This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (as (...) in Condorcet's paradox) are in large electorates. (shrink)

This is one of the best popular cosmology books ever written and Guth is now (2016) a top physics Professor at MIT. He tells the extremely complex story of inflation and related areas of particle physics in such an absorbing style that it reads like a detective novel-in fact, it is a detective novel-how he and others found out how the universe started! The interweaving of his personal story and that of many colleagues along with their photos and many wonderfully (...) clear diagrams allows just the right amount of relaxation from the intensity of the physics. In places the style reminds one of Watson´s famous book ``The Double Helix``. He tells how his work on magnetic monopoles and spontaneous symmetry breaking led to the discovery of the inflationary theory of the very early universe (ca. 10 to minus 35 seconds!). -/- Along the way you will learn many gems that should stay with you a long time such as: the observed universe(e.g., everything the Hubble telescope etc. can see out to ca. 15 billion light years when the universe began) is likely just a vanishingly tiny part of the entire inhomogeneous universe which is about 10 to the 23rd times larger; the big bang probably took place simultaneously and homogeneously in our observed universe; there probably have been and will continue to be an infinite number of big bangs in an infinite number of universes for an infinite time; when a bang happens, everything(space, time, all the elements) from the previous universe are destroyed; the stretching of space can happen at speeds much greater than the speed of light; our entire observed universe lies in a single bubble out of an endless number so there may be trillions of trillions just in our own entire(pocket) universe(and there may be an endless number of such); none of these infinite number of universes interact-i.e., we can never find out anything about the others; each universe started with its own big bang and will eventually collapse to create a new big bang; all this implies that the whole universe is fractal in nature and thus infinitely regresses to ever more universes(which can lead one to thinking of it as a giant hologram); disagreements between the endless(hundreds at least) variations of inflation are sometimes due to lack of awareness that different definitions of time are being used; some theories suggest that there was a first big bang but we can never find out what happened before it; nevertheless it appears increasingly plausible that there was no beginning but rather an eternal cycle of the destruction and creation, each being the beginning of spacetime for that universe; to start a universe you need about 25g of matter in a 10 to minus 26cm diameter sphere with a false vacuum and a singularity(white hole). -/- He deliberately spends little time on the endless variants of inflation such as chaotic, expanded and supernatural inflation or on dark matter´, supersymmetry and string theory, though they were well known at the time as you can find by reading other books such as Michio Kaku´s `Hyperspace` (see my review) and countless others. Of course much has happened since this book appeared but it still serves as an excellent background volume so cheap now it’s free for the cost of mailing. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

The Buddhist denial of the world seems hard to defend if it is confronted with empirical data. Surveys on subjective life satisfaction consistently report that the majority is satisfied with their lives. Is the desire to escape from the cycle of rebirth a sign of risk-aversion or even irrationality? How would an impartial observer evaluate the world? -/- An impartial view is achieved by interpreting the surveys on life satisfaction as probability distributions for life’s risks and chances. It turns (...) out that there is no indisputable metric for measuring risks and no reliable forecast. Given this uncertainty the denial of the world cannot easily be dismissed as being irrational. (shrink)

Interest in idealism has increased substantially since the publication of Sprigge’s Vindication of Absolute Idealism in 1984,1 and again with more vigor over the last decade in the context of the mind-body problem and panpsychism. This will probably not come as a surprise to objective idealists, among which Vittorio Hosle has proposed that philosophy cycles through stages with some form of idealism as end point of each cycle.2 More recently, David Chalmers mused about a corresponding development in the worldview (...) of single individuals from materialism over dualism and panpsychism to idealism.3 Traditional accounts of idealism include for instance those of Plato, Plotinus, Leibniz, Berkeley, or Hegel. An overview of contemporary approaches is given in the article by Chalmers, where he mentions amongst others a recent collection of essays on idealism,4 but also for instance the (recently extended5) works of Philip Goff on Russellian monism.6 A more classically oriented collection of works on idealism was edited by Hosle and Suarez Muller.7 In his article ‘Idealism and the Mind-Body Problem’, David Chalmers presents a classification of possible versions of idealism with the goal of assessing the prospects of idealism in the context of the mind-body problem without having to pay too much attention to its ‘historical baggage’. This goal seems to me highly laudable and the resulting classification an important contribution to the contemporay discussion. In addition, the conclusions drawn from the subsequent analysis seem very plausible from the viewpoints of dualistic, panpsychistic and similar thinking. I nevertheless believe that the presented classification is not really adequate to capture the core of traditional idealistic thinking, which in turn leads to somewhat distorted conclusions about the opportunities for idealism to play a role for understanding the mind-body problem: First, the distinction between micro- macro- and cosmic idealism ist not fitting well into the idealistic venture. Instead, idealism is artificially reduced to a bad alternative to panpsychism. Secondly, the initially mentioned, but afterwards not discussed again difference between subjectinvolving and non-subject-involving idealism needs to be further extended, to account for the special role of subjects in traditional accounts of objective idealism. To elaborate on this, I will first give a short summary of Chalmers classification and some of the mentioned problems with idealism. Afterwards I will come back to my two objections in more detail. (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)

Marie Oldfield, Pro Bono Economics & Refugee Council. Over half the total applications for asylum the UK receives each year are initially rejected, yet nearly a third of these initial rejections are subsequently overturned on appeal. This process that fails to get decisions right first time imposes significant costs, not just on the applicants themselves, but also more widely on UK taxpayers. Asylum seekers are not entitled to welfare benefits nor employment except in some limited cases, and are often placed (...) in unsuitable conditions with lack of appropriate support to prepare their case for asylum. These unfortunate circumstances mean that they are unable to gather and present all the required evidence first time, even when the case for asylum is legitimate. As a result, the application is rejected and thus begins a cycle of appeals that might eventually lead to a successful outcome for the asylum seeker but will, in the process, burden the taxpayer with unnecessary administrative cost and cause the asylum seeker needless distress and prevent them from accessing suitable economic opportunities. • Our study estimates that there are approximately 4,000 initial rejections that are successfully appealed each year and, with each appeal incurring direct administrative costs of around £1,000, the price tag of incorrect initial decisions adds up to a hefty £4 million per year in unnecessary administrative costs alone. • There are other costs, too, that negatively impact asylum seekers and taxpayers, albeit in a more indirect manner. The longer the appeals process is dragged out, the more delay there is to successful asylum seekers entering the labour market which means lost economic activity and forgone tax revenue for the Exchequer. Long periods of unemployment also result in skills attrition and lower the probability of the asylum seeker successfully entering the labour market in the future. • A lengthy appeals process heightens stress and worsens mental health in asylum seekers, a group arguably already more vulnerable on this front. Unnecessary human suffering aside, there is also a monetary cost borne by the taxpayer should NHS mental health services become involved. Thus, there is a pressing and viable case for providing asylum seekers a stable environment in which to complete their applications for asylum. This would increase the likelihood of reaching correct decisions in the first instance, avoid unnecessary administrative costs of an arduous appeals process, enable successful asylum seekers to access the labour market and contribute to the Exchequer, and avoid placing extra demands on already strained NHS mental health services. (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)

The Mach-Zehnder Interferometer (MZI) is chosen to illustrate the long-standing wave-particle duality problem. Why is which-way (welcher weg) information incompatible with wave interference? How do we explain Wheeler’s delayed choice experiment? Most crucially, how can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? The position advanced is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on (...) half-silvered mirrors) or diffracts (in pinholes or slits). Then there are photon probability waves that do diffract and can reinforce or cancel. Photon kinetic energy is oscillatory; its cycles require/occupy time. E = mc2 suggests that kinetic energy is physically real as occurrence in time just as rest mass is physically real as existence in space; both are quantized and both occupy/require a dimension for their occurrence or existence. Photon kinetic energy (KE) thus resides in time, but is still present/available for interactions (events) in space; rest mass (e.g., your desk) resides in space but is still present/available for interactions (events) in time. While photon probability waves progress in space and diffract there, photon KE resides in time and never diffracts in space; at reception it always arrives whole and imitates particle impact without being a particle. Photon probability waves are real; they diffract in space. Acknowledging that the photon has two identities (residing energy and progressing probability), explains photon dual nature. And wave-particle duality is central to quantum mechanics. Understanding it leads to new insights into entanglement, nonlocality and the measurement problem. A 30-minute video on nonlocality and photon dualism can be found by a google: search “youtube klevgard nonlocality”). (shrink)

In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...) Staffel and compare it to a recent competitor put forth by Moss. (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)

This paper articulates a way to ground a relatively high prior probability for grand explanatory theories apart from an appeal to simplicity. I explore the possibility of enumerating the space of plausible grand theories of the universe by using the explanatory properties of possible views to limit the number of plausible theories. I motivate this alternative grounding by showing that Swinburne’s appeal to simplicity is problematic along several dimensions. I then argue that there are three plausible grand views—theism, atheism, (...) and axiarchism—which satisfy explanatory requirements for plausibility. Other possible views lack the explanatory virtue of these three theories. Consequently, this explanatory grounding provides a way of securing a nontrivial prior probability for theism, atheism, and axiarchism. An important upshot of my approach is that a modest amount of empirical evidence can bear significantly on the posterior probability of grand theories of the universe. (shrink)

The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’s triviality proof, with (...) special attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be re-thought, and he presents alternative proposals. (shrink)

I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.

Descartes’ first book, 1618’s Compendium of Music, focuses on biomechanical reactions in the human body but also claims that the purpose of art is to arouse emotions. By the end of the 1630s, however, he had given up on precisely predicting how that arousal may occur. This article contends, though, that Descartes’ abandonment of that project is a result of using an inappropriate psychological model for such predictions. An appropriate model is developed in his last book, 1649’s The Passions of (...) the Soul. Especially by attending to generosity and desire, the probability of predicting aesthetic judgments is at least increased. In increasing it, Descartes’ abandonment need not be total. (shrink)

What are the probabilities that this universe is repeated exactly the same with you in it again? Is God invented by human imagination or is the result of human intuition? The intuition that the same laws/mechanisms (evolution, stability winning probability) that have created something like the human being capable of self-awareness and controlling its surroundings, could create a being capable of controlling all what it exists? Will be the characteristics of the next universes random or tend to something? All (...) these ques-tions that with different shapes (but the same essence) have been asked by human be-ings from the beginning of times will be developed in this paper. (shrink)

This article investigates the profound mysteries of consciousness and the afterlife, topics that have captivated humanity for centuries. Despite extensive scientific inquiry, the existence of an afterlife remains unverified, and the nature of consciousness poses significant challenges. This research presents innovative hypotheses through thought experiments grounded in empirical evidence and robust theoretical frameworks. It examines the complexities of consciousness, its intricate relationship with the brain, and advocates for interdisciplinary approaches that integrate physics, psychology, and philosophy. The study boldly posits the (...) likelihood of continuous consciousness post-death, arguing that existing evidence lends substantial support to this notion. Furthermore, it explores the practical implications of these insights, suggesting that understanding these phenomena could enhance human well-being and foster a more harmonious society. In essence, this article embarks on a quest to illuminate age-old questions surrounding consciousness and the afterlife. By employing novel methodologies, it seeks to offer fresh perspectives that may transform our understanding of existence and inspire positive advancements at both individual and societal levels. (shrink)

I discuss Richard Swinburne’s account of religious experience in his probabilistic case for theism. I argue, pace Swinburne, that even if cosmological considerations render theism not too improbable, religious experience does not render it more probable than not.

Modern humans are probably a product of social and anatomical preadaptations on the part of our Miocene australopithecine ancestors combined with the increasingly high amplitude, high frequency climate variation of the Pleistocene. The genus Homo first appeared in the early Pleistocene as ice age climates began to grip the earth. We hypothesize that this co-occurrence is causal. The human ability to adapt by cultural means is, in theory, an adaptation to highly variable environments because cultural evolution can better track rapidly (...) changing environments than can genes. High resolution ice and sediment cores published in the early 1990s showed the last ice age was characterized by high amplitude millennial and submillenial scale variation, exactly the sort of variation mathematical models suggest should favor a costly capacity for culture. More recent cores suggest that over the last several 100 thousand year glacial cycles the amount of millennial scale variation has increased rather dramatically in parallel with increases in hominin brain size and sophistication of the artifacts they made. (shrink)

The National Library of France owns an uncommon illuminated manuscript of the Book of Job : the Parisinus graecus 135. Written in Greek in 1361/62, it is illustrated with a very large iconographic cycle , which combines Byzantine and gothic styles. The examination of the historical background allows us to bring forth the general meaning of the manuscript and to locate its origin with some probability in the Papal entourage and the Byzantine latinophile circles. The analysis of the iconographic (...) cycle of the manuscript shows that it is likely inspired by the theology developed in the literal commentary of Thomas of Aquinas on the Book of Job. Remarkably, this author is intensively translated in Greek in the middle of the fourteenth century in Byzantium under the aegis of the Emperor John VI Cantacuzenus. (shrink)

Karl Popper discovered in 1938 that the unconditional probability of a conditional of the form ‘If A, then B’ normally exceeds the conditional probability of B given A, provided that ‘If A, then B’ is taken to mean the same as ‘Not (A and not B)’. So it was clear (but presumably only to him at that time) that the conditional probability of B given A cannot be reduced to the unconditional probability of the material conditional (...) ‘If A, then B’. I describe how this insight was developed in Popper’s writings and I add to this historical study a logical one, in which I compare laws of excess in Kolmogorov probability theory with laws of excess in Popper probability theory. (shrink)

Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order that they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 [2010]: 793–794), Jake H. O’Connell presents a statistical analysis of this argument, according to which the (...) probability of this correspondence occurring by chance is lower than 1%. O’Connell concludes that it is more than 99% probable that this correspondence is the result of Papias copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence, overstates the correspondence between John and Papias, wrongly assumes that if Papias did not know John he ordered the disciples randomly, and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning. (shrink)

A theory of cognitive systems individuation is presented and defended. The approach has some affinity with Leonard Talmy's Overlapping Systems Model of Cognitive Organization, and the paper's first section explores aspects of Talmy's view that are shared by the view developed herein. According to the view on offer -- the conditional probability of co-contribution account (CPC) -- a cognitive system is a collection of mechanisms that contribute, in overlapping subsets, to a wide variety of forms of intelligent behavior. Central (...) to this approach is the idea of an integrated system. A formal characterization of integration is laid out in the form of a conditional-probabilitybased measure of the clustering of causal contributors to the production of intelligent behavior. I relate the view to the debate over extended and embodied cognition and respond to objections that have been raised in print by Andy Clark, Colin Klein, and Felipe de Brigard. (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)

A few purported counterexamples to the Adams thesis have cropped up in the literature in the last few decades. I propose a theory that accounts for them, in a way that makes the connections between indicative conditionals and counterfactuals clearer.

We find a simple counterfactual acceptable, it is argued, to the extent that (i) our probability of the consequent under the thought experiment of counterfactually supposing the antecedent is high, (ii) provided the latter is on-topic with respect to the former. Counterfactual supposition is represented by Lewisian imaging. Topicality, by an algebra of subject matters. A topic-sensitive probabilistic logic is then provided, to reason about the acceptability of simple counterfactuals.

Horizontal gene transfer (HGT) has been a paramount mechanism of interest in recent literature addressing the origins of biological evolution. However, research on lightning-triggered electroporation represents the innovative and still insufficiently grasped approach to HGT (Kotnik, 2013). On the other hand, prebiotic synthesis is a fundamental process for chemical evolution. Recently, the effects of volcanic lightning on nitrogen fixation and phosphate reduction have also been considered (NavarroGonzález and Segura, 2004). This paper aims to present a top-down approach to the question (...) of the origin of life on early Earth. By considering the conditions necessary for the emergence of biological and chemical evolution, emphasizing electrostatic discharges, we will attempt to link previous theoretical and experimental research. Furthermore, we will present a recent endeavor at applying the Drake equation to calculating the probability of volcanic lightning impact on the prebiotic synthesis and derive a similar use in estimating the contribution of lightning to HGT (Weaver, 2013). We will also display that choosing a type of probability appropriate for the context of life sciences is not necessarily a quantitative issue. Finally, we will show that significant conceptual constraints, like determining the relevant factors and sources of uncertainty when considering the origin of life on early Earth, are fundamentally philosophical issues. We hope that the results of our research – deriving Drake’s equation in the domain of chemical evolution and considering Bayesian and counterfactual types as potentially more suitable candidates for calculating probabilities in the evolutionary framework – will contribute to developing new discussions in life sciences. (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)

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if (...) in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method’s sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results. (shrink)

Some recent work in philosophy of religion addresses what can be called the “axiological question,” i.e., regardless of whether God exists, would it be good or bad if God exists? Would the existence of God make the world a better or a worse place? Call the view that the existence of God would make the world a better place “Pro-Theism.” We argue that Pro-Theism is not implausible, and moreover, many Theists, at least, (often implicitly) think that it is true. That (...) is, many Theists think that various good outcomes would arise if Theism is true. We then discuss work in cognitive science concerning human cognitive bias, before discussing two noteworthy attempts to show that at least some religious beliefs arise because of cognitive bias: Hume’s, and Draper’s and Nichols’s. We then argue that, as a result of certain cognitive biases that result when good outcomes might be at stake, Pro-Theism causes many Theists to inflate the epistemic probability that God exists, and as a result, Theists should lower the probability they assign to God’s existence. Finally, based our arguments, we develop a novel objection to Pascal’s wager. (shrink)

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...) probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

In this paper it is shown that Lewis' MWD (might/would duality) and imaging principles lead to wildly implausible probability assignments for would counterfactuals.

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)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or (...) objective Bayesianism or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the (...) introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

In his recent book Warranted Christian Belief (2000), Alvin Plantinga argues that the defender of naturalistic evolution is faced with adefeater for his position: as products of naturalistic evolution, we have no way of knowing if our cognitive faculties are in fact reliably aimed at the truth. This defeater is successfully avoided by the theist in that, given theism, we can be reasonably secure that out cognitive faculties are indeed reliable. I argue that Plantinga’s argument is ultimately based on a (...) faulty comparison, that he is comparing naturalistic evolution generally to one particular model of theism. In light of this analysis, the two models either stand or fall together with respect to the defeater that Plantinga offers. (shrink)

The paper aims to explore what it means for something to be a social cycle, for a theory to be a social cycle theory, and to offer a suggestion for a simple, yet, we believe, fundamentally grounded schema for categorizing them. We show that a broad range of cycle theories can be described within the concept of disruption and adjustments. Further, many important cycle theories are true endogenous social cycle theories in which the theory provides a reason why the cycle (...) should recur. We find that many social cycle theories fit with a two-population disruption and adjustment model similar to the well-known predator-prey model. This implies that a general modeling framework could be established for creating agent-based models of many social cycle theories. (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)

In recent papers, Peter Carruthers and others have argued that the feeling of uncertainty is not metacognitive (i.e., it is not elicited by second-order cognitive appraisals) but is elicited solely by first-order likelihood estimates—a probability account of the feeling of uncertainty. In this paper, I make a case for why a probability account is sufficient to explain neither the feeling of uncertainty nor the feeling of certainty in self-reflecting humans. I argue first that humans’ feelings of (un)certainty vary (...) in ways that their probability estimates on the matter do not, and second that probability accounts elide the essentially epistemic nature of epistemic feelings. (shrink)

Sunohara Yuuri and Akita Masami’s series of six seppuku films (1990) are solely constituted by images of fictionalized death, revolving around the prolonged self-torture of a lone figure committing harakiri. I contend that the protagonist’s auto-immolation mirrors a formal death, each frame ‘killing’ the moment it represents. My analysis aims to explore how the solipsistic nature of selfhood is appositely symbolized by the isolation of the on-screen figures and the insistence with which the six films repeat the same scenario of (...) protracted agony across the cycle. The centralization of suffering, I argue, parallels the distance between viewer and image with the isolating nature of embodied existence. Thus, this article seeks to probe the relationship between form and content, asking what the image of death reveals about the death of the image. -/- . (shrink)

Providing equitable food security for a growing population while minimizing environmental impacts and enhancing resilience to climate shocks is an ongoing challenge. Here, we quantify the resource intensity, environmental impacts and nutritional output of a small (0.075 ha) low-input subsistence Mediterranean agroecological farm in a developed nation that is based on intercropping and annual crop rotation. The farm provides one individual, the proprietor, with nutritional self-sufficiency (adequate intake of an array of macro- and micro-nutrients) with limited labor, no synthetic fertilizers (...) or herbicides, and zero waste, effectively closing a full farm-table-farm cycle. We find that the agroecological farm outperforms conventional farming as practiced in the same country in terms of both lower environmental burdens, across all examined environmental metrics (63% lower on average) per kg produce, and higher nutritional score (66% higher on average). Per equal farmland, the environmental lopsidedness was even higher (79% lower than conventional farming on average), with nearly the same nutritional score (3% lower on average). Moreover, when considering total land area, which includes farmland and supporting non-agricultural lands, as well as postgate impacts and food losses, the advantage of the agroecological system over conventional farming is even more pronounced. Situated within a Mediterranean region that is undergoing rapid climate change, this food system is a unique case study of nutrition- and environment-oriented food production system. While its deployment potential is limited by lack of supportive policies, it nonetheless represents one of the most starkly bold alternatives to current food systems. (shrink)

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)

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion (...) on Independence generalizes to other views that also violate Independence. (shrink)

This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (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.

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments (...) for the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

A common objection to probabilistic theories of causation is that there are prima facie causes that lower the probability of their effects. Among the many replies to this objection, little attention has been given to Mellor's (1995) indirect strategy to deny that probability-lowering factors are bona fide causes. According to Mellor, such factors do not satisfy the evidential, explanatory, and instrumental connotations of causation. The paper argues that the evidential connotation only entails an epistemically relativized form of causal (...) attribution, not causation itself, and that there are clear cases of explanation and instrumental reasoning that must appeal to negatively relevant factors. In the end, it suggests a more liberal interpretation of causation that restores its connotations. Una objeción común a las teorías probabilísticas de la causalidad es que aparentemente existen causas que disminuyen la probabilidad de sus efectos. Entre las muchas respuestas a esta objeción, se le ha dado poca atención a la estrategia indirecta de D. H. Mellor (1995) para negar que un factor que disminuya la probabilidad de un efecto sea una causa legítima. Según Mellor, tales factores no satisfacen las connotaciones evidenciales, explicativas e instrumentales de la causalidad. El artículo argumenta que la connotación evidencial sólo implica una forma epistémicamente relativizada de atribución causal y no la causalidad misma, y que hay casos claros de explicación y razonamiento instrumental que deben apelar a factores negativamente relevantes. Se sugiere una interpretación más liberal de la causalidad que reinstaura sus connotaciones. (shrink)

I will argue that MLS theory does not provide a complete, self- sufficient approach to theorizing about evolutionary transitions. As a formal, mathematical theory about evolution within a population, it presupposes but does not address the material structure of the population that realizes the model. An MLS model might tell us whether a cooperative trait could be- come fixed in a population, for example, but it won’t be able to explain how the cooperation actually works to produce an adaptive effect (...) on the group’s fitness. It also won’t be able to account for the sources of variety in the pos- sible modes of cooperation available to a population. MLS theory can tell us when fitness has transferred from one level of units to another, but it can give misleading answers unless we have some other, principled guide for picking out units (Clarke 2012; Clarke 2014). Furthermore, it is commonly acknowl- edged among biologists that actually measuring the fitness of an individual— sometimes even obtaining and interpreting proxy measurements—is diffi- cult in practice and prone to error (Hendry 2005; Orr 2009). Hence even if MLS theory were sufficient in principle, there would still be room for other approaches in practice that avoided the difficulties and limitations of depend- ing on fitness alone. (shrink)

Evolutionary theory (ET) is teeming with probabilities. Probabilities exist at all levels: the level of mutation, the level of microevolution, and the level of macroevolution. This uncontroversial claim raises a number of contentious issues. For example, is the evolutionary process (as opposed to the theory) indeterministic, or is it deterministic? Philosophers of biology have taken different sides on this issue. Millstein (1997) has argued that we are not currently able answer this question, and that even scientific realists ought to remain (...) agnostic concerning the determinism or indeterminism of evolutionary processes. If this argument is correct, it suggests that, whatever we take probabilities in ET to be, they must be consistent with either determinism or indeterminism. This raises some interesting philosophical questions: How should we understand the probabilities used in ET? In other words, what is meant by saying that a certain evolutionary change is more or less probable? Which interpretation of probability is the most appropriate for ET? I argue that the probabilities used in ET are objective in a realist sense, if not in an indeterministic sense. Furthermore, there are a number of interpretations of probability that are objective and would be consistent with ET under determinism or indeterminism. However, I argue that evolutionary probabilities are best understood as propensities of population-level kinds. (shrink)