A collection of articles originally presented at two conferences, the first at Ventura Hall, Stanford, in April 1998; and the second at the University of Bologna in September 1999.

The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary (...) particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status.Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics.In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox. (shrink)

The difference between carnap's and de finetti's conceptions of probability does not consist of a couple of requirements, As carnap asserted in a letter to de finetti. The paper is intended to give a theoretical justification for this denial. In order to do this, The author stresses the difference between (tolerant) objectivism and (radical) subjectivism. The difference is discussed in statistical terms. The discussion is faced with respect to predictive inferences, A type of statistical inference that both carnap and de (...) finetti advocate in many occasions. (shrink)

When subjects view stimulation of a rubber hand while feeling congruent stimulation of their own hand, they may come to feel that the rubber hand is part of their own body. This illusion of body ownership is termed ‘Rubber Hand Illusion’ . We investigated sensitivity of RHI to spatial mismatches between visual and somatic experience. We compared the effects of spatial mismatch between the stimulation of the two hands, and equivalent mismatches between the postures of the two hands. We created (...) the mismatch either by adjusting stimulation or posture of the subject’s hand, or, in a separate group of subjects, by adjusting stimulation or posture of the rubber hand. The matching processes underlying body ownership were asymmetrical. The illusion survived small changes in the subject’s hand posture, but disappeared when the same posture transformations were applied to the rubber hand. Mismatch between the stimulation delivered to the subject’s hand and the rubber hand abolished the illusion. The combination of these two situations is of particular interest. When the subject’s hand posture was slightly different from the rubber hand posture, the RHI remained as long as stimulation of the two hands was congruent in a hand-centred spatial reference frame, even though the altered posture of the subject’s hand meant that stimulation was incongruent in external space. Conversely, the RHI was reduced when the stimulation was incongruent in hand-centred space but congruent in external space. We conclude that the visual–tactile correlation that causes the RHI is computed within a hand-centred frame of reference, which is updated with changes in body posture. Current sensory evidence about what is ‘me’ is interpreted with respect to a prior mental body representation. (shrink)

Réunit des textes d'auteurs français des XVIIe et XVIIIe s. évoquant Saint-Augustin.

We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an ‘alphabet of human thought’. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract objects, we (...) should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz. (shrink)

Le Traité Théologico-Politique, publié anonymement en 1670, fut sans doute le livre le plus scandaleux du XVIIe siècle, et pour cause : l'emploi d'une méthode critique radicale pour dévoiler les mystères du pouvoir théologique et politique faisait de cet ouvrage un traité aussi stimulant que polémique. Après trois cent cinquante ans, le Traité demeure un modèle de réflexion sur la politique, la philologie, la métaphysique et la religion. Dans ce volume, le lecteur trouvera un commentaire suivi de l'ouvrage. Grâce au (...) travail collectif des vingt-huit contributeurs, il pourra comprendre le détail du discours de Spinoza ainsi que saisir la trame de fond de la pensée spinoziste. L'ouvrage se compose de deux parties : le commentaire proprement dit et une section consacrée aux principaux problèmes qui animent le débat contemporain sur Spinoza. (shrink)

Multiple authorship is so common and pervasive in our world that it is tempting to take it for granted. Prior to the twentieth century, however, multiple authorship was exceedingly rare.

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the (...) intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding. (shrink)

We show that every model of IΔ0 has an end extension to a model of a theory where log-space computable function are formalizable. We also show the existence of an isomorphism between models of IΔ0 and models of linear arithmetic LA.

This article delves into Blaise Pascal’s religious philosophy, focusing on his use of the phrase “Scio cui credidi” (I know whom I have believed) to explore his understanding of faith. It analyzes Pascal’s “Memorial” and the “Summary of the Life of Jesus Christ”, highlighting how Christ is central to Pascal’s belief system. The discussion reveals the transformational nature of Pascal’s faith, particularly after his mystical experience on November 23, 1654. This experience is crucial in understanding his shift from a philosophical (...) to a deeply personal, Christ-centered faith. The article underscores Pascal’s journey from a scientific and philosophical perspective to an intimate, emotional resonance with Christian faith, demonstrating how his personal encounters with the divine profoundly shaped his religious perspective. (shrink)

Despite the burgeoning literature on the governance and impact of cross-sector partnerships in the past two decades, the debate on how and when these collaborative arrangements address globally relevant problems and contribute to systemic change remains open. Building upon the notion of wicked problems and the literature on governing such wicked problems, this paper defines harnessing problems in multi-stakeholder partnerships as the approach of taking into account the nature of the problem and of organizing governance processes accordingly. The paper develops (...) an innovative analytical framework that conceptualizes MSPs in terms of three governance processes harnessing three key dimensions of wicked problems. The Roundtable on Sustainable Palm Oil provides an illustrative case study on how this analytical framework describes and explains organizational change in partnerships from a problem-based perspective. The framework can be used to better understand and predict the complex relationships between MSP governance processes, systemic change and societal problems, but also as a guiding tool in organizing governance processes to continuously re-assess the problems over time and address them accordingly. (shrink)