An Introduction to Symbolic Logic

Rating:
Summary: Excellent introduction
Review: A truly wonderful introduction to symbolic logic. One of the best.

It covers boolean algebra, propositional calculus, and Russell and Whitehead's logistic.

A charming and delightful book.

Rating:
Summary: An "Okay" Introduction to Symbolic Logic
Review: Langer's book, An Introduction to Symbolic Logic (3rd edition) is the first book I used to teach myself. At first, symbolic logic can look really difficult, if not scary. Fortunately, this book cashes through so much information that by the time you begin to look at many of the theorems, it is not so bad after all. This book covers forms, what are propositions, propositional form, generalization, relations, and much more. One of the most important symbols that this book covers is the "included in" symbol: "<" (or implication). In doing so, the author discusses Boolean algebra, postulates, classes, deduction, class-calculus, abstractions, and prepares you for Russell and Whitehead's Principia Mathematica.

In the back there are appendices on the logic of syllogism and a brief discussion of truth-tables. To end her work, Langer writes: "It is no exaggeration, I think, to claim that every philosopher should be not only acquainted with logic, but intimately conversant with it; for the study of logic develops the art of seeing structures almost to the point of habit, and reduces to a minimum the dangers of getting lost amid abstract ideas" (333-334). I think this is a good introduction to symbolic logic if you prefer to teach yourself rather than take a whole course on it.

On the other hand, this book has its short-comings. It is a bit old, and thus takes it that Principia Mathematica is the most important work of the 20th century: this is not the case. Philosophers of mathematics have almost universally rejected "logicism;" that is, the derivation of mathematics from logic. It seems to be the case that Langer's work endorses such a view. You will find as many people today endorsing logicism as endorse logical positivism: basically no one. And so, though this book is a good introduction, there are better introductions (i.e. Copi's). If you are not interested in spending a lot of money on some of the better and more up to date books, this book is a nice place to begin.

Rating:
Summary: Very clear introduction to a difficult subject
Review: 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).

Rating:
Summary: Outstanding introduction
Review: This is a great introduction. It progresses clearly so you can always understand the new stuff in terms of the previous stuff.

Rating:
Summary: Langer triumphs
Review: This is the book that introduced me to logic. It enthused me so much that I became a professional logician, a career that I have pursued for 35 years. Langer points out that, once one becomes acquainted with modern symbolic logic, one can go on to do groundbreaking research. This is true.