
2056Philosophy of Probability: Foundations, Epistemology, and ComputationDissertation, University of Groningen. 2011.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…Read more

1558Infinitesimal ProbabilitiesIn Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology, Philpapers Foundation. pp. 199265. 2019.NonArchimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a nonArchimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

1500Fair infinite lotteriesSynthese 190 (1): 3761. 2013.This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from nonstandard analysis are brought to bear on the problem.

453Degrees of FreedomSynthese 198 (11): 1020710235. 2021.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 freewill 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 classificati…Read more

247New theory about old evidence. A framework for openminded BayesianismSynthese 193 (4). 2016.We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. Socalled openminded 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 catchall hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catchall …Read more

211NonArchimedean ProbabilityMilan Journal of Mathematics 81 (1): 121151. 2013.We propose an alternative approach to probability theory closely related to the framework of numerosity theory: nonArchimedean 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 nonArchimedean field as the range of the probability function. As a result, the property of countable additivity in Kolm…Read more

161Probability of inconsistencies in theory revisionEuropean Physical Journal B 85 (1). 2012.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 gi…Read more

141Models and simulations in material science: two cases without error barsStatistica Neerlandica 66 (3). 2012.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 platinuminduced 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 wou…Read more

139Infinitesimal ProbabilitiesBritish Journal for the Philosophy of Science 69 (2): 509552. 2016.NonArchimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a nonArchimedean 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_ Fir…Read more

120Inference to the Best Explanation versus Bayes’s Rule in a Social SettingBritish Journal for the Philosophy of Science 68 (2). 2017.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 stre…Read more

104The Snow White problemSynthese 196 (10): 41374153. 2019.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 …Read more

99Rethinking Gibbard’s Riverboat ArgumentStudia Logica 102 (4): 771792. 2014.According to the Principle of Conditional NonContradiction (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 conclu…Read more

95Inferential Conditionals and EvidentialityJournal of Logic, Language and Information 22 (3): 315334. 2013.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 argue for 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 the evidential meaning of certain English and Dutch modal expressions

89Knowledge and Approximate KnowledgeErkenntnis 79 (6): 11291150. 2014.Traditionally, epistemologists have held that only truthrelated 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 alter…Read more

86Infinite regress in decision theory, philosophy of science, and formal epistemologySynthese 191 (4): 627628. 2014.

76Ultralarge and infinite lotteriesIn B. Van Kerkhove, T. Libert, G. Vanpaemel & P. Marage (eds.), Logic, Philosophy and History of Science in Belgium II (Proceedings of the Young Researchers Days 2010), Koninklijke Vlaamse Academie Van België Voor Wetenschappen En Kunsten. 2012.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 nonstandard analysis.

74Ultralarge lotteries: Analyzing the Lottery Paradox using nonstandard analysisJournal of Applied Logic 11 (4): 452467. 2013.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 wellspecified 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 thresholdmodels that attempt to put an exact border on something that…Read more

60Measuring Graded Membership: The Case of ColorCognitive Science 41 (3): 686722. 2017.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 t…Read more

55Axioms for NonArchimedean Probability (NAP)In De Vuyst J. & Demey L. (eds.), Future Directions for Logic; Proceedings of PhDs in Logic III  Vol. 2 of IfColog Proceedings, College Publications. 2012.In this contribution, we focus on probabilistic problems with a denumerably or nondenumerably 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 nonArchimedean quantities (i.e. infinitesimals), we may call Kolmogorov's approach "Archimedean probability theory". We show that allowing nonArchimedean probabi…Read more

48Conditionals, inference, and evidentialityProceedings of the Logic and Cognition Workshop at ESSLLI 2012; Opole, Poland, 1317 August, 2012  Vol. 883 of CEUR Workshop Proceedings. 2012.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.

42Degrees of riskiness, falsifiability, and truthlikeness: A neoPopperian account applicable to probabilistic theoriesSynthese 199 (34): 1172911764. 2021.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 spec…Read more

38Demystifying the Mystery RoomThought: A Journal of Philosophy 8 (2): 8695. 2019.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 probab…Read more

38Vieri Benci and Mauro Di Nasso. How to Measure the Infinite: Mathematics with Infinite and Infinitesimal NumbersPhilosophia Mathematica 30 (1): 130137. 2022.

38The Snow White problemSynthese 196 (10): 41374153. 2019.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 …Read more

34Uniform probability in cosmologyStudies in History and Philosophy of Science Part A 101 (C): 4860. 2023.

25Moral BookkeepingErgo: An Open Access Journal of Philosophy 10 (n/a). 2023.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 verdi…Read more

25Ballonnen boven de filosofische freesmachineAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 108 (2): 245249. 2016.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.

18Zekerheid in de waarschijnlijkheidsleerAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2): 167172. 2015.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.

16Children of the Cosmos. Presenting a Toy Model of Science with a Supporting Cast of InfinitesimalsIn Anthony Aguirre, Brendan Foster & Zeeya Merali (eds.), Trick or Truth?: The Mysterious Connection Between Physics and Mathematics, Springer. 2016.Mathematics may seem unreasonably effective in the natural sciences, in particular in physics. In this essay, I argue that this judgment can be attributed, at least in part, to selection effects. In support of this central claim, I offer four elements. The first element is that we are creatures that evolved within this Universe, and that our pattern finding abilities are selected by this very environment. The second element is that our mathematics—although not fully constrained by the natural wo…Read more
Areas of Specialization
Philosophy of Physical Science 
Philosophy of Probability 
Areas of Interest
Epistemology 
Metaphysics 
Philosophy of Mathematics 