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Title: Introduction to Symbolic Logic and Its Applications by Rudolf Carnap ISBN: 0-486-60453-5 Publisher: Dover Pubns Pub. Date: 01 June, 1958 Format: Paperback Volumes: 1 List Price(USD): $9.95 |
Average Customer Rating: 4.75 (4 reviews)
Rating: 4
Summary: A real bargain by a true master
Comment: 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 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. (I should admit here that I have devised a radically simpler axiom for the truth functors, and am working on a simplification of quantification theory. Even if my theory doesn't pan out, I still believe that UG and UI suffice for quantifiers.) 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 greatest discovery. Carnap was comfortable with the notion of predicate 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.
Rating: 5
Summary: good books
Comment: 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.
Rating: 5
Summary: Learning logic as language L
Comment: Throughout his philosophical life Carnap held to the analytic character of logic and mathematics. This belief comes through in Carnap's insistence that language L deals with analytic (syntactical)relations among the functions, variables and constants of the language. Not only do you learn logic from a great philosopher, but in the end of the book Carnap takes his reader through what he understood as some philosophical applications of logic. This is a great exercise as well as that it gives the reader insight into Carnap's own understanding of the aims and uses of logic in scientific philosophy.
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Title: Introduction to Logic by Alfred Tarski ISBN: 048628462X Publisher: Dover Pubns Pub. Date: 27 March, 1995 List Price(USD): $11.95 |
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Title: An Introduction to Symbolic Logic by Susanne K. Langer ISBN: 0486601641 Publisher: Dover Pubns Pub. Date: 01 June, 1967 List Price(USD): $14.95 |
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Title: Methods of Logic by Willard V. Quine ISBN: 0674571762 Publisher: Harvard Univ Pr Pub. Date: June, 1989 List Price(USD): $21.95 |
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Title: Elementary Logic by Willard V. Quine ISBN: 0674244516 Publisher: Harvard Univ Pr Pub. Date: October, 1980 List Price(USD): $15.95 |
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Title: An Introduction to the Philosophy of Science by Rudolf Carnap ISBN: 0486283186 Publisher: Dover Pubns Pub. Date: 17 January, 1995 List Price(USD): $12.95 |
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