Edited by Alexander Miller

Logic, Language, and Mathematics
Themes from the Philosophy of Crispin Wright

Published: 05 March 2020 (Estimated)
448 Pages
234x153mm
ISBN: 9780199278343

Crispin Wright is one of the most important philosophers of the early twenty-first century
This volume brings together substantial chapters on the key themes of Wright's thought
Internationally renowned experts offer a unique insight into the cutting edge of current research
Chapters present a broad range of work in philosophy of language, logic, and mathematics
Also includes thematically organized responses by Crispin Wright, which summarize his life's work

Description

Crispin Wright is widely recognised as one of the most important and influential analytic philosophers of the twentieth and twenty-first centuries. This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics. It comprises specially written chapters by a group of internationally renowned thinkers, as well as four substantial responses from Wright. In these thematically organized replies, Wright summarizes his life's work and responds to the contributory essays collected in this book. In bringing together such scholarship, the present volume testifies to both the enormous interest in Wright's thought and the continued relevance of Wright's seminal contributions in analytic philosophy for present-day debates;

Table of contents

Part I: Frege and Neo-Logicism
1: Generality and Objectivity in Frege's Foundations of Arithmetic, William Demopoulos
2: The Logic of Frege's Theorem, Richard Kimberly Heck
3: Logicism and Logical Consequence, Jim Edwards
4: Logicism and Second Order Logic, George Boolos
4a: Postscript, Richard Kimberly Heck
5: Solving the Caesar Problem with Metaphysics, Gideon Rosen and Stephen Yablo
Part II: Vagueness
6: Vagueness and Intuitionistic Logic, Ian Rumfitt
7: Quandary and Intuitionism: Crispin Wright on Vagueness, Stephen Schiffer
Part III: Logic and Modality
8: Wright and Revisionism, Sanford Shieh
9: Inferentialism, Logicism, Harmony, and a Counterpoint, Neil Tennant
Part IV: Metaphysical Possibility
10: CCCP, Bob Hale
Replies by Crispin Wright
Foreword
Replies to Part I: Frege and Logicism
Replies to Part II: Intuitionism and the Sorites
Replies to Part III: Logical Revisionism
Replies to Part IV: The Epistemology of Metaphysical Possibility

Kuldeep Singh

Number Theory
Step by Step 1

Step-by-step explanations of concepts throughout
Enables self-study or distance learning, with explicit solutions available via companion website
Numerous examples are given to help aid understanding of number theory
Focuses on the study of positive integers using only elementary methods

Description

Number theory is one of the oldest branches of mathematics that is primarily concerned with positive integers. While it has long been studied for its beauty and elegance as a branch of pure mathematics, it has seen a resurgence in recent years with the advent of the digital world for its modern applications in both computer science and cryptography.

Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult material. The strength of the text is in its large number of examples and the step-by-step explanation of each topic as it is introduced to help aid understanding the abstract mathematics of number theory.

It is compiled in such a way that allows self-study, with explicit solutions to all the set of problems freely available online via the companion website. Punctuating the text are short and engaging historical profiles that add context for the topics covered and provide a dynamic background for the subject matter.

Table of contents

1: A Survey of Divisibility
2: Primes and Factorization
3: Theory of Modular Arithmetic
4: A Survey of Modular Arithmetic with Prime Moduli
5: Euler's Generalization of Fermat's Theorem
6: Primitive Roots and Indices
7: Quadratic Residues
8: Non-Linear Diophantine Equations

Akhmet, M., Fen, M.O., Alejaily, E.M., Middle East Technical University, Çankaya, Turkey

Dynamics with Chaos and Fractals

The Book
Stands as the first book presenting theoretical background on the
unpredictable point and mapping of fractals

Introduces the concepts of unpredictable functions, abstract self-similarity,
and similarity map

Discusses unpredictable solutions of quasilinear ordinary and functional
differential equations

Illustrates new ways to construct fractals based on the ideas of Fatou and Julia

The book is concerned with the concepts of chaos and fractals, which are within the scopes of
dynamical systems, geometry, measure theory, topology, and numerical analysis during the last
several decades. It is revealed that a special kind of Poisson stable point, which we call an
unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the
first time in the literature that the description of chaos is initiated from a single motion. Chaos
is now placed on the line of oscillations, and therefore, it is a subject of study in the
framework of the theories of dynamical systems and differential equations, as in this book. The
techniques introduced in the book make it possible to develop continuous and discrete
dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide
strong arguments for the genericity of chaos in the real and abstract universe, the concept of
abstract similarity is suggested.

1st ed. 2020, XIII, 226 p.
76 illus., 71 illus. in color.
Hardcover
ISBN 978-3-030-35853-2
Product category: Monograph
Series : Nonlinear Systems and Complexity

Alpay, D., Colombo, F., Sabadini, I., Chapman University, Orange, CA, USA

Quaternionic de Branges
Spaces and Characteristic Operator Function

This work contributes to the study of quaternionic linear operators. This study is a
generalization of the complex case, but the noncommutative setting of quaternions shows
several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators.
In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of
analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball
of quaternions or in the half space of quaternions with positive real parts. The spaces under
consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to
operator models that are also discussed. The focus of this book is the notion of characteristic
operator function of a bounded linear operator A with finite real part, and we address several
questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we
also treat the inverse problem, namely to characterize which J-contractive functions are
characteristic operator functions of an operator. In particular, we prove the counterpart of
Potapov's factorization theorem in this framework. Besides other topics, we consider canonical
differential equations in the setting of slice hyperholomorphic functions and we define the
lossless inverse scattering problem. We also consider the inverse scattering problem associated
with canonical differential equations. These equations provide a convenient unifying framework
to discuss a number of questions pertaining, for example, to inverse scattering, non-linear
partial differential equations and are studied in the last section of this book.

Due 2020-04-03
1st ed. 2020, X, 116 p.
Softcover
ISBN 978-3-030-38311-4
Product category : Brief
Series : SpringerBriefs in Mathematics


Fowler, Andrew, McGuinness, Mark, University of Limerick, Limerick, Ireland

Chaos
An Introduction for Applied Mathematicians

Fills the gap for a concise text at the beginning graduate level
Written by applied mathematicians for applied mathematics students
Takes a holistic approach with deep insights into the subject

This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for
applied mathematicians. It aims to tread a middle ground between the mathematician's rigour
and the physicist pragmatism. While the subject matter is now classical and can be found in
many other books, what distinguishes this book is its philosophical approach, its breadth, its
conciseness, and its exploration of intellectual byways, as well as its liberal and informative use
of illustration. Written at the graduate student level, the book occasionally drifts from classical
material to explore new avenues of thought, sometimes in the exercises. A key feature of the
book is its holistic approach, encompassing the development of the subject since the time of
Poincaré, and including detailed material on maps, homoclinic bifurcations, Hamiltonian
systems, as well as more eclectic items such as Julia and Mandelbrot sets. Some of the more
involved codes to produce the figures are described in the appendix. Based on lectures to
upper undergraduates and beginning graduate students, this textbook is ideally suited for
courses at this level and each chapter includes a set of exercises of varying levels of difficulty.

Due 2020-02-25
1st ed. 2019, XIV, 303 p.
118 illus., 56 illus. in color.
Softcover
ISBN 978-3-030-32537-4
Product category :Graduate/advanced undergraduate textbook