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Axiomatic Method and Category Theory

Axiomatic Method and Category Theory Author Andrei Rodin
ISBN-10 9783319004044
Release 2013-10-14
Pages 285
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This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.



Studies in the Methodology and Foundations of Science

Studies in the Methodology and Foundations of Science Author Patrick Suppes
ISBN-10 9789401731737
Release 2013-03-09
Pages 475
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The twenty-three papers collected in tbis volume represent an important part of my published work up to the date of this volume. I have not arranged the paper chronologically, but under four main headings. Part I contains five papers on methodology concerned with models and measurement in the sciences. This part also contains the first paper I published, 'A Set of Independent Axioms for Extensive Quantities', in Portugaliae Mathematica in 1951. Part 11 also is concerned with methodology and ineludes six papers on probability and utility. It is not always easy to separate papers on probability and utility from papers on measurement, because of the elose connection between the two subjects, but Artieles 6 and 8, even though they have elose relations to measurement, seem more properly to belong in Part 11, because they are concerned with substantive questions about probability and utility. The last two parts are concerned with the foundations of physics and the foundations of psychology. I have used the term foundations rather than philosophy, because the papers are mainly concerned with specific axiomatic formulations for particular parts of physics or of psychology, and it seems to me that the termfoundations more appropriately describes such constructive axiomatic ventures. Part 111 contains four papers on the foundations of physics. The first paper deals with foundations of special relativity and the last three with the role ofprobability in quantum mechanics.



Rigor and Structure

Rigor and Structure Author John P. Burgess
ISBN-10 9780191033605
Release 2015-02-12
Pages 224
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While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.



The Logic of Scientific Discovery

The Logic of Scientific Discovery Author Karl Popper
ISBN-10 9781134470020
Release 2005-11-04
Pages 480
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Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.



Berechenbarkeit der Welt

Berechenbarkeit der Welt Author Wolfgang Pietsch
ISBN-10 9783658121532
Release 2017-06-21
Pages 562
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Der Sammelband untersucht Entwicklungen in der Wissenschaft, die in den letzten Jahren durch moderne Informationstechnologien und die zunehmende Verfügbarkeit von Daten angestoßen wurden. Aufgrund dieser neuen Ansätze werden eine Reihe von Phänomenen zum Beispiel aus den Sozial- oder den Lebenswissenschaften berechenbar, die zuvor als zu komplex für eine wissenschaftliche Analyse galten. Der Band versammelt Texte aus einer Vielzahl unterschiedlicher Perspektiven, von der Physik über die Sozial- und Kulturwissenschaften bis hin zur Informatik. Neben Beiträgen, die die aktuellen Entwicklungen direkt thematisieren, untersuchen andere Aufsätze zentrale Begriffe in unmittelbarem Zusammenhang wie Komplexität oder Information.



Foundations of Statistical Natural Language Processing

Foundations of Statistical Natural Language Processing Author Christopher D. Manning
ISBN-10 0262133601
Release 1999
Pages 680
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An introduction to statistical natural language processing (NLP). The text contains the theory and algorithms needed for building NLP tools. Topics covered include: mathematical and linguistic foundations; statistical methods; collocation finding; word sense disambiguation; and probalistic parsing.



The q theory of Finite Semigroups

The q theory of Finite Semigroups Author John Rhodes
ISBN-10 9780387097817
Release 2009-04-05
Pages 666
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This comprehensive, encyclopedic text in four parts aims to give the reader — from the graduate student to the researcher/practitioner — a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.



Constructive Adpositional Grammars

Constructive Adpositional Grammars Author Federico Gobbo
ISBN-10 9781443831284
Release 2011-05-25
Pages 280
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This book presents a new paradigm of natural language grammar analysis, based on adposition as the key concept, considered a general connection between two morphemes – or group of morphemes. The adpositional paradigm considers the morpheme as the basic unit to represent morphosyntax, taken as a whole, in terms of constructions, while semantics and pragmatics are treated accordingly. All linguistic observations within the book can be described through the methods and tools of Constructive Mathematics, so that the modelling becomes formally feasible. A full description in category-theoretic terms of the formal model is provided in the Appendix. A lot of examples taken from natural languages belonging to different typological areas are offered throughout the volume, in order to explain and validate the modeling – with special attention given to ergativity. Finally, a first real-world application of the paradigm is given, i.e., conversational analysis of the transcript of therapeutic settings in terms of constructive speech acts. The main goal of this book is to broaden the scope of Linguistics by including Constructive Mathematics in order to deal with known topics such as grammaticalization, children’s speech, language comparison, dependency and valency from a different perspective. It primarily concerns advanced students and researchers in the field of Theoretical and Mathematical Linguistics but the audience can also include scholars interested in applications of Topos Theory in Linguistics.



Working with objects

Working with objects Author Trygve Reenskaug
ISBN-10 0134529308
Release 1995-06-01
Pages 366
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Working With Objects is the authoritative account of the highly successful OOram method for software analysis, design, development, maintenance and reuse. OOram has been fine-tuned over a decade on hundreds of projects by Trygve Reenskaug and his collaborators. It is supported by available CASE tools, training, and consulting. Book jacket.



Language as Calculus vs Language as Universal Medium

Language as Calculus vs  Language as Universal Medium Author Maren Kusch
ISBN-10 0792303334
Release 1989-06-30
Pages 362
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I first became interested in Husserl and Heidegger as long ago as 1980, when as an undergraduate at the Freie Universitat Berlin I studied the books by Professor Ernst Tugendhat. Tugendhat's at tempt to bring together analytical and continental philosophy has never ceased to fascinate me, and even though in more recent years other influences have perhaps been stronger, I should like to look upon the present study as still being indebted to Tugendhat's initial incentive. It was my good fortune that for personal reasons I had to con tinue my academic training from 1981 onwards in Finland. Even though Finland is a stronghold of analytical philosophy, it also has a tradition of combining continental and Anglosaxon philosophical thought. Since I had already admired this line of work in Tugendhat, it is hardly surprising that once in Finland I soon became impressed by Professor Jaakko Hintikka's studies on Husserl and intentionality, and by Professor Georg Henrik von Wright's analytical hermeneu tics. While the latter influence has-at least in part-led to a book on the history of hermeneutics, the former influence has led to the present work. My indebtedness to Professor Hintikka is enormous. Not only is the research reported here based on his suggestions, but Hintikka has also commented extensively on different versions of the manuscript, helped me to make important contacts, found a publisher for me, and-last but not least-was a never failing source of encouragement.



Science and Partial Truth

Science and Partial Truth Author Newton C. A. da Costa
ISBN-10 0198035535
Release 2003-09-18
Pages 272
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In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially rather than wholly true. They adopt a framework that sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate. The new machinery of "partial structures" that they develop offers a new perspective from which to view the nature of scientific models and their heuristic development. Their conclusions will be of wide interest to philosophers and historians of science.



The Semantic Sphere 1

The Semantic Sphere 1 Author Pierre Lévy
ISBN-10 9781118601518
Release 2013-01-22
Pages 381
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The new digital media offers us an unprecedented memory capacity, an ubiquitous communication channel and a growing computing power. How can we exploit this medium to augment our personal and social cognitive processes at the service of human development? Combining a deep knowledge of humanities and social sciences as well as a real familiarity with computer science issues, this book explains the collaborative construction of a global hypercortex coordinated by a computable metalanguage. By recognizing fully the symbolic and social nature of human cognition, we could transform our current opaque global brain into a reflexive collective intelligence.



Scientific Structuralism

Scientific Structuralism Author Alisa Bokulich
ISBN-10 9048195977
Release 2011-01-21
Pages 182
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Recently there has been a revival of interest in structuralist approaches to science. Taking their lead from scientific structuralists such as Henri Poincaré, Ernst Cassirer, and Bertrand Russell, some contemporary philosophers and scientists have argued that the most fruitful approach to solving many problems in the philosophy of science lies in focusing on the structural features of our scientific theories. Much of the work in scientific structuralism to date has been focused on the problem of scientific realism, where it has been argued that even in cases of radical theory change the most important structural features of predecessor theories are preserved. These structural realists argue that what our most successful theories get right about the world is these abstract structural features, rather than any particular ontological claims. More recently, philosophers of science have adopted structuralist approaches to many other issues in the philosophy of science, such as scientific explanation and intertheory relations. The nine articles collected in this volume, written by the leading researchers in scientific structuralism, represent some of the most important directions of research in this field. This book will be of particular interest to those philosophers, scientists, and mathematicians who are interested in the foundations of science.



A Mathematical Prelude to the Philosophy of Mathematics

A Mathematical Prelude to the Philosophy of Mathematics Author Stephen Pollard
ISBN-10 9783319058160
Release 2014-05-12
Pages 202
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This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.



Research Methods in Education

Research Methods in Education Author Louis Cohen
ISBN-10 9781315456515
Release 2017-10-12
Pages 916
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This thoroughly updated and extended eighth edition of the long-running bestseller Research Methods in Education covers the whole range of methods employed by educational research at all stages. Its five main parts cover: the context of educational research; research design; methodologies for educational research; methods of data collection; and data analysis and reporting. It continues to be the go-to text for students, academics and researchers who are undertaking, understanding and using educational research, and has been translated into several languages. It offers plentiful and rich practical advice, underpinned by clear theoretical foundations, research evidence and up-to-date references, and it raises key issues and questions for researchers planning, conducting, reporting and evaluating research. This edition contains new chapters on: Mixed methods research The role of theory in educational research Ethics in Internet research Research questions and hypotheses Internet surveys Virtual worlds, social network software and netography in educational research Using secondary data in educational research Statistical significance, effect size and statistical power Beyond mixed methods: using Qualitative Comparative Analysis (QCA) to integrate cross-case and within-case analyses. Research Methods in Education is essential reading for both the professional researcher and anyone involved in educational and social research. The book is supported by a wealth of online materials, including PowerPoint slides, useful weblinks, practice data sets, downloadable tables and figures from the book, and a virtual, interactive, self-paced training programme in research methods. These resources can be found at: www.routledge.com/cw/cohen.



Explaining Games

Explaining Games Author Boudewijn de Bruin
ISBN-10 1402099061
Release 2010-08-18
Pages 178
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Does game theory - the mathematical theory of strategic interaction - provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory - the first monograph on the philosophy of game theory - is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.



Teaching Ethics with Three Philosophical Novels

Teaching Ethics with Three Philosophical Novels Author Michael Boylan
ISBN-10 9783319557113
Release 2017-07-11
Pages 190
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This book offers a unique method for teaching ethics and social/political philosophy by combining primary texts and resource material along with three philosophical novels so that students can apply the abstract principles to real-life situations. Boylan provides a preface to introduce instructors in how to effectively put together a course in ethics using fiction. A sample syllabus and sample assignments are provided. Students often turn-off when confronted with abstract ethical principles, alone. This book allows interaction with philosophical novels that provide real-life situations that mirrors applying normative principles to lived experience. Students will be drawn into this realism and their engagement with the material will be significantly enhanced. This is an innovative textbook for teachers and students of general philosophy, ethics, business ethics, social and political philosophy, as well as students of literature and philosophy.