Philosophy of mathematics

In recent years there have been a number of books-both anthologies and monographs-that have focused on the Liar Paradox and, more generally, on the semantic paradoxes, either offering proposed treatments to those paradoxes or critically evaluating ones that occupy logical space.

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716).

Mathematical Recreations from the Tournament of the Towns contains the complete list of problems and solutions to the International Mathematics Tournament of the Towns from Fall 2007 to Spring 2021.

This book constitutes the refereed proceedings of the 20th International Conference on Group Decision and Negotiation, GDN 2020, which was planned to be held in Toronto, ON, Canada, during June 7-11, 2020.

Provides readers with experience of working on difficult unsolved problems.

This book offers a new and original hypothesis on the origin of modal ontology, whose roots can be traced back to the mathematical debate about incommensurable magnitudes, which forms the implicit background for Plato's later dialogues and culminates in the definition of being as dynamis in the Sophist.

Ludwig Wittgenstein's brief Tractatus Logico-Philosophicus (1922) is one of the most important philosophical works of the twentieth century, yet it offers little orientation for the reader.

This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728-1777) written in the 1760s: Vorlaufige Kenntnisse fur die, so die Quadratur und Rectification des Circuls suchen and Memoire sur quelques proprietes remarquables des quantites transcendentes circulaires et logarithmiques.

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other.

The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus.

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English.

An Essay on the Foundations of Geometry was first published in 1897 when Bertrand Russell was 25 years old.

If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought?

The Untold Story of Everything Digital: Bright Boys, Revisited celebrates the 70th anniversary (1949-2019) of the world "e;going digital"e; for the very first time-real-time digital computing's genesis story.

While the phrase "e;metaphysics of science"e; has been used from time to time, it has only recently begun to denote a specific research area where metaphysics meets philosophy of science-and the sciences themselves.

David Bostock presents a critical appraisal of Bertrand Russell's philosophy from 1900 to 1924--a period that is considered to be the most important in his career.

The computer science problem whose solution could transform life as we know itThe P-NP problem is the most important open problem in computer science, if not all of mathematics.

Alain Badiou has claimed that Quentin Meillassoux's book After Finitude (Bloomsbury, 2008) opened up a new path in the history of philosophy.

A mathematical sightseeing tour of the natural world from the author of THE MAGICAL MAZEWhy do many flowers have five or eight petals, but very few six or seven?

The Scholarship of Teaching and Learning: A Guide for Scientists, Engineers, and Mathematicians shows college and university faculty members how to draw on their disciplinary knowledge and teaching experience to investigate questions about student learning.

Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism.

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality?

This book introduces the reader to the mathematical core of intuitionism and to the two central topics of ''formalized intuitionism''.

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others.

The nature of reality has been a long-debated issue among scientists and philosophers.

This volume offers an English translation of all ten extant books of Diophantus of Alexandria's Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary.

Why narrative is essential to mathematicsCircles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative.

Originally published in 1967.

Originally published in 1988.

Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability.

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.

This monograph uses the concept and category of "e;event"e; in the study of mathematics as it emerges from an interaction between levels of cognition, from the bodily experiences to symbolism.

This book investigates the process of care in mathematics teaching.

This book aims to present an overview of grey system models for time series modelling and forecasting.

WHAT DOES IT MEAN TO COUNT?

To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.

This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics.

This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.

What Is Scientific Knowledge?

What is mathematics about?

Originally published in 1967.

Michael G.

To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another.

This book looks to change our thinking about thinking by looking at communication and cognition, or commognition.

Probability has fascinated philosophers, scientists, and mathematicians for hundreds of years.

Hans Vaihinger (1852-1933) was an important and fascinating figure in German philosophy in the early twentieth century, founding the well-known journal Kant-Studien.