By Susanne K. Langer
Now revised and corrected, the e-book lets you begin with the best symbols and conventions and prove with a notable seize of the Boole-Schroeder and Russell-Whitehead structures. It covers the research of types, necessities of logical constitution, generalization, sessions, and the primary kin between them, universe of periods, the deductive approach of periods, the algebra of common sense, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices disguise symbolic good judgment and the common sense of the syllogism, the development and use of truth-tables, and proofs of 2 theorems.
"One of the clearest and easiest introductions to an issue that is a great deal alive." — Mathematics Gazette.
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Additional resources for An Introduction to Symbolic Logic
CHAPTER II THE ESSENTIALS OF LOGICAL STRUCTURE i . R e l a t io n s a n d E l e m e n t s In the previous chapter, it was said that the logical form of a thing depends upon its structure, or the way it is put together; that is to say, upon the way its several parts are related to each other. Without adding or subtracting any of the factors in the composition of a thing, we may utterly change the character of that thing by changing the relations of the various factors to each other. For instance, consider the three names, “ r o n a l d , ” “ r o l a n d , ” and “ a r n o l d ” ; they contain exactly the same letters, but the relative positions of these letters — that is to say, their mutual relations of “ before” and “ after,” or “ right” and “ left” — are different in each case, and utterly different words result.
A good symbolism leads not only to a clear understanding of old ideas, but often to the discovery of new ones. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. QUESTIONS FOR REVIEW What relations are involved in the constitution of (a) a nest of tables, (6) a cluster of swarming bees, (c) a row of fence pickets, respectively? What constituents must a structure have beside relations? What is the chief use of a “logical picture” ? What is the most important kind of “logical picture” ? What is meant by the terms of a relation?
Most of us have no difficulty in seeing an order and configuration of events graphically; yet the only form which the graph and the events have in common is a logical form. They have an analogous structure, though their contents are more incongruous than cabbages and kings. It is only by analogy that one thing can represent another which does not resemble it. e. which has not a contour analogous to the map. If two things have the same logical form, one of them may represent the other, and not otherwise.
An Introduction to Symbolic Logic by Susanne K. Langer