By Susanne K. Langer
Now revised and corrected, the publication helps you to begin with the best symbols and conventions and prove with a impressive take hold of of the Boole-Schroeder and Russell-Whitehead structures. It covers the learn of varieties, necessities of logical constitution, generalization, periods, and the imperative 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 common sense and the common sense of the syllogism, the development and use of truth-tables, and proofs of 2 theorems.
"One of the clearest and least difficult introductions to an issue that is a great deal alive." — Mathematics Gazette.
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Therefore “ form” should be distinguished not from “ matter” but from “ content” The content of a logical form may be psychical, musical, temporal, or in some other way non-physical, just as well as physical. Two things which have the same logical form are analogous. e. which is analogous to it. The most important analogy is that between thought and language. Language copies the pattern of thought, and thereby is able to represent thought. To understand language requires some apprehension of logical form.
Thus form is not another constituent, but is the way the constituents are put together. . We might understand all the separate words of a sentence without understanding the sentence: if a sentence is long and complicated, this is apt to happen. In such a case we have knowledge of the constituents, but not of the form. We may also have knowledge of the form without having knowledge of the constituents. If I say, ‘Rorarius drank the hemlock/ those among you who have never heard of Rorarius (supposing there are any) will understand the form, without having knowledge of all the constituents.
To see reality as a system, or at least any part of it as belonging to some system. But before we can find order and system, we must know something about them, so as to know what we are looking for, or we shall not recognize them when we find them. Systematic patterns, however, are so much easier to study in absiracto, without the confusing irrelevancies of any particular case, that although every science may be said to deal with this topic, logic is the science of order par excellence. Philosophy and science deal with interpreted patterns; it is not hard to see that this work is greatly facilitated by a thorough command of the abstract science of forms.
An Introduction to Symbolic Logic by Susanne K. Langer