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On the Mathematics of the Jeffreys-Lindley Paradox  [PDF]
Cristiano Villa,Stephen Walker
Statistics , 2015,
Abstract: This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e. the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.
The Banach-Tarski paradox or what mathematics and religion have in common  [PDF]
Volker Runde
Mathematics , 2002,
Abstract: We give a popular account of the Banach-Tarski paradox and its connections with the axiom of choice.
A note on Gibbs paradox  [PDF]
Radhakrishnamurty Padyala
Physics , 2013,
Abstract: We show in this note that Gibbs paradox arises not due to application of thermodynamic principles, whether classical or statistical or even quantum mechanical, but due to incorrect application of mathematics to the process of mixing of ideal gases.
The Mathematics  [PDF]
Javier Guachalla H
Mathematics , 2007,
Abstract: This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of mathematics and a paradigm for education, namely Learn to structure.
Theoremizing Yablo's Paradox  [PDF]
Ahmad Karimi,Saeed Salehi
Computer Science , 2014,
Abstract: To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic.
Mathematics education and social justice
Ole Skovsmose,Paola Valero
Utbildning & Demokrati : Tidsskrift f?r Didaktik och Utbildningspolitik , 2005,
Abstract: During the last two decades there has been an increase in researchwork connecting mathematics education with society and concernsfor equity, social justice and democracy. In particular we discussthe role of mathematics education and mathematics education re-search in the ‘informational society’. This society contains contra-dictions that we express in two paradoxes. The paradox of inclu-sion refers to the fact that current processes of globalisation, al-though stating a concern for inclusion, exercise an exclusion ofcertain social sectors. The paradox of citizenship alludes to the factthat education, although seeming ready to prepare for active citi-zenship, exercises an adaptation of the individual to the given so-cial order. Much research in mathematics education ignores thesetwo paradoxes. We try to point out what it could mean for math-ematics education research to face the paradoxes of the informa-tional society in search of more just social relationships.
Mathematics of the Quantum Zeno Effect  [PDF]
Andreas U. Schmidt
Mathematics , 2003,
Abstract: We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations.
On the Flatland Paradox  [PDF]
Pierre Druilhet
Statistics , 2015,
Abstract: We revisit the flatland paradox proposed by Stone (1976). We show that the choice of a flat prior is not adapted to the structure of the parameter space and that the impropriety of the prior is not directly involved in the paradox. We also propose an analysis of the paradox by using proper uniform priors and taking the limit on the hyper-parameter. Then, we construct an improper prior based on reference priors that take into account the structure of the parameter space and the partial knowledge of the random process that generates the parameter. For this prior, the paradox disappear and the Bayesian analysis matches the intuitive reasoning.
Russell′s Early Type Theory and the Paradox of Propositions
André Fuhrmann
Principia : an International Journal of Epistemology , 2001,
Abstract: The paradox of propositions, presented in Appendix B of Russell's The Principles of Mathematics (1903), is usually taken as Russell's principal motive, at the time, for moving from a simple to a ramified theory of types. I argue that this view is mistaken. A closer study of Russell's correspondence with Frege reveals that Russell carne to adopt a very different resolution of the paradox, calling into question not the simplicity of his early type theory but the simplicity of his early theory of propositions.
Philosophy of Mathematics
Dr.Rakesh Soni
Indian Streams Research Journal , 2012,
Abstract: The philosophy of Mathematics is the branch Philosophy of that studies the philosophical assumptions, foundations, and implications of Mathematics . The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
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