Introduction to Symbolic Logic and Its Applications

by Rudolf Carnap

Book Overview

A clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. It then considers the application of symbolic logic to the clarification and axiomatization of theories in mathematics, physics, and biology. Hundreds of problems, examples, and exercises. 1958 edition.

• Format: Paperback
• Language: English
• ISBN: 0486604535
• ISBN13: 9780486604534
• Release Date: November 2011
• Publisher: Dover Publications
• Length: 272 Pages
• Weight: 0.62 lbs.
• Dimensions: 0.5" x 5.4" x 8.0"

Customer Reviews

A real bargain by a true master

Rudolf Carnap was one of the greatest philosophers of the 20th century, and the only student of Frege's worth thinking about. But what a student! This is his intro text, a doubtful first text, but full of insight for those who already know some logic. Carnap trained as a mathematician; surprisingly, his text is of value mainly for philosophers. For instance, this is the ONLY undergrad logic text I know that grapples with the intension-extension dichotomy, with the Carnap-Morris syntax-semantics-pragmatics trichotomy. Metatheory is nonexistent, and Carnap's notion of proof is emphatically too casual for my taste. The book is also dated. In its treatment of first order logic, Carnap is a bit too loyal to Principia Mathematica. His axioms are a bit pedantic, a bit inelegant for my taste. (Quantified formulae are much easier to work with than Carnap and his contemporaries realized; all you need to do with quantified variables is to instantiate them! See the "main method" of Quine's Methods of Logic.) You won't learn any natural deduction, truth trees, or Gentzen sequents here. You most definitely won't learn anything about recursion. But the exposition incorporates thoughout Carnap's greatest discovery: his formal theory of semantics. You will also learn more about the logic of relations than you will in any other undergrad text. You will be given an idea of the mathematical power of logic (infinity, continuity, numbers). You will even be introduced to the lambda calculus, Alonzo Church's great discovery. Carnap was comfortable with the notion of a predicate letter like few logicians since. Part II of the book is without parallel anywhere: an introduction to a very wide range of axiomatic theories, presented as interesting applications of modern formal logic. This is a wonderful reference for ZF set theory, Peano axioms, Tarski's axioms for the reals, the Hausdorff- Bohnenblust axioms for topology, axioms for geometry, space-time, and mirabile dictu, even mereology. Other texts present at most the first 2 items on this list.

good books

It is my experience as a reader that good books are always books that have lots of examples because they make our understanding easier. Therefore, if this math book has examples in it, then it must mean it is very good.So I recommend that whenever you have a chance to see it that you buy it.

Carnap and Vienna Circle

Rudolf Carnap is the one of the most famous analytic philosophers of 20th Century and he is one of the leaders of Vienna Circle. Learning Symbolic Logic from this classical book would be enthusiastic