Introduction to Mathematical Philosophy: Restored Classics to Go Edition

· Otbebookpublishing
Ebook
284
Pages

About this ebook

Bertrand Russell's Introduction to Mathematical Philosophy opens a strikingly clear path into the logical foundations of mathematics, treating the subject not as a sealed technical discipline but as an inquiry into what makes number, continuity, and proof possible at all. Russell contrasts the ordinary ascent from arithmetic to analysis with the philosophical descent from familiar ideas to their simplest logical components, arguing that the most obvious mathematical notions are often the least fundamental. He begins with the natural numbers and Peano's reduction of arithmetic to a few primitive ideas and axioms, including induction, showing both the power of this framework and its limits, since many different sequences can satisfy the same formal structure. From there, Russell turns to Frege's overlooked breakthrough and the problem of defining number itself. He distinguishes number from plurality, explains classes and one-one relations, and shows how equality of quantity can be established without counting. The book then develops the theory of relations, limits, and boundaries in ordered series, leading to a rigorous treatment of continuity through limiting points, perfect series, and the distinction between Dedekindian and Cantorian continuity. Throughout, Russell's aim is both explanatory and provocative: to show how mathematical logic can illuminate philosophy while demanding a deeper definition of number and structure. This edition has been fully restored with modern typesetting, custom cover design.
Bertrand Russell's Introduction to Mathematical Philosophy opens a strikingly clear path into the logical foundations of mathematics, treating the subject not as a sealed technical discipline but as an inquiry into what makes number, continuity, and proof possible at all. Russell contrasts the or...

About the author

Bertrand Russell was one of the twentieth century's most wide-ranging and influential thinkers, a philosopher, logician, mathematician, social critic, and public intellectual whose life stretched from the late Victorian era into the nuclear age. Born into an aristocratic British family in 1872, he was educated at Cambridge, where he helped transform modern logic and the philosophy of mathematics, and he spent much of his long life moving between scholarship, political activism, and moral dissent. His writing ranged from rigorous technical philosophy to essays for general readers, and he became especially celebrated for making difficult ideas about logic, knowledge, language, and human freedom feel urgent and accessible. Across his work, Russell returned again and again to themes of reason, skepticism, the search for truth, the dangers of dogma, and the ethical responsibilities of individuals in society. He argued passionately against war, religious intolerance, and intellectual complacency, and his voice remained clear and provocative in debates about education, science, and politics. Today, Russell still matters because he offers a model of thoughtfulness combined with courage: he shows how careful reasoning can serve humane ends. Readers interested in philosophy, mathematics, politics, or the challenge of thinking independently will find him especially rewarding, as will anyone drawn to writers who ask hard questions without losing their moral urgency.

Bertrand Russell was one of the twentieth century's most wide-ranging and influential thinkers, a philosopher, logician, mathematician, social critic, and public intellectual whose life stretched from the late Victorian era into the nuclear age. Born into an aristocratic British family in 1872, h...

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