Philosophy of mathematics

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Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences.

When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as "e;conflicts of conscience"e;--the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy.

There is a long tradition, in the history and philosophy of science, of studying Kant's philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant's reflections on mathematics play a role in his philosophy more generally, and in its development.

Originally published in 1967.

In this 2006 volume, Alexander Pruss examines the substantive philosophical issues raised by the Principle of Sufficient Reason.

In Alan Lightman's new book, a verse narrative, we meet a man who has lost his faith in all things following a mysterious personal tragedy.

These essays apply the core conceptual innovation underlying Frege''s theory of number to the general analysis of theoretical knowledge.

This book charts the shape of future philosophical investigation by posing the question: "e;What is the Matrix?

The philosophical positions of realism and anti-realism are difficult to distinguish, nowhere more so than in the philosophy of mathematics.

McCarthy develops a theory of radical interpretation--the project of characterizing from scratch the language and attitudes of an agent or population--and applies it to the problems of indeterminacy of interpretation first described by Quine.

Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics.

This is a charming and insightful contribution to an understanding of the "e;Science Wars"e; between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy.

'A hugely entertaining and well-written tour of the links between math and literature.

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.

This book reveals the myriad aspects of Big Data collection and analysis, by defining and clarifying the meaning of Big Data and its unique characteristics in a non-technical and easy-to-follow way.

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic; he has illuminated Aristotle's syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection; and his debunking work on the theory of descriptions is a tour de force.

Inside Mathforum.

"e;The old logic put thought in fetters, while the new logic gives it wings.

How a simple equation reshaped mathematicsLeonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules.

An engrossing look at the history and importance of a centuries-old but still unanswered math problemFor centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem.

What are the meanings of number expressions, what can they tell us about questions central to the philosophy of mathematics?

John Maynard Keynes is best known for his contributions to economics, yet he spent nearly two decades exploring the concept of probability.

Generality is a key value in scientific discourses and practices.

In his monumental 1687 work, Philosophiae Naturalis Principia Mathematica, known familiarly as thePrincipia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science.

This book presents eight papers about important historiographical issues as debated in the history of science in Islamicate societies, the history of science and philosophy of medieval Latin Europe and the history of mathematics as an academic discipline.

Do numbers, sets, and so forth, exist?

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science.

Essays on Existence and Essence presents a series of writings--including several previously unpublished--by Bob Hale on the topics of ontology and modality.

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science?

This book tells the story of the first computer exploration of Klein''s vision of infinitely repeated reflections, featuring extraordinary images.

Classical physics states that physical reality is local--a point in space cannot influence another point beyond a relatively short distance.

In The Thrilling Adventures of Lovelace and Babbage Sydney Padua transforms one of the most compelling scientific collaborations into a hilarious set of adventures The Thrilling Adventures of Lovelace and Babbage is a unique take on the unrealized invention of the computer in the 1830s by the eccentric polymath Charles Babbage and his accomplice, the daughter of Lord Byron, Ada, Countess of Lovelace.

Our words and ideas refer to objects and properties in the external world; this phenomenon is central to thought, language, communication, and science.

Originally published in 1973.

Techniques for deciphering texts by early mathematiciansWritings by early mathematicians feature language and notations that are quite different from what we're familiar with today.

There are things we routinely say that may strike us as literally false but that we are nonetheless reluctant to give up.

Seminal articles in the philosophy of mathematics by Russell, Quine, Gödel and other major thinkers.

A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.

This Festschrift includes papers presented to honour Solomon Feferman on his seventieth birthday, reflecting his broad interests and his approach to foundational research.

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.

This book offers a detailed account and discussion of Ludwig Wittgenstein's philosophy of mathematics.

What Is Scientific Knowledge?

An insightful overview of how syntactic theory was influenced by developments in the formal sciences during the twentieth Century.

This volume contains essays on the history and philosophy of probability and statistics.

Tessellations: Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists.