Pages in English

Recent preprints and publications

• S. Wenmackers, “On the limits of comparing subset sizes within ℕ,” forthcoming in the inaugural volume of Journal for the Philosophy of Mathematics (owned by The European Society for the Philosophy of Mathematics and published Open Access by the Firenze University Press).
  
  Abstract

  
  We review and compare five ways of assigning totally ordered sizes to subsets of the natural numbers: cardinality, infinite lottery logic with mirror cardinalities, natural density, generalised density, and α-numerosity. Generalised densities and α-numerosities lack uniqueness, which can be traced to intangibles: objects that can be proven to exist in ZFC while no explicit example of them can be given. As a sixth and final formalism, we consider a recent proposal by Trlifajová (2024), which we call c-numerosity. It is fully constructive and uniquely determined, but assigns merely partially ordered numerosity values. By relating all six formalisms to each other in terms of the underlying limit operations, we get a better sense of the intrinsic limitations in determining the sizes of subsets of ℕ.
• S. Wenmackers, “Remote possibilities in branching time structures,” Synthese, vol. 204, article nr. 62 (28 pages), 2024.
  
  Abstract

  
  To analyse contingent propositions, this paper investigates how branching time structures can be combined with probability theory. In particular, it considers assigning infinitesimal probabilities — available in non-Archimedean probability theory — to individual histories. This allows us to introduce the concept of ‘remote possibility’ as a new modal notion between ‘impossibility’ and ‘appreciable possibility’. The proposal is illustrated by applying it to a future contingent and a historical counterfactual concerning an infinite sequence of coin tosses. The latter is a toy model that is used to illustrate the applicability of the proposal to more realistic physical models.
• A. Algaba, C. Mazijn, V. Holst, F. Tori, S. Wenmackers, and V. Ginis, “Large language models reflect human citation patterns with a heightened citation bias”.
  
  Abstract

  
  Citation practices are crucial in shaping the structure of scientific knowledge, yet they are often influenced by contemporary norms and biases. The emergence of Large Language Models (LLMs) like GPT-4 introduces a new dynamic to these practices. Interestingly, the characteristics and potential biases of references recommended by LLMs that entirely rely on their parametric knowledge, and not on search or retrieval-augmented generation, remain unexplored. Here, we analyze these characteristics in an experiment using a dataset of 166 papers from AAAI, NeurIPS, ICML, and ICLR, published after GPT-4’s knowledge cut-off date, encompassing 3,066 references in total. In our experiment, GPT-4 was tasked with suggesting scholarly references for the anonymized in-text citations within these papers. Our findings reveal a remarkable similarity between human and LLM citation patterns, but with a more pronounced high citation bias in GPT-4, which persists even after controlling for publication year, title length, number of authors, and venue. Additionally, we observe a large consistency between the characteristics of GPT-4’s existing and non-existent generated references, indicating the model’s internalization of citation patterns. By analyzing citation graphs, we show that the references recommended by GPT-4 are embedded in the relevant citation context, suggesting an even deeper conceptual internalization of the citation networks. While LLMs can aid in citation generation, they may also amplify existing biases and introduce new ones, potentially skewing scientific knowledge dissemination. Our results underscore the need for identifying the model’s biases and for developing balanced methods to interact with LLMs in general.
• V. Holst, A. Algaba, F. Tori, S. Wenmackers, and V. Ginis, “Dataset artefacts are the hidden drivers of the declining disruptiveness in science,” preprint.
  
  Abstract

  
  Park et al. [1] reported a decline in the disruptiveness of scientific and technological knowledge over time. Their main finding is based on the computation of CD indices, a measure of disruption in citation networks [2], across almost 45 million papers and 3.9 million patents. Due to a factual plotting mistake, database entries with zero references were omitted in the CD index distributions, hiding a large number of outliers with a maximum CD index of one, while keeping them in the analysis [1]. Our reanalysis shows that the reported decline in disruptiveness can be attributed to a relative decline of these database entries with zero references. Notably, this was not caught by the robustness checks included in the manuscript. The regression adjustment fails to control for the hidden outliers as they correspond to a discontinuity in the CD index. Proper evaluation of the Monte-Carlo simulations reveals that, because of the preservation of the hidden outliers, even random citation behaviour replicates the observed decline in disruptiveness. Finally, while these papers and patents with supposedly zero references are the hidden drivers of the reported decline, their source documents predominantly do make references, exposing them as pure dataset artefacts.
• W. Lammers, S. Ferrari, S. Wenmackers, V. Pattyn, and S. Van de Walle, “Theories of uncertainty communication: an interdisciplinary literature review,” Science Communication, vol. 46, pp. 332-365, 2024.
  
  Abstract

  
  This systematic literature review presents an interdisciplinary overview of theories tested in experiments on the effects of communicating uncertainty. Using a machine learning-aided pipeline, we selected and manually coded 413 experimental studies. We discuss core assumptions and predictions of the main theories of uncertainty communication. Most normative theorizing (e.g., Bayesianism, Expected Utility Theory) is rooted in Probability Theory, which is only suitable for addressing shallow and medium uncertainty. This explains the underrepresentation of experimental research into deep uncertainty communication. To foster a more comprehensive understanding of uncertainty communication effects, we identify research questions and theories deserving greater attention.
• W. Lammers, V. Pattyn, S. Ferrari, S. Wenmackers, and S. Van de Walle, “Evidence for policy-makers: A matter of timing and certainty?” Policy Sciences, vol. 57, pp. 171-191, 2024.
  
  Abstract

  
  This article investigates how certainty and timing of evidence introduction impact the uptake of evidence by policy-makers in collective deliberations. Little is known about how experts or researchers should time the introduction of uncertain evidence for policy-makers. With a computational model based on the Hegselmann-Krause opinion dynamics model, we simulate how policy-makers update their opinions in light of new evidence. We illustrate the use of our model with two examples in which timing and certainty matter for policy-making: intelligence analysts scouting potential terrorist activity and food safety inspections of chicken meat. Our computations indicate that evidence should come early to convince policy-makers, regardless of how certain it is. Even if the evidence is quite certain, it will not convince all policy-makers. Next to its substantive contribution, the article also showcases the methodological innovation that agent-based models can bring for a better understanding of the science-policy nexus. The model can be endlessly adapted to generate hypotheses and simulate interactions that cannot be empirically tested.
• S. Wenmackers, “Uniform probability in cosmology,” Studies in History and Philosophy of Science, vol. 101, pp. 48-60, 2023.
  
  Abstract

  
  Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.

Link to full publication list.

New essay on my blog

Computer generation keeps on writing (29 May 2024).

Recent fiction

• S. Wenmackers, “How my wife got brain-hacked (again),” AcademFic, vol. 5, p. 40-43, 20 February 2024.
  
  Abstract

  
  It all started when I bought an electric toothbrush for my wife's seventieth birthday. (Speculative fiction: science fiction.)

Link to complete list of published fiction and poetry.

Upcoming talks

I am invited to give a talk at the workshop Nonlinearity, Complexity and Foundations in Mathematics at the Centro di Ricerca Matematica “Ennio De Giorgi” in Pisa, Italy at 11-13 September, 2024, where I will present my paper “On the limits of comparing subset sizes within ℕ”.

On September 12, 2024, I will give a brief online presentation to introduce my paper “On the limits of comparing subset sizes within ℕ” as part of the inauguration of the Journal for the Philosophy of Mathematics, which will take place during the 2024 Summerschool of the European Society for the Philosophy of Mathematics (ESPM) to be held at the University of Vienna, Austria.

Fedi trading card

Changes to the website

February 2024: I do not want that any parts of this website are used for training AI, so I (finally) updated my robot.txt. (For more info, see for instance Dark Visitors. Updated: August 2024.)