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Perhaps the hottest topic in the philosophy of chemistry is that of the relationship between chemistry and physics. The problem finds one of its main manifestations in the debate about the nature of molecular structure, given by the spatial arrangement of the nuclei in a molecule. The traditional strategy to address the problem is to consider chemical cases that challenge the definition of molecular structure in quantum–mechanical terms. Instead of taking that top-down strategy, in this paper we face the problem (...) |
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An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique (...) |
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L'article étudie diverses strates épistémiques de raisonnement stochastique à l'oeuvre dans l'économétrie actuelle et dans les méthodes économiques: (1) le niveau argumentatif; (2) le raisonnement fondé sur l'analogie avec les jeux de hasard; (3) les modèles basés sur le calcul analytique des probabilités, où le phénomène est tenu pour centré, son incertitude étant maîtrisée par un bruit blanc quant à sa fluctuation; (4) le calcul axiomatique. L'intrication de ces strates est observée. L'article appelle à un renforcement de la réflexion critique (...) |
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In this paper I illustrate the evolution of series theory from Leibniz and Newton to the first decades of the eighteenth century. Although mathematicians used convergent series to solve geometric problems, they manipulated series by a mere extension of the rules valid for finite series, without considering convergence as a preliminary condition. Further, they conceived of a power series as a result of a process of the expansion of a finite analytical expression and thought that the link between series and (...) |
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According to classical molecular chemistry, molecules have a structure, that is, they are sets of atoms with a definite arrangements in space and held together by chemical bonds. The concept of molecular structure is central to modern chemical thought given its impressive predictive power. It is also a very useful concept in chemistry education, due to its role in the rationalization and visualization of microscopic phenomena. However, such a concept seems to find no place in the ontology described by quantum (...) |
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Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) |
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With Humean empiricism and its agnostic stance regarding the future as a foil, I take a bird’s eye view of the links between past and future prescribed by ordinary concepts of everyday things and processes, and by scientific models of phenomenal situations. I argue that they entitle us to claim knowledge of the future—including, where appropriate, its necessary course—in a humanly affordable sense of ‘knowledge’. |
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