Beauty Problem Research Articles

A Logical Analysis of Monty Hall and Sleeping Beauty

Hintikka and Sandu’s independence-friendly (IF) logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers’ argument.

Sleeping Beauty Goes to the Lab: The Psychology of Self-Locating Evidence

Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” (“halfers”) and those endorsing the “1/3 view” (“thirders”). The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do not fit either the “1/2 view” or the “1/3 view.” Human reasoners tend to acknowledge self-locating evidence as relevant, but discount its weight significantly. Accordingly, self-locating information may trigger more cautious judgments of confirmation than familiar kinds of statistical evidence. We also discuss how these results can advance the debate by providing a more nuanced and empirically grounded account or explication of the evidential impact of self-locating information.

Philosophy and the Problem of Beauty in Heidegger’s Translation of “Justice”

Philosophy and the Problem of Beauty in Heidegger’s Translation of “Justice”

The Problem

The Problem Ryan Wilson (bio) Some bitch, some rattle ice in stormy cocktails, some read or stare into their hands' artificial glow.The good-natured, whom no one likes, make conversation. Kids kick seat-backs; babies scream.This is the part where you find out exactly who you are, as much as you will ever know,Crammed like seeds into this invaluable lemon with all the dreamed escapes you cannot help but dream. There's something wrong, some unspecified glitch, but nobody will say just what it isKeeping you stranded among strangers here on the hot tarmac, waiting,Waiting for some pronouncement, some true words that will explain your prolonged absencesFrom the air above the clouds, from flight, from the oceanfront destination everyone's anticipating. It will not last forever, your time on the ground. At some point there will come a departure.Then clouded skies will recede like sunshine, like questions, like your toddler's sticky touch, and you will be [End Page 395] Wholly invisible to the earthlings you love, who love you, an arrow shot by some blind archerBeyond the endless traffic and grocery-store pharmacy lines, long-distance calls and doctors wincing thoughtlessly. For now, take solace in the presence of the known world's flawed, forgettable, flightless things;Bless the engine's troubled heart, the brief and inexplicably beautiful problem with the wings. [End Page 396] Ryan Wilson Ryan Wilson is the editor of Literary Matters and the author of The Stranger World (Measure Press, 2017), winner of the Donald Justice Poetry Prize. His work has appeared in Birmingham Poetry Review, First Things, Five Points, the Hopkins Review, the New Criterion, the Yale Review, Best American Poetry, and other publications. He teaches at the Catholic University of America. Copyright © 2018 The University of the South

The Snow White problem

The Snow White problem is introduced to demonstrate how learning something of which one could not have learnt the opposite (due to observer selection bias) can change an agent’s probability assignment. This helps us to analyse the Sleeping Beauty problem, which is deconstructed as a combinatorial engine and a subjective wrapper. The combinatorial engine of the problem is analogous to Bertrand’s boxes paradox and can be solved with standard probability theory. The subjective wrapper is clarified using the Snow White problem. Sample spaces for all three problems are presented. The conclusion is that subjectivity plays no irreducible role in solving the Sleeping Beauty problem and that no reference to centered worlds is required to provide the answer.

Bootstrap percolation, and other automata

Many fundamental and important questions from statistical physics lead to beautiful problems in extremal and probabilistic combinatorics. One particular example of this phenomenon is the study of bootstrap percolation, which is motivated by a variety of ‘real-world’ cellular automata, such as the Glauber dynamics of the Ising model of ferromagnetism, and kinetically constrained spin models of the liquid–glass transition.In this review article, we will describe some dramatic recent developments in the theory of bootstrap percolation (and, more generally, of monotone cellular automata with random initial conditions), and discuss some potential extensions of these methods and results to other automata. In particular, we will state numerous conjectures and open problems.

Role of Information and its Processing in Statistical Analysis

This paper discusses how real-life statistical analysis/inference deviates from ideal environments. More specifically, there often exist models that have equal statistical power as the actual data-generating model, given only limited information and information processing/computation capacity. This means that misspecification actually has two problems: first with misspecification around the model we wish to find, and that an actual data-generating model may never be discovered. Thus the role information - this includes data - plays on statistical inference needs to be considered more heavily than often done. A game defining pseudo-equivalent models is presented in this light. This limited information nature effectively casts a statistical analyst as a decider in decision theory facing an identical problem: trying best to form credence/belief of some events, even if it may end up not being close to objective probability. The sleeping beauty problem is used as a study case to highlight some properties of real-life statistical inference. Bayesian inference of prior updates can lead to wrong credence analysis when prior is assigned to variables/events that are not (statistical identification-wise) identifiable. A controversial idea that Bayesianism can go around identification problems in frequentist analysis is brought to more doubts. This necessitates re-defining how Kolmogorov probability theory is applied in real-life statistical inference, and what concepts need to be fundamental.

When Sleeping Beauty First Awakes

Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga’s seminal paper on the subject. Elga’s intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a three-dimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.

David Konstan, Beauty: The Fortunes of an Ancient Greek Idea

Inês Morais The problem of beauty is vital to all those concerned with art. Even in an era in which a lot of the art that is produced seems divorced from the notion of beauty, the public and, with the public, common sense, is still sensitive to the beautiful creations of artists.

Contents

The paper proposes a novel principle of rational self-locating belief that refers to the epistemic agent’s causal context. The principle is motivated and applied to some of the most-discussed problems of self-locating belief including the Doomsday Argument, the Serpent’s Advice scenario, the Presumptuous Philosopher problem, the Sleeping Beauty problem, and the problem of confirmation in the Everett interpretation. It is shown to yield plausible verdicts in all these cases.

Sleeping Beauty’s Credences

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment.

Does Artwork Have to be Beautiful?

Beauty’s relation to art work is a contentious problem for the philosophy of art. The problem is not new to the history of philosophy. Hume and Kant attempted to tackle the question in the modern era. Contemporary philosophers have broadened the definition of art to include works that stretch modern philosophers’ conceptions. With philosophers shifting their definition from the object to the subject, they have effectively marginalized beauty in place of another good or valued concept. Considering the status quo, this paper argues that beauty is a necessary condition for art work. It argues that philosophers have a problem when their broad definition of art disregards the beautiful to incorporate art work that is intentionally ugly or is only considered art work because of its being on display. Comparing the focus of other philosophical disciplines with philosophy of art’s focus on beauty, it argues that philosophy of art blurs its vision when it directs its gaze to that other than to its proper transcendental. Examining the intelligent and elevating characteristics of the art form of sculpture, the paper compares two famous works: Michelangelo’s Pietà and Warhol’s Brillo Boxes. Because the sculptor is able to communicate the beauty of creation through his art work, a philosophy of art that changes its questions to incorporate existing objects that are deemed “art” has not fully addressed the problem of beauty’s place in art work.

Sleeping Beauty in a grain of rice

In the Sleeping Beauty problem, Beauty is woken once if a coin lands heads or twice if the coin lands tails but promptly forgets each waking on returning to sleep. Philosophers have divided over whether her waking credence in heads should be a half or a third. Beauty has centered beliefs about her world and about her location in that world. When given new information about her location she should update her worldly beliefs before updating her locative beliefs. When she conditionalizes in this way, her credence in heads is a half before and after being told it is Monday. In applications of Dutch Book arguments to the Sleeping Beauty problem, the probability of a particular outcome has often been confounded with consequences of that outcome. Heads and tails are equally likely but twice as much is at stake if the coin falls tails because Beauty is fated to make the same choice twice. As a consequence, the possibility of tails should be given twice the weight of the possibility of heads when deciding whether to bet on heads even though heads and tails are equally likely.

Can rational choice guide us to correct de se beliefs?

Significant controversy remains about what constitute correct self-locating beliefs in scenarios such as the Sleeping Beauty problem, with proponents on both the "halfer" and "thirder" sides. To attempt to settle the issue, one natural approach consists in creating decision variants of the problem, determining what actions the various candidate beliefs prescribe, and assessing whether these actions are reasonable when we step back. Dutch book arguments are a special case of this approach, but other Sleeping Beauty games have also been constructed to make similar points. Building on a recent article (James R.~Shaw. {\em De se} belief and rational choice. {\em Synthese}, 190(3):491-508, 2013), I show that in general we should be wary of such arguments, because unintuitive actions may result for reasons that are unrelated to the beliefs. On the other hand, I show that, when we restrict our attention to {\em additive} games, then a thirder will necessarily maximize her {\em ex ante} expected payout, but a halfer in some cases will not (assuming causal decision theory). I conclude that this does not necessarily settle the issue and speculate about what might.

Lost memories and useless coins: revisiting the absentminded driver

The puzzle of the absentminded driver combines an unstable decision problem with a version of the Sleeping Beauty problem. Its analysis depends on the choice between “halfing” and “thirding” as well as that between “evidential” and “causal” decision theory. I show that all four combinations lead to interestingly different solutions, and draw some general lessons about the formulation of causal decision theory, the interpretation of mixed strategies and the connection between rational credence and objective chance.

A Dutch book against sleeping beauties who are evidential decision theorists

In the context of the Sleeping Beauty problem, it has been argued that so-called "halfers" can avoid Dutch book arguments by adopting evidential decision theory. I introduce a Dutch book for a variant of the Sleeping Beauty problem and argue that evidential decision theorists fall prey to it, whether they are halfers or thirders. The argument crucially requires that an action can provide evidence for what the agent would do not only at other decision points where she has exactly the same information, but also at decision points where she has different but "symmetric" information.

Titelbaum’s Theory of De Se Updating and Two Versions of Sleeping Beauty

In his “Relevance of Self-locating Belief” (2008), Titelbaum suggests a general theory about how to update one’s degrees of self-locating belief. He applies it to the Sleeping Beauty problem, more specifically, Lewis’s (Analysis 61(3):171–176, 2001) version of that problem. By doing so, he defends the Thirder solution to the puzzle. Unfortunately, if we modify the puzzle very slightly, and if we apply his general updating theory to the thus modified version, we get the Halfer view as a result. In this paper, we will argue that the difference between the two versions of Sleeping Beauty isn’t sufficient for justifying the different verdicts on them. Since this is a counter-intuitive result, we should reject Titelbaum’s theory of de se updating.

BAROQUE AND ICONIC ECPHRASIS IN GOGOL'S "TARAS BULBA"

This article discusses the tools verbalization European Baroque painting techniques and Old icons in the Gogol's story "Taras Bulba". Narrative functions of implicit ecphrasis investigated in connection problem relatedness Catholicism and Orthodoxy in the minds of Gogol at the beginning of the 1840s. The purpose of the article analyzes the ways of verbalization and features of non-attributed implicit ecphrasis in the second edition of Gogol's "Taras Bulba" reproducing Caravaggio painting style and Old icons. Method or the methodology of work : Among research material are Gogol's "Taras Bulba" in two editions, the European Baroque paintings and ancient Russian icons. Were applied structural-typological, structural, intertextual, hermeneutical methods. Results: We describe the correlation of ecphrasis in Gogol with referents: the paintings of Caravaggio and Honthorst , and Old Russian iconography . Found that ecphrasis descriptions that appear only in the edition of 1842 are not local segments of the text and form the entire text layers, actively organizing narrative, operating plot and composition. Hidden emplisit ecphrasis is the artistic code, extending the semantic space of the text , the text translation tool of religious and philosophical ideas of the author. Valuable contraposition of baroque and iconic ecphrasis in the story reflects not only the author's reflection on the problem of beauty , inner and outer, but also a reflection of their own style. Application area: The results of our study can be used for lectures on the history of Russian literature of the XIX century, the history of Russian and European culture, cultural studies, specialized courses and electives in the problem of interaction between different kinds of art, as well as material for interdisciplinary humanities research, including in school practice teaching literature and art history.

Visual representation of rational belief revision: another look at the Sleeping Beauty problem.

The coherence of probability judgments is influenced in predictable ways by people's internal representations of problems, which may be altered by the manner in which propositions are stated or “framed” (Mandel, 2008). Likewise, several studies find that probabilistic reasoning and judgment can be improved by externally representing statistical information visually (for a review, see Garcia-Retamero and Cokely, 2013). Visual representation is thought to facilitate performance by externalizing the set-subset relations among observational data. Although some studies have examined whether visual representations can improve Bayesian reasoning, they have tended to focus on the use of natural sampling trees (Sedlmeier and Gigerenzer, 2001), Euler circles (Sloman et al., 2003), or other means of representing set-subset relations.

Generalized Conditionalization and the Sleeping Beauty Problem, II

Generalized Conditionalization and the Sleeping Beauty Problem, II