In the two-envelope problem, a reasoner is offered two envelopes, one containing exactly twice the money in the other. After observing the amount in one envelope, it can be traded for the unseen contents of the other. It appears that it should not matter whether the envelope is traded, but recent mathematical analyses have shown that gains could be made if trading was a probabilistic function of amount observed. As a problem with a purely probabilistic (...) solution, it provides a potentially interesting way to test people's consistency with probabilistic models. Three experiments did this by varying the size of both the observed and maximum amounts, and their possible distribution. The results showed that trading decisions were affected by where the observed amount in the opened envelope fell in the distribution, though its size did not always do so. This suggests that participants’ trade decisions could be affected by the perceived probabilities of different observed amounts, which is consistent with the pro.. (shrink)

The problem of determining an optimal benchmark to inefficient decision-making units is an important issue in the field of performance analysis. Previous methods for determining the projection points of inefficient DMUs have only focused on one objective and other features have been ignored. This paper attempts to determine the best projection point for each DMU when the inputs and outputs data are in stochastic form and presents an alternative definition for the best projection by considering three main aspects: (...) technical efficient, minimal cost, and maximal revenue as much as possible. Considering the important role of the electricity industry in the economic growth of each country, a practical example has been implemented on 16 regional electricity companies in Iran in 9 consecutive periods. The efficiency score along with the projection points of the three technical models ), cost, and stochastic revenue are compared with the projection point obtained from the model presented in this article, which simultaneously meets these three objectives, showing the improvement of companies’ performance. (shrink)

Four variations on Two Envelope Paradox are stated and compared. The variations are employed to provide a diagnosis and an explanation of what has gone awry in the paradoxical modeling of the decision problem that the paradox poses. The canonical formulation of the paradox underdescribes the ways in which one envelope can have twice the amount that is in the other. Some ways one envelope can have twice the amount that is in the other make it (...) rational to prefer the envelope that was originally rejected. Some do not, and it is a mistake to treat them alike. The nature of the mistake is diagnosed by the different roles that rigid designators and definite descriptions play in unproblematic and in untoward formulations of decision tables that are employed in setting out the decision problem that gives rise to the paradox. The decision maker’s knowledge or ignorance of how one envelope came to have twice the amount that is in the other determines which of the different ways of modeling his decision problem is correct. Under this diagnosis, the paradoxical modeling of the Two Envelope problem is incoherent. (shrink)

When decision makers have more to gain than to lose by changing their minds, and that is the only relevant fact, they thereby have a reason to change their minds. While this is sage advice, it is silent on when one stands more to gain than to lose. The two envelope paradox provides a case where the appearance of advantage in changing your mind is resilient despite being a chimera. Setups that are unproblematically modeled by decision tables that are (...) used in the formulation of the two envelope paradox are described, and variations on them are stipulated. The problems posed by the paradoxical modeling are then contrasted with the variations. The paper concludes with a brief explanation of why the paradoxical modeling does not gain support from the fact that one envelope has twice the amount that is in the other. (shrink)

The aim of this essay is to distinguish and analyze several difficulties confronting attempts to reconcile the fundamental quantum mechanical dynamics with Born''s rule. It is shown that many of the proposed accounts of measurement fail at least one of the problems. In particular, only collapse theories and hidden variables theories have a chance of succeeding, and, of the latter, the modal interpretations fail. Any real solution demands new physics.

Three big philosophical problems about consciousness are: Why does it exist? How do we explain and understand it? How can we explain brain-consciousness correlations? If functionalism were true, all three problems would be solved. But it is false, and that means all three problems remain unsolved (in that there is no other obvious candidate for a solution). Here, it is argued that the first problem cannot have a solution; this is inherent in the nature of explanation. (...) The second problem is solved by recognizing that (a) there is an explanation as to why science cannot explain consciousness, and (b) consciousness can be explained by a different kind of explanation, empathic or “personalistic” explanation, compatible with, but not reducible to, scientific explanation. The third problem is solved by exploiting David Chalmers“principle of structural coherence”, and involves postulating that sensations experienced by us–visual, auditory, tactile, and so on–amount to minute scattered regions in a vast, multi dimensional “space” of all possible sensations, which vary smoothly, and in a linear way, throughout the space. There is also the space of all possible sentient brain processes. There is just one, unique one-one mapping between these two spaces that preserves continuity and linearity. It is this which provides the explanation as to why brain processes and sensations are correlated as they are. I consider objections to this unique-matching theory, and consider how the theory might be empirically confirmed. (shrink)

I am inclined to think that there are three basic philosophical problems that arise in connection with consciousness. (1) Existence. Why does sentience or consciousness exist at all? Why are we not zombies? (2) Intelligibility. Granted that consciousness exists, what is it? How is it to be explained and understood? On the face of it, there could be no greater mystery than that brains should somehow produce, or be, our states of awareness, our thoughts, feelings, perceptions and desires. What (...) is so baffling and mysterious about consciousness is that each one of us knows it exists, and knows what it is, because we possess it, indeed we are it, in a certain sense; and yet, if we examine a conscious brain, we find such things as neurons and synaptic junctions, but nothing remotely like consciousness as we experience it. Consciousness is wholly apparent to the owner of the conscious brain, but bafflingly invisible and ineffable to everyone else. How is this familiar and utterly inexplicable stuff of consciousness to be explained and understood? (3) Brain-Mind Correlations. What possible explanation could there be for the way brain processes and sensations are correlated? In what follows I suggest solutions to two of these problems, and indicate why, in my view, the other problem has no solution, and thus does not deserve to be regarded as a legitimate problem. (shrink)

We prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01].

The "two-envelopes" problem has stimulated much discussion on probabilistic reasoning, but relatively little experimentation. The problem specifies two identical envelopes, one of which contains twice as much money as the other. You are given one of the envelopes and the option of keeping it or trading for the other envelope. Variables of interest include the possible amounts of money involved, what is known about the process by which the amounts of money were assigned to the envelopes, and (...) whether you are allowed to know how much money is in the envelope in hand before deciding whether to keep or trade. In an earlier study, Butler and Nickerson found that when participants were allowed to know how much was in the envelope in hand, they generally elected to trade if that amount was small relative to the range of possibilities and to keep otherwise. The present experiments showed that this propensity was independent of the amount of money in the envelopes. Participants made decisions with a strong bias for avoiding the risk of losing by trading, particularly when the amount in hand was known and large relative to the range of possible amounts, regardless of the absolute value of the gamble. The results illustrate the dependence of thinking on the context in which it occurs, and demonstrate a tendency to treat quantities that are large or small relative to a particular context in which they are encountered as though they were large or small in a more general sense. (shrink)

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincaré (...) wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)

In this paper I examine a specific way that video-conferencing modifies structures of intersubjective awareness and interaction. I focus on multi-person interactions (involving more than two people) via video-call. By unpacking some of the key features of multi-person intersubjectivity in cases of embodied co-presence, I will show where and how certain social affordances are strained or lost when multi-person interactions are transferred to the screen.

The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as -person games. The decision making is based on the same tool, namely the game theory logic based on the use of the (...) Shapley value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann-Maschler step-by-step procedure for solving the bankruptcy problem. (shrink)

Logicians disagree on (1) criteria for the presence of an argument, (2) criteria for adding implicit premises and (3) criteria for linking premises. I attempt to resolve all three problems, and in the process to remove the main obstacles to teaching diagramming. The first problem is resolved by working with real discourse that students find on their own, rather than the artificial examples and problems found in logic texts; it is further reduced by examining the different uses of (...) argument and understanding the extent to which the basic rules of diagramming are the same for the various uses. The other disagreements persist because logicians neglect to clarify the principal type of eakness we remedy by adding implicit premises and linking premises: in real discourse we do so to block substantive counterexamples, an idea correlated with that of substantive deduction, discussed by Govier, Wright and others. (shrink)

Lawrence Powers advocates a one-fallacy theory in which the only real fallacies are fallacies of ambiguity. He defines a fallacy, in general, as a bad argument that appears good. He claims that the only legitimate way that an argument can appear valid, while being invalid, is when the invalid inference is covered by an ambiguity. Several different kinds of counterexamples have been offered from begging the question, to various forms of ad hominem fallacies. In this paper, I outline three (...) potential counterexamples to Powers' theory, including one that has been addressed already by Powers, and two which are well known problems, but until now have never been applied as counterexamples to Powers' theory. I argue that there is a simpler explanation of these 'hard' cases than positing ambiguities that are not obviously there. (shrink)

Intentions matter. They have some kind of normative impact on our agency. Something goes wrong when an agent intends some end and fails to carry out the means she believes to be necessary for it, and something goes right when, intending the end, she adopts the means she thinks are required. This has even been claimed to be one of the only uncontroversial truths in ethical theory. But not only is there widespread disagreement about why this is so, there is (...) widespread disagreement about in what sense it is so. In this paper I explore an underdeveloped answer to the question of in what sense it is so, and argue that resolving an apparent difficulty with this view leads to an attractive picture about why it is so. (shrink)

I will talk here about three problems that have bothered me for a number of years, during which time I have experimented with a variety of solutions and encouraged others to work on them. I have raised each of them separately both in full and in passing in various contexts, but thought it would be worthwhile on this occasion to bring them to your attention side by side. In this talk I will explain the problems, together with some things (...) that have been tried in the past and some new ideas for their solution. (shrink)

Este trabajo es una crítica a los estudios sobre la evolución del lenguaje mediante la identificación de tres problemas epistémicos. La crítica epistémica parte de la definición del lenguaje y la unidad de evolución. El resultado es remitirnos de la pregunta por el origen del lenguaje a la pregunta por el origen del ser humano que son los otros dos problemas epistémicos. El límite superior en el estudio de la evolución del lenguaje es cómo saber qué es ser humano. De (...) esta manera, entendemos que los estudios sobre la evolución del lenguaje se refieren al proceso de cómo nos reconocemos como humanos. La falta de la definición de lenguaje para tener la unidad de evolución, con la confusión sobre el origen del lenguaje y los humanos apunta que la evolución del lenguaje aún está al nivel de una taxonomía, lejos de ser una explicación sistemática del lenguaje o la evolución. (shrink)

We consider an infinite hierarchy of systems of Alethic Modal Logic with so-called Levels of Perfection, and add to them suitable definitions of such interesting deontic categories as those of supererogation, offence, conditional obligation and conditional permission. We then state three problems concerning the proper characterization of the resulting logic(s) for our defined notions, and discuss two of these problems in some detail.

Various proposals have been made for solving The Two Envelope Problem. But even though the problem itself is easily stated and quite simple, the proposedsolutions have not been. Some involve calculus, some involve considerations about infinite values, and some are complicated in other ways. Moreover, there is not yet any one solution that is widely accepted as correct. In addition to being notable for its simplicity and its lack of a generally agreed-upon solution, The Two Envelope (...) Problem is also notable because it demonstrates that something that has been taken to be a fundamental principle of decision theory is false. The main purpose of this paper is to propose and defend a simple solution to The Two Envelope Problem. But I also want to make a start on the project of figuring out how the relevant fundamental principle of decision theory should be revised. (shrink)

After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does (...) not allow a satisfactory solution. An interpretation is made for statistical science at large. (shrink)

The Two Envelopes Problem is a beautiful and quite confusing problem in decision theory which is ca. 35 years old and has provoked at least 150 papers directly addressing the problem and displaying a surprising variety of different responses. This paper finds decisive progress in an approach of Priest and Restall in 2003, contends that the recent papers having appeared since did not really go beyond that paper, argues further that Priest’s and Restall’s solution is still not (...) complete, and proposes a completion of their solution. If the analysis is correct, this work has the potential of laying the Two Envelopes Problem at rest. (shrink)

dixerit hoc idem Epicurus, semper beatum esse sapientem … quem quidem, cum summis doloribus conficiatur, ait dicturum: ‘quam suaue est! quam nihil curo!’ non pugnem cum homine, cur tantum †habeat† in natura boni …This text, containing Cicero's oft-repeated canard, is deeply problematic. Both Reynolds and Moreschini resort to daggers here. Madvig's abeat for habeat has failed to convince, since Cicero appears to use abeo metaphorically without specifying the place of origin or destination of movement within a narrowly circumscribed semantic field (...) which does not encompass our passage. C.F.W. Müller, on the other hand, offered aberret, which can appear without such specification in the sense ‘be deceived’ or the like. Editors evidently hesitate, however, because of the difficulty of explaining the corruption. Perhaps one might rather consider the merits of haereat. haereo can mean ‘be stuck in difficulties’, but the usage is uncommon enough that it could easily have been a stumbling block for an inattentive scribe. Moreover, in some scripts where r is written with somewhat elongated hasta and an arc curving down, it can be easily confused with b; and once haebeat appeared, the ‘correction’ to habeat was all but inevitable. (shrink)

In the two feature articles for this volume, Gruber et al and Buonomano & Rovelli focus on what the former call the 'two-times problem', in short, the apparent lack of fit between time as described by physical science and our own temporal experience, where 'experience' involves things like memory, anticipation, and perception of change and motion. In this short note I'll make the case that the twotimes problem is less serious than it is often made out to be (...) in the specific case of features like 'passage ' and 'presentness' that are central to the 'A-theory' of time ---the theory that holds time to be composed of dynamic regions of 'past', 'present' and future', and for time to genuinely flow or pass.My contention is three-fold: (1) the two-times problem is better understood as a three-times problem: rather than a conflict between 'physical' and 'manifest' time, what we have in the case of time is differences between the time of physics, the time of experience, and the 'folk' concept of time. (2) Understanding the problem in this way helps deflate certain problems about the relationship of these three pictures; the time of experience and the time of physics are less obviously in a problematic conflict than often supposed; and the folk concept of time is what brings in problematic features of time hard to fit with either the time of physics of experience. (3) Understanding the time of experience as independent from the folk concept of time better fits the actual aims of the... (shrink)

Traditionally, special divine acts have been understood as involving intervention in the course of nature, so as to cause events that nature would not, or could not, otherwise produce. The concept of divine intervention has come under heavy fire in recent times, however. This has caused many philosophers and theologians either to abandon the possibility of special divine acts or to attempt to show how such acts need not be understood as interventions in natural processes. This paper argues that (...) class='Hi'>three objections typically raised against special divine acts conceived as interventions in the natural order are pseudo-problems and pose no reason to abandon the traditional conception of such acts. Further, it argues that attempted noninterventionist accounts constitute a blind alley of investigation, inasmuch as they fail to provide a secure foundation for a robust account of the possibility of special divine acts. (shrink)

It is now more than 50 years that the Goodman paradox has been discussed, and many different solutions have been proposed. But so far no agreement has been reached about which is the correct solution to the paradox. In this paper, I present the naturalistic solutions to the paradox that were proposed in Quine (1969, 1974), Quine and Ullian (1970/1978), and Stemmer (1971). At the same time, I introduce a number of modifications and improvements that are needed for overcoming shortcomings (...) of the solutions. The discussion of this improved version suggests that the Goodman paradox actually embodies three different problems; yet, one of them is not Goodman’s but Hume’s problem. The discussion also suggests that the naturalistic approach is probably the best for basing on it a theory of confirmation. Finally, I analyze one of Hume’s insights that seems to have been largely ignored. This insight shows a surprising similarity to a central feature of the naturalistic solutions. (shrink)

Both among scholars in China and abroad there have been quite a few differences of opinion on and studies into Mao Zedong's essay "On Practice". The subject of such controversies have been various - theoretical, political, and historical - and the debates on these different issues have cut across one another. The three problems of concern in this paper concern primarily the historical aspect of "On Practice".

Several fallacies of conditionalization are illustrated, using the two-envelope problem as a case in point.

Abstract: By the second half of the eleventh century, in the Christian West, the theological doctrine of St. Anslem sought to re‐establish the place of reason within the domain of faith. Anselm arrived at a possible re‐enactment of this relation under the condition regulated by the principle fides quaerens intellectum – faith seeking reason. This paper is an attempt to explore not only the possible implications of this principle but to understand the internal logic which constitutes it and holds it (...) together. It is the contention of this paper that this regulative principle (fides quaerens intellectum) could complete such a process of logically constituting itself through a violent forcing of thought which gathered and maintained within itself an anomy. This internal paradox produced a logical excess which at one hand threatened constantly to expose a crisis, inhabiting the very centre of the theological system it sought to build, but on the other hand it also became the very ground on which such a system constituted itself. To that extent this paper would try to understand the metaphysical forcing of this moment of crisis back into the theological system it sought to express and normalize at the same time. (shrink)

The central task of cognitive neuroscience to map cognitive capacities to neural mechanisms faces three interlocking conceptual problems that together frame the problem of cognitive ontology. First, they must establish which tasks elicit which cognitive capacities, and specifically when different tasks elicit the same capacity. To address this operationalization problem, scientists often assess whether the tasks engage the same neural mechanisms. But to determine whether mechanisms are of the same or different kinds, we need to solve the (...) abstraction problem by determining which mechanistic differences are and are not relevant, and also the boundary problem by distinguishing the mechanism from its background conditions. Solving these problems, in turn, requires understanding how cognitive capacities are elicited in tasks. These three problems, which have been noted and discussed elsewhere in the literature, together form a ‘cycle of kinds’ that frames the central problem-space of cognitive ontology. We describe this cycle to clarify the intellectual challenges facing the cognitive ontologist and to reveal the kind of iterative process by which ontological revision in cognitive neuroscience is likely to unfold. (shrink)

The lunar Three-Body problem is a famously intractable problem of Newtonian mechanics. The demand for accurate predictions of lunar motion led to practical approximate solutions of great complexity, constituted by trigonometric series with hundreds of terms. Such considerations meant there was demand for high speed machine computation from astronomers during the earliest stages of computer development. One early innovator in this regard was Wallace J. Eckert, a Columbia University professor of astronomer and IBM researcher. His work illustrates (...) some interesting features of the interaction between computers and astronomy. (shrink)

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated solution (...) in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package. (shrink)

-/- In Plato's work the "Sophist", Socrates, who typically occupies a central position in Plato's dialogues, is assigned a supporting role. This has led some scholars to argue for a shift in Plato's oeuvre, where he distances himself from Socrates and introduces a new main protagonist. However, this new protagonist remains unnamed and is only identified by his social position as Xenos, indicating that he is an outsider and a stranger whose identity is ambiguous. In this article, I argue that (...) Plato's decision to leave the character unnamed serves to raise a first problem: the question of whether this stranger is a friend or an adversary of philosophy. At the beginning of the dialogue, Socrates employs a series of references to Homer to bring into play a second problem: the problem of disguise. The third problem, “What is a sophist?”, is attributed to the Xenos. This is the only problem that is explicitly developed and is, therefore, the most prominent in the dialogue. If we relate these three problems to each other, it becomes clear that they represent contradictory intuitions without providing us with a strict criterion for deciding which of these intuitions is correct. By presenting these problems in their entanglement without providing a way out, Plato invites his readers to think without making explicit what the outcome of this thinking should be. -/- [In Dutch: In de "Sofist" speelt Sokrates, vaak het meest prominente personage in Plato’s dialogen, alleen maar een bijrol. Dit heeft veel interpreten ertoe verleid om een breuk in het oeuvre van Plato te postuleren, waarbij Plato afstand zou nemen van Sokrates ten behoeve van een nieuw personage. Ik zal echter laten zien dat Plato er bewust voor kiest om dit nieuwe personage naamloos te laten en hem alleen aan te duiden via zijn sociale positie als xenos (vreemdeling). Hiermee roept Plato, zo zal ik betogen, impliciet een eerste probleem op: is deze naamlo- ze Xenos een vriend of een vijand van de filosofie? Aan het begin van de dialoog wordt er door Sokrates een tweede probleem in spel gebracht: het probleem van de vermomming. Het derde probleem — ‘wat is een sofist?’ — wordt toegeschreven aan de Xenos. Dit is het enige probleem dat expliciet wordt uitgewerkt en is dan ook het meest prominent aanwezig in de dialoog. Als we deze drie problemen op elkaar betrekken dan wordt duidelijk dat ze tegenstrijdige intuïties vertolken, zonder dat we een strikt criterium krijgen aangereikt om te beslissen welke van deze intuïties de juiste is. Door deze problemen in een nog niet ontwarde kluwen te presenteren, nodigt Plato zijn lezers uit tot denken, zonder expliciet te maken wat de uitkomst van dit denken zou moeten zijn.]. (shrink)

Newtonian gravitation is studied from a discrete point of view, in that the dynamical equation is an energy-conserving difference equation. Application is made to planetary-type, nondegenerate three-body problems and several computer examples of perturbed orbits are given.

Jazz band is a 3 player superadditive game in characteristic function form. Three players have to divide the payoff they can get, while being in a grand coalition, provided their individual and duo coalitions payoffs are known. Assumptions of individual and collective rationality lead to the notion of the core of the game. We discuss offers that cannot readily be refused [OCRR] as the solutions of the game in case of an empty core, when duo coalitions are the best (...) options but only for two out of three players. The experiment shows that even in case of an empty core the most probable results are three-way coalitions and the share of the weakest player usually exceeds his OCRR. The Shapley value is introduced and its fairness is discussed as it lies at the side of the core while, on the other hand, the nucleolus lies exactly at the center of the core. We conclude that, in spite of that, the Shapley value is the best candidate for a fair sharing solution of the jazz band game and other similar games as, opposite to the other values, it is dependent both on individual and duo coalitions payoffs. (shrink)