Download or read book Paul Lorenzen Mathematician and Logician written by Gerhard Heinzmann and published by Springer Nature. This book was released on 2021-08-17 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
Download or read book A Beautiful Math written by Tom Siegfried and published by National Academies Press. This book was released on 2006-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.
Download or read book A Computational Logic written by Robert S. Boyer and published by Academic Press. This book was released on 2014-06-25 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.
Download or read book Intersection Theory written by W. Fulton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.
Download or read book Social Constructivism as a Philosophy of Mathematics written by Paul Ernest and published by SUNY Press. This book was released on 1998-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
Download or read book Constructive Measure Theory written by Errett Bishop and published by American Mathematical Soc.. This book was released on 1972 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Language in Action written by Johan van Benthem and published by MIT Press. This book was released on 1995 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.
Download or read book Handbook of Analysis and Its Foundations written by Eric Schechter and published by Academic Press. This book was released on 1996-10-24 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Download or read book Meaning Logic and Ludics written by Alain Lecomte and published by World Scientific. This book was released on 2011 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 7. Grammatical reasoning. 7.1. Motivations. 7.2. Modal preliminary. 7.3. Residuation and modalities. 7.4. Linguistic applications. 7.5. Back to quantification. 7.6. Kripke semantics. 7.7. Concluding remarks and observations. 8. A type-theoretical version of minimalist grammars. 8.1. Inserting chains. 8.2. Head movement. 8.3. Adjoining and scrambling. 8.4. Semantics without cooper storage. 8.5. Concluding remarks : Some tracks to explore. 9. Grammars in deductive forms. 9.1. Introduction. 9.2. Convergent grammars. 9.3. Labelled linear grammars. 9.4. Binding in LLG. 9.5. On phases. 9.6. Comparing CVG and LLG. 9.7. Concluding remarks. 10. Continuations and contexts. 10.1. The use of continuations in semantics. 10.2. Symmetric calculi. 10.3. Concluding remarks and further works. 11. Proofs as meanings. 11.1. From intuitionistic logic to constructive type theory. 11.2. Formalizing Montague grammar in constructive type theory. 11.3. Dynamical interpretation and anaphoric expressions. 11.4. From sentences to dialogue -- pt. IV. Ludics. 12. Interaction and dialogue. 12.1. Dialogue and games. 12.2. Ludics. 12.3. Behaviours. 13. The future in conclusion
Download or read book Second Philosophy written by Penelope Maddy and published by Oxford University Press. This book was released on 2007-04-19 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Penelope Maddy describes and practises a particularly austere form of naturalism called 'Second Philosophy'. Without a definitive criterion for what counts as 'science' and what doesn't, Second Philosophy can't be specified directly - 'trust only the methods of science!' or some such thing - so Maddy proceeds instead by illustratingthe behaviours of an idealized inquirer she calls the 'Second Philosopher'. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation and testing, working all the while to assess, correct and improve hermethods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations.Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practise SecondPhilosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.
Download or read book Logic Epistemology and the Unity of Science written by Shahid Rahman and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
Download or read book Handbook of Argumentation Theory written by Frans H. van Eemeren and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Handbook of Argumentation Theory".
Download or read book The Legacy of Kurt Sch tte written by Reinhard Kahle and published by Springer Nature. This book was released on 2020-08-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
Download or read book Mathematics Education and Philosophy written by Paul Ernest and published by Taylor & Francis. This book was released on 2003-09-02 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Currently there is a great deal of interest in philosophical issues in the teaching and learning of both mathematics and science education. In this book Ernest has collected together papers from the foremost researchers and practitioners in the philosophy of mathematics education and related areas, together with a selection of papers from the International Congress of Mathematics Education held in Quebec in 1992. Throughout, the outstanding feature of the collection is its multidisciplinary approach to the field of study. This book is the second in Paul Ernest's "Studies in Mathematics Education" series.
Download or read book The Continuum written by Hermann Weyl and published by Courier Corporation. This book was released on 1994-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.
Download or read book The Philosophy of Mathematics Education written by Paul Ernest and published by Springer. This book was released on 2016-07-15 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.
Download or read book One Hundred Years of Intuitionism 1907 2007 written by Mark van Atten and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.
