By Susanne K. Langer
Now revised and corrected, the ebook enables you to commence with the easiest symbols and conventions and prove with a impressive seize of the Boole-Schroeder and Russell-Whitehead platforms. It covers the research of kinds, necessities of logical constitution, generalization, periods, and the significant family between them, universe of periods, the deductive procedure 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 a subject matter that's a great deal alive." — Mathematics Gazette.
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Extra resources for An Introduction to Symbolic Logic
E. ,— can undergo no change, they form a solid island. But let some monstrous grinding force change their relations, so that shells which were to the right of 46 AN INTRODUCTION TO SYMBOLIC LOGIC others are now to the lefty shells which were near each other now are distant, and so forth— and what has happened? The rock is no more! Perhaps not a single one of its factors has been destroyed, but if they no longer cohere, and thus keep their spatial relations to each other rigidly unaltered, the rock is destroyed.
E. a new fundamental concept of physics, but cleverly combines the principles he has learned into a new interesting pattern; he may then construct a physical thing, or actual model, of that pattern. His abstract form— the calculation he makes on paper— is a mathematical theorem from purely conceptual principles; his application of it to the realm of physics is an interpretation; and his model is an instance of this interpreted special form (and of the THE STUDY OF FORMS 39 principles it combines).
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.