This paper considers the problem of causal explanation in classical and statistical thermodynamics. It is argued that the irreversibility of macroscopic processes is explained in both formulations of thermodynamics in a teleological way that appeals to entropic or probabilistic consequences rather than to efficient-causal, antecedental conditions. This explanatory structure of thermodynamics is not taken to imply a teleological orientation to macroscopic processes themselves, but to reflect simply the epistemological limitations of this science, wherein consequences of heat-work asymmetries are either macroscopically (...) measurable (entropy) or calculable (probabilities), while efficient-causal relationships are obscure or indeterminable. (shrink)

Richard Jeffrey’s “Conditioning, Kinematics, and Exchangeability” is one of the foundational documents of probability kinematics. However, the section entitled “Successive Updating” contains a subtle error regarding the applicability of updating by so-called relevance quotients in order to ensure the commutativity of successive probability kinematical revisions. Upon becoming aware of this error, Jeffrey formulated the appropriate remedy, but he never discussed the issue in print. To head off any confusion, it seems worthwhile to alert readers of Jeffrey’s (...) “Conditioning, Kinematics, and Exchangeability” to the aforementioned error and to document his remedy, placing it in the context of both earlier and subsequent work on commuting probability kinematical revisions.1. (shrink)

We consider Effort Games, a game-theoretic model of cooperation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, (...) called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project.We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of carrying out each task and on the boolean function that defines which task subsets complete the project, and which do not. We view this boolean function as a simple coalitional game, and call this game the underlying coalitional game. We suggest the Price of Myopia as a measure of the influence the model of rationality has on the minimal payments the principal has to make in order to motivate the agents in such a domain to exert effort.We consider the computational complexity of testing whether exerting effort is a dominant strategy for an agent, and of finding a reward strategy for this domain, using either a dominant strategy equilibrium or using iterated elimination of dominated strategies. We show these problems are generally #P-hard, and that they are at least as computationally hard as calculating the Banzhaf power index in the underlying coalitional game. We also show that in a certain restricted domain, where the underlying coalitional game is a weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time. We give bounds on PoM in weighted voting effort games, and provide simulation results regarding PoM in another restricted class of effort games, namely effort games played over Series-Parallel Graphs. (shrink)

Lewis signaling games illustrate how language might evolve from random behavior. The probability of evolving an optimal signaling language is, in part, a function of what learning strategy the agents use. Here we investigate three learning strategies, each of which allows agents to forget old experience. In each case, we find that forgetting increases the probability of evolving an optimal language. It does this by making it less likely that past partial success will continue to reinforce suboptimal practice. (...) The learning strategies considered here show how forgetting past experience can promote learning in the context of games with suboptimal equilibria. (shrink)

The heart of my dissertation project is the proposal of a new updating rule for responding to learning experiences consisting of continuous streams of evidence. I suggest characterizing this kind of learning experience as a continuous stream of stipulated credal derivatives, and show that Continuous Probability Kinematics is the uniquely coherent response to such a stream which satisfies a continuous analogue of Rigidity – the core property of both Bayesian and Jeffrey conditionalization. In the first chapter, I define (...) neighborhood norms of rationality with reference to Kenny Easwaran’s definition of neighborhood properties. I summarize and comment on some of the key arguments in the dispute between time-slice epistemologists, who argue that there are no fundamentally diachronic norms of rationality, and the proponents of diachronic norms. I am sympathetic to two of the key motivations often given in support of the synchronist position: mentalist internalism and the idea that metaphysical disputes about the identity of persons in bizarre puzzle cases should not play a central role in epistemologists’ assessments of the rationality of agents. However, I argue that time-slice epistemology cannot adequately address the rationality of temporally-extended processes like reasoning and learning. Neighborhood norms present a viable third way between these two positions, capturing much of the spirit of the previously-discussed synchronist motivations while still providing just enough temporal structure to meaningfully guide and evaluate temporally-extended rational processes. Continuous Probability Kinematics is an example of one such neighborhood norm. In the second chapter, I develop my updating rule CPK and establish many of its core properties. Of special note here are the deep connections to Jeffrey’s Probability Kinematics, as well as some key differences. The net result of any CPK updating process will always be representable as a Jeffrey shift on the refined partition generated by the propositions that the agent is receiving direct evidence concerning. However, one crucial difference is that CPK provides an intuitive account of how to combine the effects of learning experiences that are each about fundamentally different underlying partitions. In CPK’s formalism, an agent can receive simultaneous evidence streams about an arbitrary (finite) number of propositions, which can themselves be evidentially related in any way. At any given instant, the result of the combination is a simple sum of the effects that learning about the individual propositions would have separately. CPK is concerned with a novel kind of learning experience and involves a novel characterization of evidence. The third and final chapter of this dissertation is concerned with explaining what this characterization of evidence means and with arguing that it can be the basis for genuine learning. I begin by characterizing learning experiences in terms of the Value of Information, and prove a Value of Information theorem for CPK learning experiences under the assumption of a Martingale constraint on the agent’s prior distribution over the signals that they might receive. I examine Timothy Williamson’s arguments that evidence must be propositional and express my skepticism. I then explore two different routes to model agents who update by CPK as if they are learning some propositional content and updating the rest of their credences by Bayesian conditionalization on this content. The second of these two routes provides a very interesting lens to reexamine the evidential commitments that underwrite updating by CPK, which I analyze. (shrink)

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain (...) observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory. (shrink)

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the (...) accepted epistemic judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment , and the family of possible epistemic inputs . First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that (...) determines the accepted epistemic judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (pme) give a solution to the obverse Majerník problem; and (2) is Wagner correct when he claims that Jeffrey’s updating principle (jup) contradicts pme? Majerník shows that pme provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether pme also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that in (...) the special case introduced by Wagner pme does not contradict jup, but elegantly generalizes it and offers a more integrated approach to probability updating. (shrink)

Probability kinematics is the theory of how subjective probabilities change with time, in response to certain constraints . Rules are classified by the imposed constraints for which the rules prescribe a procedure for updating one's opinion. The first is simple conditionalization , and the second Jeffrey conditionalization . It is demonstrated by a symmetry argument that these rules are the unique admissible rules for those constraints, and moreover, that any probability kinematic rule must be equivalent to a (...) conditionalization preceded by a determination of the values x i to be given to the members of such a partition. Next two rival rules which can go beyond such conditionalization are described. INFOMIN and MTP . Their properties are investigated and compared. (shrink)

Making up your mind can include making up your mind about how to change your mind. Here a suggestion for coding imputations of influence into the kinematics of judgmental probabilities is applied to the treatment of Newcomb problems in The Logic of Decision framework. The suggestion is that what identifies you as treating judgmental probabilistic covariance of X and Y as measuring an influence of X on Y is constancy of your probabilities for values of Y conditionally on values (...) of X as your judgmental probability distribution for values of X changes. (shrink)

L. J. Savage and I. J. Good have each demonstrated that the expected utility of free information is never negative for a decision maker who updates her degrees of belief by conditionalization on propositions learned for certain. In this paper Good's argument is generalized to show the same result for a decision maker who updates her degrees of belief on the basis of uncertain information by Richard Jeffrey's probability kinematics. The Savage/Good result is shown to be a (...) special case of the more general result. (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.

We argue that the intractable part of the measurement problem -- the 'big' measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the (...) view that the quantum state has an ontological significance analogous to the significance of the classical state as the 'truthmaker' for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the 'big' measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW 'collapse' theorists who add structure to the theory and propose dynamical solutions to the 'big' measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic objective probabilistic constraints on correlations between events. (shrink)

Another title in the reissued Oxford Classic Texts in the Physical Sciences series, Jeffrey's Theory of Probability, first published in 1939, was the first to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Until recently the two schools of statistics were distinctly different and (...) set apart. Recent work has changed all that and today's graduate students and researchers all require an understanding of Bayesian ideas. This book is their starting point. (shrink)

Hugh Everett III proposed his relative-state formulation of pure wave mechanics as a solution to the quantum measurement problem. He sought to address the theory’s determinate record and probability problems by showing that, while counterintuitive, pure wave mechanics was nevertheless empirically faithful and hence empirical acceptable. We will consider what Everett meant by empirical faithfulness. The suggestion will be that empirical faithfulness is well understood as a weak variety of empirical adequacy. The thought is that the very idea of (...) empirical adequacy might be renegotiated in the context of a new physical theory given the theory’s other virtues. Everett’s argument for pure wave mechanics provides a concrete example of such a renegotiation. (shrink)

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. (...) A popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in a (...) way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States2 Everett and Frank3 Everett on the Nature of Physical Theories4 Conditions for Empirical Faithfulness5 The Empirical Faithfulness of Pure Wave Mechanics6 Conclusion. (shrink)

Belief-revision models of knowledge describe how to update one’s degrees of belief associated with hypotheses as one considers new evidence, but they typically do not say how probabilities become associated with meaningful hypotheses in the first place. Here we consider a variety of Skyrms–Lewis signaling game (Lewis in Convention. Harvard University Press, Cambridge, 1969; Skyrms in Signals evolution, learning, & information. Oxford University Press, New York, 2010) where simple descriptive language and predictive practice and associated basic expectations coevolve. Rather than (...) assigning prior probabilities to hypotheses in a fixed language then conditioning on new evidence, the agents begin with no meaningful language or expectations then evolve to have expectations conditional on their descriptions as they evolve to have meaningful descriptions for the purpose of successful prediction. The model, then, provides a simple but concrete example of how the process of evolving a descriptive language suitable for inquiry might also provide agents with conditional expectations that reflect the type and degree of predictive success in fact afforded by their evolved predictive practice. This illustrates one way in which the traditional problem of priors may simply fail to apply to one’s model of evolving inquiry. (shrink)

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right (...) statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm''s theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm''s theory without the distribution postulate. (shrink)

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

On Bohm's formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm's theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right (...) statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm's theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm's theory without the distribution postulate. (shrink)

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

In “Popper, Weber, and Hayek,” I claimed that the economic and political world governed by social democracy is too complex to offer hope for rational social‐democratic policy making. I extrapolated this conclusion from the claim, made by Austrian‐school economists in the 1920s and 30s, that central economic planning would face insurmountable “knowledge problems.” Israel Kirzner's Reply indicates the need to keep the Austrians’ cognitivist argument conceptually distinct from more familiar incentives arguments, which can tacitly reintroduce the assumption of omniscience against (...) which the Austrian economists rebelled. Callahan's Reply illustrates the need to keep in mind the hypothetical, conditional nature of economic arguments. Notturno's Reply changes the subject by asserting the intrinsic value of social‐democratic participation, regardless of its outcomes—even while, like Talisse's Reply, ignoring the evidence that public ignorance and elite dogmatism probably can't be mitigated by more information or by appeals to be open minded. And Hill focuses on the very real imperfections of market and other private‐sphere decision making, without weighing the shortcomings of the political alternatives. Markets and other private‐sphere decision arenas don't have to be perfect for them to improve upon public‐sector processes. In the latter, cognitive demands tend to be much greater, because of the divergence of modern social problems from the conditions that would have faced the hunter‐gatherers whose cognitive apparatus we have inherited. (shrink)

I formulate the interpretation problem of quantum mechanics as the problem of identifying all possible maximal sublattices of quantum propositions that can be taken as simultaneously determinate, subject to certain constraints that allow the representation of quantum probabilities as measures over truth possibilities in the standard sense, and the representation of measurements in terms of the linear dynamics of the theory. The solution to this problem yields a modal interpretation that I show to be a generalized version of Bohm's hidden (...) variable theory. I argue that unless we alter the dynamics of quantum mechanics, or accept a for all practical purposes solution, this generalized Bohmian mechanics is the unique solution to the problem of interpretation. (shrink)

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was the (...) impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. (shrink)

This chapter contains sections titled: Notes.

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. (...) This is surprising because based on independence assumptions the anticipated result is that it would support the opponents. It also demonstrates that opponents improperly apply independence assumptions to the problem. (shrink)

Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without introducing (...) a randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed “strict,” and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell. (shrink)

Nick Bostrom’s recently patched ‘‘simulation argument’’ (Bostrom in Philos Q 53:243–255, 2003; Bos- trom and Kulczycki in Analysis 71:54–61, 2011) purports to demonstrate the probability that we ‘‘live’’ now in an ‘‘ancestor simulation’’—that is as a simulation of a period prior to that in which a civilization more advanced than our own—‘‘post-human’’—becomes able to simulate such a state of affairs as ours. As such simulations under consid- eration resemble ‘‘brains in vats’’ (BIVs) and may appear open to similar objections, (...) the paper begins by reviewing objections to BIV-type proposals, specifically those due a presumed mad envatter. In counter example, we explore the motivating rationale behind current work in the development of psychologically realistic social simula- tions. Further concerns about rendering human cognition in a computational medium are confronted through review of current dynamic systems models of cognitive agency. In these models, aspects of the human condition are repro- duced that may in other forms be considered incomputable, i.e., political voice, predictive planning, and consciousness. The paper then argues that simulations afford a unique potential to secure a post-human future, and may be nec- essary for a pre-post-human civilization like our own to achieve and to maintain a post-human situation. Long-s- tanding philosophical interest in tools of this nature for Aristotle’s ‘‘statesman’’ and more recently for E.O. Wilson in the 1990s is observed. Self-extinction-level threats from State and individual levels of organization are compared, and a likely dependence on large-scale psychologically realistic simulations to get past self-extinction-level threats is projected. In the end, Bostrom’s basic argument for the conviction that we exist now in a simulation is reaffirmed. (shrink)

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...) in terms of a psychological effect: ambiguity aversion . The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis. (shrink)

Nearly 30 years ago, Terry Horgan and Mark Timmons published a now- popular article that combines Hilary Putnam’s Twin Earth scenario with G.E. Moore’s open question argument in an effort to show that moral naturalism – the view that moral facts are at bottom ordinary, natural facts of some sort – is probably false. Responses to Horgan and Timmons’s “revised open question argument” have been legion, but surprisingly, no one has attempted to test the core assumption upon which the argument (...) is based; namely, that competent language users univocally treat natural kind-terms as rigid designators. Here, I present evidence that the intuitions of competent English speakers are not as univocal as Horgan and Timmons need them to be to ground their argument against moral naturalism. I also briefly sketch a way that the moral naturalist can respond even if competent language speakers do treat natural-kind terms in the way that Horgan and Timmons suggest. (shrink)

Here we use generalized signaling games to model how one’s beliefs might coevolve with the language one uses to characterize those beliefs. We will start by considering how one might individuate pragmatic notions of truth and how such notions might coevolve with a descriptive language. We will then consider how agents might evolve a language that allows them to characterize their beliefs and degrees of belief. Finally, we will consider evolutionary conditions under which a principle of indifference that assigns equal (...) prior probability to each possibility that one can describe in one’s evolved language might in fact be successful. (shrink)

Nearly 30 years ago, Terry Horgan and Mark Timmons published a now- popular article that combines Hilary Putnam’s Twin Earth scenario with G.E. Moore’s open question argument in an effort to show that moral naturalism – the view that moral facts are at bottom ordinary, natural facts of some sort – is probably false. Responses to Horgan and Timmons’s “revised open question argument” have been legion, but surprisingly, no one has attempted to test the core assumption upon which the argument (...) is based; namely, that competent language users univocally treat natural kind-terms as rigid designators. Here, I present evidence that the intuitions of competent English speakers are not as univocal as Horgan and Timmons need them to be to ground their argument against moral naturalism. I also briefly sketch a way that the moral naturalist can respond even if competent language speakers do treat natural-kind terms in the way that Horgan and Timmons suggest. (shrink)

From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered (...) for use when such definite conditional probabilities are absent. (shrink)

Bayesian Epistemology is a general framework for thinking about agents who have beliefs that come in degrees. Theories in this framework give accounts of rational belief and rational belief change, which share two key features: (i) rational belief states are represented with probability functions, and (ii) rational belief change results from the acquisition of evidence. This dissertation focuses specifically on the second feature. I pose the Evidence Question: What is it to have evidence? Before addressing this question we must (...) have an understanding of Bayesian Epistemology. The first chapter argues that we should understand Bayesian Epistemology as giving us theories that are evaluative and not action-guiding. I reach this verdict after considering the popular ‘ought’-implies-‘can’ objection to Bayesian Epistemology. The second chapter argues that it is important for theories in Bayesian Epistemology to answer the Evidence Question, and distinguishes between internalist and externalist answers. The third and fourth chapters present and defend a specific answer to the Evidence Question. The account is inspired by reliabilist accounts of justification, and attempts to understand what it is to have evidence by appealing solely to considerations of reliability. Chapter 3 explains how to understand reliability, and how the account fits with Bayesian Epistemology, in particular, the requirement that an agent’s evidence receive probability 1. Chapter 4 responds to objections, which maintain that the account gives the wrong verdict in a variety of situations including skeptical scenarios, lottery cases, scientific cases, and cases involving inference. After slight modifications, I argue that my account has the resources to answer the objections. The fifth chapter considers the possibility of losing evidence. I show how my account can model these cases. To do so, however, we require a modification to Conditionalization, the orthodox principle governing belief change. I present such a modification. The sixth and seventh chapters propose a new understanding of Dutch Book Arguments, historically important arguments for Bayesian principles. The proposal shows that the Dutch Book Arguments for implausible principles are defective, while the ones for plausible principles are not. The final chapter is a conclusion. (shrink)

Joseph Margolis, a relativist with respect to aesthetic qualities, has argued that nonrelativists must produce a theory of perception capable of providing a basis for the distinction between an object’s actually possessing a specified aesthetic quality and an object’s only seeming to possess it. Although I think Margolis is probably right on the point, my concern is not with the need for the non relativist to produce such a theory; rather, it is with the need for the relativist to give (...) an account of the perception of aesthetic qualities. (shrink)

This article considers the ethical aspects of the question: should a scientist engage in war-related research, particularly use-inspired or applied research directed at the development of the means for the better waging of war? Because scientists are simultaneously professionals, citizens of a particular country, and human beings, they are subject to conflicting moral and practical demands. There are three major philosophical views concerning the morality of war that are relevant to this discussion: realism, just war theory and pacifism. In addition, (...) the requirements of professional codes of ethics and common morality contribute to an ethical analysis of the involvement of scientists and engineers in war-related research and technology. Because modern total warfare, which is facilitated by the work of scientists and engineers, results in the inevitable killing of innocents, it follows that most, if not all, war-related research should be considered at least as morally suspect and probably as morally prohibited. (shrink)

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are in conflict with (...) either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example. (shrink)

This chapter contains sections titled: Pascal's Wager Other Prominent Pragmatic Arguments Pragmatic Arguments and the Ethics of Belief Works cited.

This article discusses bertrand russell's book "human knowledge". This discussion is focused on the problem of probability, In relation to russell's discussion of it in his book. (staff).

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In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Report from the Front Lines: Conversations on Public Theology. A Festschrift in Honor of Robert Benne, and: Explorations in Christian Theology and Ethics: Essays in Conversation with Paul L. LehmannJeffrey P. GreenmanA Report from the Front Lines: Conversations on Public Theology. A Festschrift in Honor of Robert Benne Edited by Michael Shahan Grand Rapids, Mich.: Eerdmans, 2009. 184 pp. $30.00.Explorations in Christian Theology and Ethics: Essays in (...) Conversation with Paul L. Lehmann Edited by Philip G. Ziegler and Michelle J. Bartel Farnham, Surrey, UK: Ashgate, 2009. 206 pp. $99.95.The volumes reviewed here each recognize an important thinker in Christian social ethics in America: Robert Benne, emeritus professor of religion at Roanoke College, a Lutheran social ethicist; and Paul L. Lehmann (1906–94), a Presbyterian who was an influential teacher associated with Princeton Theological Seminary, Harvard University Divinity School, and Union Theological Seminary in New York.The first volume honors Benne’s seventieth birthday. His major writings include The Ethic of Democratic Capitalism: A Moral Reassessment (1981), Ordinary Saints: An Introduction to the Christian Life (1988), The Paradoxical Vision: A Public Theology for the Twenty-First Century (1995), Quality with Soul: How Six Premier Colleges and Universities Keep Faith with Their Religious Traditions (2001), and most recently, Good and Bad Ways to Think about Religion and Politics (2010). Since Benne is known for his traditionalist moral views, some unmistakably conservative voices, including a number of prominent Lutherans and neoconservative political thinkers, are represented in this book. The broad theme is public theology, working from Benne’s definition of public theology as “the engagement of a living religious tradition with its public environment—the economic, political, and cultural spheres of our common life.”The book has three parts. The first section, “The Imperative of a Public Theology,” includes essays by editor Michael Shahan, Carl Braaten, Jean Bethke Elshtain, and Richard John Neuhaus. Shahan’s essay provides a helpful exposition of Benne’s intellectual trajectory. Braaten offers a defense of the historic, bodily resurrection of Jesus as the “crux of Christianity’s case.” Elshtain takes [End Page 206] up C. S. Lewis’s concerns in his Abolition of Man (1944) as she diagnoses the “cultural disorder” reflected in current debates about euthanasia and abortion. Neuhaus’s wistful essay looks back over his efforts in the public square, stating that he and Benne have shared a common concern: “A renewal of Christian confidence in providing a morally informed philosophy for a more just and virtuous society in the tradition of liberal democracy” (47). Taken together, these four chapters sketch the assumed intellectual and cultural landscape that sets the context for the volume as a whole.The second section, “The Lutheran Necessity in Public Theology,” begins with a largely autobiographical essay by James Nuechterlein about his journey in Lutheranism and the value of its theological distinctives, especially the famous simul. Next is Gilbert Meilaender’s account (exploring an insight from Kierkegaard) of the place for a Lutheran “corrective” within the wider normative tradition, then Mark Noll’s chapter that underscores the value of robust Lutheran social thinking against the backdrop of the more revivalist and pietist tendencies of Protestant evangelicalism.The final section, “Contested Issues in Public Theology,” includes chapters by Paul Hinlicky, Ronald Thiemann, Gerald McDermott, Donald Schmeltekopf and Michael Beaty, and Joseph Swanson. The chapters by Hinlicky on Luther’s relation to liberal political theory, and by Thiemann on the idea of the public theologian’s prophetic role as “connected critic,” are the most densely argued material in the book. These two essays will probably be of the most interest for scholars in theological ethics. The chapter by McDermott deals with Lutheran church-related colleges. A coauthored essay by Schmeltekopf and Beaty champions the vocation of Christian university education. Swanson situates Benne’s economic writings within neo-conservative thought.The book takes up some of Benne’s favorite themes and interest areas, but only rarely do the authors engage Benne’s own thought. Virtually nowhere do they prod Benne to become clearer, to strengthen his arguments, or to modify his conclusions. I would have preferred a deeper engagement with Benne’s ideas; in several... (shrink)