Founding Mathematics On Semantic Conventions
DOWNLOAD
AUDIOBOOK
Download Founding Mathematics On Semantic Conventions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Founding Mathematics On Semantic Conventions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Founding Mathematics On Semantic Conventions
DOWNLOAD
AUDIOBOOK
Author : Casper Storm Hansen
language : en
Publisher: Springer Nature
Release Date : 2021-11-04
Founding Mathematics On Semantic Conventions written by Casper Storm Hansen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Mathematics categories.
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Doing Mathematics
DOWNLOAD
AUDIOBOOK
Author : Martin H. Krieger
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015-01-21
Doing Mathematics written by Martin H. Krieger and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-21 with Mathematics categories.
Doing Mathematics discusses some ways mathematicians do their work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians, all depend on mathematics what will work out and what won't. And how mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, rigorous proofs of the stability of matter, solutions to the two-dimensional Ising model of ferromagnetism, and their connection to the Langlands program in number theory and representation theory and a relationship of number theory, function theory, and analysis begun by Dedekind. This second edition deepens each chapter: mathematical rigor and the philosophy of mathematics; finance and big data in statistics; the need for perseverance and the inevitable inelegance in a first proof; the recurrent appearance of the Bethe Ansatz and Hopf algebras in these lattice models; solutions of the Kondo model as epitomizing these themes; analogies between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics; Edward Frenkel's use of the Weil threefold-analogy in the geometric Langlands program; the warehouse of mathematical objects and how it is enlarged; and how recent developments in set theory are analogous with developments in systematic theology as attempts to be articulate about what others take as vague or beyond analysis.
Language And Philosophical Problems
DOWNLOAD
AUDIOBOOK
Author : Sören Stenlund
language : en
Publisher: Taylor & Francis
Release Date : 2013-01-11
Language And Philosophical Problems written by Sören Stenlund and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Philosophy categories.
Language and Philosophical Problems investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, Sren Stenlund demonstrates a strategy for tracing out and resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many prima facie different kinds of problems are shown to have common roots, and should thus be dealt and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem.
The Philosophy Of Mathematics Education
DOWNLOAD
AUDIOBOOK
Author : Paul Ernest
language : en
Publisher: Routledge
Release Date : 2002-11-01
The Philosophy Of Mathematics Education written by Paul Ernest and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-01 with Education categories.
Although many agree that all teaching rests on a theory of knowledge, there has been no in-depth exploration of the implications of the philosophy of mathematics for education. This is Paul Ernest's aim. Building on the work of Lakatos and Wittgenstein it challenges the prevalent notion that mathematical knowledge is certain, absolute and neutral, and offers instead an account of mathematics as a social construction. This has profound educational implications for social issues, including gender, race and multiculturalism; for pedagogy, including investigations and problem solving; and challenges hierarchical views of mathematics, learning and ability. Beyond this, the book offers a well-grounded model of five educational ideologies, each with its own epistemology, values, aims and social group of adherents. An analysis of the impact of these groups on the National Curriculum results in a powerful critique, revealing the questionable assumptions, values and interests upon which it rests. The book finishes on an optimistic note, arguing that pedagogy, left unspecified by the National Curriculum, is the way to achieve the radical aims of educating confident problem posers and solvers who are able to critically evaluate the social uses of mathematics.
Mathematical Reviews
DOWNLOAD
AUDIOBOOK
Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The Foundations Of Mathematics
DOWNLOAD
AUDIOBOOK
Author : Kenneth Kunen
language : en
Publisher:
Release Date : 2009
The Foundations Of Mathematics written by Kenneth Kunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Principia Mathematica
DOWNLOAD
AUDIOBOOK
Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Computing With Words
DOWNLOAD
AUDIOBOOK
Author : Paul P. Wang
language : en
Publisher: Wiley-Interscience
Release Date : 2001
Computing With Words written by Paul P. Wang and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
Fuzzy logic refers to a computer's ability to make decisions involving "grey" or "fuzzy" areas. As linguistics contains numerous "grey" areas, computing with words through the use of fuzzy logic is an extremely hot topic in database and Internet research. This book explores the state of the art in linguistic computation, discussing how current research findings are extending the application of fuzzy logic beyond control engineering and intelligent systems into the use of language on a computer. Fuzzy logic pioneer, Dr. Lofti Zadeh, provides the introduction for this thought-provoking work.
Mathematical Writing
DOWNLOAD
AUDIOBOOK
Author : Donald E. Knuth
language : en
Publisher: Cambridge University Press
Release Date : 1989
Mathematical Writing written by Donald E. Knuth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Language Arts & Disciplines categories.
This book will help those wishing to teach a course in technical writing, or who wish to write themselves.
The Formal Semantics Of Programming Languages
DOWNLOAD
AUDIOBOOK
Author : Glynn Winskel
language : en
Publisher: MIT Press
Release Date : 1993-02-05
The Formal Semantics Of Programming Languages written by Glynn Winskel and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-05 with Computers categories.
The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.
