Synopses & Reviews
This book, written by one of philosophy's preeminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. Hintikka's new logic is highly original and will prove appealing to logicians, philosophers of mathematics, and mathematicians concerned with the foundations of the discipline.
Review
"Every thoughtful mathematician or student of the philosophy of science or mathematics will want to read this book....superbly lucid and well-presented work....highly recommended for upper division undergraduate through professional collections." Choice"In this engaging, provocative manifesto, Professor Hintikka breaks the ground for what he hopes will be a revolution in logic, in much the same "critical and constructive" spirit as motivted Bertrand Russell...Hintikka claims that present-day logic, with its basis in a beautiful proof theory, is the result of abandoning the idea that logic can have any major role to play in mainstream mathematical...this highly readable, wide-ranging book deserves a great deal of attention and debate." Modern Logic May 2000- Oct 2001
Synopsis
Hintikka proposes a new logic and uses it to explore the foundations of mathematics.
Description
Includes bibliographical references (p. 271-279) and indexes.
Table of Contents
1. The functions of logic and the problem of truth definition; 2. The game of logic; 3. Fregeâs fallacy foiled: Independence-friendly logic; 4. The joys of independence: Some uses of IF logic; 5. The complexities of completeness; 6. Whoâs afraid of Alfred Tarski? Truth-definitions for IF first-order languages; 7. The liar belied: negation in IF logic; 8. Axiomatic set theory: Frankensteinâs monster?; 9. IF logic as a framework for mathematical theorizing; 10. Constructivism reconstructed; 11. The epistemology of mathematical objects.