An Introduction to Symbolic Logic

by Susanne K. Langer

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.

Genres: Philosophy, Logic, Science, Mathematics, Nonfiction, Linguistics, Reference

384 pages, Paperback

First published January 1, 1967

About the author

Susanne Katherina Langer (née Knauth) (December 20, 1895 – July 17, 1985) was an American philosopher of mind and of art, who was influenced by Ernst Cassirer and Alfred North Whitehead. She was one of the first women to achieve an academic career in philosophy and the first woman to be popularly and professionally recognized as an American philosopher. Langer is best known for her 1942 book entitled, Philosophy in a New Key. (wikipedia)

Reviews

[path · Rating 4 out of 5]

It is going to be difficult to separate my thoughts about the book from my thoughts about symbolic logic and the system of thought that it represents, but at least I know this: although I had some elementary notion of what symbolic logic was, Langer's book absolutely crystallized it for me. She begins with common sense perceptions about the world and the structured relationships between parts of a whole that come together in a logic that allows us to recognize wholes as such. Langer takes the reader, systematically, through basic assumptions about logic, simple definitions of elements, variables, and classes and then builds out to the more complex logical relationships that afford more complex perception and proposition-based thinking. Although the common symbology used in logic has changed a bit from the time of this book's publication, the principles hold true.

It is because of Langer that I have a much better appreciation of formal logic and can recognize how it simultaneously (and paradoxically) makes the world infinitely larger in the sense that model-able logical relationships exist everywhere but also more manageable in distilling those logics to fundamental functions from which more complex, propositional logic is built. The application and utility of symbolic logic was immediately and clearly apparent to me after reading this book. I see so many applications and will be reading further to be sure.

All of the above being true, I am not ready to follow the train of thought to suppose that all structure and relationships in the world are reducible to math. There is too much that is true about the world that is irrational and ineffable that any correspondence to mathematical expression would likely be coincidental than designed. Nevertheless, the influence of formal logical is undeniable and evident. The utility and certainty of formal logic is absolutely an underpinning of modern education on a variety of topics.

[Manny Tingplants · Rating 5 out of 5]

Langer's conversational tone and clear style make the topic about as accessible as I can imagine it being. It's essentially written as an introduction to the works of Russell, Whitehead, Frege, etc. The paragraphs and formulas are also spaced well, as to make the text more readable.

After reading this I was hungry for more, picked up Russell's Principia Mathematica, and couldn't help but grimace from Russell's unnecessarily convoluted sentence structure, lack of text parsing, and generally disorganized presentation of what is essentially a system of absolute organization. Warning: if you're new to the field, Langer's style will spoil you.

My understanding of language (both human and computer) have been expanded by this text.

[Jonah · Rating 3 out of 5]

Pretty interesting intro-type stuff... Maybe just start at like chapter seven or so, as a lot of it is real basic foundational stuff that you don't really need to know / can figure out on your own from the context. Quick, easy, if unsatisfying, and has gotten me hungry for more and more up-to-date stuff.

[Lucille Nguyen · Rating 4 out of 5]

Conversational and readable, a bit out of date with the logicist approach to mathematics, nonetheless a good introduction to the subject and the thought of early 20th century logicians of the Russell and Whitehead.