By Susanne K. Langer
Now revised and corrected, the publication helps you to begin with the easiest symbols and conventions and prove with a outstanding seize of the Boole-Schroeder and Russell-Whitehead platforms. It covers the examine of types, necessities of logical constitution, generalization, sessions, and the valuable family members between them, universe of sessions, the deductive process of periods, the algebra of good judgment, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices conceal symbolic common sense and the good judgment of the syllogism, the development and use of truth-tables, and proofs of 2 theorems.
"One of the clearest and least difficult introductions to a subject matter that's greatly alive." — Mathematics Gazette.
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Additional resources for An Introduction to Symbolic Logic
So the study of relations is neces sarily bound up with a study of discourse. But if the latter obscures and disguises relations, as it often does, there is no escape from error, except by adopting another sort of discourse altogether. Such a new medium of expression is the symbolism of logic. In this ideography, the four pro positions wherein “ is” really names a relation would not appear to have a common form, but would wear the badge of their distinctions plainly in view: (3) (4) (5) (6) Barbarossa = Frederick I Barbarossa c legendary hero To sleep c to dream E!
3. What is a “logical picture” ? How does it differ from an ordinary picture? 4. What is a “ construct” ? Is it always something that has been put together? Is a cloud a “ construct” ? 5. What is meant by “ content” ? What is its relation to form, to “stuff” ? May two forms have the same content? May one form have different contents ? 6. What is meant by calling two things “ analogous” ? What is the importance of analogy? 44 AN INTRODUCTION TO SYMBOLIC LOGIC 7. Why is the grammatical structure of language important?
Therefore “ form” should be distinguished not from “ matter” but from “ content” The content of a logical form may be psychical, musical, temporal, or in some other way non-physical, just as well as physical. Two things which have the same logical form are analogous. e. which is analogous to it. The most important analogy is that between thought and language. Language copies the pattern of thought, and thereby is able to represent thought. To understand language requires some apprehension of logical form.