Akikazahn And we get a first look at the ideas of effectiveness and computability. It is intended for the reader who has not studied logic previously, but A Mathemarical Introduction to Logic, Second Editionoffers mthematical flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. Chapter 1, which covers sentential propositional logic, also has a short section on applications to circuit design, providing some much-welcome motivation for the material. Get fast, free shipping with Amazon Prime. There was a problem providing the content you requested May 28, at 4: Like the First Edition, this book is an introduction to the concepts of proof, truth, and computability.

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Verified Purchase There are two types of mathematical texts: source code definition-theorem-proof-remark-definition For this he automatically earns 2 stars -- though in any field except mathematics, this would earn him nothing.

The prose itself is easy to follow, and makes suitable use of cross-references -- you will not find yourself stumped for 30 minutes trying to substantiate a casual statement made half-way through the book, as with some mathematical authors.

Chapter 1, which covers sentential propositional logic, also has a short section on applications to circuit design, providing some much-welcome motivation for the material. Model theory is also integrated with the discussion of first-order logic in chapter 2, which is preferable to having it relegated to a later section as in some texts. The book also gives heavy emphasis to computational topics, and even gets into second-order logic in the final chapter -- a very complete coverage for such a small introductory text.

These virtues combine to earn it a third star. My primary complaint is the manner in which rigor is emphasized in the text to the neglect rather than supplement of a coherent big picture -- losing two full stars. For instance, in chapter 1, 10 pages are spent very early on induction and recursion theorems, to put intuitive ideas like "closure" on firm ground.

And yet the words "deduction" and "completeness" -- arguably the whole reason we want to study logic in the first place -- do not appear until after the entirety of the rigorous discussion of propositional logic, and even then only as an exercise. Most readers will reach page before realizing that logicians care about deduction or soundness at all. These complex and highly detailed definitions remove ambiguity from mathematical discourse, and are essential -- but are best viewed as fungible reference material.

After all, many alternative renditions of the formalism exist. I found it difficult to see the forest for the trees in this book. I would have much preferred to see examples of deduction proofs -- with exercises in making use of axioms of natural deduction, discharged assumptions, etc -- and a brief discussion of completeness up front.

The next three sections will set to that task via many small steps. But perhaps that is too much to ask, since mathematics educators are uniquely in academia not accustomed to contextualizing their material as part of a wider intellectual enterprise.

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