By Susanne K. Langer
Now revised and corrected, the booklet permits you to begin with the best symbols and conventions and turn out with a awesome snatch of the Boole-Schroeder and Russell-Whitehead structures. It covers the research of kinds, necessities of logical constitution, generalization, periods, and the vital kinfolk between them, universe of sessions, the deductive method of sessions, the algebra of common sense, 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 least difficult introductions to a subject matter that's greatly alive." — Mathematics Gazette.
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Extra info for An Introduction to Symbolic Logic
This may be done by adding a numerical subscript; for example, “ kd2” means that “ killing” is dyadic, “ bt3” th a t“ between” is triadic. ” Furthermore, natural language has a strong tendency to let one word embody many meanings. This fallacy, which we exploit in making puns and twisting arguments, seems, at first sight, to be another of those weaknesses of language against which we ought to be guarded by common sense and the vigilance of English teachers. We are supposed to know that “ The morning breaks, and with it breaks my heart,” involves an amphibolous use of the word “ breaks” — a change from one meaning to another, neither of which, in this case, happens to be the “ real” (or literal, or primary) meaning.
We learn them as they apply to certain things; we learn number by counting things, shapes by fitting objects together, qualities by comparing various articles, rules of conduct by gradually collecting and judging instances of good and evil. The easiest way to teach a formula is to present several instances and point out their common formal properties. But this is not the easiest way to discover new patterns, which no one points out to us. There are, essentially, two ways in which new forms of things are discovered: (i) by abstraction from instances which nature happens to collect for us (the power to recognize a common form in such a chance collection is scientific genius); (2) by interpretation of empty forms we have quite abstractly constructed.
If you watch a young child playing with blocks, you will see him experimenting with the various relations into which the blocks may enter with one another, and learning to identify the forms which result. He piles one upon another, and a third upon this, and a fourth upon that; by using only the single relation we call “ upon,” he constructs a column. He sets one block to the right of another and puts a third one across the two; the result is the simplest sort of lintel. And so he proceeds, to a wall, a house, a pyramid.