
11Vieri Benci and Mauro Di Nasso. How to Measure the Infinite: Mathematics with Infinite and Infinitesimal NumbersPhilosophia Mathematica 30 (1): 130137. 2022.

26Degrees 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

199Degrees 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

7Children 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, . 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

99Infinitesimal 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

81Inference 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

65Knowledge and Approximate KnowledgeErkenntnis 79 (S6): 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

3Impedimetric, diamondbased immmunosensor for the detection of Creactive proteinSensors and Actuators B, Chemical 157 (1). 2011.The high prevalence of cardiovascular diseases demands a reliable and sensitive risk assessment technique. In order to develop a fast and labelfree immunosensor for Creactive protein, a risk factor for this condition, antiCRP antibodies were physically adsorbed to the hydrogen terminated surface of nanocrystalline diamond. An EnzymeLinked ImmunoSorbent Assay reference technique showed that this was a suitable substrate for antibodyantigen recognition reactions. Electrochemical Impedance Sp…Read more

35Measuring 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

14The 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

848Infinitesimal ProbabilitiesIn Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology, Philpapers Foundation. pp. 199265. 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.

Lost in Space and Time: A Quest for Conceptual Spaces in PhysicsIn Peter Gärdenfors, Antti Hautamäki, Frank Zenker & Mauri Kaipainen (eds.), Conceptual Spaces: Elaborations and Applications, Springer Verlag. 2019.

23Demystifying 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

7Herkansing voor infinitesimalen?Algemeen Nederlands Tijdschrift voor Wijsbegeerte 110 (4): 491510. 2018.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 realvalued probabilities is limited to countably infini…Read more

55The 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

11Zekerheid in de waarschijnlijkheidsleerAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2): 167172. 2015.

1104Fair 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.

51Ultralarge 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

128Models 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

16Ballonnen boven de filosofische freesmachineAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 108 (2): 245249. 2016.

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

1557Philosophy 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

183New 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

173NonArchimedean 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

75Ultralarge 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.
Areas of Specialization
Philosophy of Physical Science 
Philosophy of Probability 
Areas of Interest
Epistemology 
Metaphysics 
Philosophy of Mathematics 