This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically (...) vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness. (shrink)

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

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

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...) of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

This article compares inference to the best explanation with Bayes’s rule in a social setting, specifically, in the context of a variant of the Hegselmann–Krause model in which agents not only update their belief states on the basis of evidence they receive directly from the world, but also take into account the belief states of their fellow agents. So far, the update rules mentioned have been studied only in an individualistic setting, and it is known that in such a setting (...) both have their strengths as well as their weaknesses. It is shown here that in a social setting, inference to the best explanation outperforms Bayes’s rule according to every desirable criterion. 1 What Is Inference to the Best Explanation?2 Judging the Rules—By Which Lights?3 From an Individualistic to a Social Perspective 3.1 The Hegselmann–Krause model 3.2 A probabilistic extension of the Hegselmann–Krause model 3.3 Simulations4 Results and Discussion5 Interpretation6 Conclusion. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...) _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix. (shrink)

Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards (...) the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it. (shrink)

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by (...) a different type of infinite additivity. (shrink)

This paper considers Kamp and Partee's account of graded membership within a conceptual spaces framework and puts the account to the test in the domain of colors. Three experiments are reported that are meant to determine, on the one hand, the regions in color space where the typical instances of blue and green are located and, on the other hand, the degrees of blueness/greenness of various shades in the blue–green region as judged by human observers. From the locations of the (...) typical blue and typical green regions in conjunction with Kamp and Partee's account follow degrees of blueness/greenness for the color shades we are interested in. These predicted degrees are compared with the judged degrees, as obtained in the experiments. The results of the comparison support the account of graded membership at issue. (shrink)

By exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. We solve the 'adding problems' that occur in these two contexts using a similar strategy, based on non-standard analysis.

According to the Principle of Conditional Non-Contradiction (CNC), conditionals of the form “If p, q” and “If p, not q” cannot both be true, unless p is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to violate CNC. He concluded from this that conditionals lack truth conditions. We argue that this conclusion is (...) rash by proposing a new diagnosis of what is going on in Gibbard’s argument. We also provide empirical evidence in support of our proposal. (shrink)

We present a model for studying communities of epistemically interacting agents who update their belief states by averaging the belief states of other agents in the community. The agents in our model have a rich belief state, involving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, (...) an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study. (shrink)

We discuss two research projects in material science in which the results cannot be stated with an estimation of the error: a spectroscopic ellipsometry study aimed at determining the orientation of DNA molecules on diamond and a scanning tunneling microscopy study of platinum-induced nanowires on germanium. To investigate the reliability of the results, we apply ideas from the philosophy of models in science. Even if the studies had reported an error value, the trustworthiness of the result would not depend on (...) that value alone. (shrink)

Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.

The Mystery Room problem is a close variant of the Mystery Bag scenario. It is argued here that dealing with this problem requires no revision of the Bayesian formalism, since there exists a solution to this problem in which indexicals or demonstratives play no essential role. The solution does require labels, which are internal to the probabilistic model. While there needs to be a connection between at least one label and one indexical or demonstrative, that connection is external to the (...) probabilistic model that is used to determine the relevant conditional probability; hence, it does not complicate the update procedure. (shrink)

A New Chance for Infinitesimals? This article discusses the connection between the Zenonian paradox of magnitude and probability on infinite sample spaces. Two important premises in the Zenonian argument are: the Archimedean axiom, which excludes infinitesimal magnitudes, and perfect additivity. Standard probability theory uses real numbers that satisfy the Archimedean axiom, but it rejects perfect additivity. The additivity requirement for real-valued probabilities is limited to countably infinite collections of mutually incompatible events. A consequence of this is that there exists no (...) standard probability function that describes a fair lottery on the natural numbers. If we reject the Archimedean axiom, allowing infinitesimal probability values, we can retain perfect additivity and describe a fair, countable infinite lottery. The article gives a historical overview to understand how the first option has become the current standard, whereas the latter remains ‘non-standard’. (shrink)

Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.

There is widespread agreement among philosophers about the Mens Rea Asymmetry (MRA), according to which praise requires intent, whereas blame does not. However, there is evidence showing that MRA is descriptively inadequate. We hypothesize that the violations of MRA found in the experimental literature are due to what we call “moral compositionality,” by which we mean that people evaluate the component parts of a moral problem separately and then reach an overall verdict by aggregating the verdicts on the component parts. (...) We have subjected this hypothesis to the test and here report the results of our experiment. We explore several explanations of the experimental findings and conclude that they present a puzzle to moral theory. (shrink)

In this contribution, we focus on probabilistic problems with a denumerably or non-denumerably infinite number of possible outcomes. Kolmogorov (1933) provided an axiomatic basis for probability theory, presented as a part of measure theory, which is a branch of standard analysis or calculus. Since standard analysis does not allow for non-Archimedean quantities (i.e. infinitesimals), we may call Kolmogorov's approach "Archimedean probability theory". We show that allowing non-Archimedean probability values may have considerable epistemological advantages in the infinite case. The current paper (...) focuses on the motivation for our new axiomatization. (shrink)

At least many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to revive an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on two Dutch linguistic markers.

In this paper, we take a fresh look at three Popperian concepts: riskiness, falsifiability, and truthlikeness of scientific hypotheses or theories. First, we make explicit the dimensions that underlie the notion of riskiness. Secondly, we examine if and how degrees of falsifiability can be defined, and how they are related to various dimensions of the concept of riskiness as well as the experimental context. Thirdly, we consider the relation of riskiness to truthlikeness. Throughout, we pay special attention to probabilistic theories (...) and we offer a tentative, quantitative account of verisimilitude for probabilistic theories. (shrink)

Traditionally, epistemologists have held that only truth-related factors matter in the question of whether a subject can be said to know a proposition. Various philosophers have recently departed from this doctrine by claiming that the answer to this question also depends on practical concerns. They take this move to be warranted by the fact that people’s knowledge attributions appear sensitive to contextual variation, in particular variation due to differing stakes. This paper proposes an alternative explanation of the aforementioned fact, one (...) that allows us to stick to the orthodoxy. The alternative applies the conceptual spaces approach to the concept of knowledge. With knowledge conceived of spatially, the variability in knowledge attributions follows from recent work on identity, according to which our standards for judging things (including concepts) to be identical are context-dependent. On the proposal to be made, it depends on what is at stake in a context whether it is worth distinguishing between knowing and being at least close to knowing. (shrink)

The high prevalence of cardiovascular diseases demands a reliable and sensitive risk assessment technique. In order to develop a fast and label-free immunosensor for C-reactive protein, a risk factor for this condition, anti-CRP antibodies were physically adsorbed to the hydrogen -terminated surface of nanocrystalline diamond. An Enzyme-Linked ImmunoSorbent Assay reference technique showed that this was a suitable substrate for antibody-antigen recognition reactions. Electrochemical Impedance Spectroscopy was used to electronically detect CRP recognition. The specificity of the immunosensor was demonstrated by incubation (...) with CRP and plasminogen as reference molecule. A different impedance behavior was observed in real-time after CRP addition as compared to plasminogen addition: the impedance increased only during CRP incubation. Fitting the data showed that this corresponded with a decrease in capacitance of the molecular layer due to its increased thickness by specific CRP recognition. Sensitivity experiments in real-time showed a clear discrimination between 1 μM, 100 nM, and 10 nM of CRP after 10 min at 100 Hz. Since, 10 nM of CRP was still clearly distinguishable from buffer solution, our CRP-directed immunosensor prototype reaches a sensitivity that is within the physiologically relevant concentration range of this biomarker in healthy controls and CVD patients. Moreover, this prototype displayed real-time discriminating power between spiked and unspiked serum, and thus also shows its applicability in this biological matrix. © 2011 Elsevier B.V. All rights reserved. (shrink)

This chapter analyses the theology of Soren Kierkegaard. It explains that Kierkegaard was trained in the theology of the Evangelical Lutheran Church of Denmark and was well-versed in the subject, but did not consider himself as a theologian. The chapter suggests that his main theological project was the reintroduction of Christianity into Christendom or the ecclesiastical-sociopolitical established order. Kierkegaard believes that Christianity is not a doctrine but an ‘existence-communication’ and a subjective truth that is to be actualized in existence with (...) the object of existing in it through faith. (shrink)

This collection of essays on Kierkegaard consists of various articles published in academic journals over the course of several decades. They address dominant and consistent themes in Kierkegaard's authorship, demonstrating the importance of these topics for understanding his authorship as a whole and for contemporary discussions of these issues. In particular, these articles seek to bring his thought into conversation with woman and gender studies in contemporary feminist philosophy and hermeneutics as well as other forms of interpretation. Many of the (...) essays appeared in the International Kierkegaard Commentary edited by fellow Kierkegaard scholar, Robert L. Perkins, and it is in his memory that they are dedicated. (shrink)

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption—implicit in standard Bayesianism—that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new (...) catch-all. As will be seen, this motivates a second update rule, besides Bayes’ rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, “keep[s] an open mind, but not so open that your brain falls out”. (shrink)

Difficile à lire, connu de réputation pour ses objections aux Méditations de Descartes, sa réhabilitation d'Épicure et des atomes, voire le caractère ambigu de ses relations avec les "libertins", Pierre Gassendi est un personnage un peu flou dans notre galerie de portraits imaginaire. Il fut cependant un auteur important, lu, connu, approuvé ou critiqué dans toute l'Europe, surtout par les savants qui voulaient fonder efficacement leur physique moderne sans renier pour autant les acquis des anciens. Les études réunies ici ont (...) cherché comme la trace et le reflet de l'œuvre de Gassendi dans les écrits d'autres auteurs qui ont vécu de son temps et jusqu'à la fin des Lumières - non seulement en France -, mais aussi en Angleterre (comme Walter Charleton, John Locke, David Hume ou Robert Boyle), en Hollande (professeurs d'Université), en Allemagne (Leibniz), en Pologne (Sociniens et "libertins"), en Italie du Nord (comme le jésuite milanais Thommaso Ceva), en Italie du Sud (comme le fondateur de l'Accademia degli Investiganti Tommaso Cornelio ou Giambattista Vico), en Espagne enfin (comme le médecin Martínez). Aujourd'hui encore Gassendi fait des adeptes parmi ceux que séduisent les chemins non battus de l'effort gratuit et de l'érudition austère, ceux que ravit absolument une certaine esthétique baroque de l'esprit pur. (shrink)

USA. Monograph examining the dilemmas of power (incl. Workplace power) and ethics in business management - demonstrates manifestations of power in sciences, business and political power, shows the channels for its control in human relations, and analyses creative uses in negotiation, etc.

This collection of essays analyzes relations of social inequality that appear to be logical extensions of a "natural order," and in the process demonstrates that a revitalized feminist anthropology of the 1990s has much to offer the field of feminist theory. Fashioned as a response to the lack of cultural analysis in feminist scholarship, the contributors question the category of gender within the inclusive context of the structural dynamics of inequality. They also examine how cultural identities, domains and institutions affect (...) our perception of gender in society. The first selection of essays addresses how ideas of family and kinship have fostered society's hierarchies and legitimized the status quo. In part two, the essays show how several dimensions of inequality are implicit in the construction of identities that are based upon ideas of social solidarity. Contributors: Susan McKinnon, University of Virginia; Kath Weston, Arizona State West; Rayna Rapp, New School for Social Research; Janet Dolgin, Hofstra University; Harriet Whitehead, Duke University; Carol Delaney, Stanford University; Brackette Williams, University of Arizona; Sylvia Yanagisako, Stanford University; Phyllis Chock, Catholic University; Sherry Ortner, University of Michigan; Anna Tsing, University of California, Santa Cruz. (shrink)

I respond to H. M. Collins's claim (1985, 1990, 1993) that experimental inquiry cannot be objective because the only criterium experimentalists have for determining whether a technique is "working" is the production of "correct" (i.e., the expected) data. Collins claims that the "experimenters' regress," the name he gives to this data-technique circle, cannot be broken using the resources of experiment alone. I argue that the data-technique circle, can be broken even though any interpretation of the raw data produced by techniques (...) is theory-dependent. However, it is possible to break this circle by eliminating dependence on even those theoretical presuppositions that are shared by an entire scientific community through the use of multiple independently theory-dependent techniques to produce robust bodies of data. Moreover, I argue, that it is the production of robust bodies of data that convinces experimentalists of the objectivity of their data interpretations. (shrink)

Rasmussen (1993) argues that, because electron microscopists did not use robustness and would not have been warranted in using it as a criterion for the reality or the artifactuality of mesosomes, the bacterial mesosome serves as a test case for robustness that it fails. I respond by arguing that a more complete reading of the research literature on the mesosome shows that ultimately the more robust body of data did not support the mesosome and that electron microscopists used and were (...) warranted in using robustness as a criterion for the artifactuality of mesosomes. (shrink)

Noradrenergic pathways are involved in mediating the central and peripheral effects of physiological arousal. The aim of the present study was to investigate the role of noradrenergic transmission in moral decision-making. We studied the effects in healthy volunteers of propranolol (a noradrenergic beta-adrenoceptor antagonist) on moral judgement in a set of moral dilemmas pitting utilitarian outcomes (e.g., saving five lives) against highly aversive harmful actions (e.g., killing an innocent person) in a double-blind, placebo-controlled, parallel group design. Propranolol (40 mg orally) (...) significantly reduced heart rate, but had no effect on self-reported mood. Importantly, propranolol made participants more likely to judge harmful actions as morally unacceptable, but only in dilemmas where harms were ‘up close and personal’. In addition, longer response times for such personal dilemmas were only found for the placebo group. Finally, judgments in personal dilemmas by the propranolol group were more decisive. These findings indicate that noradrenergic pathways play a role in responses to moral dilemmas, in line with recent work implicating emotion in moral decision-making. However, contrary to current theorising, these findings also suggest that aversion to harming is not driven by emotional arousal. Our findings are also of significant practical interest given that propranolol is a widely used drug in different settings, and is currently being considered as a potential treatment for post-traumatic stress disorder in military and rescue service personnel. (shrink)

Entrevista realizada durante a conferência proferida por Sylvia Serbin nas atividades do “Congresso Internacional Territorialidade e Saude: desigualdades raciais e sociais em contextos locais e globais”, organizado e coordenado pelo Nucleo de Estudos e Pesquisa em Psicanalise, Identidade, Negritude e Sociedade, ocorrido de 03 a 7 de setembro de 2014, no Centro de Ciências da Saude da Universidade Federal do Recôncavo da Bahia, em Santo Antonio de Jesus/BA.