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Research Interests: Computer Science, Theory Of Computation, Formal Methods (Formal Verification), Philosophy, Philosophy of Mind, and 9 morePhilosophy of Science, Verification and Validation, Scientific Models, Holism, Model validation, Computer Simulation, Philosophy and Religious Studies, Psychology and Cognitive Sciences, and Minds & Machines
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The finite-size scaling (FSS) theory is a relatively new and important attempt to study critical phenomena; this paper aims to contribute to clarifying the philosophical significance of this theory. We maintain that, contrary to initial... more
The finite-size scaling (FSS) theory is a relatively new and important attempt to study critical phenomena; this paper aims to contribute to clarifying the philosophical significance of this theory. We maintain that, contrary to initial appearances and to some recent claims in the literature, the FSS theory cannot arbitrate the debate between the reductionists and antireductionists about phase transitions. Although the theory allows scientists to provide predictions for finite systems, the analysis we carry on here shows that it involves the intertwinement of both finite and infinite systems. But, we argue, the FSS theory has another virtue, as it provides quantitative predictions and explanations for finite systems close to the critical point; it thus complements in a distinctive manner the standard Renormalization Group qualitative approach relying on infinite systems.
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Research Interests:
Various errors can affect scientific code and detecting them is a central concern within computational science. Could formal verification methods, which are now available tools, be widely adopted to guarantee the general reliability of... more
Various errors can affect scientific code and detecting them is a central concern within computational science. Could formal verification methods, which are now available tools, be widely adopted to guarantee the general reliability of scientific code? After discussing their benefits and drawbacks, we claim that, absent significant changes as regards features like their user-friendliness and versatility, these methods are unlikely to be adopted throughout computational science, beyond certain specific contexts for which they are well-suited. This issue exemplifies the epistemological heterogeneity of computational science: profoundly different practices can be appropriate to meet the reliability challenge that rises for scientific code.
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Can Brownian motion arise from a deterministic system of particles? This paper addresses this question by analysing the derivation of Brownian motion as the limit of a deterministic hard-spheres gas with Lanford's theorem. In particular,... more
Can Brownian motion arise from a deterministic system of particles? This paper addresses this question by analysing the derivation of Brownian motion as the limit of a deterministic hard-spheres gas with Lanford's theorem. In particular, we examine the role of the Boltzmann-Grad limit in the loss of memory of the deterministic system and compare this derivation and the derivation of Brownian motion with the Langevin equation.
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In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other,... more
In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided.
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It has been argued that the Duhem problem is renewed with computational models since model assumptions having a representational aim and computational assumptions cannot be tested in isolation. In particular, while the Verification and... more
It has been argued that the Duhem problem is renewed with computational models since model assumptions having a representational aim and computational assumptions cannot be tested in isolation. In particular, while the Verification and Validation methodology is supposed to prevent such holism, Winsberg (Philos Compass 4:835-845, 2009; Science in the age of computer simulation, University of Chicago Press, Chicago, 2010) argues that verification and validation cannot be separated in practice. Morrison (Reconstructing reality: models, mathematics, and simulations , Oxford University Press, Oxford, 2015) replies that Winsberg overstates the entanglement between the steps. The paper aims at arbitrating these two positions, by stressing their respective validity in relation to domains of application. It importantly argues for an increasing use of formal methods in verification, that makes dis-entanglement possible.
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The transference theory reduces causation to the transmission (or regular manifestation) of physical conserved quantities, like energy or mo-menta. Although this theory aims at applying to all fields of physics, we claim that it fails to... more
The transference theory reduces causation to the transmission (or regular manifestation) of physical conserved quantities, like energy or mo-menta. Although this theory aims at applying to all fields of physics, we claim that it fails to account for a quantum electrodynamic effect, viz. the Aharonov-Bohm effect. After having argued that the Aharonov-Bohm effect is a genuine counterexample for the transference theory, we offer a new physicalist approach of causation, ontic and modal, in which this effect is embedded.
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It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g., Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that... more
It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g., Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al. 2000). Based on this theory, we argue for the plausibility for eliminating the infinite limit for studying phase transitions. We offer a new account for phase transitions in finite systems, and we argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.
Keywords infinite idealizations · phase transitions · finite systems · ineliminability · approximation · zeros of partition function
Keywords infinite idealizations · phase transitions · finite systems · ineliminability · approximation · zeros of partition function
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Uffink and Valente (2015) claim that there is no time-asymmetric ingredient that, added to the Hamiltonian equations of motion, allows to obtain the Boltzmann equation within the Lanford's derivation. This paper is a discussion and a... more
Uffink and Valente (2015) claim that there is no time-asymmetric ingredient that, added to the Hamiltonian equations of motion, allows to obtain the Boltzmann equation within the Lanford's derivation. This paper is a discussion and a reply to that analysis. More specifically, I focus on two mathematical tools used in this derivation, viz. the Boltzmann-Grad limit and the incoming configurations. Although none of them are time-asymmetric ingredients , by themselves, I claim that the use of incoming configurations, as taken within the Boltzmann-Grad limit, is such a time-asymmetric ingredient. Accordingly, this leads to reconsider a kind of Stoßzahlansatz within Lanford's derivation.
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An important task in mathematical sciences is to make quantitative predictions, which is often done via the solution of differential equations. In this paper, we investigate why, to perform this task, scientists sometimes choose to use... more
An important task in mathematical sciences is to make quantitative predictions, which is often done via the solution of differential equations. In this paper, we investigate why, to perform this task, scientists sometimes choose to use numerical methods instead of analytical solutions. Via several examples, we argue that the choice for numerical methods can be explained by the fact that, while making quantitative predictions seems at first glance to be facilitated with analytical solutions, this is actually often much easier with numerical methods. Thus we challenge the widely presumed superiority of analytical solutions over numerical methods.
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In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer... more
In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer two objections that could be made against this solution. First, I argue that the discrete solution is not an ad hoc solution. It is embedded in a discrete formulation of classical mechanics. Second, I show that the discrete solution cannot be falsified experimentally.
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As an important innovation of the last decades, there exists nowadays an intrinsically discrete physical theory called Discrete Mechanics. It is intrinsically discrete since it does not originate in the discretization of continuous... more
As an important innovation of the last decades, there exists nowadays an intrinsically discrete physical theory called Discrete Mechanics. It is intrinsically discrete since it does not originate in the discretization of continuous equations but is rather built upon already discrete fundamental principles. DM is a new, variational theory of classical motion. The purpose of the paper is to examine the consequences of adopting this discrete physical theory on the way we can represent time in physics. We focus on two main consequences. The first is the use of a discrete representation of time, the second is the representation of time as a dynamical variable rather than a parameter.
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Dans La structure du temps, William H. Newton-Smith avance la thèse selon laquelle il est impossible de décider si la structure du temps est continue ou simplement dense. L’objectif de cet article est d’examiner dans quelle mesure la... more
Dans La structure du temps, William H. Newton-Smith avance la thèse selon laquelle il est impossible de décider si la structure du temps est continue ou simplement dense. L’objectif de cet article est d’examiner dans quelle mesure la thèse de Newton-Smith est justifiée. D’un côté, je soutiens que l’argumentation qu’il propose est insuffisamment convaincante. D’un autre côté, je montre comment pallier cette critique et, dans ce nouveau contexte, je propose une révision des conséquences de sa thèse de l’indécidabilité.
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Dans cet article, j'examine une pratique de la recherche en mathématiques constructives, celle qui consiste à reformuler constructivement les théories physiques. Je discute plus précisément trois aspects de cette pratique. Je montre... more
Dans cet article, j'examine une pratique de la recherche en mathématiques constructives, celle qui consiste à reformuler constructivement les théories physiques. Je discute plus précisément trois aspects de cette pratique. Je montre d’abord que celle-ci a la particularité d’être motivée par des considérations philosophiques et comment la physique est utilisée pour arbitrer un débat de philosophie des mathématiques entre constructivisme et classicisme. Ensuite, j’identifie la méthodologie de la recherche en mathématiques que cette pratique implique et montre qu’il s’agit, selon une terminologie empruntée à Poincaré, d’une méthodologie de « logiciens ». Enfin, je montre que dans cette pratique, les théories physiques ont un rôle heuristique sur le développement des mathématiques constructives. Elles permettent avec succès de stimuler la recherche d’énoncés constructifs et d’orienter la recherche en mathématiques constructives vers de nouveaux domaines.
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La méthode scientifique : éclairages en philosophie des sciences OBJECTIFS : Connaître les grandes conceptions philosophiques de la méthode scientifique-Être capable de définir certaines notions-clés en philosophie des sciences... more
La méthode scientifique : éclairages en philosophie des sciences
OBJECTIFS : Connaître les grandes conceptions philosophiques de la méthode scientifique-Être capable de définir certaines notions-clés en philosophie des sciences (hypothèse, modèle, inférence, causalité, corrélation, confirmation, déduction, induction) et de les mobiliser pour éclairer un problème concret-Savoir mesurer l'importance de la mise en oeuvre d'une méthode pour résoudre un problème concret-Être capable de distinguer et de hiérarchiser les différents aspects de la représentation d'un phénomène (outils mathématiques, facteurs causaux, contexte)-Savoir mesurer l'importance de la communication au sein d'une équipe et entre différentes équipes pour résoudre efficacement un problème PUBLIC Ingénieurs, cadres scientifiques.
PREREQUIS : Connaissances de base en physique, mathématiques et philosophie (niveau Bac scientifique).
OBJECTIFS : Connaître les grandes conceptions philosophiques de la méthode scientifique-Être capable de définir certaines notions-clés en philosophie des sciences (hypothèse, modèle, inférence, causalité, corrélation, confirmation, déduction, induction) et de les mobiliser pour éclairer un problème concret-Savoir mesurer l'importance de la mise en oeuvre d'une méthode pour résoudre un problème concret-Être capable de distinguer et de hiérarchiser les différents aspects de la représentation d'un phénomène (outils mathématiques, facteurs causaux, contexte)-Savoir mesurer l'importance de la communication au sein d'une équipe et entre différentes équipes pour résoudre efficacement un problème PUBLIC Ingénieurs, cadres scientifiques.
PREREQUIS : Connaissances de base en physique, mathématiques et philosophie (niveau Bac scientifique).