Paradoxes and inconsistent mathematics / Zach Weber.

Format:

Book

Author/Creator:

Weber, Zach, author.

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Inconsistency (Logic).

Dialetheism.

Paradox.

Physical Description:

1 online resource (xii, 324 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.

Contents:

Introduction to an inconsistent world

Paradoxes; or, "Here in the presence of an absurdity"

In search of a uniform solution

Metatheory and naive theory

Prolegomena to any future inconsistent mathematics

Set theory

Arithmetic

Algebra

Real analysis

Topology

Ordinary paradox.

Notes:

Title from publisher's bibliographic system (viewed on 11 Oct 2021).

ISBN:

1-108-99902-6

1-108-99924-7

1-108-99313-3

OCLC:

1266204914