I defend a new argument for causal finitism, the view that nothing can have an infinite causal history. I begin by defending a number of plausible metaphysical principles, after which I explore a host of novel variants of the Littlewood-Ross and Thomson’s Lamp paradoxes that violate such principles. I argue that causal finitism is the best solution to the paradoxes.

In this article, I argue that it is impossible to complete infinitely many tasks in a finite time. A key premise in my argument is that the only way to get to 0 tasks remaining is from 1 task remaining, when tasks are done 1-by-1. I suggest that the only way to deny this premise is by begging the question, that is, by assuming that supertasks are possible. I go on to present one reason why this conclusion (that supertasks are (...) impossible) is important, namely that it implies a new verdict on a decision puzzle propounded by Jeffrey Barrett and Frank Arntzenius. (shrink)

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece. Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise. This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation (...) as manifested in different presentations and normative interpretations or resolutions of well-known paradoxes of infinity. Paradoxes have been described as occasioning major epistemological reconstructions, and I highlight such occasions as they emerged for both novices and experts with connection to current conceptualisations of objectivity. Of interest is the perception that one single objective truth about “actual” mathematical infinity exists – indeed, this is brought to question at an axiomatic level with both theoretical and empirical research implications. (shrink)

The first aim of this paper is to introduce a new way of looking at supertasks in the light of special relativity which makes use of the elementary dynamics of relativistic point particles subjected to elastic binary collisions and constrained to move unidimensionally. In addition, this will enable us to draw new physical consequences from the possibility of supertasks whose ordinal type is higher than the usual ω or ω * considered so far in the literature. Thus, the paper shows (...) how an entire collection of infinitely many particles may place itself spontaneously in motion (mechanical self-acceleration) or even reach the speed of light in a way compatible with special relativity. Interesting implications for classical mechanics are also derived, particularly the possibility of a system of particles disappearing spontaneously in spatial infinity even under the condition of the non-existence of non-collision singularities. (shrink)

It is a generally accepted idea that strict finitism is a rather marginal view within the community of philosophers of mathematics. If one therefore wants to defend such a position (as the present author does), then it is useful to search for as many different arguments as possible in support of strict finitism. Sometimes, as will be the case in this paper, the argument consists of, what one might call, a “rearrangement” of known materials. The novelty lies precisely in the (...) rearrangement, hence on the formal-axiomatic level most of the results presented here are not new. In fact, the basic results are inspired by and based on Mycielski (1981). (shrink)

Dans cet article je réponds à deux questions philosophiques soule­vées par la thèse suivante appelée « thèse de l’hyper-calcul » : il est possible de construire physiquement un modèle d’hyper-calcul. La première question est liée aux enjeux de cette thèse. Puisque la construction physique d’un modèle de calcul dépasse le cadre mathématique initial de la théorie de la calculabilité, j expliquerai pourquoi il est nécessaire de construire physiquement un modèle d’hyper-calcul. La seconde question concerne le problème de la vérification : (...) à supposer que l’on dispose d’un modèle d’hyper-calcul construit physiquement, il serait impossible de vérifier que ce modèle calcule une fonction non calculable par machine de Turing. Je proposerai une analyse de ce problème dans le but de montrer qu’il ne remet pas en cause de façon explicite la thèse de l’hyper-calcul. (shrink)