Probabilistic Reasoning

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)

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)

This paper investigates the question of how subjective probability should relate to binary belief. We propose new distance minimization methods, and develop epistemic decision-theoretic accounts. Both approaches can be shown to get “close” to the truth: the first one by getting “close” to a given probability, and the second by getting expectedly “close” to the truth. More specifically, we study distance minimization with a refined notion of Bregman divergence and expected utility maximization with strict proper scores. Our main results reveal (...) that the two ways to get “close” to the truth can coincide. (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)

Trước những khó khăn và thách thức của các nhà khoa học trẻ và các nhà khoa học ở những nước đang phát triển do thiếu tài nguyên và cơ hội được tiếp cận với các kiến thức và phương pháp nghiên cứu bài bản…, các nhà khoa học Việt Nam đã phát triển nền tảng Cổng thông tin SM3D hỗ trợ đào tạo phương pháp nghiên cứu khoa học xã hội cho các nhà khoa học. Sau gần 2 năm (...) được triển khai, Cổng thông tin SM3D được đánh giá là một trong những sáng kiến đóng góp tiêu biểu của khoa học Việt Nam cho cộng đồng khoa học quốc tế, đặc biệt là đối với các nước đang phát triển. (shrink)

This paper explores the derogatory uses of nicknames within closely-knit social settings such as villages, households, and schools. By examining ethnographic and psychological data on nicknaming practices, this paper contends that pejorative nicknames and slurs share structural and functional attributes. On the one hand, pejorative nicknames and slurs can elicit deep offence regardless of the speaker’s intentions or whether they occur within speech reports. On the other, pejorative nicknames can contribute to creating and reinforcing unjust intra-group hierarchies, hence mirroring the (...) role of slurs within a smaller social scale. To explain these shared attributes, this paper argues (i) that both forms of verbal aggression index multiple dimensional qualities such as ‘negative valence’, ‘neutral arousal’, and ‘high dominance’ rather than discrete emotional categories such as ‘contempt’ or ‘anger’, and (ii) that the expression of high dominance in social interactions underlies their capacity to offend. Then, it translates this hypothesis into a Bayesian model of sociolinguistic variation inspired by Heather Burnett’s work on identity construction, thus integrating pragmatic reasoning into a psychologically informed framework for interpreting emotional cues. By studying both phenomena in tandem, this paper shows how understanding nicknaming dynamics within smaller speech-act communities can contribute to our comprehension of the derogatory impact of slurs in more intricate social contexts. (shrink)

The notions of psychological similarity and probabilistic learning are key posits in cognitive, computational, and developmental psychology and in machine learning. However, their explanatory relationship is rarely made explicit within and across these research fields. This opinionated review critically evaluates how these notions can mutually inform each other within computational cognitive science. Using probabilistic models of concept learning as a case study, I argue that two notions of psychological similarity offer important normative constraints to guide modelers’ interpretations of representational primitives. (...) In particular, the two notions furnish probabilistic models of cognition with meaningful interpretations of what the associated subjective probabilities in the model represent and how they attach to experiences from which the agent learns. Similarity representations thereby provide probabilistic models with cognitive, as opposed to purely mathematical, content. (shrink)

A conjunction of two hypotheses may provide a better explanation than either one of them individually, even if each already provides a good explanation on its own. An appropriate measure of explanatory power should reflect this, but none of the measures discussed in the literature do so because they only consider how much an explanatory hypothesis reduces our surprise at the evidence – which is problematic. This chapter introduces and defends a class of coherentist measures of explanatory power, and shows (...) that one particular such measure that combines different intuitions underlying the epistemological notion of coherence overcomes the aforementioned problems of surprise reduction measures. (shrink)

Do people tend to be overconfident? Many think so. They’ve run studies on whether people are calibrated: whether their average confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically ‘over-calibrated’—for example, of the opinions they’re 80% confident in, only 60% are true. From this empirical over-calibration, it’s inferred that people are irrationally overconfident. My question: When and why is this inference warranted? Answering it requires articulating a general connection between being (...) rational and being right—something extant studies have not done. I show how to do so using the notion of deference. This provides a theoretical foundation for calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is standardly assumed, since rational people can often be expected to be miscalibrated. Thus we can’t test whether people are overconfident by simply testing whether they are over-calibrated; instead, we must try to predict the rational deviations from calibration, and then compare those predictions to people’s performance. I show how this can be done—and that doing so complicates the interpretation of robust empirical effects. (shrink)

We illustrate how a variety of logical methods and techniques provide useful, though currently underappreciated, tools in the foundations and applications of reasoning under uncertainty. The field is vast spanning logic, artificial intelligence, statistics, and decision theory. Rather than (hopelessly) attempting a comprehensive survey, we focus on a handful of telling examples. While most of our attention will be devoted to frameworks in which uncertainty is quantified probabilistically, we will also touch upon generalisations of probability measures of uncertainty, which have (...) attracted a significant interest in the past few decades. (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)

The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to which (...) this limitation can be overcome. Building on the best arguments in finite domains, I present two accuracy arguments for probabilism that are perfectly general—they apply to credence functions with arbitrary domains. I then discuss how the arguments’ premises can be challenged. We will see that it is particularly difficult to characterize admissible accuracy measures in infinite domains. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

In natural language, conditionals are frequently used for giving explanations. Thus the antecedent of a conditional is typically understood as being connected to, being relevant for, or providing evidential support for the conditional's consequent. This aspect has not been adequately mirrored by the logics that are usually offered for the reasoning with conditionals: neither in the logic of the material conditional or the strict conditional, nor in the plethora of logics for suppositional conditionals that have been produced over the past (...) 50 years. In this paper I survey some recent attempts to come to terms with the problem of encoding evidential support or relevance in the logic of conditionals. I present models in a qualitative-modal and in a quantitative-probabilistic setting. Focussing on some particular examples, I show that no perfect match between the two kinds of settings has been achieved yet. (shrink)

Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.

La epistemología bayesiana tiene como concepto capital la condicionalización simple. Para comprender de buena forma cómo opera esta regla, se debe dar cuenta de la concepción subjetiva de la probabilidad. Sobre la base de lo anterior es posible esclarecer alcances y límites de la condicionalización simple. En general, cuando esta regla enfrenta una dificultad se hacen esfuerzos por resolver dicha particular cuestión, pero no es usual encontrar propuestas unificadas con la intención de resolver varias de las complicaciones subyacentes al bayesianismo (...) ortodoxo. Por lo mismo, el propósito de esta investigación es justamente proponer aquello: un marco bayesiano ampliado que tendrá por objeto solucionar más de una cuestión particular. Más específicamente, el problema de la incorregibilidad, el problema del surgimiento del cero, el problema de la evidencia antigua y el problema de las teorías nuevas. Lo anterior se logrará adicionando al bayesianismo ortodoxo dos cuestiones, a saber, la condicionalización épsilon y una reconstrucción racional. Palabras clave: Probabilidad Subjetiva, Grados de Creencia, Dogmatismo Bayesiano, Evidencia Antigua, Nuevas Teorías. (shrink)

Academia is a competitive environment. Early Career Researchers (ECRs) are limited in experience and resources and especially need achievements to secure and expand their careers. To help with these issues, this book offers a new approach for conducting research using the combination of mindsponge innovative thinking and Bayesian analytics. This is not just another analytics book. 1. A new perspective on psychological processes: Mindsponge is a novel approach for examining the human mind’s information processing mechanism. This conceptual framework is used (...) to construct models in studies. The framework is highly flexible and widely applicable for many different types of information processes. The mindsponge approach can help researchers discover interesting ideas or even formulate their very own theories when investigating psychosocial phenomena. This approach brings a fresh wind to the current landscape of social sciences and humanities (SSH). 2. Easy-to-follow analysis protocol: The Bayesian Mindsponge Framework (BMF analytics) is useful in terms of computing and visualizing power but also easy to learn and apply. Contrary to being intimidating, the Bayesian analytics section of this book is presented in a reader-friendly manner with a detailed yet clear step-by-step procedure. Examples are from published BMF articles, allowing readers to immediately practice the method and quickly create their own applications. With educational purposes in mind, the book is very suitable for ECRs who are looking to innovate their research methods. 3. Advocating for low-cost, high-quality research: Doing science can be very costly. Mindsponge innovative thinking and BMF analytics help produce impactful studies using openly available data on online repositories. This is based on the authors’ previous works and experiences. The book presents examples of employing the open R package bayesvl on secondary data from different sources. With less financial constraints, researchers can have more freedom of thought to pursue their curiosity and creativity. ECRs in low- and middle-income countries may find this aspect crucial in their careers. 4. Support and collaboration: The authors share their insights from experiences in the academic publishing system to help readers get through the processes of manuscript writing and peer-reviewing more easily. The authors are also ready to support other researchers with further inquiries and collaboration opportunities at the following website, mindsponge(dot)info. This book is for: a) ECRs whose only abundant resources are their innovation capacity and strength of will; b) Researchers in SSH who want to explore a novel approach to thinking and study conducting; c) Low- and middle-income countries’ researchers looking for a cost-effective research protocol; and, d) Innovative thinkers who want to turn their interesting thoughts into good publications. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause (...) for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist. -/- Friends of the KCA have sought to defend their view that physical reality began to exist in two distinct ways. As I discuss in chapter 2, the first way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a priori arguments meant to show that, as a matter of metaphysical necessity, the past must be finite. If the past is necessarily finite, then the past history of physical reality is necessarily finite. And if having a finite past suffices for having a beginning, then, since the past history of physical reality is necessarily finite, physical reality necessarily began to exist. I show that the arguments which have been offered thus far for the view that the past is necessarily finite do not succeed. Moreover, as I elaborate on in chapter 5, having a finite past does not suffice for having a beginning. -/- As I discuss in chapter 3, the second way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a posteriori arguments meant to show that we have empirical evidence that physical reality has a finite past history. For example, the big bang is sometimes claimed to have been the beginning of physical reality and, since we have excellent empirical evidence for the big bang, we have excellent empirical evidence for the beginning of physical reality. The big bang can be understood in two ways. On the one hand, the big bang can be understood as a theory about the history and development of the observable universe. Understood in that sense, then I agree that the big bang is supported by excellent empirical evidence and by a scientific consensus. On the other hand, some authors (particularly science popularizers, science journalists, and religious apologists) have wrongly interpreted big bang theory as a theory about the beginning of the whole of physical reality. As I argue, while a beginning of physical reality may be consistent with classical big bang theory, classical big bang theory does not provide good reason for thinking that physical reality began to exist. -/- In part II, I turn to discussing three necessary, but not necessarily sufficient, conditions for physical reality to have a beginning. Before discussing the three conditions, in chapter 4, I introduce three metaphysical accounts of the nature of time (A-theory, B-theory, and C-theory) as well as some formal machinery that will subsequently become useful in the dissertation. I introduce the first of the three conditions in chapter 5. According to the Modal Condition, physical reality began to exist only if, at the closest possible worlds without time, physical reality does not exist. I show that this condition helps us to make sense of various views in both theology and philosophy of physics. In chapter 6}, I introduce the second of my three conditions, the Direction Condition, according to which, roughly, physical reality began to exist only if all space-time points agree about the direction of time, so that all space-time points can agree that physical reality's putative beginning took place in their objective past. In chapter 7, I discuss the third condition, the Boundary Condition, according to which physical reality began to exist only if there is a past temporal boundary such that physical reality did not exist before the boundary. I show that there are two senses in which physical reality could be said to have had a past temporal boundary. Lastly, in chapter 8, I show that there is a relationship between my three conditions and classical big bang theory, even though the relationship is not the one usually identified in the literature. -/- In part III, I present four arguments for the view that, at the present stage of philosophical and scientific inquiry, we cannot know whether physical reality satisfies the three necessary conditions to have had a beginning and, consequently, we cannot know whether physical reality had a beginning. As I will prove in chapter 9, no set of observations that we currently have, when conjoined with General Relativity, entails that physical reality satisfies the Direction or Boundary Conditions. As I show in chapter 10, considerations in the philosophical foundations of statistical mechanics entail either that the Cosmos violates the Modal Condition or else that there is a transcendental condition on the possibility of our knowledge of the past that prevents our access to data we would need to gather to determine whether physical reality satisfies the Boundary Condition. In chapter 11, I show that there are a number of live cosmological models according to which physical reality does not satisfy the Boundary Condition. As long as we don't know whether any of those cosmological models are correct, we do not know whether physical reality satisfies the Boundary Condition. Lastly, I turn to confirmation theory and show that, at our present stage of inquiry, ampliative inferences for the conclusion that physical reality satisfies the Modal, Direction, and Boundary Conditions are not successful. (shrink)

The interplay between the virus, infected cells and immune responses to SARS-CoV-2 is still under debate. By extending the basic model of viral dynamics, we propose here a formal approach to describe neutralisation versus weak (or non-)neutralisation scenarios and compare them with the possible effects of antibody-dependent enhancement (ADE). The theoretical model is consistent with the data available in the literature; we show that both weakly neutralising antibodies and ADE can result in final viral clearance or disease progression, but that (...) the immunodynamics are different in each case. As a significant proportion of the world’s population is already naturally immune or vaccinated, we also discuss the implications for secondary infections after vaccination or in the presence of immune system dysfunctions. (shrink)

I argue that we can get evidence for the temporal ontology of the universe simply by looking at the time. The argument is an extension of the ‘epistemic objection’ towards Growing Block theories.

A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.

This paper models knowledge in cases where an agent has multiple experiences over time. Using this model, we introduce a series of observations that undermine the pretheoretic idea that the evidential significance of experience depends on the extent to which that experience matches the world. On the basis of these observations, we model knowledge in terms of what is likely given the agent’s experience. An agent knows p when p is implied by her epistemic possibilities. A world is epistemically possible (...) when its probability given the agent’s experiences is not significantly lower than the probability of the actual world given that experience. (shrink)

In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical generalisation. In this (...) paper, I show that Moss's account of legal proof crucially depends on a moral norm called the rule of consideration. I argue that we have a number of reasons to be sceptical of this rule. Once we reject the rule, it is not clear that Moss's account of legal proof is either plausible or attractive. (shrink)

The present paper focuses on the work of Adolphe Quetelet (1796-1874), the Belgian author of the Social Physics who worked in the tradition of the French mathématique sociale, and of Otto Neurath (1882-1945), the Vienna Circle’s member who supported a “sociology within physicalism”. They shared some important philosophical and methodological positions: an empiricist approach to the social sciences, a unitary conception of the natural and the social sciences, and the appreciation of statistics as a tool for investigating and also reforming (...) society. My paper analyses these elements of continuity between the two authors, in order to highlight how an empirical-quantitative approach to society was (at least partially) inherited by Austrian sociology from an earlier French tradition. On the contrary, most German statisticians refused such an approach at the time in which social sciences were developing in Germany, and they strongly believed in an in-principle difference between natural and social sciences. From a systematic point of view, my paper devotes a special attention to the relationship between the application of statistics (praxis) and a unitary conception of the sciences (theory). Both in Quetelet’s and in Neurath’s work these two aspects support each other. Nevertheless Neurath can be said to have turned Quetelet’s reasoning upside-down: While Quetelet appealed to statistics to claim that the social sciences can reach the same objectivity and determinacy as the natural ones, Neurath referred to statistics to argue that the natural sciences – exactly like the social ones – are characterized by a certain degree of indeterminacy and underdetermination. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...) can help us make progress on the problem of induction. (shrink)

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...) a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)