By Susanne K. Langer
Now revised and corrected, the booklet permits you to commence with the easiest symbols and conventions and turn out with a awesome grab of the Boole-Schroeder and Russell-Whitehead structures. It covers the research of varieties, necessities of logical constitution, generalization, periods, and the central family between them, universe of periods, the deductive method of sessions, 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 good judgment 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 topic that's a great deal alive." — Mathematics Gazette.
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Additional info for An Introduction to Symbolic Logic
In a symbolically expressed pro position the relation is merely named, and the fact that it is asserted to hold is (for the present) always understood. Since symbols may have meanings arbitrarily assigned, it is necessary to state what each sign equals by interpretation. 62 AN INTRODUCTION TO SYMBOLIC LOGIC Ideographic signs may be freely invented or adopted within the limits of the following principles of symbolic expression: (1) Radical distinction between term signs and relation signs. (2) Avoidance of false suggestion.
The narrow dash that represents a window is not intended to look like one; it resembles the object for which it stands only by its location in the plan, which must be analogous to the location of the window in the room. The dissimilarity in appearance between a “ logical picture” and what it represents is even more marked in the case of a graph. Supposing a graph in the newspaper conveys to you the growth, acceleration, climax and decline of an epidemic. The graph is spatial, its form is a shape, but the series of events does not have shape in a literal sense.
We do not try to make an architect’s drawing look as much as possible like the house; that is, even if the floor is to be brown, the floor-plan is not con sidered any better for being drawn in brown; and if the house is to be large, the plan need not convey an impression of vastness. All that the plan must do is to copy exactly the proportions of length and width, the arrangement of rooms, halls and stairs, doors and windows. The narrow dash that represents a window is not intended to look like one; it resembles the object for which it stands only by its location in the plan, which must be analogous to the location of the window in the room.