Alzheimer’s disease (AD) in its most common form results in cognitive changes in memory function leading to dementia due to underlying neurodegenerative disease. Recent research advancements in AD...

The program of Reverse Mathematics (Simpson 2009) has provided us with the insight that most theorems of ordinary mathematics are either equivalent to one of a select few logical principles, or provable in a weak base theory. In this paper, we study the properties of the Dirac delta function (Dirac 1927; Schwartz 1951) in two settings of Reverse Mathematics. In particular, we consider the Dirac Delta Theorem, which formalizes the well-known property \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${\int_\mathbb{R}f(x)\delta(x)\,dx=f(0)}$$\end{document} of the Dirac delta function. We show that the Dirac Delta Theorem is equivalent to weak König’s Lemma (see Yu and Simpson in Arch Math Log 30(3):171–180, 1990) in classical Reverse Mathematics. This further validates the status of WWKL0 as one of the ‘Big’ systems of Reverse Mathematics. In the context of ERNA’s Reverse Mathematics (Sanders in J Symb Log 76(2):637–664, 2011), we show that the Dirac Delta Theorem is equivalent to the Universal Transfer Principle. Since the Universal Transfer Principle corresponds to WKL, it seems that, in ERNA’s Reverse Mathematics, the principles corresponding to WKL and WWKL coincide. Hence, ERNA’s Reverse Mathematics is actually coarser than classical Reverse Mathematics, although the base theory has lower first-order strength. (shrink)

Those who comment on modern scientific institutions are often quick to praise institutional structures that leave scientists to their own devices. These comments reveal an underlying presumption that scientists do best when left alone—when they operate in what we call the ‘scientific state of nature’. Through computer simulation, we challenge this presumption by illustrating an inefficiency that arises in the scientific state of nature. This inefficiency suggests that one cannot simply presume that science is most efficient when institutional control is (...) absent. In some situations, actively encouraging unpopular, risky science would improve scientific outcomes. 1 Introduction2 Scientists and Bandits3 Choosing an ϵ4 Structure of Communication5 Discussion. (shrink)

In On the Origin of Species, Charles Darwin put forward his theory of natural selection. Conventionally, Darwin's argument for this theory has been understood as based on an analogy with artificial selection. But there has been no consensus on how, exactly, this analogical argument is supposed to work – and some suspicion too that analogical arguments on the whole are embarrassingly weak. Drawing on new insights into the history of analogical argumentation from the ancient Greeks onward, as well as on (...) in-depth studies of Darwin's public and private writings, this book offers an original perspective on Darwin's argument, restoring to view the intellectual traditions which Darwin took for granted in arguing as he did. From this perspective come new appreciations not only of Darwin's argument but of the metaphors based on it, the range of wider traditions the argument touched upon, and its legacies for science after the Origin. (shrink)

William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deeper twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. His works are of enormous historical importance; they remain also a source of inspiration and information. The works of his contemporaries, such as Klein, Frobenius, Schur, have been published as also have the works of his (...) immediate successors such as Phillip Hall. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. This is the first reference volume of Burnside's collected papers, enhanced by a series of critical essays on his work, and is important for group theorists and historians and philosophers of mathematics and fills the gap in this area of literature. (shrink)

The origins and nature of the judicial role of the senate in cases which under the republic were the business of the permanent quaestiones have been the subject of long debate, and a satisfactory explanation has yet to be found for the change that had undoubtedly taken place by the reign of Tiberius. The discovery and publication of the senatorial decree which concluded the investigation into the charge brought in A.D. 20 against Cn. Piso following the murder of Germanicus,2 in (...) addition to the wealth of new material it provides for the political history of the period and the understanding of the methods of the historian Tacitus, allows an insight into the relation of the senate to the quaestio maiestatis which may prove useful in unravelling some of the puzzles which have troubled scholars hitherto. (shrink)

The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.

This paper is a response to Nicholas Dixon's defence of the moderate partisan as the ideal fan of team sports. For Dixon, the moderate partisan is someone who combines a partisan fan's loyalty for a particular team with a purist fan's desire to see fair and skilful play by all participants. My aim is to argue that there is no ideal fan of team sports. In particular, there is nothing specially commendable about the moderate partisan's loyalty that justifies the claim (...) to be the ideal fan. There are many other ways of being a fan than being a purist or a partisan as described by Dixon. None of them is morally superior to the other, assuming that they meet basic requirements of respect for others and for fair play. I argue that the commitment of partisan fans to particular teams is better explained by other values than the moral virtue of loyalty. A better explanation and justification of partisanship, and indeed of fan interest in sport generally, is found in the human attachment to narrative as a way of creating meaning in our lives. (shrink)

This comprehensive and important volume includes contributions by activists, journalists, lawyers and scholars from twenty-one countries. The essays map the directions the movement for women's rights is taking--and will take in the coming decades--and the concomittant transformation of prevailing notions of rights and issues. They address topics such as the rapes in former Yugoslavia and efforts to see that a War Crimes Tribunal responds; domestic violence; trafficking of women into the sex trade; the persecution of lesbians; female genital mutilation; and (...) reproductive rights. (shrink)

This paper approaches the problem of testimony from a new direction. Rather than focusing on the epistemic grounds for testimony, it considers the problem from the perspective of an individual who must choose whom to trust from a population of many would-be testifiers. A computer simulation is presented which illustrates that in many plausible situations, those who trust without attempting to judge the reliability of testifiers outperform those who attempt to seek out the more reliable members of the community. In (...) so doing, it presents a novel defense for the credulist position that argues one should trust testimony without considering the underlying reliability of the testifier. (shrink)

In seeking to explain the evolution of social cooperation, many scholars are using increasingly complex game-theoretic models. These complexities often model readily observable features of human and animal populations. In the case of previous games analyzed in the literature, these modifications have had radical effects on the stability and efficiency properties of the models. We will analyze the effect of adding spatial structure to two communication games: the Lewis Sender-Receiver game and a modified Stag Hunt game. For the Stag Hunt, (...) we find that the results depart strikingly from previous models. In all cases, the departures increase the explanatory value of the models for social phenomena. (shrink)

Three questions of major historical interest may be asked concerning the neglect and the rediscovery of Mendel's work.1. Why was it so little noticed between its publication in 1866 and its rediscovery in 1900?2. What factors determined its rediscovery?3. What factors favoured the rapid growth of Mendelian genetics?It is with the second and third of these questions that this paper is concerned.