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An Introduction to Symbolic Logic, 3rd Edition, by Susanne K. Langer
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This is probably the clearest book ever written on symbolic logic for the philosopher, the general scientist, and the layman. For years it has received the appreciation of those who have been rebuffed by other introductory works because of insufficient mathematical training. No special knowledge of mathematics is required here; even if you have forgotten most of your high school algebra, you can learn to use mathematical logic by following the directions in this book.
Now revised and corrected, the book allows you to start with the simplest symbols and conventions and end up with a remarkable grasp of the Boole-Schroeder and Russell-Whitehead systems. It covers the study of forms, essentials of logical structure, generalization, classes, and the principal relations among them, universe of classes, the deductive system of classes, the algebra of logic, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices cover symbolic logic and the logic of the syllogism, the construction and use of truth-tables, and proofs of two theorems.
"One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
- Sales Rank: #429874 in Books
- Published on: 1967
- Released on: 2011-10-27
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .80" w x 5.51" l, .83 pounds
- Binding: Paperback
- 384 pages
From the Back Cover
This is probably the clearest book ever written on symbolic logic for the philosopher, the general scientist, and the layman. For years it has received the appreciation of those who have been rebuffed by other introductory works because of insufficient mathematical training. No special knowledge of mathematics is required here; even if you have forgotten most of your high school algebra, you can learn to use mathematical logic by following the directions in this book.
Now revised and corrected, the book allows you to start with the simplest symbols and conventions and end up with a remarkable grasp of the Boole-Schroeder and Russell-Whitehead systems. It covers the study of forms, essentials of logical structure, generalization, classes, and the principal relations among them, universe of classes, the deductive system of classes, the algebra of logic, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices cover symbolic logic and the logic of the syllogism, the construction and use of truth-tables, and proofs of two theorems.
"One of the clearest and simplest introductions to a subject which is very much alive."—Mathematics Gazette.
About the Author
Langer is research scholar and professor emeritus of philosophy at Connecticut College.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Excellent logic book
By JR Crombez, Ph.D.
Read the chapter summaries first, read the chapters next, read the chapter exercises and do them. This is an excellent book!
17 of 19 people found the following review helpful.
Very clear introduction to a difficult subject
By A Customer
Symbolic Logic can be a very daunting study, even to those already familiar with traditional Aristotelian logic. Langer's book, however, makes symbolic logic comprehensible to the average educated person, so that the array of logical symbols and mathematical formulae employed in symbolic logic seem not so intimidating after all. Clarity of presentation is this book's chief virtue. Admittedly, it is a bit dated, but for someone approaching the study of symbolic logic for the first time, it cannot be surpassed. It would make a suitable textbook for an introductory course in Logic, perhaps in combination with Mary Michael Spangler's "Logic: An Aristotelian Approach" (a good choice for traditional deductive logic).
28 of 28 people found the following review helpful.
High Marks for Clarity, Good for Self-Tutorial - Offers Historical Perspective
By Michael Wischmeyer
An Introduction to Symbolic Logic by Susanne K. Langer is quite useful for self-tutorial purposes. The author's informal, wordy, enthusiastic, narrative style is quite engaging, and should appeal to readers new to this topic. Her explanations are detailed and carefully constructed.
However, Langer's classic text is now rather dated; her first edition (1937) is credited with being the first introductory level text on symbolic logic. The second (1953) and third (1967) editions offer new prefaces, updated reading lists, and expanded appendices, but are not dramatically changed. The third edition (1967) is still available in an inexpensive Dover reprint.
Symbolic logic was a young discipline when Langer was writing her first edition. The classic work of Boole, De Morgan, Schroeder, Peano, and Frege had all occurred in previous seven decades. Not everyone agreed, but many logicians still viewed Whitehead and Russell's monumental Principia Mathematica (1910-1913) as the detailed reduction of all of mathematics to logic.
Susanne Langer's personal choice of some symbols now seems idiosyncratic, but to be fair it should be noted that even today's textbooks have yet to agree fully on a standard set of logic symbols. What really dates Langer's text is her effusive admiration for the "logistic masterpiece" of Whitehead and Russell. Not surprisingly, her text culminates, after much preparation, in two final chapters devoted to Principia Mathematica and logistics. Reading Langer is like reading history. (And I for one do enjoy reading classic mathematical texts, monographs, and papers.)
Langer's early chapters include the essentials of logical structures, generalization, classes, principal relations among classes, and the universe of classes. The latter half is more challenging with chapters titled The Deductive System of Classes, The Algebra of Logic, Abstraction and Interpretation, The Calculus of Propositions, and of course, The Assumptions of Principia Mathematica. Readers already familiar with the fundamentals of symbolic logic might skip the early chapters.
Langer made no mention of Godel's incompleteness theorem despite its direct reference to Russell and Whitehead's work. Godel's classic 1931 paper was titled "On formally undecidable propositions of Principia Mathematica and other related systems". Perhaps, Godel's work was judged too technical for an introductory text.
My review refers to the second edition of An Introduction to Symbolic Logic. My 1953 soft cover Dover edition, a library discard, is still in surprisingly good condition.
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