hypothesis testing to make their decisions to believe or not in scientific knowledge. We borrow this method to believe in Christianity. Therefore, we need evidence to make our decision of belief. We mention some evidence from past miracles to help us to make decisions. These include Eucharistic miracles, Marian apparitions, incorruptible corpses, etc. After we decide to believe in Christianity, we work out a theory of Christianity based on the salvation plan of God. We try to substantiate the principles in the theory by referencing testimonies from the Bible and from evidence of miracles that happened. We show that these principles are related to models and experiments that we formulate based on our beliefs in Christianity. Having obtained an understanding of Christianity like a (historical) science, we formulate our practice as a Christian. (shrink)

Die kumulative Habilitation besteht aus einer philosophiegeschichtlichen Arbeit (G), drei vorwiegend theoretischen Arbeiten (T1–T3) und vier anwendungsorientierten Arbeiten (A1–A4).

This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While talk of qualitative vs. quantitative may be suggestive, we identify a robust and meaningful boundary in the space by distinguishing systems that encode (at most) additive reasoning from those that encode additive and multiplicative reasoning. The latter includes not only languages with explicit multiplication but also languages expressing notions of dependence and (...) conditionality. We show that the distinction tracks a divide in computational complexity: additive systems remain complete for NP, while multiplicative systems are robustly complete for ∃ℝ. We also address axiomatic questions, offering several new completeness results as well as a proof of non-finite-axiomatizability for comparative probability. Repercussions of our results for conceptual and empirical questions are addressed, and open problems are discussed. (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is (...) based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (shrink)

Many philosophers accept that, as well as having a right that others not harm us, we also have a right that others not subject us to a risk of harm. And yet, when we attempt to spell out precisely what this ‘right against risk imposition’ involves, we encounter a series of notorious puzzles. Existing attempts to deal with these puzzles have tended to focus on the nature of rights – but I propose an approach that focusses instead on the nature (...) of risk. The key move is to distinguish two different ways in which to conceptualise the risk that a given action presents – one of which is linked to the notion of probability and the other to the notion of normalcy. (shrink)

Probabilistic actual causation is a theory about actual causal relations in probabilistic scenarios. Compared with general (or type) causal connections, actual (or token, singular) causation involves specific and actual events occurring in a particular time and space. Halpern and Pearl proposed three mathematical definitions on actual causation via structural equation models (or causal models). Fenton-Glynn extended one of their definitions into a probabilistic version by following the probability-raising principle in the tradition of theorizing about probabilistic causation. The basic idea of (...) this principle is that a cause shall raise the probability of its effect. He adopted interventional probabilities to analyse actual causation in causal Bayesian networks. According to Pearl, interventional probabilities of the form P(Y = yX=x) are used to form type-level causal claims, while it is counterfactual probabilities of the form P(Y = yX=x | X = x1, Y = y1) that help us characterize token-level causal relations as the conditionalization part takes actual situations into account; the more facts we condition upon, the closer we come to actual causation. In this dissertation, we modify Fenton-Glynn’s probabilistic definition of actual causation in probabilistic causal models by employing counterfactual probability raising instead of his interventional probability raising. Our new definitions PAC and PAC’ are capable of dealing with a number of probabilistic versions of causal examples in which Fenton-Glynn’s definition fails, such as voting, overlapping, trumping, etc. Alternatively, we can exploit elaborate and plausible counterfactual definitions of actual causation, once counterfactuals are interpreted probabilistically, essentially we turn the deterministic theories of actual causation into their indeterministic versions. That can be seen as the second or new approach to defining probabilistic actual causation compared with the traditional straightforward probability-raising approach. In order to realize this idea, we propose a probabilistic semantics for causal counterfactuals in probabilistic causal models using counterfactual probabilities. Causal counterfactuals or interventional sentences have the form [X ←x]Y = y with the meaning “if X is manipulated to take value x, Y has value y.” Causation definitions in the causal modeling framework take interventional sentences as counterfactuals. Our proposed semantics for [X ← x]Y = y is its corresponding counterfactual probability being very high (e.g. P(Y = yX=x | e) = 1). For this semantics, we provide a sound and complete axiomatization. Based on this logical result, Halpern’s latest definition of actual causation can be translated as a probabilistic version by interpreting interventional statements in it with our semantics. The difference between definitions from this approach and the traditional one turns out to be the extent of probability increase, namely, slight (traditional approach) or significant (new approach) probability raising. We compare the logical properties of our conception PAC of probabilistic actual causation and the new indeterministic version of Halpern’s latest actual causation by treating these two definitions as the semantics for causal conditionals. (shrink)

The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people’s performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based (...) on computational requirements for solving a problem. According to the EPO framework, current methods for improving probabilistic reasoning are of two kinds: First, reduction of Bayesian problems to a type of probabilistic problems requiring less conceptual and procedural competencies. Second, enhancing people’s utilization competence by fostering the application of quantitative inference schemas. The approach suggests new applications, including the teaching of probabilistic reasoning, using analogical problem solving in probabilistic reasoning, and new methods for analyzing errors in probabilistic problem solving. (shrink)

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. (...) Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection (Moss, 2021). I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity Reflection from (...) the assumption that you defer to someone whenever you consider their doxastic state to be better than yours, in the sense of leading to better decision-making. (shrink)

By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'" or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.

Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.

Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle of (...) suspension, I argue that all possible credal accounts face serious challenges. They either (i) falsify central claims that uphold the credal picture itself or (ii) do not permit suspension in cases where it is permissible or (iii) rule out the possibility of plainly possible confidence comparisons. (shrink)

A stereotype is a belief or claim that a group of people has a particular feature. Stereotypes are expressed by sentences that have the form of generic statements, like “Canadians are nice.” Recent work on generics lends new life to understanding generics as statements involving probabilities. I argue that generics (and thus sentences expressing stereotypes) can take one of several forms involving conditional probabilities, and these probabilities have what I call a naturalness requirement. This is the natural probability theory of (...) stereotypes. Each of the two components of the theory entails a family of fallacies that contributes to the spurious reinforcement of stereotypes: inferential slippage within and between the different generic forms, and inferential slippage from facts about frequencies of group traits to beliefs about natural propensities or dispositions of groups. Empirical research suggests that we often commit these fallacies. Moreover, this theory can referee a vitriolic debate between some psychologists, who hold that stereotypes are always false and stereotyping is always wrong, and other psychologists, who hold that stereotypes are often accurate and stereotyping is often reasonable. (shrink)

This article examines how Facebook’s Feed, its dynamic user interface, incorporates and refashions the capacity to temporalize cultural material and experience that has classically been attributed to subjectivity. I problematize the ambiguous historicity of digital culture across the experience of the ordinary that it produces by arranging the subjective time and ‘ruined’ bits of cultural material into algorithmic timelines. Drawing on recent media theory, I underscore the irreducible alienness of algorithmic temporalizations, which undermine habitual normalization. I show subjectivity moves beyond (...) identity and narrative closure through an unconscious affective investment in extremely popular algorithmic timelines. (shrink)

General epistemic polarization arises when the beliefs of a population grow further apart, in particular when all agents update on the same evidence. Epistemic factionalization arises when the beliefs grow further apart, but different beliefs also become correlated across the population. I present a model of how factionalization can emerge in a population of ideally rational agents. This kind of factionalization is driven by probabilistic relations between beliefs, with background beliefs shaping how the agents’ beliefs evolve in the light of (...) new evidence. Moreover, I show that in such a model, the only possible outcomes from updating on identical evidence are general convergence or factionalization. Beliefs cannot spread out in all directions: if the beliefs overall polarize, then it must result in factionalization. (shrink)