Leo Horovitz's Reviews > Logic, Language, and Meaning, Volume 1: Introduction to Logic

Logic, Language, and Meaning, Volume 1 by L.T.F. Gamut
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Jan 17, 12

bookshelves: logic, philosophy, philosophy-of-language, philosophy-of-logic, formal-science, formal-language, science, non-fiction, favorites
Read from November 04, 2011 to January 17, 2012 — I own a copy, read count: 1

An excellent book covering many different aspects of logic in an exhaustive manner. It is the first volume of two, with the somewhat misleading subtitle "Introduction to Logic". It should perhaps rather have been called "Introduction to a formal treatment of logic" or something along those lines. As a first book on logic, it is not a good choice. A word might be necessary on my use of the word "formal" here. Any treatment of logic is of course in a certain sense "formal". Arguments in natural language are often translated as examples to illustrate the meaning of the logical constants. But this does not amount to a formal treatment of logic itself. This book explains the use of mathematical induction to prove things about formulas, which relies on a formal definition on the syntax of the language of logic, gives extensive treatments on logical semantics and goes into some discussions about the correspondence between the model theoretic (semantic) approach (Tarski's beautiful truth definition is there) and proof theoretic (syntactic) approach to logical inference. In this connection some metalogical results are explained.

It is written with a strong linguistic focus. The ability of the formalisms to encode natural language is always a central issue, as opposed to the situation in more mathematically inclined books on logic where the translation of natural language sentences seems to often be more of a pedagogical thing. Towards the end, after the thorough treatment of classical logic, follows a few chapters on some other topics, with a more brief treatment. A chapter on various extensions and deviations on classical logic along with an explanation of the motivations of these (again, translations of natural language sentences are in focus) comes first. Then follows one on the pragmatics on logic and language, and finally, a chapter on the formal theory of grammar with a very brief explanation of the language hierarchy initially developed by Chomsky and its connection to types of automata.

This is an great text for the reader who already has a basic understanding of classical logic and wishes to delve a bit deeper, perhaps before getting into an even more formal treatment of logic in a course on metalogic (which is exactly what I'm about to do myself in about two weeks).
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