David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics. This approach promises to resolve some long-standing problems with probability in EQM, but it has faced plenty of resistance. One kind of objection charges that the requisite notion of decision-theoretic uncertainty is unavailable in the Everettian picture, so that the argument cannot gain any traction; another kind of objection grants the proof’s applicability and targets the premises. In this article I propose (...) some novel principles connecting the physics of EQM with the metaphysics of modality, and argue that in the resulting framework the incoherence problem does not arise. These principles also help to justify one of the most controversial premises of Wallace’s argument, ‘branching indifference’. Absent any a priori reason to align the metaphysics with the physics in some other way, the proposed principles can be adopted on grounds of theoretical utility. The upshot is that Everettians can, after all, make clear sense of objective probability. 1 Introduction2 Setup3 Individualism versus Collectivism4 The Ingredients of Indexicalism5 Indexicalism and Incoherence5.1 The trivialization problem5.2 The uncertainty problem6 Indexicalism and Branching Indifference6.1 Introducing branching indifference6.2 The pragmatic defence of branching indifference6.3 The non-existence defence of branching indifference6.4 The indexicalist defence of branching indifference7 Conclusion. (shrink)

Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schrödinger and Born, are in tension with one another but are not incompatible. Schrödinger’s idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to (...) determine atomic and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schrödinger’s electron charge density can be incorporated into many different interpretations of quantum mechanics. (shrink)

The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.

This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency (...) and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics. (shrink)

It has been alleged that Bayesian usage of prior probabilities allows one to obtain empirical statements on the basis of no evidence whatever. We examine this charge with reference to several examples from the literature, arguing, first, that the difference between probabilities based on weighty evidence and those based on little evidence can be drawn in terms of the variance of a distribution. Moreover, qua summaries of vague prior knowledge, prior distributions only transmit the empirical information therein contained and, (...) therefore, their consequences for long-run frequency behavior are "a priori" in at best a Pickwickian sense. (shrink)

Pruss uses an example of Lester Dubins to argue against the claim that appealing to hyperreal-valued probabilities saves probabilistic regularity from the objection that in continuum outcome-spaces and with standard probability functions all save countably many possibilities must be assigned probability 0. Dubins’s example seems to show that merely finitely additive standard probability functions allow reasoning to a foregone conclusion, and Pruss argues that hyperreal-valued probability functions are vulnerable to the same charge. However, Pruss’s argument (...) relies on the rule of conditionalisation, but I show that in examples like Dubins’s involving nonconglomerable probabilities, conditionalisation is self-defeating. (shrink)

Tacitus traces a series of conflicts between Agrippina the Elder and her father-in-law Tiberius. After the death of her husband Germanicus in Syria, Agrippina returned to Rome with their children. Germanicus' lingering popularity with the armies and people meant that his widow Agrippina and their children enjoyed a level of popular support as well—one that eventually became a threat in Tiberius' mind. Agrippina, moreover, refused to embrace the modest, retiring role that her father-in-law expected of her. Tiberius was, moreover, ‘never (...) gentle toward the house of Germanicus’ and his concerns were augmented by the machinations of Sejanus, who reported that the people were dividing themselves into factions, some even calling themselves members of the partes Agrippinae. The combination of Agrippina's high birth—the only still-living grandchild of Augustus—and her status as widowed daughter-in-law of the emperor, therefore mother of the emperor's probable heir, along with her persistent independence and sometimes unfeminine strength of character made her seem an intolerable political threat. This paper examines the culmination of these conflicts, when Agrippina is subjected to criminal prosecution and penalty in a.d. 27 and 29 at the instigation of Sejanus, with the overt approval of Tiberius. Of primary concern is the timing and the order of the charges brought against Agrippina. (shrink)

In order adequately to refute the charge that relativism makes against any absolute answer to problems of science, it will be necessary for us to generalize upon the principal theme and attempt a characterization of experimental methodology. Only by thus determining what constitutes experimental inquiry in general can we hope to define that particular aspect of it which involves the concept of probability.

Salutary reading for all philosophers, and not only for inductive logicians, philosophers of science and law, this important book presents an elaborate theory of inductive reasoning whose substantive features are as strikingly original as the approach is rare. First, the theory is based on concrete, real, actual, and significant instances of inductive reasoning, e.g., Karl von Frisch’s work on bees; that is, though its aim is genuinely theoretical in the sense that it engages in the proper amounts of idealization, abstraction, (...) systematization, precision, and rigor, it never loses sight of the fact that "theories in the philosophy of science, like theories in science itself, have to face up to the challenge of appropriately accredited experience within their appointed domains". Second, a central subject matter being analyzed is legal reasoning, that is, the types of proofs and arguments used by juries, judges, and lawyers in the Anglo-American system of jurisprudence, where criminal charges have to be proved beyond reasonable doubt and civil cases have to be argued on the balance of probability. Thus, in effect, Cohen’s synthesis of juridical and of scientific reasoning is an admirable example of the bridging of two "cultures." Third, and most importantly, the concept of "inductive probability," in terms of which Cohen makes sense out of his subject matter, is incommensurable with that of "mathematical probability," namely the classical calculus of chance according to which probability is measurable, additive, transitive, and obeys a multiplicational principle for conjunction and a complementational one for negation. This is not to say that "inductive probability" is a hazy, mysterious, or unstructured concept, and Cohen goes to great lengths to show that it is ordinal, modal, and formally analyzable; what it does mean is that essential types of reasoning in science and in law involve probable inferences whose probabilities are nonquantitative. Hence, though Cohen does not stress the qualitative nature of inductive probability, his book will be welcome by those who conceive of philosophy as scientia qualitatum. Specific conclusions reached by Cohen are that, in general, probability may be conceived as degree of provability, that differences in proof-rules generate different special cases of probability, that inductive probability may be viewed as the special case where the proof-rules are incomplete, that inductive probability is to inductive support as deducibility is to logical truth, and that some recent epistemological scepticism may be refuted by Cohen’s inductive logic. Finally, he sees himself in the British inductivist tradition, interpreting his predecessors as groping toward a logic of inductive support and probability rather than a methodology of discovery: from Bacon he develops the notion of eliminative induction but rejects that of induction by enumeration; Mill’s canons are analyzed as special cases of Cohen’s own "method of relevant variables," except for the method of residues, which is rejected as invalid ; he takes his critique of mathematical probability as a vindication of Hume’s thesis that "probability or reasoning from conjecture may be divided into two kinds, viz., that which is founded on chance and that which arises from causes" ; Whewell’s consilience of induction is justified ; and from Keynes, he develops the notion of the "weight" of evidence but rejects his mathematicist approach.—M. A. F. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. The (...) differences between the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Logic of Probabilities in Hume's Argument against Miracles Fred Wilson The position is often stated that Hume's discussion of miracles is inconsistent with his views on the logical or ontological status oflaws ofnature and with his more general scepticism. Broad, for one, has so argued.1 Hume's views on induction are assumed to go somethinglike this. Any attempt to demonstrate knowledge ofmatters offact presupposes causal reasoning, but the latter (...) is based not on any perception of necessary connections, but on an unreasoned expectation that because events have been constantly conjoined in the past they will be constantly conjoined in the future. The fact that our past experience gives rise to certain expectations provides absolutely no reason to think that these expectations will be fulfilled. But this is forgotten as soon as he turns to the topic of miracles where the argument requires certain assumptions about laws of nature. Here he claims that the laws of nature arebased upon afirm andunalterable experience and dismisses what he apparently admits to be strong evidence for miracles on the basis of the claim that such events are absolutely impossible. The inconsistency between the discussion of miracles and the earlier discussions of induction and causality is clear. Nonetheless, there is a certain implausibility to this claim that makes it a difficult one to entertain seriously, since it is unlikely that a philosopher as careful as Hume would have failed to recognize the inconsistency if it existed. What I propose here to argue is that there is in fact no inconsistency, and that this becomes clear once one places the discussion ofmiracles in the broader context ofthe overall argument ofthe first Enquiry. In particular, the charge ofinconsistency disappears once one eliminates the caricature ofHume's views on causal reasoning upon which it rests. To come to grips with the discussion of miracles in Hume it is necessary to place that discussion in its historical context. In the generally empiricist atmosphere that developed in Britain following the mid-seventeenth century civil wars, the general defence of the reasonableness of Christianity consisted of two parts. First, it washeldthatrational argument, whether causal or teleological orboth, could yield a reasonable belief that a deity ofa more or less traditional sort existed. Then, second, in order to establish further that Jesus was the Son ofGod it was held that one could rely upon a chain oftestimony Volume XV Number 2 255 FRED WILSON leading back from the present to the past to infer the existence of miracles testifying to the divinity ofJesus. Hume attacks this second inference in the essay on miracles andthe first in the essay that follows in the Enquiries on God's particular providence (the themes of which are developed more fully in the Dialogues on Natural Religion). Given the central place that the appeal to miracles held in Christian apologetics in the 17th and 18th centuries, Hume's systematic attack on the argument from miracles constituted a clear attack on Christianity. To be sure, Hume's argument would never have persuaded JohnWesley, but that would hardly have surprised Hume himself, nor should it surprise us: those in the grips of religious enthusiasm, whether it be John Wesley or Jimmy Swaggart, will hardly be persuaded by rational argument, however much it is still true that they ought to be persuaded by it. The appeal to miracles tojustify specifically Christian beliefs had a long history. One can find it already in the late Roman period in Eusebius. Muslim thinkers were to challenge this traditional defence by arguing that chains oftestimony become more unreliable the longer they become. As for their own Islamic beliefs, these they admitted had also to be justified by an appeal to miracles, but there was, it was claimed, a unique self-justifying miracle in the Koran, the specially revealed Word of God. The critical theme of the Muslim apologists, that the longer a chain of testimony the less assurance it gives of the fact that a miracle had occurred, was developed in Britain in the 17th and 18th centuries.6 It seems to have been introduced by the Oxford orientalist Edward Pocock who had discovered this line of Muslim apologetics while... (shrink)

The charge that the limit-frequency theory of probability is inconsistent due to incompatibility between the required features of randomness and limit convergence is inapplicable when probability sequences are taken to be empirically (i.e., extensionally) generated, as they must be on a strictly empirical conception of probability. All past attempts to meet this charge by formulating constructive definitions of randomness that would still allow for a demonstrable limit-convergence have, in their exclusive concern with logically (i.e., intensionally) (...) prescribed sequences, left the logic of extensional classes essentially untouched. In the light of a strict differentiation between intensional and extensional classes a generalized approach is possible under which several closely connected senses of randomness, i.e., the formal, material, restricted and unrestricted senses may be easily distinguished and related to the notion of relevance. (shrink)

Judgments of symmetry lay at the heart of the classical theory of probability. It was by direct appeal to the symmetries exhibited by the processes underlying simple games of chance that the earliest theorists of probability were able to justify the initial assumptions of equiprobability which allowed them to compute the probabilities of more complex events using combinatorial methods, i.e., by simply counting cases. Nevertheless, in spite of the role that symmetry played in the earliest writings on the (...) subject, in light of the fact it is only in highly contrived settings that a direct appeal to symmetries can suffice to determine the probabilities of events, many philosophers have been led to conclude that the concept of symmetry itself has, at best, a limited role to play in a general theory of probability. In this essay, I argue that this view of the matter is mistaken, and that judgments of symmetry, in fact, have an indispensible role to play in all probabilistic reasoning. In chapter 1, I provide a detailed account of symmetry-based reasoning and argue against the view that the judgments of relevance on which such reasoning is based must be construed in subjective terms if symmetry-based reasoning is to be applied to deterministic processes. In chapter 2, I argue that the two most plausible proposals for how to avoid an appeal to symmetry in the assignment of probabilities (viz., those which are based on a priori principles of epistemic conservatism or the observed frequencies of events) must themselves rely on implicit assumptions of symmetry if they are to defend themselves against the charges of incoherency and arbitrariness. In chapter 3, I consider a decision-theoretic example of symmetry-based reasoning, in which the appeal to symmetry arises in the context of an agent's choice of a deliberative methodology. In this context, the principle of symmetry amounts to the requirement that the agent avoid adopting a biased deliberative methodology, i.e., one which treats two equally legitimate sources of information differently. In the specific context of the exchange paradox, I propose an account of how biased information is to be handled, which, despite suffering from some important defects, does, I believe, capture some of our general intuitions about how a rational agent ought to adjust his expectations to correct for the effects of bias. (shrink)

Jon Elster reports that in 1940, and again in 1970, the U.S. draft lottery was challenged for falling short of the legally mandated ‘random selection’. On both occasions, the physical mixing of the lots appeared to be incomplete, since the birth dates were clustered in a way that would have been extremely unlikely if the lots were fully mixed. There appears to have been no suspicion on either occasion that the deficiency in the mixing was intended, known, or believed to (...) favor or disfavor any identifiable group. If the selection was non-random in the way charged, Elster asks, was it unfair? (shrink)

Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

Here, we continue the discussion in [1], about infinities in Physics. Our goal is to create a Mathematical system to give a probable explanation for infinities in QED, based on Fuzzy time. This Mathematical system should be sufficiently satisfactory and Simple. In general, our goal of these series, is to provide more reasons to consider time as a fuzzy concept in a way that is explained in [4], [5], [6].

We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed (...) in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wave function cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wave function is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)

In ‘An Almost Absolute Value in History’ John T. Noonan criticizes several attempts to provide a criterion for when an entity deserves rights. These criteria, he argues are either arbitrary or lead to absurd consequence. Noonan proposes human conception as the criterion of rights, and justifies it by appeal to the sharp shift in probability, at conception, of becoming a being possessed of human reason. Conception, then, is when abortion becomes immoral.The article has an historical and a philosophical goal. (...) The historical goal is to carefully present the probability argument in a charitable manner. The philosophical goal is to offer a unique criticism of Noonan's probability argument against abortion. I argue that, even on a very charitable reading of Noonan's argument for the conception criterion, this criterion is also susceptible to charges of arbitrariness and absurdity. Noonan's claim that probability shifts have anything to do with the moral rights of fetuses cannot be made coherent. I also show that there are problems with Noonan's assumptions about moral rights and the potential to become a being possessed of human reason. (shrink)

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but (...) also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model. (shrink)

Christopher Fuchs has recently offered a provocative version of quantum mechanical realism, which is based on the suggestion that quantum probabilities merit a subjective interpretation. His proposal, however, has been charged with inconsistency by Amit Hagar (2003), who argues that interpreting quantum probabilities subjectively is inconsistent with the realist claims Fuchs wants to maintain for the quantum system and the dimensionality of the Hilbert space that accompanies it. In this paper I first outline the fundamentals of Fuchs's approach and then (...) take up the task of rebutting Hagar's charge by demonstrating the internal coherence of Fuchs's realism. (shrink)

Christopher Fuchs has recently offered a provocative version of quantum mechanical realism, which is based on the suggestion that quantum probabilities merit a subjective interpretation. His proposal, however, has been charged with inconsistency by Amit Hagar, who argues that interpreting quantum probabilities subjectively is inconsistent with the realist claims Fuchs wants to maintain for the quantum system and the dimensionality of the Hilbert space that accompanies it. In this paper I first outline the fundamentals of Fuchs’s approach and then take (...) up the task of rebutting Hagar’s charge by demonstrating the internal coherence of Fuchs’s realism. (shrink)

Teddy Seidenfeld recently claimed that Kolmogorov's probability theory transgresses the Substitutivity Law. Underscoring the seriousness of Seidenfeld's charge, the author shows that (Popper's version of) the law, to wit: If (∀ D)(Pr(B,D)=Pr(C,D)), then Pr(A,B)=Pr(A,C), follows from just C1. 0≤ Pr(A,B)≤ 1 C2. Pr(A,A)=1 C3. Pr(A & B,C)=Pr(A,B & C)× Pr(B,C) C4. Pr(A & B,C)=Pr(B & A,C) C5. Pr(A,B & C)=Pr(A,C & B), five constraints on Pr of the most elementary and most basic sort.

A proposed 4-space Dirac theory requires modified definitions of expected value and Hermitian operator, because the charge density is not positive definite. However, this does not imply negative probability.

Bernoulli’s 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model Mθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}_{{{\varvec{\uptheta}}}} \left( {\mathbf{x}} \right)$$\end{document}, defining the inductive premises of inference. It is argued that several widely-accepted claims relating to the golden theorem and frequentist inference are either misleading or erroneous: (a) Bernoulli solved the problem of inference ‘from probability to frequency’, and thus (b) the golden (...) theorem cannot justify an approximate Confidence Interval (CI) for the unknown parameter θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}, (c) Bernoulli identified the probability PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\left( A \right)$$\end{document} with the relative frequency 1n∑k=1nxk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{n}\sum\nolimits_{k = 1}^{n} {x_{k} }$$\end{document} of event A as a result of conflating f(x0|θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f({\mathbf{x}}_{0} |\theta )$$\end{document} with f(θ|x0),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(\theta |{\mathbf{x}}_{0} ),$$\end{document} where x0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{x}}_{0}$$\end{document} denotes the observed data, and (d) the same ‘swindle’ is currently perpetrated by the p value testers. In interrogating the claims (a)–(d), the paper raises several foundational issues that are particularly relevant for statistical induction as it relates to the current discussions on the replication crises and the trustworthiness of empirical evidence, arguing that: [i] The alleged Bernoulli swindle is grounded in the unwarranted claim θ^nx0≃θ∗,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\theta }_{n} \left( {{\mathbf{x}}_{0} } \right) \simeq \theta^{*},$$\end{document} for a large enough n, where θ^nX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\theta }_{n} \left( {\mathbf{X}} \right)$$\end{document} is an optimal estimator of the true value θ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta^{*}$$\end{document} of θ. [ii] Frequentist error probabilities are not conditional on hypotheses (H0 and H1) framed in terms of an unknown parameter θ since θ is neither a random variable nor an event. [iii] The direct versus inverse inference problem is a contrived and misplaced charge since neither conditional distribution f(x0|θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f({\mathbf{x}}_{0} |\theta )$$\end{document} and f(θ|x0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(\theta |{\mathbf{x}}_{0} )$$\end{document} exists (formally or logically) in model-based (Mθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}_{{{\varvec{\uptheta}}}} \left( {\mathbf{x}} \right)$$\end{document}) frequentist inference. (shrink)

This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability of the loss. (...) Second, it shows that insurers are sensitive to sources of ambiguity. The participants indeed, charged a higher premium when ambiguity came from conflict and disagreement regarding the probability of the loss than when ambiguity came from imprecision (imprecise forecast about the probability of the loss). This research thus documents the presence of both ambiguity aversion and conflict aversion in the field of insurance, and discuses economic and psychological rationales for the observed behaviours. (shrink)

We define an ultraproduct of metric structures based on a maximal probability charge and prove a variant of Łoś theorem for linear metric formulas. We also consider iterated ultraproducts.

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The (...) essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. (...) What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”. (shrink)

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is (...) not continuous but discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for (...) Bayesian reasoning with idealized models in science. (shrink)

This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...) that we make by drawing an analogy with de Finetti's argument against mandating countable additivity. Having presented the best version of the Orgulity Argument, our second aim is to develop a reply to it. We extend Elga's idea of appealing to finitely additive probability to show that the challenge posed by the Orgulity Argument can be met. (shrink)

A synchronic probability is the probability at a time that an outcome occurs at that very time. Common sense invokes synchronic probabilities with values between 0 and 1, as do scientific theories such as classical statistical mechanics. Recently, philosophers have argued about whether any synchronic probabilities are best interpreted as objective chances. I add to this debate an underappreciated reason we might have to believe in synchronic chance; it might turn out that the best interpretation of our common (...) sense and scientific theories is one in which the macrophysical properties of physical systems are partly determined by synchronic chance distributions over microphysical properties of those systems. Additionally, I argue against the common charge that synchronic probability fails to satisfy various platitudes about chance—most notably Lewis’s Principal Principle. (shrink)

The concept of "fitness" is a notion of central importance to evolutionary theory. Yet the interpretation of this concept and its role in explanations of evolutionary phenomena have remained obscure. We provide a propensity interpretation of fitness, which we argue captures the intended reference of this term as it is used by evolutionary theorists. Using the propensity interpretation of fitness, we provide a Hempelian reconstruction of explanations of evolutionary phenomena, and we show why charges of circularity which have been levelled (...) against explanations in evolutionary theory are mistaken. Finally, we provide a definition of natural selection which follows from the propensity interpretation of fitness, and which handles all the types of selection discussed by biologists, thus improving on extant definitions. (shrink)

The most frequent charges brought against moral relativism are probably that it is inconsistent, that it has morally repugnant implications, and that it leads to amoralism, or the breakdown of morality altogether. A less frequent but still common objection is more conceptual in nature: relativism cannot make any sense of a certain species of comparative moral judgment, namely those that morally compare two moral codes. The general form of this kind of judgment is: ‘Moral code A is morally superior to (...) moral code B.’ Stace lodges this objection, and others have as well. Is it cogent? Using Stace as a springboard for discussion, I critically examine three related arguments against relativism that claim that comparative judgments of the sort in question are impossible on relativism. (shrink)

Conspiracy has probably become one of the key notions—or fantasies—of our times. Conspiracy, in the modern acceptation of the word, as in "conspiracy theory," has not only filled the mediasphere in which we live and breathe but it has also overshadowed—maybe we should say repressed—its ancient meaning. Surprisingly, this forgotten sense was revived on a poster lithographed by Andy Warhol in 1969 for a group exhibition in a Chicago gallery. The poster was meant to benefit the legal defense fund for (...) the Chicago Seven (who were charged by the federal government with conspiracy for organizing anti-Vietnam War protests). Warhol used the image of an electric chair (as he did in a series of paintings titled Little... Read More. (shrink)

Suárez was probably the first theologian to propose a political understanding of the order of subordination among the demons. According to Aquinas, this subordination immediately reflects the natural differences in perfection between the demons. Suárez charged that a natural-based order of demonic subordination could not ground the capacity of the demons’ ruler—Lucifer—to use his power to impose civic obligations on fellow demons so as to pursue their joint evil goals. But can there be obligations ad malum? This paper explores a (...) number of possible paths seemingly available to Suárez to defend his controversial view. I argue that the most promising interpretation of Suárez is one according to which the obligations created by Lucifer’s commands are not obligations in conscience but rather what we may call “non-moral obligations.”. (shrink)

Critics of conspiracy theories often charge that such theories are implausible because conspiracies of the kind they allege tend to fail. Thus, according to these critics, conspiracy theories that have been around for a while would have been, in all likelihood, already exposed if they had been real. So, they reason, they probably are not. In this article, I maintain that the arguments in support of this view are unconvincing. I do so by examining a list of four sources (...) recently cited in support of the claim that conspiracies tend to fail. I pay special attention to two of these sources, an article by Brian Keeley, and, especially, an article by David Grimes, which is perhaps the single “best” article in support of the idea that conspiracies tend to fail. That is, it offers the most explicit and elaborate attempt to establish this view. Further, that article has garnered significant (uncritical) attention in the mainstream press. I argue that Grimes's argument does not succeed, that the common assertion that conspiracies tend to fail remains poorly supported, and that there are good reasons to think that at least some types of conspiracies do not tend to fail. (shrink)

To judge from the rash of recent law review articles, it is a miracle that research with human subjects in the U.S. continues to draw breath under the asphyxiating heel of the rent-seeking, creativity-stifling, jack-booted bureaucrethics that is the current system of research ethics oversight and review. Institutional Review Boards, sometimes called Research Ethics Committees, have been accused of perpetrating “probably the most widespread violation of the First Amendment in our nation's history,” resulting in a “disaster, not only for academics, (...) but for the whole nation.” One member of the President's Council on Bioethics went so far as to assert, “There has been no greater damage to academic freedom in the United States in my lifetime. And my lifetime encompasses McCarthy and it encompasses political correctness, both.” Locked in the bureaucratic “iron cage” of IRB oversight, critics charge that researchers have been transformed into a vulnerable, exposed population, subject to domination, that has been likened in one case to a kind of “Tuskegee in reverse.”. (shrink)

According to Paul Draper and Ryan Nichols the practice of philosophy of religion—and especially its theistically committed practitioners—regularly violate norms of rationality, objectivity, and impartiality in the review, assessment, and weighing of evidence. (Draper and Nichols, 2013). We consider the charge of epistemic partisanship and show that the observational data does not illustrate a norm-violating form of inquiry. The major oversight in the charge of epistemic partiality is the epistemically central role of prior probabilities in determining the significance (...) of incongruent evidence. We argue that reasonably divergent views on the likelihood of theism on incongruent evidence can also account for differences in significance. We conclude that it is an epistemic requirement that committed theists regard incongruent evils as much less significant evidence against theism than do lukewarm theists, agnostics, or atheists. Differences in the significance of evidence quite properly reflect differences in commitments to theism. (shrink)

The previous chapters have provided a detailed overview of the variety of ethical challenges posed by the development of ICTs. By way of conclusion, in this epilogue I would like to invite the reader to look into the possible future of Information and Computer Ethics. More specifically, I shall try to forecast how the convergence of two fundamental trends of our times, globalization and the development of the information society, may interact with the ethical problems analysed in this book. The (...) exercise will not be based on some untenable technological determinism. Humanity is, and will remain, firmly in charge of its destiny and hence be responsible for it. Rather, it will mean adopting the farmer's view that, with enough intelligence, toil and a bit of luck, one might be able to tell today what one will probably reap tomorrow. Before trying to ‘look into the seeds of time, and say which grain will grow and which will not’ (Shakespeare, Macbeth, Act I, Scene III, 59–62), two clarifications might be in order. First, the future of globalization is a phenomenon too complex even to sketch in this brief epilogue. For a synthetic, well-balanced and informed overview, the reader may wish to consult Held and McGrew (2001) and consider that this chapter is written from what Held et al. (1999)) have defined as a ‘transformationalist perspective’, according to which ‘globalization does not simply denote a shift in the extensity or scale of social relations and activity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THIS MESSAGE IS FOR YOU. MAYBE. by Joseph Agassi There is a mood often enough conjured in science fiction literature to be familiar to every fan, the mood of seemingly intentional yet probably remdom contact between two individuals across immense space-time expanses. The hero of a complicated chase story has lost contact with the mother planet, has long ago leuided on a strange pleuiet, emd there, right now, just (...) walking across the plaza he sees a huge poster, with a piece of commercial advertisement or some similar message of purely local import printed on it. The poster is decorated with an arabesque which puzzles him, quickens his pulse, intrigues him, fascinates him — until it hits him insteinteuneously in full force: the arabesque is a message, written in his own native language, telling him how to reestablish contact. The story, as I say, has many veurietnts. And it has, it seems, a very widespread appeal. It is couched in terms of adventure stories, but its mood is not diat of adventure. The mood is more of die one associated with the idea of the eterned return, die idea of timelessness or of time standing still (and space vanishing), the idea the western philosophies usually associate with the ideas of Nicholas, the Renaissance mystic bishop ofCusa, though it is a recurrent idea in many cultures, of the identity of the vanishingly smedl and the infinitely large. Indeed, the meeting of the message and the recipient is symbolized by the meeting of the infinite line and the point of vanishing length. Whence this universality? I suppose it is a fact of biological nature. Think of the scent a living thing, be it a fish or em emtelope, leaves behind to contact a possible mate. It is a few complex molecules in a sea of molecules of astronomical numbers: just this room contains more molecules than you can imagine. And the animal follows a long tortuous path to find its mate. According to Willietm Craig and Konrad Lorenz, an animal does not have the slightest clue what it is after. Even while building a nest it has no complete 95 96Philosophy and Literature picture of its task. In each of its stages it goes after diverse kinds of things, yet it knows not which things, let alone their inborn rigidly fixed sequence. Yet the animal in charge of a tetsk, whether of finding a mate or of finding a twig for a nest, will be resdess — say Craig and Lorenz — and move about, and try to read the message in any piece of arabesque, until one day one piece of arabesque will med«: sense and enable its finder to complete die next step in the mysterious complex task and open up die search for the next message, the next step further along die unfolding series of preordained ordeals that life is strewn widi. Consider writing proper, like my writing this message for you right now. We do not know the background to literacy, much less its actual origins, except that these were far from unique: though many cultures eire illiterate or have acquired literacy from more evolved neighbors, mere eire many places on earth where literacy evolved independently. Yet even here we see a sequence: many independent ideographic scripts, some ofthem evolving into syllabic scripts and one or two of these evolving into an alphabet proper. How and why, we do not know. There is room for speculation, though. It is hard to imagine how the very first writer conceived of the very first message he wrote without consulting his recipient first. There are a few possible explemations here. First, that writer and recipient are one: writing was a form ofmemorizing, or ofconsigning matters to memory more stable than that of the human brain — the granite rock, for instance. The ancient Egyptian god of literacy was the god of memory. Primitive shepherds use knots in their rope and cuts on their sticks as aides memoire, as bookkeeping of sorts, and scholars consider these the origins of writings. This is evidenced by the runic writings of the Norse, whose letters are images of sticks with cuts on them. Yet runic writing is alphabetic and... (shrink)

Goldman and Olsson ( 2009 ) have responded to the common charge that reliabilist theories of knowledge are incapable of accounting for the value knowledge has beyond mere true belief. We examine their “conditional probability solution” in detail, and show that it does not succeed. The conditional probability relation is too weak to support instrumental value, and the specific relation they describe is inessential to the value of knowledge. At best, they have described conditions in which knowledge (...) indicates that additional epistemic value is likely to be forthcoming in the future. We also argue that their motive analogy breaks down. The problem, we conclude, is that being produced by a reliable process is not sufficient for a belief to be justified. (shrink)