Philosophy of mathematics

Mathematical Meditations identifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing.

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry.

Originally published in 1966.

This book presents a new nominalistic philosophy of mathematics: semantic conventionalism.

Written within the tradition of Wittgenstein's work, these eight original essays in philosophical psychology are either by-products of efforts to understand Wittgenstein's later writings or applications of techniques and approaches derived from Wittgenstein to problems about which he did not say a great deal.

A dozen world-renowned researchers explore the concept of infinity through the prism of mathematics and beyond.

This book highlights and develops a hitherto neglected area of Hans Blumenberg's contributions, i.

A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

Today, most money is credit money, created by commercial banks.

This Element shows that Plato was not a mathematical Platonist, and kept a clear distinction between mathematical and metaphysical realism.

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period.

Philosophy of science studies the methods, theories, and concepts used by scientists.

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

This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools.

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities.

The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.

Developing mathematical thinking is one of major aims of mathematics education.

What is the nature of mathematical knowledge?

Originally published in 1923 Chance and Error examines the vagaries of chance, and how this is the result of the interference of yes and no.

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems.

While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail.

This monograph explores the logical systems of early logicians in the Arabic tradition from a theoretical perspective, providing a complete panorama of early Arabic logic and centering it within an expansive historical context.

Das mathematische Werk des Cusanus ist vor allem von seinem Interesse an metaphysisch-theologischen Fragestellungen geprägt.

Mathematics is as much a science of the real world as biology is.

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds.

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.

Numbers: A Cultural History provides students with a compelling interdisciplinary view of the development of mathematics and its relationship to world cultures over 4,500 years of human history.

Head hits cause brain damage - but not always.

This volume brings together 12 essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant.

Mathematical and philosophical thought about continuity has changed considerably over the ages.

This book provides a comprehensive investigation into the concept of typicality and its significance for physics and the philosophy of science.

Simply stated, this book bridges the gap between statistics and philosophy.

Hex: The Full Story is for anyone - hobbyist, professional, student, teacher - who enjoys board games, game theory, discrete math, computing, or history.

The seventeenth century saw dramatic advances in mathematical theory and practice.

Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century.

Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics.

Classroom interaction has a significant influence on teaching and learning.

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content.

Not all scientific explanations work by describing causal connections between events or the world's overall causal structure.

In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel''s work on the foundations and philosophy of mathematics.

Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent.