By Susanne K. Langer
Now revised and corrected, the ebook permits you to commence with the easiest symbols and conventions and turn out with a extraordinary grab of the Boole-Schroeder and Russell-Whitehead structures. It covers the examine of varieties, necessities of logical constitution, generalization, sessions, and the vital family 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 hide 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 easiest introductions to a topic that is greatly alive." — Mathematics Gazette.
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Additional info for An Introduction to Symbolic Logic
We might as well have written i, 2, 3, 4 for our elements, or a, j8, y, 8; and the relation “ br” might have been expressed by a picture of a playing card, and “ ch” by a chess-pawn, or any other sign that suggested itself. But certain general principles of symbolization should be borne in mind in the selection of logical characters: (1) Signs for elements and signs for relations should be different in kind. * W h e n a relatio n is used, th e su b scrip t is o m itte d , becau se th e co n stru ct its e lf r evea ls th e degree o f th e relation.
8. In t e r p r e t a t io n The latter of these two procedures, finding applications for concepts, is called interpretation of an abstract form. It is a process of looking about for kinds of things to which a certain form belongs. If, for instance, we would interpret the abstract concept of “ rotation," we would think of the rolling of a wheel, the motion of a heavenly body, the spinning of a top, the whirl of a propeller. " In one sense, two exactly similar spinning tops might be taken as two contents for one form, but in order to avoid confusion I shall call them two instances of one content for the same form.
If we speak simply of a couple, without reference to any content, or simply of “ two-ness” or “ two,” we are treating of this form in abstracto. Or again, if we consider the order in which hours of a day follow each other— always one after another, never two at once following the same predecessor — and then regard the order of inches on a ruler, or rungs on a ladder, or the succession of volumes of the Encyclopaedia Britannica, or the sequence of Presidents of the United States, we see at once that there is a common form in all these progressions.
An Introduction to Symbolic Logic by Susanne K. Langer