A classical probabilistics explanation for a typical quantum effect in Hardy's paradox is demonstrated.

Topicality of the research topic. As a result of the COVID-19 pandemic, there is an increase in the instability of the structure of ecosocial systems. Technological innovations have led to a sharp deterioration in natural social ecodynamics. The aim of the research is the conceptual modeling of the proliferation of biopolitics from the social sphere to the field of international relations with the subsequent transformation into a systemic factor of the global evolutionary process. Research methods and results. The model is (...) based on our previously proposed concept of a three-module stable evolutionary strategy of technogenic civilization. In relation to the triple spiral of anthropo-socio-technogenesis, i.e., the historical development of the cultural-ecological niche of Homo sapiens, constructed by him, this means the following. Periods of stable progressive growth of evolutionary and civilizational success are replaced by periods of various scales crisis, up to civilizational or even biological-evolutionary singularity. During the crisis, the importance of the political factor increases sharply, and over the past 50 years, this primarily relates to the field of biopolitics. The regional differentiation of the biopolitical sphere reconstruction during the fight against the pandemic will inevitably complicate international relations not only between regions that belong to different cultural and civilizational types. Probably less so, the same problems will affect the reconciliation of differences caused by geopolitical, interethnic, religious and even economic (competition) reasons. The first phase of the adaptive civilizational response is to reduce the degree of connection between the individual socio-cultural elements of modern civilization, i.e., slowing down the globalization process and intensifying interregional conflicts of various contents. In particular, such contradictions will be most acute in the post-Soviet geopolitical space, where the conditions of the civilizational rift are imposed on the conflicts of the transition period. Due to the specifics of modern high technologies, the process will enter the phase of global socio-techno-ecological self-developing systems reconstruction, which includes man as its element. And the obvious conclusion will be the transition of the development of biopolitical issues to a new, no longer international, but global-evolutionary level. In our understanding, transbiopolitics is a political issue related to the rationalization of the global evolutionary process. The latter will become a bearing element of the global process of evolution of the noosphere with the subsequent complication and increase of cohesion between separate sociocultural types which are a part of system of the modern globalizing civilization. (shrink)

In recent decades, several authors have claimed that an epoch-making change in the development of science is taking place. A closer examination of this claim shows that these authors take different – and problematic – concepts of an epochal break as their points of departure. In order to facilitate an evaluation of the current development of science, I would like to propose a concept of an epochal change according to which it is not necessarily a discontinuous process that typically begins (...) in a subarea of the sciences, has far-reaching consequences for the entire system of the sciences, and can be observed by contemporaries as early as during its initial phase. Taking this concept as my point of departure, I discuss various candidates for the status of an epochal transformation in the recent development of the sciences. Although there are sound reasons to doubt that an epochal break is currently taking place, one must concede that the sciences are probably in a profound transformation, which could unfold in various directions, perhaps even leading to epoch-making new characterizations of the sciences. (shrink)

The author argues that consciousness may never be defined or explained with entities or their properties, neither with brains, neurons, and biomacromolecules, nor with particles, waves, and fields. Instead, the author proposes a system with matter, energy, and lives as its components, and with all its components defined as changes. Based on the systematic relationships among these three components, a triple definition or explanation of consciousness is reached: • Ontologically, consciousness is universal, since it is the systematic distinction between (...) matter and energy. • Epistemologically, consciousness is unique, since it is the energy systematically formalized, qualified, or diversified by the matter. • Semantically, consciousness is a meaningless language with lives as its only meaning. In other words, only lives are, but consciousness is not, the cause or effect of mental activities. From this definition or explanation, the author deduces that consciousness is the same as action, but not the same as mental states, especially not the same as the experiences of a unique self in its unique world. Therefore, the author argues that many theories of consciousness have explained something other than consciousness itself. (shrink)

An analysis of the physical implications of abstractness reveals the reality of three interconnected modes of existence: abstract, virtual and concrete, corresponding in physics to information, energy and matter. This triple-aspect monism clarifies the ontological status of subatomic quantum particles. It also provides a non-spooky solution to the weirdness of quantum physics and a new outlook for the mind-body problem. The ontological implications are profound for both physics and philosophy.

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.

This paper develops an information-sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional If A, then C equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that rational (...) agents update their credences via conditionalization. We offer a new rule of update, Hyperconditionalization, which agrees with Conditionalization whenever nonmodal statements are at stake but differs for modal and conditional sentences. (shrink)

I conjecture that the probability amplitudes of a quantum state are fractions of the Planck frequency, stemming from the rich dynamics at the Planck scale. This offers a means to indirectly measure the fundamental properties of quantum spacetime and potentially resolves the measurement problem.

The importance of this article for society lies in its exploration of the intersection between ethics and aesthetics as a foundation for quality education. In today's rapidly evolving and complex world, there is a pressing need to cultivate individuals who are not only knowledgeable but also ethically conscious and culturally sensitive. By integrating ethical and aesthetic considerations into educational practices, this article advocates for a holistic approach that fosters the full development of human personality and promotes a culture of peace. (...) Such an interdisciplinary approach to education can inspire both personal growth and social responsibility. It encourages the development of critical thinking, moral discernment, and a deeper appreciation for cultural diversity. As societies become increasingly interconnected, the ability to navigate ethical and aesthetic dimensions becomes crucial in nurturing well-rounded individuals capable of contributing positively to their communities and beyond. Ultimately, the insights presented in this article aim to reshape educational paradigms, making them more relevant and impactful in addressing the challenges of our time. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities (...) of conditionals violate standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory (...) and that the rival restrictor theory can avoid these problematic assumptions. In doing so, I argue that recent extensions of the triviality arguments to restrictor conditionals fail, making assumptions which are only justified on the operator theory. (shrink)

I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had (...) B as their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

Although probabilistic statements are ubiquitous, probability is still poorly understood. This shows itself, for example, in the mere stipulation of policies like expected utility maximisation and in disagreements about the correct interpretation of probability. In this work, we provide an account of probabilistic predictions that explains when, how, and why they can be useful for decision-making. We demonstrate that a calibration criterion on finite sets of predictions allows one to anticipate the distribution of utilities that a given policy (...) will yield. Based on this, we specify assumptions under which expected utility maximisation is a sensible decision criterion. We also introduce the notion of prediction methods, highlighting the dependence on schemes of abstraction, and argue that all probabilities are outputs of such prediction methods. This helps explain how the calibration criterion can be satisfied and shows that also supposedly objective probabilities are model-dependent. We compare our account of probability with conventional interpretations and show that it recovers key intuitions behind the latter. We, thus, provide a general account of what probabilities are and how they can enable successful decision-making under uncertainty. (shrink)

We have ignored for a century that the incompleteness of Quantum Theory (QT) is inseparable from the incompleteness of Special Relativity (RT). In this article, I claim that the latter has been gravely incomplete vis à vis the former from 1927 until today. But completing RT in the light of QT is not as simple as merely postulating nonlocality and stochasticity as “elements of reality” (which is de facto done by most physicists and pragmatic philosophers); otherwise, RT would not still (...) be in a “peaceful” conflict with QT after a century. Vice versa, I contend that QT is incomplete vis à vis RT, though not for the reasons claimed in the iconic EPR paper. We then show how to complete the Ontology, Foundation, and Structure of both RT and QT and merge them into an internally consistent embracive theory I call QR/TOPI. This theory offers a more cogent and simpler avenue to integrate RT with QT than positing exotic causal structures like ‘retrocausality’, ‘future-input dependence’, ‘superdeterminism’ – not to mention the extravagant ‘Many-Worlds’, ‘Many-Minds’, ‘Parallel-Lives’, and other interpretations of QT like Many-Histories, QBism, etc. -/- QR/TOPI provides the “radical conceptual renewal” wished by John Bell so as to integrate probability and nonlocality into an upgraded RT and, reciprocally, to integrate Frame-Invariance into QT while at the same time, as demanded by 2022 Nobel laureate Anton Zeilinger, providing basic physical meaning to the resulting encompassing theory. The old outcast notion of absolute simultaneity is resurrected without any conflict with Einstein’s relative simultaneity, while Frame-Invariance is preserved via our Quantumlike Transformation (QLT), which is an extension of the Lorentz Transformation (LT): QLT includes what LT excludes: nonlocality. -/- Section 1 examines the philosophical foundations of Space and Time, focusing on RT, its plethora of empirical validations, and the tenets which make it incompatible with QT. Section 2 incorporates stochasticity into RT. Sections 3 through 5 gradually introduce QR/TOPI for mono-, bi-, and tri-quanton systems, with full consideration of Bell Theorem, nonlocality, teleportation, and their implications. Section 6 attempts to review the current status quo. Section 7 makes the case for the incompleteness of RT and QT. Section 8 explains how to complete and integrate both theories so as to formally develop QR/TOPI. Finally, in Section 9, via multiple experimental setups, I zero in on Zeilinger’s basic question: “what does this really mean in a basic way?”. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

People are ‘biased toward the future’: all else being equal, we typically prefer to have positive experiences in the future, and negative experiences in the past. Several explanations have been suggested for this pattern of preferences. Adjudicating among these explanations can, among other things, shed light on the rationality of future-bias: For instance, if our preferences are explained by unjustified beliefs or an illusory phenomenology, we might conclude that they are irrational. This paper investigates one hypothesis, according to which future-bias (...) is explained by our having a phenomenology that we describe, or conceive of, as being as of time robustly passing. We empirically tested this hypothesis and found no evidence in its favour. Our results present a puzzle, however, when compared with the results of an earlier study. We conclude that although robust passage phenomenology on its own probably does not explain future-bias, having this phenomenology and taking it to be veridical may contribute to future-bias. (shrink)

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely (...) thought to undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work (...) in neuroscience and behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (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)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be (...) borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of (...) class='Hi'>probability through a heterogeneous sample of thinkers who adopted his interpretation. This sample consists of Frederick C. Benenson, Roy Harrod, Donald C. Williams, Henry E. Kyburg and David Stove. The ideas of Keynes prove to be adaptable to their diverse theories of probability. My discussion indicates both the robustness of Keynes’s probability theory and the importance of its influence on the philosophers whom I describe. I also discuss the Problem of the Priors. I argue that none of those I discuss have obviously improved on Keynes’s theory with respect to this issue. (shrink)

Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences (...) of human agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism. (shrink)

We will flip a fair coin infinitely many times. Al calls the first flip, claiming it will land heads. Betty calls every odd numbered flip, claiming they will all land heads. Carl calls every flip bar none, claiming they will all land heads. Pre-theoretically, it seems that Al's claim is infinitely more likely than Betty's, and that Betty's claim is infinitely more likely than Carl's. But standard, real-valued probability theory says that, while Al's claim is infinitely more likely than (...) Betty's, Betty's claim is exactly as likely as Carl's. I use John Conway's surreal numbers to capture these pre-theoretic judgements about the relative probabilities of Al's, Betty's, and Carl's claims. Surreal-valued probabilities also allow us to calculate precise numerical values for those claims. For instance, we will see that Betty's claim has a probability equal to the reciprocal of the product of the square root of cardinality of the continuum and the fourth root of 2. The article provides a 'user's guide' to surreal-valued probabilities and raises questions for further research. (shrink)

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- ditional counterparts) (...) cannot generate a sufficiently interesting logical system. Here, we will describe results dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams’s classical approach allow for the construction of a logic of evidential conditionals with distinctive fea- tures, which is also well-behaved and reasonably strong. (shrink)

A set D subset of V(G) is a dominating set of a graph G if for all x ϵ V(G)\D, for some y ϵ D such that xy ϵ E(G). A dominating set D subset of V(G) is called a connected dominating set of a graph G if the subgraph <D> induced by D is connected. A connected domination number of G, denoted by γ_c(G), is the minimum cardinality of a connected dominating set D. The triple repetition sequence denoted (...) by {S_n:n ϵ Z+} is a sequence of positive integers which is repeated thrice, i.e., {S_n}={1,1,1,2,2,2,3,3,3, ...}. In this paper, we construct a combinatorial explicit formula for the triple repetition sequence of connected domination numbers of a triangular grid graph. (shrink)

When examining the human being as a conscious being, we are still to arrive at an understanding of, firstly, the conditions required whereby physical processes give rise to consciousness and secondly, how consciousness is something fundamental to life as an intrinsic part of nature. Humans are complex organisms with myriad interacting systems whereby the convergence of the activities toward the support and development of the whole organism requires a high level of organisation. Though what accounts for the dynamic unity of (...) the human being? From an empirical perspective the question remains unanswered. The aim of this paper is to conceptually establish a fundamental biophysical organising principle to account for the unity and organisation of the human being. To this end I draw from David Bohm’s interpretation of quantum theory to provide an adapted and adjunct conceptual scheme in the form of a Triple-Aspect-Theory (TAT) of Being as a grounding ontology. David Bohm presented a holistic view of two interwoven orders of existence defined as the Explicate material world and the Implicate (quantum) enfolded world from which the former materialises. Consistent with David Bohm’s idea that matter at a fundamental level consists of a kind of protointelligence, the TAT facilitates a perspective based on aspect conditions of the human organism intended to furnish an explanation of the constitutive mechanism (TAT) inherent in the evolving human being. The TAT operates as an organising principle by which evolution inherently proceeds and maintains itself in an interactive relation between the Implicate and Explicate orders. The accumulated effect of natural selection is to produce adaptations, but without an organising principle: ‘Consciousness’, ‘Body-of-Experience’ and ‘Intellect-Reflective’ (the terms for the engaged coexistent aspects of being) it is argued could not occur. (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data (...) will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

In this paper, we illustrate some serious difficulties involved in conveying information about uncertain risks and securing informed consent for risky interventions in a clinical setting. We argue that in order to secure informed consent for a medical intervention, physicians often need to do more than report a bare, numerical probability value. When probabilities are given, securing informed consent generally requires communicating how probability expressions are to be interpreted and communicating something about the quality and quantity of the (...) evidence for the probabilities reported. Patients may also require guidance on how probability claims may or may not be relevant to their decisions, and physicians should be ready to help patients understand these issues. (shrink)

Stalnaker's Thesis about indicative conditionals is, roughly, that the probability one ought to assign to an indicative conditional equals the probability that one ought to assign to its consequent conditional on its antecedent. The thesis seems right. If you draw a card from a standard 52-card deck, how confident are you that the card is a diamond if it's a red card? To answer this, you calculate the proportion of red cards that are diamonds -- that is, you (...) calculate the probability of drawing a diamond conditional on drawing a red card. Skyrms' Thesis about counterfactual conditionals is, roughly, that the probability that one ought to assign to a counterfactual equals one's rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. This thesis also seems right. If you decide not to enter a 100-ticket lottery, how confident are you that you would have won had you bought a ticket? To answer this, you calculate the prior chance--that is, the chance just before your decision not to buy a ticket---of winning conditional on entering the lottery. The central project of this article is to develop a new uniform theory of conditionals that allows us to derive a version of Skyrms' Thesis from a version of Stalnaker's Thesis, together with a chance-deference norm relating rational credence to beliefs about objective chance. (shrink)

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero probability. Chapters (...) 3–6 discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both beliefs (...) are plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

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.

This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential even (...) for philosophers whose work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson (...) is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the (...) density matrices induced by the experiments or `measurements' is the Lüders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over ℤ₂, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over ℤ₂ that can model many characteristic non-classical results of QM. (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)

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided (...) that (ii) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)

Complexity may not be defined or explained with entities and properties. Instead, a system is proposed ontologically, epistemologically, and semantically as the definition or explanation in this paper, with matter, energy and lives as its components, and with all its components defined as changes, which might improve upon our prediction in/with complexity. -/- .

The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; (...) population size problems; equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities (...) are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

El presente artículo analiza los principales argumentos de la reacción comunitarista frente al liberalismo, debido a su enfoque individualista y su defensa del modelo contractual. Se destaca la presencia de una triple raíz que se hunde hasta la filosofía política de Aristóteles, Hegel y Marx. Finalmente, se analizarán los l ́ımites dela frontera entre ambas comprensiones de la política, as ́ı como los riesgos en que incurren las democracias modernas al omitir la presencia del libertarismo como ideología depositaria de (...) principios tanto liberales como comunitaristas. (shrink)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the (...) usefulness of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

This project retraces activations of Kierkegaard in the development of polit­ical theology. It suggests alternative modes of states of exception than those attributed to him by Schmitt, Taubes and Agamben. Several Kierkegaardian themes open themselves to 'something like pure potential' in Agamben, namely: living death, animality, criminality, auto-constitution, modification, liturgy, love and certain articulations of improbabilities. Attention is drawn to a modal ontology and auto-constitution at work in Kierkegaard's writings, as well as a complicated and indissociable operation between killing and (...) letting-live in legalist exceptionalism, comparable to similar functions found in Foucault regarding the biopowers and necropolitics of territorial and governmental apparatuses. It closes in consideration of Kierkegaard's critique of enumeration, large numbers, and statistical probability alongside contemporary tele-technoscientific social controls via the online datafication of people by surveillance or platform capitalisms. After Kierkegaard, such apparatuses are perhaps suspect as calculated to tranquilize humanity into more docile subhumans as it fools folk into becoming part of its numbers. (*Accompanying file includes only front matter, abstract, and endnotes*). (shrink)

Abstract. In this article is presented a model of the change of the probability of the global catastrophic risks in the world with exponentially evolving technologies. Increasingly cheaper technologies become accessible to a larger number of agents. Also, the technologies become more capable to cause a global catastrophe. Examples of such dangerous technologies are artificial viruses constructed by the means of synthetic biology, non-aligned AI and, to less extent, nanotech and nuclear proliferation. The model shows at least double exponential (...) growth of the probability of the global catastrophe which means that the accumulated probability of the catastrophe will grow from negligible to overwhelming at the period of a few doubling times of the technological capabilities. For biotech and AI, such doubling time roughly corresponds to the doubling period of Moore’s law and its analogues in other technologies and is around 2 years. Thus the global catastrophe in the exponential technologies world will most likely happen during a “dangerous decade”. Such a dangerous decade could start as early as in the 2020s. We also found that the double exponential growth in the model makes the model less sensitive to its initial conditions, like the number of dangerous agents or initial probabilities constants. The model also shows that smaller catastrophes could happen earlier than larger ones, and such a smaller catastrophe may be able to stop the technological growth before larger ones become possible, thus global risks will be self-limiting. However, if the growth of the number of dangerous agents will be very quick, the multiple smaller catastrophes could happen simultaneously and will be equal to a global catastrophe. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that (...) probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the (...) conventional wisdom about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

This paper argues that the technical notion of conditional probability, as given by the ratio analysis, is unsuitable for dealing with our pretheoretical and intuitive understanding of both conditionality and probability. This is an ontological account of conditionals that include an irreducible dispositional connection between the antecedent and consequent conditions and where the conditional has to be treated as an indivisible whole rather than compositional. The relevant type of conditionality is found in some well-defined group of conditional statements. (...) As an alternative, therefore, we briefly offer grounds for what we would call an ontological reading: for both conditionality and conditional probability in general. It is not offered as a fully developed theory of conditionality but can be used, we claim, to explain why calculations according to the RATIO scheme does not coincide with our intuitive notion of conditional probability. What it shows us is that for an understanding of the whole range of conditionals we will need what John Heil (2003), in response to Quine (1953), calls an ontological point of view. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect (...) whether it is the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)