Philosophical Introduction To Set Theory
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Set Theory and its Philosophy
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Philosophical Introduction to Set Theory
Set theory is the primary mechanism for ideological and theoretical unification in modern mathematics. By offering a clear statement of basic questions and problems in this volume, Stephen Pollard aims to make the study of the philosophy of set theory less anarchic.
Philosophical Introduction to Set Theory
Author: Stephen Pollard
language: en
Publisher: Courier Dover Publications
Release Date: 2015-07-20
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.