16,862 research outputs found

    Duhem Before Breakfast

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    This essay traces some of Pierre Duhem's motives for his celebrated "Quine- Duhem thesis" to a specific worry about theory underdetermination that arises within classical mechanics, concerned with the rivalry between Duhem's own thermomechanical approach and the more narrowly "mechanical" treatment pursued by Hertz and others. In the context of the treatments of "physical infinitesimals" common at the time, these two approaches seem empirically indistinguishable. After an exposition of the basic issues, this alleged "underdetermination" is then evaluated from a more modern perspective

    Determinism and the Mystery of the Missing Physics

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    This article surveys the difficulties in establishing determinism for classical physics in the context of several distinct foundational approaches to the discipline. It also explains that such formulations commonly appear in an incomplete condition due to a deeper problem of "missing physics.

    Congruence successions in compositions

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    A \emph{composition} is a sequence of positive integers, called \emph{parts}, having a fixed sum. By an \emph{mm-congruence succession}, we will mean a pair of adjacent parts xx and yy within a composition such that x≡y(modm)x\equiv y(\text{mod} m). Here, we consider the problem of counting the compositions of size nn according to the number of mm-congruence successions, extending recent results concerning successions on subsets and permutations. A general formula is obtained, which reduces in the limiting case to the known generating function formula for the number of Carlitz compositions. Special attention is paid to the case m=2m=2, where further enumerative results may be obtained by means of combinatorial arguments. Finally, an asymptotic estimate is provided for the number of compositions of size nn having no mm-congruence successions
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