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.
Recent astrophysical findings suggest that the era during which the universe is habitable has just begun. This raises the question whether the entire universe may at some point in the future be filled with intelligent life. Hanson et al. (2021) argued that we can be confident that the universe will, by cosmic standards, soon be dominated by imperialist civilizations which expand rapidly, persist long, and make drastic changes to the volumes they control. The main motivation for this “grabby civilizations” hypothesis is that it supposedly provides a good explanation of why we are so early in cosmic history. In this paper, we criticise this motivation and suggest that it fails, for reasons analogous to why the notorious Doomsday argument fails. In the last part of the paper we broaden our discussion and argue that it may be rational to assign a rather low prior probability to the grabby civilizations hypothesis. For instance, if there are any civilizations that expand rapidly and indefinitely, they may well not make any drastic changes to the volumes they inhabit, potentially for strategic reasons. Hence, we call for epistemic caution and humility regarding the question of the long-term evolution of intelligence in the universe.
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 inthe 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.
Isaac Asimov (1920-1992) wrote Foundation, a science-fiction series about a galactic empire. The books are now being televised by Apple TV+: the first season premiered in 2021 and a second season is planned. The plot of Foundation crucially revolves around a fictional science that is supposed to predict the future course of large populations.
Would psychohistory have been developed if Hari Seldon hadn’t existed? Pondering psychohistory easily prompts the old question: how much of history is contingent and how much of it is inevitable? This chapter applies the question to the mathematics underlying the Foundation itself and offers reasons to think the answer may be affirmative. The analysis also helps us to understand why Seldon postulated that the predictions of psychohistory should be kept a secret and why it only works at the level of large groups of people, such as the Galactic Empire.
The purview of mathematics and statistics has profoundly changed throughout history. Ancient thinkers, such as Plato and Aristotle, believed that mathematics could only describe and predict heavenly motions. This belief continued throughout medieval times. Only in the seventeenth century, natural philosophers such as Galileo and Newton formulated mathematical laws that apply to objects on Earth as well as elsewhere in the universe.
Newtonian laws are deterministic, which means that an exact specification of the world at one time in principle allows us to compute the situation at all other times, past and future. Laplace explained this deterministic worldview using a thought experiment, now known as Laplace’s demon. Newcomb’s paradox explores one perplexing consequence of this idea. It involves a television show that employs a very accurate predictor of human behaviour, much like Laplace’s demon.
Yet, determinism does not automatically lead to predictability in practice. Poincaré was among the first to study chaotic systems, in which small changes in initial conditions may blow up to gigantic differences in the long run. Meanwhile, it was discovered that indeterminism may give rise to very stable and predictable patterns. Allegedly, Poincaré was able to prove his baker was committing fraud with the weight of his baguettes by looking at their weight distribution.
The nineteenth century also gave rise to statistical mechanics, which studies collections of particles of which the positions and velocities aren’t known exactly, but their probability distributions are. As a result, the particles do exhibit lawlike behaviour at the collective level. Another watershed occurred when Quetelet realized that not just particles and baguettes, but also people can be characterized by statistical distributions.
Both in fiction and in reality, the notion of statistical determinism makes us wonder how much an individual can really change the course of history. It invites further reflection not merely on Salvor Hardin or the Mule, but also on how free Seldon could have been in coming up with psychohistory and in designing his Plan in the first place.
Link to the book on the publisher’s website.
Link to full publication list.
During a workshop on “Discreteness and Precision in Physics” in Paris 8-10 November 2023, I gave a talk on infinitesimal probabilities.
On May 5th, 2023, I gave an OLOFOS/CEFISES seminar in Louvain-la-Neuve on non-conglomerability in cosmology. You can view it on YouTube here.
Treintrots (23 augustus 2023).
Solarpunk (24 juni 2023).
Twee eeuwen eeuwigheid (19 mei 2023).
Torenhoog spelplezier (25 april 2023).
Moet er nog zand zijn? (30 maart 2023).
Mastodonten op het web (17 februari 2023).
Van myriade tot quetta (22 januari 2023).
Kleine handen (13 december 2022).
Een hoop onbeduidendheden (12 december 2022).
Academische babystapjes (11 december 2022).
Raadselachtige groei (10 december 2022).
Tussen alles en niets (9 december 2022).
Kan wetenschap de wereld redden? (9 november 2022).
Vierkante wielen (28 oktober 2022).
Op 28 augustus 2023 gaf ik een lezing over wetenschapsfilosofie in de module “Eeuwige vragen” tijdens de Zomerschool Filosofie aan het Hoger Instituut Wijsbegeerte in Leuven.
Op 4 juli gaf ik de lezing “Let’s talk methodology” over de rol van de wetenschappelijke methode in wetenschapscommunicatie voor Let’s talk science in Gent. Je kunt mijn lezing hier herbekijken.
Op 16 juni 2023 gaf ik in het Paleis der Academiën in Brussel de presentatie “Prinses Papierzak” tijdens een event van de Jonge Academie over de beeldvorming van wetenschappers.
Op 5 mei 2023 gaf ik in het Paleis der Academiën in Brussel een presentatie over Waarheid en (on-)waarschijnlijkheid tijdens een symposium van de Lentecyclus georganiseerd door het Academisch Cultureel Forum. Je kunt het hier herbekijken.
Op 27 mei 2023 nam ik deel aan een panel van Eos tijdens Nerdland in Wachtebeke: onder het motto “Los het op!” werd ons gevraagd het fileprobleem op te lossen. Je kunt het hier herbeluisteren als podcast. Kim Verhaeghe schreef er dit verslag over.
Waarom alle wetenschap met elkaar verbonden is. Laat je onderdompelen in een wonderlijke, wetenschappelijk bestudeerde wereld, en ontdek de verborgen samenhang van de wetenschap.
Wetenschap bestaat uit een hele familie van uiteenlopende disciplines, van astronomie tot zoölogie. Op het eerste gezicht lijkt er tussen pakweg sociologie en wiskunde weinig verwantschap te bestaan. Wie de wetenschappelijke stamboom van dichtbij bekijkt, ziet echter dat er meer aan de hand is.
In Wetenschap maak je kennis met de boom van de wetenschap en haar vele vertakkingen. Het boek gaat op zoek naar de drijfveren achter de verschillende wetenschappelijke disciplines en welke vragen ze behandelen. Bovenal leer je hoe ze antwoorden zoeken op die ene, moeilijke vraag: hoe zit de werkelijkheid in elkaar?