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Elwes R: The Story of Huge Numbers

The Story of Huge Numbers

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

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

This Element explores medieval arguments for the impossibility of infinity, focusing on the early stages of the development of the notion of 'infinities of different sizes'. The Equality Argument and Mapping Argument, initially proposed in opposition to infinity, have played significant roles in the historical evolution of this concept.

Medieval Finitism

A fascinating new take on the world of Shakespeare.

Much Ado About Numbers

WHAT DOES IT MEAN TO COUNT? WHY ARE HUMANS THE ONLY SPECIES ON EARTH THAT CAN DO IT? WHERE DID COUNTING COME FROM? HOW HAS IT SHAPED SOCIETIES ALONG THE WAY? AND WHY DOES IT MATTER?

Humans, History and the Infinite Lives of Numbers

Counting

This volume brings together twelve essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant. Its broad historical sweep also facilitates comparisons between different figures.

This volume brings together twelve essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant. Its broad historical sweep also facilitates comparisons between different figures.

Definition and Essence from Aristotle to Kant

Rules to Infinity defends the thesis that mathematics contributes to the explanatory power of science by expressing conceptual rules that allow for the transformation of empirical descriptions. It claims that mathematics should not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional Platonists have thought.

This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. 

One of the central aims of science is to provide explanations of natural phenomena. What role does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis that mathematics contributes to the explanatory power of science by expressing conceptual rules that allow for the transformation of empirical descriptions. It claims that mathematics should not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional Platonists have thought. 

This view, which Mark Povich calls "mathematical normativism," is updated with contemporary philosophical tools, which are used to form the argument that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the Platonistic idea that there exist abstract mathematical objects that explain such truths. There is a distinction between scientific explanations that are in some sense distinctively mathematical--those that explain natural phenomena in some uniquely mathematical way--and those that are only standardly mathematical, and Povich defends a particular account of this distinction. 

Rules to Infinity compares normativism to other prominent views in the philosophy of mathematics, such as neo-Fregeanism, fictionalism, conventionalism, and structuralism, and offers an entry point into debates at the forefront of philosophy of science and mathematics as it defends its novel positions.

The Normative Role of Mathematics in Scientific Explanation

Rules to Infinity

Bloomsbury Studies in the Aristotelian Tradition

Aristotle's Organon in Old and New Logic 1800-1950 explores the reception and interpretation of Aristotle's logic over the last two centuries. The volume covers seminal works during this period by logicians, historians of logic, and historians of philosophy, including John Lloyd Akrill, Francesco Barone, Günther Patzig, Enrico Berti, and Mario Mignucci. Contributors consider the reception of the Organon in old logic and chart the appearance of formal approaches to logic beginning with Boole. This in-depth study of Aristotelianism also covers logic in Kant and Hegel, alongside the problems and projects of interpreting Aristotle in the new logic after Boole and Frege. The background of modern debates concerning induction and abduction provides further insight into Aristotelian logic during the period. By filling gaps in our understanding of Aristotelian logic, this book provides a fundamental missing link in 21st century studies of the history of Aristotelianism. It brings together scholars of both ancient and modern logic to understand the interpretation of ancient logic before and after the development of the modern, algebraic approach to logic.

Aristotle’s Organon in Old and New Logic 1800–1950 explores the reception and interpretation of Aristotle’s logic over the last two centuries. The volume covers seminal works during this period by logicians, historians of logic, and historians of philosophy, including John Lloyd Akrill, Francesco Barone, Günther Patzig, Enrico Berti, and Mario Mignucci. Contributors consider the reception of the Organon in old logic and chart the appearance of formal approaches to logic beginning with Boole. This in-depth study of Aristotelianism also covers logic in Kant and Hegel, alongside the problems and projects of interpreting Aristotle in the new logic after Boole and Frege. The background of modern debates concerning induction and abduction provides further insight into Aristotelian logic during the period. By filling gaps in our understanding of Aristotelian logic, this book provides a fundamental missing link in 21st century studies of the history of Aristotelianism. It brings together scholars of both ancient and modern logic to understand the interpretation of ancient logic before and after the development of the modern, algebraic approach to logic.

1800–1950

Aristotle’s Organon in Old and New Logic

?If you have ever wondered why an airliner bound from London to Los Angeles flies over Greenland, how we know what lies inside the Earth, or how computers correct errors, then this is for you' John Gribbin, author of Six Impossible Things How does a delivery driver distribute hundreds of packages in a single day? Why can maps help to win elections? Where should we look for serial killers? The answers lie in the crucial connection between maps and maths. In Mapmatics, mathematician Dr Paulina Rowinska embarks on a fascinating journey to discover the mathematical foundations of cartography and cartographical influences on mathematics. From a sixteenth-century map that remains an indispensable navigation tool on our phones to public transport maps that both guide and mislead passengers, she reveals how maps and maths shape not only our sense of space and time but also our worldview. In entertaining stories, surprising real-world examples, maps, illustrations and a cast of unforgettable characters, Mapmatics helps us to appreciate the mathematical methods and ideas behind maps - and leaves us better equipped to look after them. ?A wonderfully readable adventure' Edward Brooke-Hitching, author of The Phantom Atlas ?This book blew my mind, again and again' Roma Agrawal, author of Built ?Entertaining, illuminating . . . An engaging look at a fascinating subject' New Scientist ?An expansive journey through time and place' The Observer

How We Navigate the World Through Numbers

Mapmatics

This Element looks at Quine's arguments against the concepts of analyticity. It mentions Boghossian's distinction between epistemic and metaphysical accounts of analyticity. It shows how analyticity is related to truth, necessity and questions of ontology. The relation of analyticity to the axiomatic method in mathematics is mentioned.

This Element looks at Quine's arguments against the concepts of analyticity. It mentions Boghossian's distinction between epistemic and metaphysical accounts of analyticity. It shows how analyticity is related to truth, necessity and questions of ontology. The relation of analyticity to the axiomatic method in mathematics is mentioned.

Mathematics is (mostly) Analytic

This book introduces students and researchers to the philosophical issues at play in the growing field of Bayesian epistemology. It focuses not on how to do particular calculations but instead on the philosophical foundations at the convergence of belief and mathematical representation. Its central questions are: What is the nature of quantifying belief? What is the source of its norms? How is it reasonable to represent belief numerically? Accessible to those without any mathematical background, this book will become a much used classic in the field.

This book introduces students and researchers to the philosophical issues at play in the growing field of formal (or Bayesian) epistemology. It focuses not on how to do particular calculations but instead on the philosophical foundations at the convergence of belief and mathematical representation. Its central questions are: What is the nature of quantifying belief? What is the source of its norms? How is it reasonable to represent belief numerically? Accessible to those without any mathematical background, this book will become a much used classic in the field.

A Philosophical Introduction

The Foundations of Bayesian Epistemology

This Element explores the philosophical role of definitions in mathematical knowledge, examining their origins, epistemic roles, and formal constraints. It explores explicit, implicit, and axiomatic definitions, and their potential to yield mathematical knowledge.

This Element explores the philosophical role of definitions in mathematical knowledge, examining their origins, epistemic roles, and formal constraints. It explores explicit, implicit, and axiomatic definitions, and their potential to yield mathematical knowledge.

Definitions and Mathematical Knowledge

The Story of Huge Numbers

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