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By Susanne K. Langer

ISBN-10: 0486601641

ISBN-13: 9780486601649

This is among the clearest e-book ever written on symbolic common sense for the thinker, the final scientist, and the layman. For years it has got the appreciation of these who've been rebuffed by means of different introductory works as a result of inadequate mathematical education. No distinctive wisdom of arithmetic is needed the following; whether you could have forgotten such a lot of your highschool algebra, you could discover ways to use mathematical good judgment by way of following the instructions during this book.
Now revised and corrected, the ebook helps you to begin with the easiest symbols and conventions and prove with a extraordinary clutch of the Boole-Schroeder and Russell-Whitehead structures. It covers the examine of kinds, necessities of logical constitution, generalization, periods, and the important relatives between them, universe of sessions, the deductive method 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 easiest introductions to a topic that's a great deal alive." — Mathematics Gazette.

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Sample text

Every structure is at least ideally composed of elements. In a musical scale, the elements are tones; in orthography, letters; in penmanship, they would be the height, curvature and slant of lines which compose letters. Note that in this last case the elements are not parts, but merely abstractable factors; properties, not portions, of writing. " Like­ wise, in judging a musical instrument, say a violin, one considers the proportions among certain attributes of its sound— the timbre, clarity, volume, and so forth— rather than the relations of individual tones to each other.

Do you think it has any value for everyday life ? SUGGESTIONS FOR CLASS WORK (a v o id e x a m p l e s g iv e n in th e t e x t ) 1. 2. 3. 4. Name three things that may appear in different forms. " Give an example of a “construct" not deliberately made. Name two things, one material and one immaterial, which are analogous in form. 5. What name would you give to the structure exemplified by (1) a string-quartet, (2) a group of bridge-players, (3) a “good-luck" clover? 6. g. different sciences) do they belong?

In the previous chapter I pointed out that the elements in a structure need not be physically separate, first existing alone and then brought into combination. They must only be conceptually distinguishable; and ideal parts are geo­ metrically distinguishable, though they be set off from each other by artificial, or even purely imaginary, lines. Therefore, even though a column be not composed of pieces set one upon another, it does allow us to conceive of its possible sections as ranged in this fashion; and it is simply on the basis of such a conception that we call an upright beam, or an obelisk, or even the air in a chimney or the mercury in a thermometer tube, a column.

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An Introduction to Symbolic Logic by Susanne K. Langer


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