Philosophy of Probability

It is possible that you are living in a simulation—that your world is computer-generated rather than physical. But how likely is this scenario? Bostrom and Chalmers each argue that it is moderately likely—neither very likely nor very unlikely. However, they adopt an unorthodox form of reasoning about self-location uncertainty. Our main contention here is that Bostrom’s and Chalmers’ premises, when combined with orthodoxy about self-location, yields instead the conclusion that you are almost certainly living in a simulation. We consider how (...) this (surprising) conclusion might be resisted, and show that the analogy between Sleeping Beauty cases and simulation cases provides a new way of evaluating approaches to self-location uncertainty. In particular, we argue that some conditionalization-based approaches to self-location are problematically limited in their applicability. (shrink)

The study of belief and its norms of rationality is central to contemporary epistemology. But belief is just one of many doxastic states. When it comes to the class of doxastic states, epistemologists commonly distinguish between our outright doxastic states and our graded doxastic states. The outright doxastic states include believing that p, thinking that p, having the opinion that p, and being certain that p, while the graded doxastic states include degrees of confidence, credences, and perhaps certain degreed phenomenal (...) states. But in addition to the standard doxastic states mentioned above we also have *conviction* – i.e. *the state of being convinced that something is the case*. The concept of conviction was central to Kant’s way of thinking about outright doxastic states. However, conviction has not been regarded as a distinctive doxastic mental state in recent philosophy of mind and epistemology. But there are a number of reasons to think that conviction plays a central role in understanding the nature of all of the outright doxastic states mentioned above. Linguistic evidence from both English and German strongly suggests that conviction comes in degrees and that the fundamentality of conviction is part of our folk theory of mind. This book will explain the variety of reasons there are to think that conviction plays a central role in understanding (i) the nature of all of the outright doxastic states mentioned above, (ii) the relation between conviction and belief, and (iii) how degrees of conviction are distinct from familiarly referenced degreed doxastic states (degrees of confidence, credences, and other relevant degreed phenomenal states). This book goes on to introduce readers to the widely held idea that doxastic states are related to dispositions to rely on propositions, and shows how this holds a key to providing an adequate metaphysical account of degrees of conviction, and thereby an adequate metaphysical account of our outright doxastic states. An upshot of this is the emergence of an often overlooked species of the suspension of our outright states, one that yields new theoretical options for epistemologists wrestling with old problems. (shrink)

“If the tower is any taller than 320 ms, it may collapse,” Eiffel thinks out loud. Although understanding this counterfactual poses no trouble, the most successful interventionist semantics struggle to model it because the antecedent can come about in infinitely many ways. My aim is to provide a semantics that will make modeling such counterfactuals easy for philosophers, computer scientists, and cognitive scientists who work on causation and causal reasoning. I first propose three desiderata that will guide my theory: it (...) should be general, yet conservative, yet useful. Next, I develop a formalization of events in the form of an algebra. I identify an event with all the ways in which it can be brought about and provide rules for determining the referent of an arbitrary event description. I apply this algebra to counterfactuals expressed using underdeterministic causal models-models that encode non-probabilistic causal indeterminacies. Specifically, I develop semaphore interventions, which represent how the target system may be modified from without in a coordinated fashion. This, in turn, allows me to bring about any event within a single model. Finally, I explain the advantages of this semantics over other interventionist competitors. (shrink)

A number of authors, including me, have argued that the output of our most complex climate models, that is, of global climate models and Earth system models, should be assessed possibilistically. Worries about the viability of doing so have also been expressed. I examine the assessment of the output of relatively simple climate models in the context of discovery and point out that this assessment is of epistemic possibilities. At the same time, I show that the concept of epistemic possibility (...) used in the relevant studies does not fit available analyses of this concept. Moreover, I provide an alternative analysis that does fit the studies and broad climate modelling practices as well as meshes with my existing view that climate model assessment should typically be of real possibilities. On my analysis, to assert that a proposition is epistemically possible is to assert that it is not known to be false and is consistent with at least approximate knowledge of the basic way things are. I, finally, consider some of the implications of my discussion for available possibilistic views of climate model assessment and for worries about such views. I conclude that my view helps to address worries about such assessment and permits using the full range of climate models in it. (shrink)

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...) by introducing the concept of Type I error rates and distinguishing between statistical errors and theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ underestimation of theoretical errors and misinterpretation of statistical errors. (shrink)

The Objective of “Tranquillity’s Secret” Is To Present A New More Veridical Way Of Understanding The World, And The Meditation Technique And Its Unexcelled Support That Directly Leads One To See The World Differently. -/- In our rational attempts to understand ourselves and our world today, it is the case that in comparison to matter, which is so definite, measurable, actual, and sometimes literally concrete, we have ‘mind’ and ‘consciousness’, which is exactly the opposite: it is indefinite, unmeasurable, undiscoverable, and (...) abstract. And yet, it is the reverse within our lived experience in which it is our being aware that is actual, indisputable, irrefutable, true, and well-grounded, while matter is only an abstraction from our experiences, that is wholly contingent, and about which everything is unsure. So why do we search for ‘consciousness’ by reasoning about the world, rather than meditating upon our immediate lived experience? ‘Consciousness’ is an abstraction taken from our experience, so we cannot use ‘consciousness’ to explain experience. A contemplative science would. -/- The meditation technique that Tranquillity’s Secret presents uses Inner Spontaneous Sound as its support. These uncaused sounds which are always available to meditate with, have no material basis, and so their very presence calls into question our faith that only matter matters. These sounds appear in different forms in the myriad of contemplative traditions which have employed them for millennia and have universally acknowledged them as the most efficacious path to a direct experience of the nature of Reality. Unfortunately, during modern times, the correct use of these sounds has been almost lost, along with the reasons why they were claimed to be so highly effective. The primary condition for this loss is the mechanical materialism which frames what is allowable for thought, and constrains our reasoning to only consider reductionist mechanical explanations in every case. Even those who believe they have escaped from the limitations of this understanding, continue to be enframed because our language has been structured by it, so that there is no true escape via a simple substitution or redefinition of concepts. Instead, Tranquillity’s Secret presents a new understanding that supersedes mechanical materialism and its paradigm of physical causality. It begins with an acceptance that Time is only a formalism, and does not exist in the sense of either an arrow or a stream. This leads to a radical reorientation of what it means to be aware and conscious, and the discovery of a revolutionary understanding of coherent Responsive Naturing that supplants the never-solved paradoxes of ‘consciousness’ and ‘causal change over time’ with coherent and immediate processual reconfigurations based upon contextual conditions, potentials, and probabilities — and the recognition of each reconfiguration. -/- Thus, Responsive Naturing provides a sound foundation for veridical science, so that both science and spirituality can be founded upon a common understanding of ‘how things work’. This empowers us in ways that our disjointed and parochial schools of thought lock us out of completely, while opening up new possible methods of looking at problems and finding solutions across disciplines. (shrink)

In this article, Joey Lawsin argues that intelligence, behaviors, perceptions, awareness, consciousness, and other related mental interims can be processed without the need of the brain. His claims are built upon the concepts of Inscription by Design and Generated Interim Emergence. The former deals with Intuitive Systems, Embedded Inscriptions, and Generated Interims while the latter deals with the new seven evolutionary criteria of life namely: (i) Mechanical Aliveness, (ii) Sensoric Awareness, (iii) Logical Intuitiveness, (iv) Aneural Consciousness, (v) Information Inlearness, (vi) (...) Symbiotic Living, and (vii) Self-Emergence. From his findings comparing autognorics, biotronics, animals, plants, molds, and machines' intuitive anueral networks, Lawsin concluded that a network of logics produces intelligence, thinking does not need to emanate from the brain, sequential inscriptions give rise to behavioral experiences, and mother nature, which includes all living things, comes with a brain without the brain. He also concluded that an intuitive memory network can be lateral or open like a memory circuit board and can evolve into spherical or close like the human brain. (shrink)

TS. Nguyễn Minh Hoàng (ĐH Phenikaa), đã giảng bài về tiếp cận tính toán sử dụng bayesvl và ứng dụng BMF cho công việc nghiên cứu KHXH.

On November 3 and 4, 2023, Dr. Nguyen Minh Hoang (Phenikaa University), co-author of the BMF Analytics [1], gave a lecture on computational approaches using bayesvl and BMF application for social science research.

This paper will attempt to offer a defence of to the Multiverse (MV) hypotheses, in the context of the theistic Fine Tuning Argument (FTA). It will be argued that theistic proponents of the FTA who argue that the MV hypothesis commits the Inverse Gambler’s Fallacy (IGF) are, themselves, guilty of moving the goalposts when it comes to assessing the validity of the MV hypothesis. The Cosmic Slot Machine analogy will be used to demonstrate how the This Universe Objection (TUO), first (...) outlined by White (2000) and further clarified by Draper et al (2007), fails to adequately account for the anthropic principle (or selection effect). (shrink)

This paper explores the functions and features of nicknaming practices, with a particular emphasis on their capacity to derogate and establish power differentials within a group. Upon analysing data from ethnographic and psychological studies, this investigation argues that some pejorative nicknames, due to their capacity to foster unjust forms of intra-group hierarchies, can function analogously to slurs. That is, expressions which target social groups singled out based on gender or ethnicity and which, among other features, elicit deep offense autonomously from (...) the speaker’s intentions and irrespective of whether the term is used or mentioned within speech-reports. Building upon this premise, the paper proposes a unified theory that posits both forms of verbal aggression as indexing multiple dimensional qualities such as “negative valence”, “neutral arousal,” and “high dominance” rather than unique discrete emotional categories such as “contempt” or “anger” and contends that the expression of high dominance states within social interactions is at the root of their capacity to warrant offense. Moreover, the paper translates this hypothesis into a Bayesian model of sociolinguistic variation, drawing inspiration from Heather Burnett’s pioneering work on identity construction. This new approach not only accounts for slurs and nicknames’ uniform offensive profile but also situates pragmatic reasoning within a psychologically grounded framework for the interpretation of emotional signals. (shrink)

Slurs’ meaning is highly unstable. A slurring utterance like ‘Hey, F, where have you been?’ (where F is a slur) may receive a wide array of interpretations depending on various contextual factors such as the speaker’s social identity, their relationship to the target group, tone of voice, and more. Standard semantic, pragmatic, and non-content theories of slurs have proposed different mechanisms to account for some or all types of variability observed, but without providing a unified framework that allows us to (...) understand how different contextual factors simultaneously influence slurs’ interpretation. To address this issue, I argue that slurs convey dimensional qualities such as, e.g., ‘negative valence, neutral arousal, high dominance’ instead of discrete emotional categories such as ‘contempt’. Then, I translate this hypothesis into a game-theoretic model of slurs’ interpretation inspired by Heather Burnett’s pioneering work on identity construction. This new model, called ‘Affective Meaning Games’ (AMG), captures the variability of slurs and integrates pragmatic reasoning within an independently motivated psychological understanding of emotional states. (shrink)

De mens is irrationeel. Verliefd op zijn eigen gelijk. Doof voor feiten argumenten. Verblind door honderden denkfouten. Een makkelijke prooi voor nepnieuws. Gevangen in filterbubbels. Zo is het heersende idee. Maar klopt het wel? In dit boek verweeft filosoof Maarten van Doorn de jongste inzichten uit de psychologie, communicatiewetenschappen, filosofie en politicologie. Hij neemt ons mee op een reis langs verrassende onderzoeksresultaten en scherpzinnige filosofen en geeft nieuwe antwoorden op dringende vragen: Waarom geloven we wat we geloven? Hoe veranderen mensen (...) van mening? Zijn we echt in een post-truth tijdperk aanbeland? Hoe gevaarlijk is misinformatie? Zijn onze emoties of onze ratio de baas in ons hoofd en in onze maatschappij? Waarom we beter denken dan we denken biedt een hoopvol geluid in een gepolariseerde wereld. (shrink)

Swear words are highly colloquial expressions that have the capacity to signal the speaker's affective states, i.e., to display the speaker's feelings with respect to a certain stimulus. For this reason, swear words are often called 'expressives'. Which linguistic mechanisms allow swear words display affective states, and, more importantly, how can such 'affective content' be characterized in a theory of meaning? Even though research on expressive meaning has produced models that integrate the affective aspects of swear words in a compositional (...) framework, there is extensive evidence that swear words cannot be assigned a single or stable affective interpretation across contexts. For example, even though expletive adjectives (e.g., 'damn'), particularistic insults (e.g., 'bastard') and slurs (e.g., 'wop') typically express (and elicit) negatively valenced affective states, they can also be interpreted positively in some contexts. Thus, inspired in recent developments in formal sociolinguistics, I propose an 'indexical' approach to affective meaning. Under this approach, an affective expression is associated with a set of affective qualities, anyone of which may emerge at a given context depending on the interpreter's prior assumptions about the speaker's affective states and/or relation with the target of the swear word. To define this set, also called 'indexical field', I will use the dimensions pleasure, arousal and dominance, standardly employed in cognitive psychology to characterize and measure affective episodes. In this dissertation, thus, the affective meaning of an expression is given by the set of affective states it typically conveys within a linguistic community, but its interpretation at a given context is established by taking into account the interpreter's prior assumptions about the speaker's affective states and/or attitudes with respect to the target of the affective expression. (shrink)

Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic "level-bridging" principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

Lewis’s Principal Principle says that one should usually align one’s credences with the known chances. In this paper I develop a version of the Principal Principle that deals well with some exceptional cases related to the distinction between metaphysical and epistemic modal­ity. I explain how this principle gives a unified account of the Sleeping Beauty problem and chance-­based principles of anthropic reasoning. In doing so, I defuse the Doomsday Argument that the end of the world is likely to be nigh. (...) GPI Working Paper No. 8-2021. (shrink)

This paper develops a trivalent semantics for indicative conditionals and extends it to a probabilistic theory of valid inference and inductive learning with conditionals.} On this account, (i) all complex conditionals can be rephrased as simple conditionals, connecting our account to Adams's theory of p-valid inference; (ii) we obtain Stalnaker's Thesis as a theorem while avoiding the well-known triviality results; (iii) we generalize Bayesian conditionalization to an updating principle for conditional sentences. The final result is a unified semantic and probabilistic (...) theory of conditionals with attractive results and predictions. (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)

Many philosophers sympathetic with a Humean understanding of laws of nature have thought that, in the final analysis, the fundamental laws will include not only the traditional dynamical equations, but also two additional principles: the Past Hypothesis and the Statistical Postulate. The former says that the universe began in a particular very-low-entropy macrostate M(0), and the latter posits a uniform probability distribution over the microstates compatible with M(0). Such a view is arguably vindicated by the orthodox Humean Best System Account (...) (BSA). However, I argue here that recent developments of the BSA render the Past Hypothesis otiose. In particular, the trend among Humeans toward a more pragmatic view of laws — according to which the best system is the one that is maximally effective at helping creatures like us amplify our information about the world — does not support the idea that the Past Hypothesis is a law of nature. (shrink)

Speakers typically use the sentence “I will go to the store” to simultaneously express an intention to go to the store and a belief that they will go to the store. This is consonant with two popular theses about intentions: first, intending to j implies believing that one will j; second, intending to j commits one to j-ing. In this paper, I argue that at least one of these theses is false. I do so by exploring what speakers express when (...) they utter a sentence with a slightly different form, like “I will probably go to the store” in a typical situation. After laying down a framework for thinking about this sort of communication, I explore some different things speakers might express with this sentence in different situations. Most importantly, I argue that in some typical situations speakers express either ordinary intentions but not beliefs or partial intentions that don’t commit them to performing the intended action. Either way, at least one of the popular theses is false. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their (...) performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

The explanation for everything in Nature, everything in human history, future, and-or, past, is the conservation of a circle, proven by, the circular-linear relationship between, the solstice and the equinox.

Космовізі — це термін, який має означати набір основ, з яких виникає системне розуміння Всесвіту, його складових як життя, світу, в якому ми живемо, природи, людського феномену та їхніх взаємозв’язків. Таким чином, це галузь аналітичної філософії, що живиться науками, метою якої є це сукупне та епістемологічно стійке знання про все, що ми є і що містить у собі, що оточує нас і що будь-яким чином до нас відноситься. Це щось таке ж давнє, як людська думка, і, окрім використання елементів наукової (...) космології, воно охоплює все у філософії та науці, що стосується Всесвіту та життя. Космогляд — це не набір ідей, гіпотез і припущень, а система, заснована на спостереженнях, аналізі, доказах і демонстраціях. Жодне космобачення не має на меті визначати, встановлювати чи пропонувати, а лише розуміти, аналізувати та інтерпретувати. Кожен з нас будує і транспортує своє космогляд протягом життя, не встановлюючи форми, як фон для нашого мислення і поведінки . Лінгвістично термін «космовізія» походить від німецької мови, що еквівалентно поняттю « Weltanschauung», яке використовували кілька філософів. Однак цей лінгвістичний зв’язок незастосовний, оскільки він суперечить тому, що ми пропонуємо як космовізію. Це німецьке слово відноситься до дологічного або протоекспериментального бачення реальності з інтуїтивним контекстом і далеко не критичним знанням, яке ще не існувало на момент його формулювання. Безсумнівно, космовізії, у тому сенсі, як ми їх розуміємо, містять і використовують ці протоекспериментальні або до-логічні елементи, які включають історію, колективне несвідоме та всі архетипи, які ми носимо. Однак у концепції, яку ми тут застосовуємо, космовізія виходить далеко за межі цього змісту, по-перше, постійно підпорядковуючи його теперішньому критичному мисленню і, нарешті, роблячи аналітичний досвід (а не саму думку чи інтуїцію) своїм справжнім всесвітом. У цій роботі ми прагнемо окреслити космогляд, заснований на реаліях, які пропонує сьогодні наука. Ми ніколи не пропонуємо займатися наукою; або теоретизувати філософію, але ми завжди будемо прагнути отримати їхню підтримку або, принаймні, захистити їх від когнітивних викривлень, які ми зазвичай несемо. (shrink)

The usefulness of the statistic known as the p-value, as a means of quantify-ing the strength of evidence for the presence of an effect from empirical data has long been questioned in the statistical community. In recent years there has been a notable increase in the awareness of both fundamental and practical limitations of the statistic within the target research fields, and especially biomedicine. In this article I analyse the recently published article which, in summary, argues that with a better (...) understand-ing and thus more appropriate use of the statistic, many of the aforementioned limitations can be addressed. In particular, I demonstrate that the (often implicit) premises of this counterargument are questionable, in some cases arguably inconsistent, and that therefore the counterargument provides little if any justification for the continued use of the p-value. Additionally, my analysis should help researchers seeking to interpret their empirical data by illustrating the nuanced nature and the multiplicity of statistical, methodological, and epistemological issues which must be considered in this process. (shrink)

This book puts forward a novel, unified cognitive account of skeptical doubt. Historically, most philosophers have tried to tackle this difficult topic by directly arguing that skeptical doubt is false. But N. Ángel Pinillos does something different. He begins by trying to uncover the hidden mental rule which, for better or worse, motivates our skeptical inclinations. He then gives an account of the broader cognitive purpose of having and applying this rule. Based on these ideas, he shows how we can (...) give a new response to the traditional problem of global skepticism. He also argues that philosophical skepticism is not just something that comes up during philosophical reflection, as David Hume, Charles Sanders Peirce and other philosophers have urged. Instead, it is of great practical significance. The rule which produces skepticism may itself be operative in certain pathologies such as obsessive-compulsive disorder, in creative endeavors, and in conspiratorial thinking. The rule can also explain some of our reluctance to trust statistical evidence, especially in legal settings. More broadly, this volume aims to breathe new life into a classic problem in philosophy by tackling it from a new perspective and exploring new areas of application. The book will be of interest to philosophers, psychologists and anyone interested in the human capacity to doubt and to question our beliefs. (shrink)

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons (...) to be uncertain about updating, rationality can require you to prefer ignorance. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...) reduced to probabilities, but deriving these probabilities involves more than just statistics. (shrink)

It is a common opinion that chance events cannot be understood in causal terms. Conversely, according to a causal view of chance, intersections between independent causal chains originate accidental events, called “coincidences”. Firstly, this book explores this causal conception of chance and tries to shed new light on it. Such a view has been defended by authors like Antoine Augustine Cournot and Jacques Monod. Second, a relevant alternative is provided by those accounts that, instead of acknowledging an intersection among causal (...) lines, claim to track coincidences back to some common cause. Third, starting from Herbert Hart and Anthony Honoré’s view of coincidences (Causation in the Law. Clarendon Press, Oxford, 1959). This book provides a more detailed account of coincidences, according to which coincidental events are hybrids constituted by ontic (physical) components, which is the intersection between independent causal chains, plus epistemic aspects, including but not limited to, access to information, expectations, relevance, significance, desires, which in turn are psychological aspects. -/- The main target of the present work is to show that the epistemic aspects of coincidences are, together with the independence between the intersecting causal chains, a constitutive part of coincidental phenomena. This book aims to introduce and discuss recent work in psychology concerning one’s judgment about coincidences; this data offers further materials and reasons to reflect upon our understanding of coincidences and to refine our hybrid conception. (shrink)

I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable _A_ and _B_. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables _A_ and _B_, so this is _AB_-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the (...) _AB_-entangled states as amplitude non-factorisable states. In the tensor product case, _AB_-entanglement implies standard entanglement, but not vise verse. _AB_-entanglement for dichotomous observables is equivalent to their correlation, i.e., \(\langle AB\rangle _{\psi} \not = \langle A\rangle _{\psi} \langle B\rangle _{\psi}.\) We describe the class of quantum states that are \(A_{u} B_{u}\) -entangled for a family of unitary operators (_u_). Finally, observables entanglement is compared with dependence of random variables in classical probability theory. (shrink)

Wlodek Rabinowicz suggested in an e-mail conversation (2001) to me that one might be able to use a particular Hats Puzzle to make a Dutch Book against a group of individually rational persons. I present a fanciful story here that has the same structure as Rabinowicz’s Dutch Book.

The treatise on justice in Nicomachean Ethics 5 reports that the 6th C. sage Bias claimed that “ruling shows the man” (ἀρχὴ ἄνδρα δείξει [EN 5.1.1130a1–2]). How ought we understand such a claim? Prominent, in the last thirty years, are interpretations that claim that Aristotle espouses a doctrine of “political naturalism” that views the political community as “natural” (rather than a social contract, like the conventionalism found in theorists such as Hobbes, Locke, and Rousseau) in which individuals make quasi-rights claims (...) against others, including those in political power who rule over them, based on a natural teleology that governs humans. Rather than interpret Bias’ pithy remark through the anachronistic hermeneutical lens of “political naturalism” (a term that appears nowhere in Aristotle’s writings), my book examines the remark (and Aristotle’s philosophy of human things more generally) within an historic-critical hermeneutical framework that aims to understand Aristotle’s treatises within the historical context of 4th C. BCE Greece. The book includes chapters on both Nicomachean Ethics 5 and all books of the Politics. (shrink)

Many philosophers have been attracted to a restricted version of the principle of indifference in the case of self-locating belief. Roughly speaking, this principle states that, within any given possible world, one should be indifferent between different hypotheses concerning who one is within that possible world, so long as those hypotheses are compatible with one’s evidence. My first goal is to defend a more precise version of this principle. After responding to several existing criticisms of such a principle, I argue (...) that existing formulations of the principle are crucially ambiguous, and I go on to defend a particular disambiguation of the principle. According to the disambiguation I defend, how we should apply this restricted principle of indifference sensitively depends on our background metaphysical beliefs. My second goal is to apply this disambiguated principle to classical skeptical problems in epistemology. In particular, I argue that Eternalism threatens to lead us to external world skepticism, and Modal Realism threatens to lead us to inductive skepticism. (shrink)

I argue for a connection between two debates in the philosophy of probability. On the one hand, there is disagreement about conditional probability. Is it to be defined in terms of unconditional probability, or should we instead take conditional probability as the primitive notion? On the other hand, there is disagreement about how additive probability is. Is it merely finitely additive, or is it additionally countably additive? My thesis is that, if conditional probability is primitive, then it is not countably (...) additive. (shrink)

Climate scientists often apply statistical tools to a set of different estimates generated by an “ensemble” of models. In this paper, I argue that the resulting inferences are justified in the same way as any other statistical inference: what must be demonstrated is that the statistical model that licenses the inferences accurately represents the probabilistic relationship between data and target. This view of statistical practice is appropriately termed “model-based,” and I examine the use of statistics in climate fingerprinting to show (...) how the difficulties that climate scientists encounter in applying statistics to ensemble-generated data are the practical difficulties of normal statistical practice. The upshot is that whether the application of statistics to ensemble-generated data yields trustworthy results should be expected to vary from case to case. (shrink)

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms.

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called generalized stochastic systems, collectively encompass many important kinds of stochastic processes, including Markov chains and random dynamical systems. This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system. This theorem therefore leads to a new formulation of (...) quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability formulations. The theorem also provides a first-principles explanation for why quantum systems are based on the complex numbers, Hilbert spaces, linear-unitary time evolution, and the Born rule. In addition, the theorem suggests that by selecting a suitable Hilbert space, together with an appropriate choice of unitary evolution, one can simulate any generalized stochastic system on a quantum computer, thereby potentially opening up an extensive set of novel applications for quantum computing. (shrink)