Logic - Techniques of Formal Reasoning | |

Kalish (Donald), Montague (Richard), Mar (Gary) | |

This Page provides (where held) the Abstract of the above Book and those of all the Papers contained in it. | |

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**BOOK ABSTRACT: **

- Thomson Learning, Wadsworth Publishing Company, Inc., Belmont, California; Second Edition; 1980
- Very nice hardback, reprint after 1992, when the copyright was renewed by Kalish & Helen S. Schofield.

- I was originally introduced to the 1964 edition of Kalish and Montague's
*Logic: Techniques of Formal Reasoning*in early 1970. As an undergraduate taking elementary logic for the first time, needless to say I found the demands of sentential and predicate calculus and theorem-proving in general to be daunting and not a little painful. It was many years later after receiving advanced degrees and teaching logic courses myself, along with researching some of the theoretical horizons in artificial intelligence^{1}, that I turned back to this most precious of textbooks. Finding that a second edition had been published, I eagerly bought a copy and set out to re-prove all those theorems. - Sharpening one's logic skills can be a struggle, but it is one well worth undergoing especially with the demands for reasoned discipline imposed by Kalish, Montague, and Mar. Every so often, I go back to this text to prove the theorems once again (though I occasionally skip over a few in the first three chapters). I've found just a few suggestions I would make to the authors, if they were still around, or to whoever may edit it in the future. These pertain only to the first 5 chapters.
- The transition from the 125 theorems of the sentential calculus to those of the predicate calculus is a bit rough-going. Almost immediately, one is expected to engage in abbreviated theorem-proving which certainly assumes a command of all those theorems that came before. It would seem that a few more exercises would help students acquire more familiarity with those theorems and with abbreviated proofs. Moreover, one is introduced to more complex inference rules, such as separation of cases, for which few exercises have prepared one, at least up to that point. These may be minor quibbles, but they can cause a lot of confusion, especially to students introduced to logic for the first time.
- Additionally, well into Chapter III, it is possible to construct a proof of one of the advanced theorems with the use of hypothetical syllogism. In theorem T235 (corresponding to the Aristotelian syllogism Barbara), one can derive two pure hypothetical statements permitting the application of hypothetical syllogism (the law of transitivity) to deduce a third. Yet neither hypothetical syllogism as a specific rule of inference nor the concept of transitivity has been introduced in previous pages. In fact, hypothetical syllogism as such (including explanations of pure and mixed syllogisms) is never introduced, though principles of syllogism are. The law of transitivity is not introduced until late in Chapter V. Of course, one can derive them, but this can cause confusion for a beginner.
- I highly recommend this text over all others that are commonly used in basic undergraduate or even graduate courses. Though
*Logic: Techniques of Formal Reasoning*is more demanding than, say, any of the Copi books, those demands result in more disciplined reasoning, proofs, and a broader understanding of logic and its relation to mathematics.

… Myrna L. Estep, Ph.D.

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- Blue: Text by me; © Theo Todman, 2021
- Mauve: Text by correspondent(s) or other author(s); © the author(s)

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