- Paperback: 404 pages
- Publisher: Oxford University Press, USA (9 Oct. 1997)
- Language: English
- ISBN-10: 0198751427
- ISBN-13: 978-0198751427
- Product Dimensions: 15.5 x 2.8 x 23.1 cm
- Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
- Amazon Bestsellers Rank: 956,695 in Books (See Top 100 in Books)
Intermediate Logic Paperback – 9 Oct 1997
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This textbook covers the fundamental proof-theoretical and model-theoretical aspects of classical propositional and first-order logic. . . .The book is clearly written and ideally suited for an intermediate course on the subject, requiring just some elementary knowledge of proof theory and model theory. (Mathematical Reviews)
From the Back Cover
Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding.See all Product description
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Top Customer Reviews
Clearly written, yet in no way dumbing down. It is obvious that a great deal of time was put into this wonderful book.
I started out with Lemmon's "Beginning Logic" which is superb and am now straight into this. All in all - wonderful stuff.
Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)
Bostock's writing will seem dense and technical to anyone without much formal background, but it's really pretty expository compared to other presentations. Non-mathematics students will need to read slowly and carefully, but that's the nature of the material.
Although the material is basic mathematical logic, it's not written in the style of math texts- Bostock doesnt describe things in terms of set theory or take for granted common mathematical terminology. The tone is descriptive and explanatory rather than formal and systematic. And there are a few philosophically-minded discussions about the relation of formal logic to real language. Math majors might find it a little verbose and soft on rigor, but its not sloppy- Bostock's proofs are clear and he is attentive to small details. What I liked most is that he often presents alternative ways of setting things up, and discusses the pros and cons of each choice.
Part I covers all the basic syntax and semantics of formal logic, and is no better or worse than most logic texts. Until the end of the book, the first-order logic used has no equality and no function signs, which simplifies things considerably. He decides upon a semantics that avoids formulas with free variables after a discussion of the other approach.
Part II (pg 139-321) is the meat of the book, and covers _four_ different formal proof systems in detail. Each is presented first for propositional logic and then extended to first-order logic. This section is clear and easy reading and there are quite a few examples. The systems given are:
1) Semantic Tableux. Completeness proofs are given. (For a more sophisticated presentation of tableaux see Smullyan's FOL).
2) Axiomatic (Hilbert-style). A lot of time is spent considering different axiom schemes and axiom independence. Completeness is shown for propositional logic- with a notably simple and direct proof.
3) Natural Deduction. A tree-style system is given and then collapsed into linear form.
4) Sequent Calculi. He shows how proofs in tableau or ND form can be easily adapted to different sequent systems. The completeness of tableaux thus gives completeness for the (cut-free Gentzen) sequent system, and with a little hand-waving completeness of natural deduction is also shown. Finally he gives a system (Kneale) is which branching occurs both upwards and downwards.
I'd recommend all beginning students of mathematical logic learn several proof systems. A lot of books present just the cumbersome Hilbert-style, rush through it in a race to the completeness theorem, and then discard formal proofs as too unwieldy. Learning the other systems too gives you a firmer grasp of working with predicate logic.
Part III briefly introduces equality and function signs into the logic, and then has a philosophically motivated discussion about allowing empty domains and names that dont reference anything.
Logic, by which I mean the mathematics of truth functors and quantifiers, is a tool that ought to be better known and more widely used. Maybe Bostock will move us toward that goal.
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