The principle of Anteriority says that prospects that are identical from the perspective of every possible person’s welfare are equally good overall. The principle enjoys prima facie plausibility, and has been employed for various theoretical purposes. Here it is shown using an analogue of the St Petersburg Paradox that Anteriority is inconsistent with central principles of axiology.

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the (...) class='Hi'>paradox, the slope at zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough. (shrink)

This paper aims to consider the meaning of the dismal theorem, as presented by Martin Weitzman [(2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91, 1–19]. The theorem states that a standard cost–benefit analysis breaks down if there is a possibility of catastrophes occurring. This result has a significant influence on debates regarding the economics of climate change. In this study, we present an intuitive similarity between the dismal theorem and the St. (...) Petersburg paradox using a simple discrete probability distribution. (shrink)

In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion (...) rather than a positive model of decision making processes. (shrink)

In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ. The deduction of those fees is the main result of Section 2. We (...) then propose a Bayesian approach to the problem. When the probability of heads is θ the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in, for in this case there is a paradox. (shrink)

I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.

How much would you pay to play a lottery with an “infinite expected payoff?” In the case of the century old, St. Petersburg Paradox, the answer is that the vast majority of people would only pay a small amount. The authors seek to understand this paradox by providing an explanation consistent with a broad, process‐level model of human decision‐making under risk.

One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.

In this paper I add a new twist to Colyvan's version of the Petrograd paradox.

Written and set on the banks of the Neva, St Petersburg Dialogues is a startlingly relevant analysis of the human prospect in the twenty-first century. As the literary critic George Steiner has remarked, "the age of the Gulag and of Auschwitz, of famine and ubiquitous torture... nuclear threat, the ecological laying waste of our planet, the leap of endemic, possibly pandemic, illness out of the very matrix of libertarian progress" is exactly what Joseph de Maistre foretold. In the Dialogues (...) Maistre addressed a number of topics that are discussed briefly or not at all in his other works already available in English. These include an apologetic for traditional Christian beliefs about providence, reflections on the social role of the public executioner and the "divinity" of war, a critique of John Locke's sensationalist psychology, meditations on prayer and sacrifice, and a mini-course on "illuminism." The literary form is that of the "philosophical conversation" – one that allowed Maistre to be deliberately provocative and to indulge his taste for paradox, a "methodical extravagance" that he judged particularly appropriate for the eighteenth-century salon. Translator and editor Richard Lebrun provides a full scholarly edition of this classic work, complete with an introduction, chronology, critical bibliography, and generous explanatory notes. The Dialogues will be of interest to scholars of literary history as well as the history of ideas. (shrink)

Written and set on the banks of the Neva, St Petersburg Dialogues is a startlingly relevant analysis of the human prospect at the end of the twentieth century. As the literary critic George Steiner has remarked, "the age of the Gulag and of Auschwitz, of famine and ubiquitous torture,... nuclear threat, the ecological laying waste of our planet, the leap of endemic, possibly pandemic, illness out of the very matrix of libertarian progress" is exactly what Maistre foretold. In the (...) Dialogues Maistre addressed a number of topics which are discussed briefly or not at all in his other works already available in English. These include an apologetic for traditional Christian beliefs about providence, reflections on the social role of the public executioner and the "divinity" of war, a critique of John Locke's sensationalist psychology, meditations on prayer and sacrifice, and a mini-course on "illuminism." The literary form is that of the "philosophical conversation" -- one that allowed Maistre to be deliberately provocative and to indulge his taste for paradox, a "methodical extravagance" that he judged particularly appropriate for the eighteenth-century salon. Translator and editor Richard Lebrun provides a full scholarly edition of this classic work, complete with an introduction, chronology, critical bibliography, and generous explanatory notes. The Dialogues will be of interest to scholars of literary history as well as the history of ideas. (shrink)

This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to (...) the St. Petersburg puzzle and related puzzles. The result will be a decision theory that gives a novel, but well-motivated, reason for discounting small probabilities when making decisions. We examine the merits and demerits of such a decision theory. (shrink)

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

A variety of evidence demonstrates that memory is a reconstructive process prone to errors and distortions. However, the complex relationship between memory encoding, strength of memory reactivation, and the likelihood of reporting true or false memories has yet to be ascertained. We address this issue in a setting that mimics a real-life experience: We asked participants to take a virtual museum tour in which they freely explored artworks included in the exhibit, while we measured the participants’ spontaneous viewing time of (...) each explored artwork. In a following memory reactivation phase, participants were presented again with explored artworks, followed by novel artworks not belonging to the same exhibit. For each of these objects, participants provided a reliving rating that indexed the strength of memory reactivation. In the final memory recognition phase, participants underwent an old/new memory task, involving reactivated vs. baseline targets, and activated and baseline lures. The results showed that those targets that were spontaneously viewed for a longer amount of time were more frequently correctly recognized. This pattern was particularly true for reactivated targets associated with greater memory strength. Paradoxically, however, lures that were presented after targets associated with higher reliving ratings in the reactivation phase were more often erroneously recognized as artworks encountered during the tour. This latter finding indicates that memory intrusions, irrespective of the viewing time, are more likely to take place and be incorporated into true memories when the strength of target memory is higher. (shrink)

Sorensen provides a panoramic view of paradoxes of theoretical and practical rationality. These puzzles are organized as apparent counterexamples to attractive principles such as the principle of charity, the transitivity of preferences, and the principle that we should maximize expected utility. The following paradoxes are discussed: fearing fictions, the surprise test paradox, Pascal’s Wager, Pollock’s Ever Better wine, Newcomb’s problem, the iterated prisoner’s dilemma, Kavka’s paradoxes of deterrence, backward inductions, the bottle imp, the preface paradox, Moore’s problem, Buridan’s (...) ass, Condorcet’s paradox of cyclical majorities, the St. Petersburg paradox, weakness of will, the Ellsberg paradox, Allais’s paradox, and Peter Cave’s puzzle of self-fulfilling beliefs. (shrink)

In this article, we re-examine Pascal’s Mugging, and argue that it is a deeper problem than the St. Petersburg paradox. We offer a way out that is consistent with classical decision theory. Specifically, we propose a “many muggers” response analogous to the “many gods” objection to Pascal’s Wager. When a very tiny probability of a great reward becomes a salient outcome of a choice, such as in the offer of the mugger, it can be discounted on the condition (...) that there are other symmetric, non-salient rewards that one may receive if one chooses otherwise. (shrink)

The two envelope paradox can be dissolved by looking closely at the connection between conditional and unconditional expectation and by being careful when summing an infinite series of positive and negative terms. The two envelope paradox is not another St. Petersburg paradox and that one does not need to ban talk of infinite expectation values in order to dissolve it. The article ends by posing a new puzzle to do with infinite expectations.

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which (...) we call *Countable Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

Personality and prayer are both conceptualized as focusing on issues of connectivity with the self and beyond. Individual participants each recruited a peer to join the study . Participants rated themselves according to multi-item scales that detail five personality factors . They also responded to an instrument specifying eight foci of the inward, outward, and upward cognitive content of prayer ; these eight foci were reduced to three prayer themes: internal concerns, embracing paradox, and bold assertion. Finally, respondents reported (...) the strength of six "basic" emotions that may be experienced during their typical prayer. Using the same instruments, each peer rated her or his matched participant. Results reveal discrete patterns between self and peer ratings, with respect to links among prayer and personality variables. Both self and peer ratings emphasize a relation between prayer and the personality traits of agreeableness and conscientiousness . Several concluding points highlight the value of the present conceptualization of personality and prayer with relation to connectivity, potential differences between personal and corporate prayers, and the potential role of sex differences in the disclosure of prayer's content and emotional influence. (shrink)

Personality and prayer are both conceptualized as focusing on issues of connectivity with the self and beyond. Individual participants each recruited a peer to join the study . Participants rated themselves according to multi-item scales that detail five personality factors . They also responded to an instrument specifying eight foci of the inward, outward, and upward cognitive content of prayer ; these eight foci were reduced to three prayer themes: internal concerns, embracing paradox, and bold assertion. Finally, respondents reported (...) the strength of six "basic" emotions that may be experienced during their typical prayer. Using the same instruments, each peer rated her or his matched participant. Results reveal discrete patterns between self and peer ratings, with respect to links among prayer and personality variables. Both self and peer ratings emphasize a relation between prayer and the personality traits of agreeableness and conscientiousness . Several concluding points highlight the value of the present conceptualization of personality and prayer with relation to connectivity, potential differences between personal and corporate prayers, and the potential role of sex differences in the disclosure of prayer's content and emotional influence. (shrink)

It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.

Why does Derek Parfit, a philosopher very much associated with the University of Oxford, use pictures of St. Petersburg on the covers of volumes of On What Matters? Perhaps it is because he regards his agony argument as like something from Russian literature. But I can envisage a response to the argument from such literature.

In spite of its infinite expectation value, the St. Petersburg game is not only a gamble without supply in the real world, but also one without demand at apparently very reasonable asking prices. We offer a rationalizing explanation of why the St. Petersburg bargain is unattractive on both sides (to both house and player) in the mid-range of prices (finite but upwards of about $4). Our analysis – featuring (1) the already-established fact that the average of finite ensembles (...) of the St. Petersburg game grows with ensemble size but is unbounded, and (2) our own simulation data showing that the debt-to-entry fee ratio rises exponentially – explains why both house and player are quite rational in abstaining from the St. Petersburg game. The house will be unavoidably (and intentionally) exposed to very large ensembles (with very high averages, and so very costly to them), while contrariwise even the well-heeled player is not sufficiently capitalized (as our simulation data reveals) to be able to capture the potential gains from large-ensemble play. (Smaller ensembles, meanwhile, enjoy low means, as others have shown, and so are not worth paying more than $4 to play, even if a merchant were to offer them at such low prices per trial.) Both sides are consequently rational in abstaining from entry into the St. Petersburg market in the mid-range of asking prices. We utilize the concept of capitalization vis-à-vis a gamble to make this case. Classical analyses of this question have paid insufficient attention to the question of the propriety of using expected values to assess the St. Petersburg gamble. And extant analyses have not noted the average-maximum-debt-before-breaking-even figures, and so are incomplete. (shrink)

The image of St. Petersburg is an integral part of Russian art, in particular, in watercolor painting. This article is devoted to the analysis of the work of Russian watercolor artists, identifying the specifics and characteristic features of the image of the city on the Neva in their work. The object of the study is watercolors by Russian artists, the subject is expressive means, techniques and methods through which the image of St. Petersburg is embodied. On the example (...) of watercolor works by E.P. Gau, I.A. Vladimirova, A.S. Vedernikov, A.P. Ostroumova-Lebedeva, P.P. Grigoryants, G.P. Fitingof, A. Ermolaev, V.V. Proshkin, K. Kuzema, V. Kolbasov, O. Litvinenko, etc. the historical transformation of the artistic image of St. Petersburg, its conditionality by cultural and historical factors and the nature of the life of the inhabitants of the city is shown. The study concluded that the image of St. Petersburg is important for Russian artists, as well as a significant variety of its creative interpretations. Each watercolor work demonstrates the subjective attitude of artists to St. Petersburg, thanks to which real urban landscapes acquire spirituality and unique expressiveness. The complex historical fate of this cultural and artistic center of Russia, which was once a magnificent capital, experienced revolutionary events and went through military destruction, determined the versatility of creative approaches to the embodiment of the city, as a result of various turns of history, it lost, then regained its greatness, beauty and attractiveness. Petersburg in watercolors is invariably filled with vitality, lyrical feelings and the love of artists. (shrink)

The article presents results of an ongoing study of centers of intellectual innovations in post-Soviet Russia. Using the European University at St. Petersburg as the main object of their analysis, the authors demonstrate how new models of academic careers, which became available in the 1980s and 1990s, were eventually institutionalized as new models of knowledge production and educational practices. Supported by American foundations, this private university had to invent a new institutional structure and to position itself within the field (...) of higher education, still mostly dominated by the state. (shrink)

The St. Petersburg Theological Academy was the first of the four academies in the early years of the nineteenth century to undergo a remodeling along the lines of a new charter for the empire’s church-affiliated educational institutions. Instruction in philosophy was mandated, but the academy faced staffing issues at the outset. Courses were taught following Wolffian guidebooks that many found to be antiquated, raising pedagogical dilemmas for the teachers. Nevertheless, a divorce between faith and reason was proscribed, and adherence (...) to a Christianized Plato remained prescribed and seen as central to the Orthodox religion. (shrink)

Khoryev regards Petersburg, a collection of essays by Jarosław Iwaszkiewicz, published in 1976, as a windup of the writer’s complex ties with Russian culture and literature, which he was widely known to have loved and known in depth. It is a book where, through the legendary city on the river Neva, Iwaszkiewicz takes a look at a number of essential issues of Russian history and its ties with the history of Poland and the Polish people. Iwaszkiewicz avoids unequivocal judgments, (...) noticing the antinomian nature of St. Petersburg, seen as a being full of contrast but at the same time the center of revolutions and despotism, a manifestation of imperial power and the highest achievements of sophisticated art. These contrasts reveal, in Khoryev’s opinion, the multi-faceted and fullest picture of St. Petersburg and its individuality: so mysterious, overpowering and unique. (shrink)

This is the first complete translation of this work of Maistre's into the English language. It also includes Maistre's shorter piece, "Elucidation on Sacrifices," which has traditionally been appended to these philosophical dialogues. Maistre himself had divided his writing into eleven numbered dialogues, each of which formally represents an evening of conversation, as well as a "Sketch of a Final Dialogue," in which the participants say their farewells. The debating figures are called "the Count", "the Senator", and "the Chevalier." There (...) is an elaborate apparatus surrounding the work, consisting of the footnotes and endnotes to each dialogue that Maistre himself had written, as well as explanatory footnotes and endnotes to each dialogue by the translator. Lebrun has traced virtually all of the references Maistre had made, and in some cases has been able to point out slight errors and misstatements in Maistre's own citations. He has also translated into English all the passages in languages other than French, which follow immediately after their appearance in the text in their original tongue. Lebrun has also provided fine supplements to Maistre's writing--a preface, scholarly introductory essay, chronology, critical bibliography, a well as a note on the text. There is also a very fine index, which includes virtually every work and author cited or mentioned in Maistre's text. The quality of Lebrun's translation is excellent indeed, clearly aware of a variety of nuances in Maistre's language, and based squarely on a life-long study of the thinker. (shrink)

RESUMO O artigo discute os princípios fundamentais de elaboração do projeto e anotação de corpora de fala no âmbito da Escola Fonológica de São Petersburgo e fornece os exemplos de utilização de dados de vários corpora na pesquisa em fonética. Um dos princípios fundamentais é analisar as amostras em todos os níveis: desde o segmento até a entoação, incluindo as disfluências da fala. Durante a anotação fonética, sugerimos ouvir cada som isoladamente e confiar nos dados do espectrograma. Na anotação silábica, (...) é crucial considerar a ressilabificação. Durante a anotação prosódica, sugerimos confiar na percepção do ouvinte e analisar as curvas melódicas. Um corpus de fala que segue esses princípios é uma fonte valiosa de dados fonéticos, uma vez que os fatores segmentais e prosódicos estão em constante interação e não se pode analisar as unidades de um nível de anotação sem fazer referência aos outros. (shrink)

Khoryev regards Petersburg, a collection of essays by Jarosław Iwaszkiewicz, published in 1976, as a windup of the writer’s complex ties with Russian culture and literature, which he was widely known to have loved and known in depth. It is a book where, through the legendary city on the river Neva, Iwaszkiewicz takes a look at a number of essential issues of Russian history and its ties with the history of Poland and the Polish people. Iwaszkiewicz avoids unequivocal judgments, (...) noticing the antinomian nature of St. Petersburg, seen as a being full of contrast but at the same time the center of revolutions and despotism, a manifestation of imperial power and the highest achievements of sophisticated art. These contrasts reveal, in Khoryev’s opinion, the multi-faceted and fullest picture of St. Petersburg and its individuality: so mysterious, overpowering and unique. (shrink)

The art historian Alessandro Giovanardi has recently published a monograph on one of the important representatives of the Russian religious-philosophical renaissance of the beginning of 20th century – Vladimir Nikolayevich Zabugin. This volume, written in Italian, aims to provide a comprehensive overview of Zabugin's intellectual biography, philosophical and aesthetic ideas and opens up a completely unknown corpus of the author’s works as well as the history of the reception of his heritage. The monograph underlines the contribution of Vladimir Zabugin in (...) Italian and European humanitarian culture and defines his heritage as a rare synthesis of the finest erudition and Christian spirituality. (shrink)

By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena game over (...) the Pasadena game, and that would have been claimed for the St Petersburg game over the Altadena, can be contradicted without fear of inconsistency with the axioms of utility theory. However, insistence upon dominance can be made to yield a contradiction of the Archimedean axiom of utility theory. CiteULike Connotea Del.icio.us What's this? (shrink)

A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision (...) theory might be supplemented; the role of simulations of such infinite games; the role of small probabilities, and of idealization, in decision theory; tolerance about practical norms; and alternative ways of understanding decision theory's job description. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...) then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

This book contains 86 essays and papers by the Russian sculptor and hermeneutic philosopher Vladimir Zimmerling (1931-2017) addressed the issues in aesthetics, ethics and cultural history. The apparatus includes the introductory article, the commentary, the name and the subject indexes prepared by the book editor, Anton Zimmerling. The appendix contains 70 pictures of Vladimir Zimmerling's sculptures. Vladimir Zimmerling's conception is build on the combination of the empiricism principle with the elements of hermeneutics and metalinguistic criticism. His essays and papers focus (...) on the foundations of aesthetics and ethics. Vladimir Zimmerling was one of the pioneers of the analytic approach to the poetics of Ossip Mandelstam with his paper "Промер" ["The Measurement"], (1974-1975) devoted to 10 difficult Mandelstam's poems including "Грифельная Ода", "Слепая ласточка бросается к ногам", "Я слово позабыл, что я хотел сказать". (shrink)

This paper is partly a tribute to Richard Jeffrey, partly a reflection on some of his writings, The Logic of Decision in particular. I begin with a brief biography and some fond reminiscences of Dick. I turn to some of the key tenets of his version of Bayesianism. All of these tenets are deployed in my discussion of his response to the St. Petersburg paradox, a notorious problem for decision theory that involves a game of infinite expectation. Prompted (...) by that paradox, I conclude with some suggestions of avenues for future research. (shrink)