One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

Lexical Semantics is about the meaning of words. Although obviously a central concern of linguistics, the semantic behaviour of words has been unduly neglected in the current literature, which has tended to emphasize sentential semantics and its relation to formal systems of logic. In this textbook D. A. Cruse establishes in a principled and disciplined way the descriptive and generalizable facts about lexical relations that any formal theory of semantics will have to encompass. Among the topics covered in depth are (...) idiomaticity, lexical ambiguity, synonymy, hierarchical relations such as hyponymy and meronymy, and various types of oppositeness. Syntagmatic relations are also treated in some detail. The discussions are richly illustrated by examples drawn almost entirely from English. Although a familiarity with traditional grammar is assumed, readers with no technical linguistic background will find the exposition always accessible. All readers with an interest in semantics will find in this original text not only essential background but a stimulating new perspective on the field. (shrink)

A record of the words and teachings of Confucius, _The Analects_ is considered the most reliable expression of Confucian thought. However, the original meaning of Confucius's teachings have been filtered and interpreted by the commentaries of Confucianists of later ages, particularly the Neo-Confucianists of the Song dynasty, not altogether without distortion.In this monumental translation by Professor D. C. Lau, an attempt has been made to interpret the sayings as they stand. The corpus of the sayings is taken as an organic (...) whole and the final test of the interpretation rests on the internal consistency it exhibits. In other words, _The Analects_ is read in the light of _The Analects._This results in a truer understanding of Confucius' thought than the traditional interpretation and paves the way for a re-assessment of its importance in the history of Chinese thought and its relevance to the present day world.This volume also contains an introduction to the life and teachings of Confucius, and three appendices on the events in the life of Confucius, on his disciples, and on the composition of _The Analects._. (shrink)

"By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis. I found it to be challenging, fascinating, infuriating, and provocative, but certainly not dull."--James H, Brown, University of New Mexico "This book is unquestionably mandatory reading not only for every living biologist but for generations of biologists to come."--Jack P. Hailman, Animal Behaviour , review of the first (...) edition "An important contribution to modern evolutionary thinking. It fortifies the place of Evolutionary Theory among the other well-established natural laws."--R.Gessink, TAXON. (shrink)

This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other (...) possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization. (shrink)

This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.

This book examines the history of the concept of irony from the first appearance of?eironeia? in Plato to the modern era. It isolates and discusses the basic features of irony and the variable features that determine the kind and in part the effect or quality. It distinguishes carefully between the two main types : instrumental irony (of which verbal irony is the most common form) and observable irony (which includes dramatic irony, irony of events, general irony and other situational ironies). (...) A distinction is also drawn between open and closed irony. (shrink)

Leading philosopher of religion D. Z. Phillips argues that intellectuals need not see their task as being for or against religion, but as one of understanding it. What stands in the way of this task are certain methodological assumptions about what enquiry into religion must be. Beginning with Bernard Williams on Greek gods, Phillips goes on to examine these assumptions in the work of Hume, Feuerbach, Marx, Frazer, Tylor, Marett, Freud, Durkheim, Le;vy-Bruhl, Berger and Winch. The result exposes confusion, but (...) also gives logical space to religious belief without advocating personal acceptance of that belief, and shows how the academic study of religion may return to the contemplative task of doing conceptual justice to the world. Religion and the Hermeneutics of Contemplation extends in important ways D. Z. Phillips' seminal 1976 book Religion Without Explanation. It will be of interest to scholars and students of philosophy, anthropology, sociology and theology. (shrink)

Introduction What is the point of studying Aristotle's theory of moral virtue? In the first place, many interesting questions are raised, in metaphysics, ...

RésuméLa croyance que l'on est (ou pas) dans un état de douleur est singulière en ceci qu'elle semble pouvoir être qualifiée d'infaillibilité ou d'incorrigibilité logique, de même que le cogito. Mais comment se peut-il que l'existence d'une croyance (vraie) et l'existence du fait qui est l'objet de cette croyance puisssent constituer la même existence? Je propose ici une réponse à cette question. Parfois, une croyance peut être un désir.

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

A comprehensive introduction to the ways in which meaning is conveyed in language. Alan Cruse covers semantic matters, but also deals with topics that are usually considered to fall under pragmatics. A major aim is to highlight the richness and subtlety of meaning phenomena, rather than to expound any particular theory. Rich in examples and exercises, Meaning in Language provides an invaluable descriptive approach to this area of linguistics for undergraduates and postgraduates alike.

Preface: The Shameful face of Philosophy In fact, Socrates talks about laden asses, blacksmiths, cobblers and tanners1 Whether one looks for a ...

We propose a kernel method for using combinations of features across example pairs in learning pairwise classifiers. Pairwise classifiers, which identify whether two examples belong to the same class or not, are important components in duplicate detection, entity matching, and other clustering applications. Existing methods for learning pairwise classifiers from labeled training data are based on string edit distance or common features between two examples. However, if two examples from the same class have few common features, these methods have difficulties (...) in finding these pairs and achieving high recall. One typical example is to check whether two abbreviated author names in different citations refer to the same person or not. Since similarities between examples from the same class become close to zero, classifiers fail to distinguish positive pairs from negative pairs. One approach to avoiding the problem of zero similarities is using conjunctions of different features across examples, but implementing this idea straightforwardly makes the computational cost prohibitive for practical problems. Using a kernel on pair instances, our method can use feature conjunctions across examples without actually doing feature mappings, which are computationally expensive. The kernel is a tensor product of two inner products on the original feature space. The corresponding feature mapping generates conjunctions of features only across the two different examples while that of the conventional polynomial kernel also generates conjunctions of features from the same example, which are irrelevant to pairwise classification and cause deterioration of accuracy. Our experiments on the author matching problem show that this method can give a precision 4 to 8 times higher than that of previous methods at medium recall levels. (shrink)

This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and (...) sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text. (shrink)

Without denying the contradictory character of Marx s thought, the French philosopher Daniel Bensaid sets out to demonstrate that it was not a philosophy of the ...

Engaging Polanyi’s embeddedness–disembeddedness framework, this study explored the work experiences of Bhil children employed in Indian Bt cottonseed GPNs. The innovative visual technique of drawings followed by interviews was used. Migrant children, working under debt bondage, underwent greater exploitation and perennial and severe depersonalized bullying, indicative of commodification of labour and disembeddedness. In contrast, children working in their home villages were not under debt bondage and underwent less exploitation and occasional and mild depersonalized bullying, indicative of how civil society organizations, (...) along with the state, attempt to re-embed economic activities in the social context. Polanyi’s double movement was evident. ‘Place’ emerged as the pivotal factor determining children’s experiences. A ‘protective alliance’ of community controls and social power, associated with in-group affiliations and cohesive ties, stemming from a common village and tribal identity, aided children working at home for Bhil farmers. ‘Asymmetric intergroup inequality’ due to pronounced social identity and class differences, coupled with locational constraints and developmental disadvantage, made migrant children vulnerable targets. Social embeddedness influences how child workers are treated because it forces employers to be ethical and not engage in bullying. However, by shifting production to children’s home villages, there is an attempt to obscure the difference between child labour and child work. Thus, the seeds of disembeddedness are sown through the very act of re-embeddeding, potentially hampering future interventions. (shrink)

This paper presents two proposals to improve the text of an important passage in Manilius’ Astronomica, 1.456–68, in which the poet explains natura's rationale for arranging the stars in such a way as to create only a partial, rather than a full, representation of the constellation figures. The text of line 464 is repunctuated in order to give proper emphasis to natura's parsimonious disposition of the stars. Scholars have noted that the sentence atque ignibus ignes | respondent in 466–7 is (...) not consistent with the poet's account of how the constellation figures were delineated nor with what an observer sees in the heavens. The conjecture insignibus (neuter plural), for the transmitted atque ignibus in line 466, is offered to indicate that it is the distinctive features (insignia) of the figures to which specific stars correspond and by means of which the figures are described. Attention is also drawn to a striking paronomasia in 466–7, designat … insignibus ignes, which creates a meaningful phonetic constellation of celestial fire (ignis), sign (signum) and insigne (distinctive feature) and thus provides evidence, on the linguistic level, of natura's providentia. (shrink)

In this paper I respond to Robert Taylor's argument that a Rawlsian framework does not support strong affirmative action programs. The paper makes three main arguments. The first disputes Taylor's claim that strong AA would not be needed in ideal conditions. Private racial discrimination, I suggest, might still exist in such conditions, so strong AA might be needed there. The second challenges Taylor's claims that pure procedural justice constrains Rawlsian nonideal theory. I argue that this rests on a fetishizing of (...) pure procedural justice that is absent from Rawls's work. I also show that a revised formulation of Taylor's concern here also fails. My third argument makes a positive Rawlsian case for strong AA in nonideal conditions that builds on a Taylor concession. Taylor suggests that the goal of nonideal theory is to create a world in which ideal theory can be applied. My argument begins by showing that another permissible goal of Rawlsian nonideal theory is to ameliorate injustice. I then argue that Rawls's contractualist framework supports the strongest forms of AA when category 3 interventions are blocked. (shrink)