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Navigating Across Mathematical Cultures
And Times: Exploring The Diversity Of Di

Navigating Across Mathematical Cultures And Times: Exploring The Diversity Of Discoveries And Proofs

Publications of the Austrian Ludwig Wittgenstein Society – New Series

This volume covers the origin, interpretations, and reception of Wittgenstein's Tractatus Logico-Philosophicus and offers a critical assessment of the related research and contemporary historiography. Moreover, open philosophical, ethical, and (un

This volume covers the origin, interpretations, and reception of Wittgenstein’s Tractatus Logico-Philosophicus and offers a critical assessment of the related research and contemporary historiography.The authors deal with an evaluation of research on Wittgenstein’s philosophy, life, and work, as well as of the editions of his work published since his death. This includes upcoming editions with a special focus on the availability of Wittgenstein’s (digital) Nachlass. Special attention is given to the reception of and references to the Tractatus in the middle and later Wittgenstein, as well as the reception by other philosophers. Moreover, open philosophical, ethical, and (unresolved) scientific questions are addressed with a critical investigation of current research. Furthermore, the complex, diverse, and mutual relation of Wittgenstein and the Vienna Circle of Moritz Schlick, Otto Neurath, Friedrich Waismann and others are addressed.

Proceedings of the 44th International Ludwig Wittgenstein Symposium

100 Years of ›Tractatus Logico-Philosophicus‹ – 70 Years after Wittgenstein’s Death

Indo-Arabic Numerals and the Making of Practical Knowledge in Early Modern Europe

Working Numbers

Leibniz from Oxford

This volume gathers together the philosophical journal articles that appeared during Leibniz's lifetime, as a companion to Leibniz: Journal Articles on Natural Philosophy (OUP, 2023). The articles include seminal original works, responses to criticisms, and series of critical discussions of Descartes and Cartesian philosophy.

This volume gathers together the philosophical journal articles that appeared during Leibniz's lifetime, as a companion to Leibniz: Journal Articles on Natural Philosophy (OUP, 2023). The articles include seminal original works, responses to criticisms, and series of critical discussions of Descartes and Cartesian philosophy.

Leibniz: Journal Articles on Philosophy

"Deflationary" theories are views about truth that are often, but not always, characterized as accounts that accept the utility of the truth predicate without granting the metaphysical or epistemological assumptions that usually go along with it. The Deflationary Approach to Truth: A Guide presents a detailed, up-to-date, and historically informed survey and critical explication of the deflationary approach to the topic of truth, paying special attention to the wide range of different deflationary theories.

"Deflationary" theories are views about truth that are often, but not always, characterized as accounts that accept the utility of the truth predicate without granting the metaphysical or epistemological assumptions that usually go along with it. The Deflationary Approach to Truth: A Guide presents a detailed, up-to-date, and historically informed survey and critical explication of the deflationary approach to the topic of truth, paying special attention to the wide range of various deflationary theories. 

In Part One, Bradley Armour-Garb and James A. Woodbridge explain what the deflationary approach to truth involves and develop a useful framework that clarifies how it differs from the traditional, "inflationary" approach. The framework illuminates certain general deflationary themes in terms of what Armour-Garb and Woodbridge call broad four-dimensional deflationism. This analysis reveals four different dimensions that any deflationary account must satisfy: Linguistic Deflationism, Metaphysical Deflationism, Conceptual Deflationism, and Paradox Treatment Deflationism. Armour-Garb and Woodbridge examine the degree to which these dimensions are displayed in early, "proto-deflationary" accounts before explaining the different contemporary deflationary views and assessing the degree to which these accounts adhere to the four deflationary dimensions, differ from inflationism, and differ from each other. 

In Part Two, Armour-Garb and Woodbridge examine various challenges to deflationism, systematizing them by considering each deflationary dimension and grouping the challenges in terms of which dimension they target. For each challenge, they explain its historical development and investigate the extent to which the most prominent contemporary deflationary accounts answer, or fail to answer, that challenge. In Part Three, Armour-Garb and Woodbridge explore fruitful new directions for deflationism and develop a version of the approach that they think best handles the challenges that are examined in Part Two. The result is an accessible yet comprehensive overview of the challenges to and merits of the deflationary approach to truth.

A Guide

The Deflationary Approach to Truth

Princeton Mathematical Series

Princeton Legacy Library

An authoritative introduction to the essential features of étale cohomology A. Grothendieck’s work on algebraic geometry is one of the most important mathematical achievements of the twentieth century. In the early 1960s, he and M. Artin introduced étale cohomology to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry but also in several different branches of number theory and in the representation theory of finite and p-adic groups. In this classic book, James Milne provides an invaluable introduction to étale cohomology, covering the essential features of the theory. Milne begins with a review of the basic properties of flat and étale morphisms and the algebraic fundamental group. He then turns to the basic theory of étale sheaves and elementary étale cohomology, followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Milne proves the fundamental theorems in étale cohomology—those of base change, purity, Poincaré duality, and the Lefschetz trace formula—and applies these theorems to show the rationality of some very general L-series.

Étale Cohomology

Series on Advances in Mathematics for Applied Sciences

This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging.As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types.Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.

Mathematical Modelling: Selected Objects And Processes

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

A Mathematical Tour

Elements in the Philosophy of Mathematics

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.

This Element explores the preference for pure proofs in mathematics since antiquity, focusing on geometry and number theory. It discusses different types of purity, reasons for preferring pure proofs, and the importance of local purity. It also touches on translation issues and the relationship between purity and local considerations.

Elements of Purity

English and Maths Made Simple

2 books in 1! Help your child make progress in English and mathstopics with this essential practice and revision title covering keyknowledge and skills from the whole school year. Recap all theessential content, then check your skills with practice questionsand activities.

Navigating Across Mathematical Cultures And Times: Exploring The ...

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